Molecular Light Scattering And Optical Activity 2nd Ed Rev And Enl Laurence D Barron

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MOLECULAR LIGHT SCATTERING
AND OPTICAL ACTIVITY
Using classical and quantum methods with a strong emphasis on symmetry prin-
ciples, this book develops the theory of a variety of optical activity and related
phenomena from the perspective of molecular scattering of polarized light. In addi-
tion to the traditional topic of optical rotation and circular dichroism in the visible
and ultraviolet region associated with electronic transitions, the newer topic of op-
tical activity associated with vibrational transitions, which may be studied using
both infrared and Raman techniques, is also treated. Ranging from the physics of
elementary particles to the structure of viruses, the subject matter of the book re-
ﬂects the importance of optical activity and chirality in much of modern science
and will be of interest to a wide range of physical and life scientists.
Laurence Barron worked with Professor Peter Atkins for his doctorate in
theoretical chemistry from Oxford University, followed by postdoctoral work with
Professor David Buckingham at Cambridge University. He was appointed to a fac-
ulty position at Glasgow University in 1975, where he is currently the Gardiner
Professor of Chemistry. His research interests are in the electric, magnetic and op-
tical properties of molecules, especially chiral phenomena including Raman optical
activity which he pioneered and is developing as a novel probe of the structure and
behaviour of proteins, nucleic acids and viruses.

MOLECULAR LIGHT SCATTERING
AND OPTICAL ACTIVITY
Second edition, revised and enlarged
LAURENCE D. BARRON, f.r.s.e.
Gardiner Professor of Chemistry, University of Glasgow

  
Cambridge, New York, Melbourne, Madrid, Cape Town, Singapore, São Paulo
Cambridge University Press
The Edinburgh Building, Cambridge  , UK
First published in print format
- ----
- ----
© L. D. Barron 2004
2004
Information on this title: www.cambrid
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e.or
g
/9780521813419
This publication is in copyright. Subject to statutory exception and to the provision of
relevant collective licensing agreements, no reproduction of any part may take place
without the written permission of Cambridge University Press.
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Cambridge University Press has no responsibility for the persistence or accuracy of s
for external or third-party internet websites referred to in this publication, and does not
guarantee that any content on such websites is, or will remain, accurate or appropriate.
Published in the United States of America by Cambridge University Press, New York
www.cambridge.org
hardback
eBook (NetLibrary)
eBook (NetLibrary)
hardback

ForSharon

There are some enterprises in which a careful disorderliness is the true method.
Herman Melville,Moby Dick

Contents
Preface to the ﬁrst edition page xi
Preface to the second edition xv
List of symbols xviii
1Ahistorical review of optical activity phenomena
1.1 Introduction
1.2 Natural optical rotation and circular dichroism
1.3 Magnetic optical rotation and circular dichroism
1.4 Light scattering from optically active molecules
1.5 Vibrational optical activity
1.6 X-ray optical activity
1.7 Magnetochiral phenomena
1.8 The Kerr and Cotton–Mouton effects
1.9 Symmetry and optical activity
Spatial symmetry and optical activity•Inversion symmetry and
physical laws
•Inversion symmetry and optical rotation•Inversion
symmetry and optical activity in light scattering
•Motion-dependent
enantiomorphism: true and false chirality
•Symmetry violation: the
fall of parity and time reversal invariance
•Chirality and relativity•
Chirality in two dimensions
2Molecules in electric and magnetic ﬁelds
2.1 Introduction
2.2 Electromagnetic waves
Maxwell’s equations•Plane monochromatic waves•Force and
energy
•The scalar and vector potentials
2.3 Polarized light
Pure polarization•Partial polarization
2.4 Electric and magnetic multipole moments
vii

viii Contents
Electric multipole moments
•Magnetic multipole moments•Static
electric multipole ﬁelds
•Static magnetic multipole ﬁelds•
Dynamic electromagnetic multipole ﬁelds
2.5 The energy of charges and currents in electric and
magnetic ﬁelds
Electric and magnetic multipole moments in static ﬁelds•Electric
and magnetic multipole moments in dynamic ﬁelds
2.6 Molecules in electric and magnetic ﬁelds
Amolecule in static ﬁelds•Amolecule in a radiation ﬁeld•A
molecule in a radiation ﬁeld at absorbing frequencies
•
Kramers–Kronig relations•The dynamic molecular property tensors
in a static approximation
2.7 A molecule in a radiation ﬁeld in the presence of
other perturbations
2.8 Molecular transition tensors
The Raman transition polarizability•The adiabatic approximation•
The vibrational Raman transition tensors in Placzek’s approximation•
Vibronic interactions: the Herzberg–Teller approximation
3Molecular scattering of polarized light
3.1 Introduction
3.2 Molecular scattering of light
3.3 Radiation by induced oscillating molecular multipole moments
3.4 Polarization phenomena in transmitted light
Refraction as a consequence of light scattering•Refringent
scattering of polarized light
•Simple absorption•Linear dichroism
and birefringence (the Kerr effect)
•Electric ﬁeld gradient-induced
birefringence: measurement of molecular electric quadrupole
moments and the problem of origin invariance
•Natural optical
rotation and circular dichroism
•Magnetic optical rotation and
circular dichroism
•Magnetochiral birefringence and dichroism•
Nonreciprocal (gyrotropic •The Jones birefringence•
Electric optical rotation (electrogyration
3.5 Polarization phenomena in Rayleigh and Raman
scattered light
Nonrefringent scattering of polarized light•Symmetric scattering•
Antisymmetric scattering•Natural Rayleigh and Raman optical
activity
•Magnetic Rayleigh and Raman optical activity•Electric
Rayleigh and Raman optical activity
4Symmetry and optical activity
4.1 Introduction
4.2 Cartesian tensors

Contents ix
Scalars, vectors and tensors
•Rotation of axes•Polar and axial
tensors
•Some algebra of unit tensors•Isotropic averages of tensor
components
•Principal axes
4.3 Inversion symmetry in quantum mechanics
Space inversion•Time reversal•The parity and reversality
classiﬁcation of optical activity observables
•Optical enantiomers,
two-state systems and parity violation
•Symmetry breaking and
symmetry violation
•CPviolation and molecular physics
4.4 The symmetry classiﬁcation of molecular
property tensors
Polar and axial, time-even and time-odd tensors•Neumann’s
principle
•Time reversal and the permutation symmetry of molecular
property and transition tensors
•The spatial symmetry of molecular
property tensors
•Irreducible cartesian tensors•Matrix elements of
irreducible spherical tensor operators
4.5 Permutation symmetry and chirality
Chirality functions•Permutations and the symmetric group•
Chirality functions: qualitative completeness•Chirality functions:
explicit forms
•Active and inactive ligand partitions: chirality
numbers
•Homochirality•Chirality functions: concluding remarks
5Natural electronic optical activity
5.1 Introduction
5.2 General aspects of natural optical rotation and
circular dichroism
The basic equations•Optical rotation and circular dichroism through
circular differential refraction
•Experimental quantities•Sum rules
5.3 The generation of natural optical activity within molecules
The static coupling model•The dynamic coupling model•Exciton
coupling (the degenerate coupled oscillator model)
5.4 Illustrative examples
The carbonyl chromophore and the octant rule•The Co
3+
chromophore: visible, near ultraviolet and X-ray circular dichroism•
Finite helices: hexahelicene
5.5 Vibrational structure in circular dichroism spectra
Introduction•The vibronically perturbed rotational strength•The
carbonyl chromophore
6Magnetic electronic optical activity
6.1 Introduction
6.2 General aspects of magnetic optical rotation and
circular dichroism
The basic equations•Interpretation of the FaradayA-,B-and
C-terms

x Contents
6.3 Illustrative examples
Porphyrins•Charge transfer transitions in Fe(CN
3−
6
•
The inﬂuence
of intramolecular perturbations on magnetic optical activity: the
carbonyl chromophore
6.4 Magnetochiral birefringence and dichroism
7Natural vibrational optical activity
7.1 Introduction
7.2 Natural vibrational optical rotation and circular dichroism
The basic equations•The ﬁxed partial charge model•The bond
dipole model
•Aperturbation theory of vibrational circular dichroism
7.3 Natural vibrational Raman optical activity
The basic equations•Experimental quantities•Optical activity in
transmitted and scattered light
•The two-group model of Rayleigh
optical activity
•The bond polarizability model of Raman optical
activity
•The bond polarizability model in forward, backward and
90
◦
scattering
7.4 The bond dipole and bond polarizability models applied to
simple chiral structures
Asimple two-group structure•Methyl torsions in a hindered
single-bladed propellor
•Intrinsic group optical activity tensors
7.5 Coupling models
7.6 Raman optical activity of biomolecules
8Antisymmetric scattering and magnetic Raman optical activity
8.1 Introduction
8.2 Symmetry considerations
8.3 A vibronic development of the vibrational Raman
transition tensors
8.4 Antisymmetric scattering
The antisymmetric transition tensors in the zeroth-order
Herzberg–Teller approximation
•Resonance Rayleigh scattering in
atomic sodium
•Resonance Raman scattering in totally symmetric
vibrations of iridium (IV
•Antisymmetric transition
tensors generated through vibronic coupling
•Resonance Raman
scattering in porphyrins
8.5 Magnetic Rayleigh and Raman optical activity
The basic equations•Resonance Rayleigh scattering in atomic
sodium
•Vibrational resonance Raman scattering in IrCl
2−
6
and
CuBr
2−
4
:Spin-ﬂip transitions and Raman electron paramagnetic
resonance
•Electronic resonance Raman scattering in uranocene•
Resonance Raman scattering in porphyrins
References 423
Index 436

Preface to the ﬁrst edition
Scientists have been fascinated by optical activity ever since its discovery in the
early years of the last century, and have been led to make major discoveries in
physics, chemistry and biology while trying to grapple with its subtleties. We can
think of Fresnel’s work on classical optics, Pasteur’s discovery of enantiomeric pairs
of optically active molecules which took him into biochemistry and then medicine,
and Faraday’s conclusive demonstration of the intimate connection between elec-
tromagnetism and light through his discovery of magnetic optical activity. And of
course the whole subject of stereochemistry, or chemistry in space, has its roots
in the realization by Fresnel and Pasteur that the molecules which exhibit optical
rotation must have an essentially helical structure, so from early on molecules were
being thought about in three dimensions.
Asystem is called ‘optically active’ if it has the power to rotate the plane of
polarization of a linearly polarized light beam, but in fact optical rotation is just
one of a number of optical activity phenomena which can all be reduced to the
common origin of a different response to right- and left-circularly polarized light.
Substances that are optically active in the absence of external inﬂuences are said
to exhibit ‘natural’ optical activity. Otherwise, all substances in magnetic ﬁelds are
optically active, and electric ﬁelds can sometimes induce optical activity in special
situations.
It might be thought that a subject originating at the start of the nineteenth century
would be virtually exhausted by now, but nothing could be further from the truth.
The recent dramatic developments in optical and electronic technology have led
to large increase in the sensitivity of conventional optical activity measurements,
and have enabled completely new optical activity phenomena to be observed and
applied. Traditionally, optical activity has been associated almost exclusively with
electronic transitions; but one particularly signiﬁcant advance over the last decade
has been the extension of natural optical activity measurements into the vibrational
spectrum using both infrared and Raman techniques. It is now becoming clear
xi

xii Preface to ﬁrst edition
that vibrational optical activity makes possible a whole new world of fundamental
studies and practical applications quite undreamt of in the realm of conventional
electronic optical activity.
Optical activity measurements are expected to become increasingly important
in chemistry and biochemistry. This is because ‘conventional’ methods have now
laid the groundwork for the determination of gross molecular structure, and em-
phasis is turning more and more towards the determination of the precise three-
dimensional structures of molecules in various environments: in biochemistry it is
of course the ﬁne detail in three dimensions that is largely responsible for biological
function. Whereas X-ray crystallography, for example, provides such information
completely, it is restricted to studies of molecules in crystals in which the three
dimensional structures are not necessarily the same as in the environment of interest.
Natural optical activity measurements are a uniquely sensitive probe of molecular
stereochemistry, both conformation and absolute conﬁguration, but unlike X-ray
methods can be applied to liquid and solution samples, and even to biological
moleculesin vivo.The signiﬁcance of magnetic optical activity measurements, on
the other hand, can probably be summarized best by saying that they inject addi-
tional structure into atomic and molecular spectra, enabling more information to
be extracted.
Following the recent triumph of theoretical physics in unifying the weak and
electromagnetic forces into a single ‘electroweak’ force, the world of physics has
also started to look at optical activity afresh. Since weak and electromagnetic forces
have turned out to be different aspects of the same, more fundamental, uniﬁed
force, the absolute parity violation associated with the weak force is now thought
to inﬁltrate to a tiny extent into all electromagnetic phenomena, and this can be
studied in the realm of atoms and molecules by means of delicate optical activity
experiments. So just as optical activity acted as a catalyst in the progress of science
in the last century, in our own time it appears set to contribute to further fundamental
advances. One could say that optical activity provides a peephole into the fabric of
the universe!
In order to deal with the optical properties of optically active substances in a
uniﬁed fashion, and to understand the relationship between the conventional ‘bire-
fringence’ phenomena of optical rotation and circular dichroism and the newer
‘scattering’ phenomena of Rayleigh and Raman optical activity, the theory is de-
veloped in this book from the viewpoint of the scattering of polarized light by
molecules. In so doing, a general theory of molecular optics is obtained and is ap-
plied to the basic phenomena of refraction, birefringence and Rayleigh and Raman
scattering. Optical activity experiments are then regarded as applications of these
phenomena in ways that probe the asymmetry in the response of the optically active
system to right- and left-circularly polarized light. As well as using the results of the

Preface to ﬁrst edition xiii
general theory to obtain expressions for the observables in each particular optical
activity phenomenon, where possible the expressions are also derived separately in
as simple a fashion as possible for the beneﬁt of the reader who is interested in one
topic in isolation.
There are several important topics within the general area of optical activity that
Ihaveeither omitted or mentioned only brieﬂy, mainly because they are outwith
the theme of molecular scattering of polarized light, and also because of my lack
of familiarity with them. These include circular polarization of luminescence, and
chiral discrimination. I have also not treated helical polymers: to do justice to this
very important topic would divert us too far from the fundamental theory. Where I
have discussed speciﬁc atomic or molecular systems, this has been to illuminate the
theory rather than to give an exhaustive explanation of the optical activity of any
particular system. For a much broader view ofnaturaloptical activity, including
experimental aspects and a detailed account of a number of speciﬁc systems, the
reader is referred to S. F. Mason’s new book ‘Molecular Optical Activity and the
Chiral Discriminations’ (Mason, 1982).
So this is not a comprehensive treatise on optical activity. Rather, it is a personal
view of the theory of optical activity and related polarized light scattering effects
that reﬂects my own research interests over the last 14 years or so. During the earlier
part of this period I was fortunate to work with, and learn from, two outstanding
physical chemists: Dr P. W. Atkins in Oxford and Professor A. D. Buckingham in
Cambridge; and their inﬂuence extends throughout the book.
Iwish to thank the many colleagues who have helped to clarify much of the
material in this book through discussion and correspondence over the years. I am
particularly grateful to Dr J. Vrbancich for working through the entire manuscript
and pointing out many errors and obscure passages.
Glasgow
May 1982

Preface to the second edition
Interest in optical activity has burgeoned since the ﬁrst edition of this book was
published in 1982. The book anticipated a number of new developments and helped
to fuel this interest, but has become increasingly hard to ﬁnd since going out of print
in 1990. Numerous requests about where a copy might be found, often accompa-
nied by ‘our library copy has been stolen’ and the suggestion that a second edition
would be well-received, have encouraged me to prepare this new edition. The book
has been considerably revised and enlarged, but the general plan and style remain
as before.
Traditionally, the ﬁeld of optical activity and chirality has been largely the pre-
serve of synthetic and structural chemistry due to the inherent chirality of many
molecules, especially natural products. It has also been important in biomolecu-
lar science since proteins, nucleic acids and oligosaccharides are constructed from
chiral molecular building blocks, namely the L-amino acids and the D-sugars,
and the chemistry of life is exquisitely stereospeciﬁc. The ﬁeld is becoming in-
creasingly important in these traditional areas. For example, chirality and enan-
tioselective chemistry are now central to the pharmaceutical industry since many
drugs are chiral and it has been recognized that they should be manufactured as
single enantiomers; and chiroptical spectroscopies are used ever more widely for
studying the solution structure and behaviour of biomolecules, a subject at the
forefront of biomedical science. But in recent years optical activity and chiral-
ity have also been embraced enthusiastically by several other disciplines. Physi-
cists, for example, are becoming increasingly interested in the ﬁeld due to the
subtle new optical phenomena, linear and nonlinear, supported by chiral ﬂuids,
crystals and surfaces. Furthermore, since homochiral chemistry is the signature
of life, and considerable effort is being devoted to searches for evidence of life,
or at least of prebiotic chemistry, elsewhere in the cosmos including interstellar
xv

xvi Preface to second edition
dust clouds, cometary material and the surfaces of extrasolar planets, chirality
has captured the interest of some astrophysicists and space scientists. It has even
caught the attention of applied mathematicians and electrical engineers on ac-
count of the novel and potentially useful electromagnetic properties of chiral
media.
Although containing a signiﬁcant amount of new material the second edition, like
the ﬁrst, is not a comprehensive treatise on optical activity and remains a personal
view of the theory of optical activity and related polarized light scattering effects
that reﬂects my own research interests. The material on symmetry and chirality has
been expanded to include motion-dependent enantiomorphism and the associated
concepts of ‘true’ and ‘false’ chirality, and to expose productive analogies between
the physics of chiral molecules and that of elementary particles which are further
emphasized by considering the violation of parity and time reversal invariance.
Another signiﬁcant addition is a detailed treatment ofmagnetochiralphenomena,
which are generated by a subtle interplay of chirality and magnetism and which
were unknown at the time of writing the ﬁrst edition. Since vibrational optical
activity has now ‘come of age’ thanks to new developments in instrumentation and
theory in the 1980s and 1990s, the treatment of this topic has been considerably
revised and expanded. Of particular importance is a new treatment of vibrational
circular dichroism in Chapter 7; serious problems in the quantum chemical theory,
now resolved, were unsolved at the time of writing the ﬁrst edition, which contains
an error in the way in which the Born–Oppenheimer approximation was applied.
The revised material on natural Raman optical activity now reﬂects the fact that it
has become an incisive chiroptical technique giving information on a vast range
of chiral molecular structures, from the smallest such as CHFClBr to the largest
such as intact viruses. New developments in magnetic Raman optical activity are
also described which illustrate how it may be used as a novel probe of magnetic
structure.
Another subject to come of age in recent years is nonlinear optical activity, man-
ifest as a host of different optical phenomena generated by intense laser beams
incident on both bulk and surface chiral samples. However the subject has become
too large and important, and too specialized with respect to its theoretical devel-
opment, to do it justice within this volume which is therefore conﬁned to linear
optical activity phenomena.
Ihavebeneﬁted greatly from interactions with many colleagues who have helped
directly and indirectly with the identiﬁcation and correction of errors in the ﬁrst edi-
tion, and with the preparation of new material. I am especially grateful in this respect
to E. W. Blanch, I. H. McColl, A. D. Buckingham, J. H. Cloete, R. N. Compton,
J. D. Dunitz, K.-H. Ernst, R. A. Harris, L. Hecht, W. Hug, T. A. Keiderling, L. A.

Preface to second edition xvii
Naﬁe, R. D. Peacock, P. L. Polavarapu, M. Quack, R. E. Raab, G. L. J. A. Rikken,
A. Rizzo, P. J. Stephens, G. Wagni`ere and N. I. Zheludev.
Ihope that workers in many different areas of pure and applied science will ﬁnd
something of value in this second edition.
Glasgow
2004

Symbols
The symbols below are grouped according to context. In some cases the same
symbol has more than one meaning, but it is usually clear from the context which
meaning is to be taken. A tilde above a symbol, for example˜A,denotes a complex
quantity, the complex conjugate being denoted by an asterisk, for example˜A
∗
.A
dot over a symbol, for example˙A,denotes the time derivative of the corresponding
quantity. An asterisk is also used to denote an antiparticle or an antiatom, for
exampleν
∗
and Co
∗
.
Historical review
α optical rotation angle
[α] speciﬁc rotation
ψ ellipticity
[ψ] speciﬁc ellipticity
∇ decadic molar extinction coefﬁcient
g dissymmetry factor
V Verdet constant
← dimensionless Rayleigh or Raman circular intensity difference
R,S absolute conﬁguration in the Cahn–Ingold–Prelog notation. (R)-(+)etc.
speciﬁes the sense of optical rotation associated with a particular
absolute conﬁguration
P,M helicity designation of the absolute conﬁguration of helical molecules
Electric and magnetic ﬁelds and electromagnetic waves
λ wavelength
c velocity of light
v wavevelocity
ω angular frequency, magnitude 2πv/
λ(2πc/ λin free space)
n refractive index, magnitudec/v
n
ψ
absorption index
xviii

List of symbols xix
˜n complex refractive indexn+in
ψ
n propagation vector, magnituden
κ wavevector, magnitudeω/v(may be writtenωn/c)
E electric ﬁeld vector in free space
B magnetic ﬁeld vector in free space
D electric ﬁeld vector within a medium
H magnetic ﬁeld vector within a medium
ρ electric charge density
J electric current density
N Poynting vector
I intensity (time average of|N|)
φ scalar potential
A vector potential
P bulk polarization
M bulk magnetization
Q bulk quadrupole polarization
∇ dielectric constant
µ magnetic permeability
∇
0 permittivity of free space
µ
0 permeability of free space
Polarized light
η ellipticity of the polarization ellipse
θ azimuth of the polarization ellipse
S
0,S1,S2,S3 Stokes parameters
P degree of polarization
˜Π complex polarization vector
˜ρ
αβ complex polarization tensor
Geometry and symmetry
i,j,k unit vectors along space-ﬁxed axesx,y,z.
I,J,K unit vectors along molecule-ﬁxed axesX,Y,Z.
r position vector
l
λ
ψ
α direction cosine between theλ
ψ
andαaxes (cos
−1
lλ
ψ
αis the angle
between the
λ
ψ
andαaxes)
δ
αβ Kronecker delta
ε
αβ γ alternating tensor
T
αβ ...∇α∇β...R
−1
P parity operation
T classical time reversal operation

xx List of symbols
C charge conjugation operation
p eigenvalue ofP
2πb helix pitch
a helix radius
[
2
] symmetric part of the direct product of the representationwith itself
{
2
} antisymmetric part of the direct product of the representationwith
itself
D
(j)
irreducible representation of the proper rotation groupR
+
3
T
k
q
irreducible spherical tensor operator
Classical mechanics
v velocity vector
p linear momentum vector
L angular momentum vector
F Lorentz force vector
W total energy
T kinetic energy
V potential energy
L Lagrangian function
H Hamiltonian function
p
ψ
generalized momentum vector
Q
p normal coordinate for thepth normal mode of vibration
P momentum conjugate toQ
p,namely˙Q p
sq qth internal vibrational coordinate
L vibrationalL-matrix
Quantum mechanics
h Planck constant
¯hh /2π
ψ wavefunction
H Hamiltonian operator
e
j,vj,rjelectronic, vibrational, rotational parts of thejth quantum state
j,m general angular momentum quantum number, associated magnetic
quantum number, of a particle
l,m
l orbital angular momentum quantum number, associated magnetic
quantum number, of a particle
s,m
s spin angular momentum quantum number, associated magnetic
quantum number, of a particle
J,M total angular momentum quantum number, associated magnetic
quantum number, of an atom or molecule

List of symbols xxi
K quantum number specifying the projection of the total angular
momentum onto the principal axis of a symmetric top
g
i g-value of theith particle spin
Θ quantum mechanical time reversal operator
∇ eigenvalue of
Θ
2
A
T
transpose of operatorA
A
†
=A
T∗
Hermitian conjugate of operatorA
Y
lm spherical harmonic function
2δ tunnelling splitting
2∇ parity-violating energy difference between chiral enantiomers
G Fermi weak coupling constant
α ﬁne structure constant
g weak charge
Q
W effective weak charge
θ
W Weinberg electroweak mixing angle
σ Pauli spin operator
Z proton number
[a,b] commutatorab−ba
{a,b} anticommutatorab+ba
Molecular properties
e
i electric charge of theith particle (+efor the proton,−efor the
electron)
q net charge or electric monopole moment
µµ electric dipole moment vector
m magnetic dipole moment vector
Θαβ traceless electric quadrupole moment tensor
α
αβ real part of the electric dipole–electric dipole polarizability tensor
α
ψ
αβ
imaginary part of the electric dipole–electric dipole polarizability
tensor
G
αβ real part of the electric dipole–magnetic dipole optical activity tensor
G
ψ
αβ
imaginary part of the electric dipole–magnetic dipole optical
activity tensor
A
α,βγ real part of the electric dipole–electric quadrupole optical activity
tensor
A
ψ
α,βγ
imaginary part of the electric dipole–electric quadrupole optical
activity tensor
G
αβ real part of the magnetic dipole–electric dipole optical activity tensor
G
ψ
αβ
imaginary part of the magnetic dipole–electric dipole optical
activity tensor

xxii List of symbols
Aα,βγ real part of the electric quadrupole–electric dipole optical activity
tensor
A
ψ
α,βγ
imaginary part of the electric quadrupole–electric dipole optical
activity tensor
˜α
αβ,etc. complex polarizabilityα αβ−iα
ψ
αβ
,etc. (the minus sign arises from
the choice of sign in the exponents of the complex dynamic electric
and magnetic ﬁelds)
α isotropic invariant ofα
αβ
G
ψ
isotropic invariant ofG
ψ
αβ
β(α)
2
anisotropic invariant ofα αβ
β(G
ψ
)
2
anisotropic invariant ofG
ψ
αβ
β(A)
2
anisotropic invariant ofA α,βγ
κ dimensionless polarizability anisotropy
Spectroscopy
[θ] speciﬁc rotation
η ellipticity
I
R
,I
L
Rayleigh or Raman scattered intensity in right (R
(L
D(j←n)dipole strength for thej←ntransition
R(j←n)rotational strength for thej←ntransition
¯hδ Zeeman splitting
A,B,C FaradayA-,B-andC-terms

1
Ahistorical reviewof optical activityphenomena
Yet each in itself–this wastheuncanny,theantiorganic,thelife-denying
characterof them all –eachof them was absolutely symmetrical, icily
regular inform.Theywere tooregular, as substanceadaptedtolifenever
wasto this degree–theliving principleshudderedatthis perfe
ctpreci-
sion,found itdeathly,thevery marrowofdeath – Hans Castorpfelthe
understoodnowthereason whythebuildersofantiquity purposely and
secretly introduced minutevariationsfrom absolutesymmetry intheir
co
lumnar structures.
Thomas Mann(TheMagic Mountain)
1.1Introduction
InthePreface,anoptical activityphenomenon was deﬁnedasonewhoseorigin may
bereducedtoadifferentresponseofa systemtoright- and left-circularly polarized
light.This ﬁrstchapterprovidesareview,from a historical p
erspective,of themain
featuresofa rangeofphenomenathatcan beclassiﬁed as manifestationsof optical
activity,togetherwithafeweffectsthatarerelatedbutarenotstrictlyexamples
of optical activity.Th
ereaderisreferredto thesplendid books by Lowry (1935
Partington (1953 on (1982forfurther historical details.
Thesymbols and unitsemployedinthis reviewarethoseencounteredinthe
earlierliterature, which uses CGS units almostexclusively; buttheseare
notnec-
essarilythesameasthoseusedintherestofthebook in whichthetheoryofmany
of thephenomena includedinthereviewaredevelopedindetailfromtheuniﬁed
viewpointofthemolecular scatteringofpo
larized light. In particular,thetheoretical
developmentin subsequentchaptersemploys SI units sincethesearecurrently in
favour internationally.
1

2 Ahistorical review of optical activity
1.2Natural opticalrotationandcirculardichroism
Optical activity was ﬁrstobserved by Arago(1811theformofcolours in sunlight
thathad passedalongtheoptic axisofa quartz crystal placedbetweencrossed
polarizers. SubsequentexperimentsbyBi
ot(1812)establishedthatthecolours
wereduetotwodistincteffects:optical rotation,thatistherotationof theplaneof
polarizationofa linearly polarized lightbeam; andoptical rotatory dispersion,that
istheun
equal rotationof theplaneofpolarizationoflightofdifferentwavelengths.
Biotalsodiscoveredasecondformofquartz which rotatedtheplaneofpolarization
intheoppositedirection. Biot(1818ecognized subsequent
lythattheangleof
rotationαwas inversely proportionalto thesquareofthewavelength
λof thelight
foraﬁxedpathlengththroughthequartz.Themoreaccurate experimental data
availabletoDrude(1902)enabled himtoreplaceBiot’s lawofinversesquaresby
α=
λ
j
Aj
λ
2
−λ
2
j
, (1.2.1)
whereA
jis a constantappropriate to thevisibleornear ultravioletabsorption
wavelength
λj.Modern moleculartheoriesof optical rotation all provideequations
of thisformfortransparentregions.
Optical rotation was soon discoveredinorganic liquids such asturpentine(Biot,
1815), as well as in alcoholic solutionsofcamphor and aqueous soluti
onsofsugar
andtartaric acid,thelastbeing reported in 1832 (Lowry, 1935). Itwas appreciated
thattheoptical activityofﬂuids mustresideintheindividual molecules, and may
beobservedevenwhenthemoleculesareoriented in randomfashion; whereast
hat
ofquartzisapropertyof thecrystal structureand not of theindividual molecules,
sincemolten quartzisnot optically active. As discussedindetail in Section 1.9
below, itwaseventually realizedthatthesourceofnaturaloptical activityisa
chiral(hande
d) molecularor crystal structurewhich ariseswhenthestructurehas
asufﬁciently low symmetrythatitis notsuperposableonits mirror image.Thetwo
distinctformsthatcanexistaresaidtohaveoppositeabsolute conﬁgurations, and
thesegenera
te optical rotationsof equal magnitudebutoppositesenseatagiven
wavelength.
Therelationship between absoluteconﬁguration andthesenseofoptical rota-
tion is subtleand hasexercisedtheoreticiansforagood many years.Th
emodern
systemforspecifyingtheabsoluteconﬁgurationofmostchiral molecules is based
ontheR(forrectus) andS(forsinister) systemofCahn, Ingold and Prelog, sup-
plementedwiththeP(for plus) andM(for minus) designationformole
culesthat
haveaclear helical structure.Thesenseofoptical rotation (usually measuredat
thesodium D-linewavelengthof589 nm) associatedwith a particular absolute
conﬁgurationisgiven in brackets,forexample(R)-(−)or(S)-(+). Eliel and Wilen
(1994 ec
onsultedforfurtherdetails.Thedeﬁnitivemethodofdetermining

1.2 Natural optical rotation 3
z
Fig. 1.1Theinstantaneouselectric ﬁeld vectorsofa right-circularly polarized
lightbeam propagating alongz.Avectorinaﬁxed planerotatesclockwisewhen
viewedinthe−zdirection.
absoluteconﬁguration is via anomalous X-ray scattering associatedwiththepres-
enceofarelatively heavy atom substitutedinto themolecule, ﬁrstdemonstrated
by Bijvoetet al.(1951 tudyofsodium rubidiumtartrate.However, many
chiral moleculesaren
otaccessibletoX-ray crystallography:forthesecasesopti-
cal activityphenomena such asoptical rotation, which areintrinsically sensitiveto
molecular chirality, arebeing usedwith increasing success. Anoptical methodthat
can differentiatebetweenthetw
oenantiomersofa chiral compound is referredto
as achiropticaltechnique.
Fresnel’s celebratedtheoryof optical rotation (Fresnel, 1825)followedfrom his
discoveryofcircularly polarized light. In a circularly polarized lightbeam,thetipof
theelectric ﬁeld ve
ctorinaﬁxed planeperpendicularto thedirectionofpropagation
tracesouta circlewithtime:traditionally,thecircular polarization is saidtoberight
handed(positive)orlefthanded(negative)dependingonwhethertheel
ectric ﬁeld
vectorrotatesclockwiseoranticlockwise,respectively, whenviewedinthis plane
by anobserverlookingtowardsthesourceofthelight.Atagiven instant,the
tipsof theelectric ﬁeld vectors distributedalongthe
directionofpropagationofa
circularly polarized lightbeam constituteahelix, as shown in Fig. 1.1. Sincethe
helix movesalongthedirectionofpropagation, butdoesnotrotate,theprevious
deﬁnitionofrightand lefthandedn
ess corresponds withthehandednessof thehelix,
forasthehelix movesthroughtheﬁxed plane,thepointofintersectionof thetipof
theelectric ﬁeld vectorwhenviewedtowardsthelightsourcer
otatesclockwisefor
a right-handedhelix and anticlockwiseforaleft-handedhelix. A particularly clear
accountofcircularly polarized lightandof thepitfallsthatmay arisein its graphical
description may befound inthebook by Kliger, Lewis and Randall (1990
Fresnelrealizedthatlinearly polarized lightcan beregarde
d as a superposition
ofcoherentleft- and right-circularly polarized lightbeamsof equal amplitude,the
orientationof theplaneofpolarizationbeing afunctionof therelativephasesof the
twocomponents.This is illustra
ted in Fig. 1.2a.Heattributedoptical rotationtoa

4 Ahistorical review of optical activity
E
E
(a)( b)
E
L E
R
E
R
E
L

α
θ
L
θ
R
Fig. 1.2(a)Theelectric ﬁeld vectorofa linearly polarized lightbeam decomposed
intocoherentright- and left-circularly polarizedcomponents.Thepropagation
directionisoutoftheplaneofthepaper. (b)Ther
otatedelectric ﬁeld vectorat
somefurtherpointintheoptically activemedium.Takenote ofFig. 1.1 ifconfused
by Fig. 1.2b.
differenceinthevelocityofpropagationof theleft- and right-circularly polarized
componentsof thelinearly polarizedbeam inthemedium,fortheintroductionof
a phasedifferencebetweenthecircularly polarizedco
mponentswould changethe
orientationof theplaneofpolarization, as shown in Fig. 1.2b. Supposethata linearly
polarized lightbeamofangularfrequencyω=2πc/
λenters atransparentoptically
activemedium atz=0. If,at a given instant,theelectric ﬁeld vectorsof theright-
and left-circularly polarizedcomponentsatz=0areparallelto thedirectionof
polarizationof thelinearly polarized lightbe
am,thenat the same instanttheelectric
ﬁeld vectorsof theright- and left-circularly polarizedcomponentsatsomepoint
z=lintheoptically activemedium areinclinedatanglesθ
R
=−2πcl/ λv
R
and
θ
L
=2πcl/ λv
L
,respectively,to this direction, wherev
R
andv
L
arethevelocities
of theright- and left-circularly polarizedcomponentsinthemedium.Theangleof
rotation in radians isthen
α=
1
2
(θ
R
+θ
L
)=
πcl
λ
∗
1
v
L
−
1
v
R
θ
. (1.2.2)
Sincetherefractiveindexisn=c/v,theangleofrotation in radians per unitlength
(measuredinthesameunitsas
λ) can bewritten
α=
π
λ
(n
L
−n
R
), (1.2.3)
and isthereforeafunctionof thecircular birefringenceof themedium,thatisthe
differencebetweentherefractiveindicesn
L
andn
R
forleft- and right-circularly
polarized light.

1.2 Natural optical rotation 5
Inthechemistry literature,themedium is saidtobedextro rotatoryiftheplane
ofpolarizationrotatesclockwise(positiveangleofrotation), andlaevo rotatoryif
theplaneofpolarizationrotatesanticlockwise(negativeangleofrotation), whe
n
viewedtowardsthesourceofthelight.Thepathofa linearly polarized lightbeam
in atransparentoptically activemedium is characterizedbyahelical patternof
electric ﬁeld vectors, sincetheorientationof eachelectric ﬁeld vectorisaf
unction
onlyofitspositioninthemedium, although its amplitudeis afunctionof time.
Theformof theDrudeequation (1.2.1followsfrom (1.2.3fanexpressionfor
thewavelengthdependenceoftherefractiveind
ex such as
n
2
=1+
λ
j
Cjλ
2
λ
2
−λ
2
j
(1.2.4)
is used, whereC
jisaconstantappropriate to thevisibleornear ultravioletab-
sorptionwavelength
λj.This is a versionofSellmeier’sequation (1872Thus if
theC
jsareslightly differentfor right- and left-circularly polarized light,anex-
pressionfor(n
L
)
2
−(n
R
)
2
isfound. But(n
L
)
2
−(n
R
)
2
=(n
L
−n
R
)(n
L
+n
R
), and
sincen
L
andn
R
arecloseton,therefractiveindexfor unpolarized light,thevalue
of(n
L
+n
R
) may betakenas2n, and Drude’sequation (1.2.1obtainedwith
A
j=πλ(C
L
j
−C
R
j
)/2n.This simpleargumentservestoillustratehowoptical ro-
tation can begeneratedifamechanismexists givingC
L
j
ω=C
R
j
.
Sincerefraction and absorptionareintimately related, anoptically activemedium
should absorb right- and left-circularly polarized lightdifferently.This was ﬁrst
observed by Haidinger (1847 ethystquartz crystals, and laterbyCotton
(1895olutionsofcopper and chromiumtartrate. Fur
thermore, linearly polarized
lightbecomeselliptically polarizedinanabsorbingoptically activemedium: since
elliptically polarized lightcan bedecomposedintocoherentright- and left-circularly
polarizedcomponentsofdifferentamplitud
e, as illustrated in Fig. 1.3,thetraditional
theory ascribesthegenerationofanellipticitytoadifferenceintheabsorptionof
thetwocircular components.Theellipticityψisobtainedfromtheratioofthe
minor and maj
oraxesof theellipse, which aresimplythedifferenceand sumof
theamplitudesof thetwocircular components:
tanψ=(E
R−EL)/(ER+EL). (1.2.5)
WhenE
R>EL,ψis deﬁnedtobepositive,correspondingtoaclockwiserotation
of theelectric ﬁeld vectorof theelliptically polarizedbeam in a ﬁxed plane.The
attenuationof theamplitudeofa lightbeam by an absorbing medium is relatedto
theabso
rption indexn
θ
and pathlengthlby
E
l=E0e
−2πn
θ
l/λ
. (1.2.6)

6 Ahistorical review of optical activity
E
L
E
R
ψ
Fig. 1.3Elliptical polarization, speciﬁedbytheangleψ,resolvedintocoherent
right- and left-circular polarizationsofdifferentamplitude.
Theellipticityisthen
tanψ=
e
−2πn
θR
l/λ
−e
−2πn
θL
l/λ
e
−2πn
θR
l/λ
+e
−2πn
θL
l/λ
=
e
π(n
θL
−n
θR
)/λ
−e
−πl(n
θL
−n
θR
)/λ
e
πl(n
θL
−n
θR
)/λ
+e
−πl(n
θL
−n
θR
)/λ
=tanh
ψ
πl
λ
(n
θL
−n
θR
)
η
, (1.2.7)
wheren
θL
andn
θR
aretheabsorption indicesforleft- and right-circularly polarized
light.For smallellipticities, in radians per unitlength(measuredinthesameunits
as
λ),
ψ≈
π
λ
(n
θL
−n
θR
). (1.2.8)
Theellipticityisthereforeafunctionof(n
θL
−n
θR
),thecircular dichroismof the
medium.
Apartfromthefactthattheyaresigned quantities, circular dichroism andoptical
rotatory dispersionhavewavelengthdependencecurvesintheregionofanelec-
tronic absorptionvery similarto thoseforc
onventional absorption and refraction,
respectively.Theseareillustrated in Fig. 1.4. Circular dichroism,togetherwiththe
anomalousoptical rotatory dispersion which accompaniesitintheabsorptionre-
gion, areknown collect
ively astheCotton effect.Theellipticity maximum coincides
withthepointofinﬂectioninthecurveofoptical rotatory dispersion, which ideally
coincideswiththemaximumofanelectronic absorption band at
λj.Theellipticity

1.2 Natural optical rotation 7
0
ellipticity
rotation
λ
j λ
Fig. 1.4Theellipticity and anomalousoptical rotatory dispersionintheregion
of theelectronic absorptionwavelength
λj.Thesigns shown herecorrespondtoa
positiveCottoneffect.
andoptical rotatory dispersion curves always havetherelativesigns shown in
Fig. 1.4foranisolated absorption band in a given sample.Atwavelengthsfar re-
movedfromany
λj,therotatory dispersionisgivenbytheDrudeequation (1.2.1
butintheanomalous regiontheDrudeequation mustbemodiﬁedtoremovethe
singularity andtoallowfortheﬁniteabsorption width. Ifthereareseve
ral adjacent
absorption bands,thenetCottoneffectwill bea superpositionof theindividual
Cottoneffectcurves.
Optical rotationmeasurementsareusually presentedasthespeciﬁc optical ro-
tatory power(often called simplythespeciﬁc rotation)
[α]=
αV
ml
, (1.2.9)
whereαistheoptical rotationindegrees,Visthevolumecontaining a massmof
theoptically activesubstance, andlisthepathlength. In muchof thechemistry
literature, CGS unitsareused andlis speciﬁedindecimetres. Similarly, circular
dichr
oism measurementsareusually presentedasthespeciﬁc ellipticity
[ψ]=
ψV
ml
, (1.2.10)
whereψis measuredindegrees. Circular dichroism is now usuallyobtained directly
by measuringthedifferenceinthedecadic molarextinctioncoefﬁcients
ψ=
1
cl
log
I
0
Il
, (1.2.11)
whereIistheintensityof thelightwaveandcistheconcentrationofabsorbing
moleculesinmolesperlitre,ofseparateleft- and right-circularly polarized light
beams, ratherthan viatheellipticity inducedinaninitially linearly polariz
ed light
beam. Sincetheintensityofawaveis proportionalto thesquareoftheamplitude,
therelationship betweenextinctioncoefﬁcientand absorption indexisobtained

8 Ahistorical review of optical activity
from (1.2.6 ting
I
l=I0e
−2.303ψcl
=I0e
−4πn
θ
l/λ
, (1.2.12)
from which itfollowsthat
n
θ
=
2.303
λcψ
4π
. (1.2.13)
Thefollowingexpression, givingtherelationship betweentheellipticityindegrees
andthedecadic molar circular dichroism, isoftenencounteredinthechemistry
literature:
[θ]=3300(ψ
L
−ψ
R
)=3300ηψ. (1.2.14)
Thisobtainsfrom (1.2.8 fCGS unitsareused and itis
rememberedthatthepathlengthisspeciﬁedindecimetres.
Auseful dimensionless quantityisthedissymmetry factor(Kuhn, 1930)
g=
ψ
L
−ψ
R
ψ
=
ψ
L
−ψ
R
1
2
(ψ
L
+ψ
R
)
, (1.2.15)
which istheratioofthecircular dichroismto theconventional absorption.The
constantsthatariseinthedeterminationofabsoluteabsorptionintensitiestherefore
cancelout, andgoftenreducestosimpl
eexpressions involving justthemolecular
geometry. Sincecircular dichroism isofnecessity always determinedinthepresence
ofabsorption,gis alsoan appropriatecriterionofwhetherornotcircular dichroism
in a particular absorption band is measurable,giventheavailableinstrum
ental
sensitivity.
Althoughoptical rotatory dispersion and circular dichroism havebeenknown
formorethan 100 years, untilthemiddleofthetwentiethcentury mostapplica-
tions in chemistry utilized justtheoptical rotationatsometransparent
wavelength,
usuallythesodium D lineat589 nm.Thenintheearly 1950s a revolutioninthe
studyof optically activemolecules was broughtaboutthroughtheintroductionof
instrumentstomeasureoptical rotatory dispersionro
utinely:this was possibleas
aresultofdevelopmentsinelectronics, particularlytheadventofphotomultiplier
tubes, sothattherecordingofvisibleand ultravioletspectra nolongerdepended
ontheuseofphotographic plate
s. Steroid chemistry wasoneoftheﬁrstareasto
beneﬁt, mainly as a resultofthepioneering workofDjerassi (1960truments
tomeasurecircular dichroism routinely weredevelopedintheearly 1960s when
electro-optic modulators, which switchth
epolarizationof theincidentlightbe-
tween rightand leftcircular ata suitablefrequency, becameavailable, andthis
techniqueis nowgenerally preferredoveroptical rotatory dispersionbecauseit
providesbetter discriminationbetweenoverlapping abso
rption bands (thecircular

1.2 Natural optical rotation 9
dichroism lineshapefunctiondropstozeromuch morerapidlythantheoptical
rotatory dispersion lineshapefunction).
Conventionaloptical rotation and circular dichroism utilizevisibleorultra-
violetradiation: sincethisexcitestheelectro
nic statesof themolecule,these
techniques can beregardedasformsofpolarizedelectronic spectroscopy.Thus itis
thespatial distributionof theelectronic statesresponsiblefor a particular circular
dichroism band,forexample,
thatis probed.This canoftenberelatedto thestere-
ochemistryof themolecular skeletoninwaysthatareelaboratedinlater chapters.
Itisoftenstatedthatoptical rotatory dispersion and circular dichroism areusedto
lookatthestereochemis
tryof themoleculethroughtheeyesof thechromophore
(thestructural group absorbingthevisibleornear ultravioletradiation).Theﬁrst
successful applicationof this anthropomorphic viewpointwasthecelebrate
doctant
ruleofMofﬁtet al.(1961 elatesthesign and magnitudeofCottoneffects
inducedintheinherentlyoptically inactivecarbonyl chromophorebythespatial
arrangementofperturbing groups intherestofthemolecule.Thetheor
etical basis
of theoctantruleis discussedindetail in Chapter5.
Therearetwotopics closely relatedtocircular dichroismthatshould bemen-
tioned, namely circular polarizationofluminescence, and ﬂuorescencedetected
circular dichroism.Thelatter is simply an alternativemeth
odofmeasuring circu-
lar dichroism in samples, usually biological, withpoortransmission, and involves
measurementofadifferenceintheﬂuorescenceintensityexcited by right- and
left-circularly polarized incidentlightwithwavelengthinthevicinityofanelec-
tronic abs
orption band (Turner,Tinocoand Maestre, 1974).Theformerrefersto
a circularly polarizedcomponentinthelightspontaneouslyemittedfromanop-
tically activemoleculein anexcitedstate.Thewell-known relationship bet
ween
theEinstein coefﬁcientsfor absorption and spontaneousemission suggeststhatthe
circular dichroism and circular polarizationofluminescenceassociatedwith a par-
ticular molecularelectronictransition will provideidentical structural informati
on.
However, differencesbetweentheseobservables willoccur whenthestructureof
themoleculeinthegroundelectronic statediffersfromthestructureintheexcited
luminescentsta
te.Thus circular dichroism is a probeofground statestructureand
circular polarizationofluminescenceis a probeofexcitedstatestructure. Under
certain conditions, circular polarizationofluminescencecan beusedtostudy as-
pectsof excitedstatem
olecular dynamics such as photoselection and reorientational
relaxation. A detaileddevelopmentofthesetopics isoutsidethescopeofthis book,
andtheinterestedreaderisreferredtoreviews by Richardson and Metcalf(2000)
and Dekkers (2000
An inte
resting variantofﬂuorescencedetected circular dichroism has been
mooted: circular differential photoacoustic spectroscopy (Saxe, Faulkner and
Richardson, 1979). In conventional photoacoustic spectroscopy, lightenergy is

10 Ahistorical review of optical activity
absorbed by a sample, andthatportionof theabsorbedenergy which is subse-
quently dissipatedintoheatis detectedinthefollowing manner. Iftheexciting
lightis modulatedintime,thesampleheating and cooling will alsobemodulated.
Theresulting
temperatureﬂuctuations leadto thetransformationof thethermal
energy intomechanicalenergy carriedbysound wavesinthesamplewhich are
detectedwith a microphone. In circular differential photoacoustic spectroscopy,
thepolarizationof t
heincidentlightis modulatedbetween right- and left-circular
andtheintensityofany sound wavesdetectedatthemodulationfrequency will
beafunctionof thecircular dichroismof theabsorbing chiral sample.Itcould be
morewidely applicablethan ﬂuorescenced
etected circular dichroism becausea
ﬂuorescing chromophoreis notrequired, and could beparticularly attractivefor
studying moleculeson surfaces.
As well astheir general importancein stereochemistry, naturaloptical activity
techniques,especially ultravi
oletcircular dichroism, havebecomecentral physical
methods in biochemistry and biophysics sincetheyaresensitivetothedelicate
stereochemicalfeaturesthatdeterminebiologicalfunction (Fasman, 1996; Berova,
Nakanishi and Woody, 2000).
1.3Magneticopticalrotatio
nandcirculardichroism
Faraday’s convictionof theconnectionbetweenelectromagnetism and lightled him
to thediscoveryof therotationof theplaneofpolarizationofa linearly polarized
lightbeamontraversing a r
odoflead borateglass placedbetweenthepolesofan
electromagnet(Faraday, 1846). A Faraday rotationisfound when lightistransmitted
through any medium, isotropicororiented, inthedirectionofa magnetic ﬁeld.
Thesenseofrotationde
pendsontherelativedirectionsof thelightbeam and
themagnetic ﬁeld, and is reversedonreversingeitherthedirectionof thelight
beamorthemagnetic ﬁeld.Thus magnetic rotatory powerdiffersfromna
tural
rotatory powerinthattherotations areadded, ratherthan cancelled,onreﬂecting
thelightbackthroughthemedium. Itwas soon discoveredthatmagneticoptical
rotation variesinversely withthesquareoft
hewavelength, in accordancewith
Biot’s lawfornaturaloptical rotation; although itwas subsequentlyfoundthata
better approximationisprovidedbyaformula similartoDrude’sequation (1.2.1
ThequantitativeinvestigationsofVerdet(1854
esummarizedinVerdet’s law
fortheangleofrotationper unitpathlength in a magnetic ﬁeldBmaking an angle
θwiththedirectionofpropagationof thelightbeam:
α=VBcosθ, (1.3.1)
whereVistheVerdetconstantforthe
materialfor a givenwavelength andtemper-
ature.For lightpassingthroughthemedium inthedirectionof themagnetic ﬁeld
(northpoletosouthpole)mostdiamagnetic materials rotate theplaneofpolarization

1.3Magnetic optical rotation 11
ellipticity
rotation
ellipticity
rotation
0 0
(a)( b)
λ
j
λ
jλ λ
Fig. 1.5Themagneticellipticity and anomalousoptical rotatory dispersionshown
by (a) diamagnetic and (b) paramagnetic samplesintheregionof theelectronic
absorptionwavelength
λj.
in an anticlockwisesensewhenviewedtowardsthelightsource,correspondingto
anegativerotationinthechemistry convention.Thisoptical rotationisinthesame
senseasthecirculationofcurrentin a s
olenoid producing anequivalentmagnetic
ﬁeld.
Magneticoptical rotation can bedescribedintermsofdifferentrefractiveindices
forleft- and right-circularly polarized light, and (1.2.3esequally wellto
natural and magnetic rotation, althoughtheoriginof thecircular birefringe
nce
is differentinthetwocases. In regionsofabsorptionthereisadifferenceinthe
absorptionofleft- and right-circularly polarized lightinthedirectionof themagnetic
ﬁeld, and linearly polarized lightacquiresanellipticitygivenbyt
hesameequation
(1.2.8)thatdescribesnatural circular dichroism.
Verdetalsodiscoveredthatiron salts in aqueous solutionshow a magnetic rota-
tion which is intheoppositesensetothatofwater, arisingfromtheparamagnetism
ofiron salts. In general,onlyth
emagnetic rotatory dispersionsofdiamagnetic mate-
rialsfollowthelawsofDrudeand Verdet;thoseofparamagnetic materials aremore
complicated.Theinﬂuenceoftemperatureonthemagnetic rotationofdiamagnetic
materials is slight,butparamagnetic materials showaprono
unced variationwith
temperaturewhich is relatedto thetemperaturedependenceofparamagnetism.
Thedispersionwithwavelengthof themagnetic rotation andellipticityina
regionofabsorptiondependsontherelat
ivemagnitudesof thediamagnetic and
paramagnetic contributions.Thetwoideal casesareillustrated in Fig. 1.5.The
diamagnetic rotation curveshown is actuallytheresultantoftwoequal andopposite
optical rotatory dispersion curvesfortwoadjacentelec
tronic absorption bands, and
is usually symmetric.Theparamagnetic rotation curveis likeanoptical rotatory
dispersion curvefor a singleabsorption band, and is usually unsymmetric.
Faraday had lookedfortheeffectofa magnetic ﬁeldonasourceofradiation, but
withoutsuccess becausestrong ﬁelds and sp
ectroscopesofgoodresolutionwerenot
availabletohim.TheﬁrstpositiveresultswereobtainedbyZeeman (1896 ere
describedasabroadeningof thetwolinesof theﬁrstprincipal doublet fromasodium

12 Ahistorical review of optical activity
||
L R
(a)( b)
Intensity
Intensity
λ
j −
∇
λ λ
j −
∇
λλ
j +
∇
λ λ
j +
∇
λλ
j λ λ
j λ
⊥⊥
Fig. 1.6Thenormal Zeemaneffect(a)for lightemittedperpendicularto the
magnetic ﬁeld and (b)for lightemittedinthedirectionof themagnetic ﬁeld.
ﬂameplacedbetweenthepolesofapowerfulelectromagnet.Soonafterwards,
Lorentzshowedthathiselectrontheoryofradiation and matter accommodatedthis
observation: whenviewedperpendicularto t
hemagnetic ﬁeld,thespectral lines
should besplitinto threelinearly polarizedcomponentswiththecentral (unshifted)
linelinearly polarized parallel( )to theﬁeld andtheothertwolines linearly
polarizedperpendicular (⊥)to the
ﬁeld; whenthemagnetic ﬁeld pointstowardsthe
observer,thereshould betwolinesoneither sideoftheoriginal linewiththehigh and
lowwavelength linesshowing right- and left-circular polarizations, respectively.
This is illustrated in Fig. 1.6.Th
edisplacements≠ λshould beproportionalto the
magnetic ﬁeld strength.Thesepredictions wereveriﬁedlaterbyZeeman, butonly
forcertain spectral linesshowing whatis now calledthenormalZeemaneffect;
other lines (includingthecomponent
sof theﬁrstprincipal sodium doublet) split
intoagreater numberofcomponents and aresaidtoshowtheanomalousZeeman
effect.Thenormaleffectis simply a special casein whichtheeffectsof electron
spin areabsent.
Sincetheright- and left-circularly polarizedcompo
nentsoflightemittedbyan
atominthepresenceofa magnetic ﬁeld aredifferentiated,theZeemaneffectcan
beregarded as a manifestationof optical activity. Indeed, itwas soonrecognized
thatthemainfeaturesof theFaradayeffec
tcan beexplainedintermsof theZeeman
effect. Sinceright- and left-circularly polarized lightbeams arealsoabsorbedat
theslightly differentwavelengths
λ
R
j
=λj+≠λandλ
L
j
=λj−≠λin a magnetic
ﬁeld alongthedirectionofpropagationof theincidentbeam,onecould use,for
example,equation (1.2.4fortherefractiveindexwithtwoabsorptionwavelengths
λ
R
j
andλ
L
j
:
(n
L
)
2
−(n
R
)
2
=Cjλ
2
′
1
λ
2
−
πλ
L
j

2
−
1
λ
2
−
πλ
R
j

2

, (1.3.2)

1.3Magnetic optical rotation 13
0
α
A
j
________________ A
j
________________
λ
2

− (
)
2
λ
R
j
λ
L
j λ
R
j
λ
2

− (
)
2
λ
L
j
λ
Fig. 1.7Thediamagneticoptical rotatory dispersion curvegeneratedfromtwo
equal andoppositeDrude-typecurvescentredon
λ
L
j
andλ
R
j
.Thesign shown here
obtains whenthemagnetic ﬁeld is inthedirectionofpropagationof thelightbeam.
which is simplythesumof twoequal andopposite optical rotatory dispersion curves
centredon
λ
L
j
andλ
R
j
,sothat
α≈
πC
jλ
2n
′
1
λ
2
−
πλ
L
j

2
−
1
λ
2
−
πλ
R
j

2

. (1.3.3)
If(1.3.3odiﬁedtoremovethesingularities and allowfor a ﬁniteabsorption
width,thegeneralformofa diamagneticoptical rotation curveis reproduced, as
illustrated in Fig. 1.7. Similarly,thegeneralformofa diamagneticellipticity curve
is repro
ducedfromthesumof twoequal andopposite ellipticity curvescentredon
λ
L
j
andλ
R
j
.
Noticethatin justifying Drude’sequation (1.2.1forthedispersionofnatural
optical rotationweinvoked a slightdifferenceintheconstantsC
jin Sellmeier’s
equation (1.2.4fortherefractiveindicesfor right- and left-circularly polarized
light,butassumedthattheresonancewavelengths werethesame,whereas in de-
velopingtheform (1.3.3forthediamagnetic rotation curvew
eassumedthatthe
C
jsarethesamefortheoppositecircular polarizations butthattheresonance
wavelengths aredifferent.This illustratestwodistinctmechanisms by whichopti-
cal rotation (and circular dichroism) can begenerated, and weshall seelater, when
general quantum mechanical
theoriesaredeveloped,thatanaloguesofbothmech-
anisms can contribute tobothnatural and magneticoptical rotation and circular
dichroism.
Themain signiﬁcanceofmagneticoptical activityinchemistry isthatitprovides
informationaboutground andexci
tedelectronic statesofatoms and molecules. As
indicatedabove, magnetic circular dichroism isthedifferencebetweenleft- and

14 Ahistorical review of optical activity
right-circularly polarizedZeeman spectra andthereforeprovidesnonewinforma-
tionwhentheZeeman componentsofatransitionareresolved. Butsincemagnetic
circular dichroism can bemeasuredinbroad bands whereconventional Zeeman
effect
sareundetectable,theessenceofits valueis inextendingthecircularly po-
larizedZeemanexperimenttobroad spectra.Thesimplestuseofmagnetic circular
dichroism isfordetecting weaktransitions which areeither buried underastronger
transition
orarejust tooweaktobeobservedinconventional absorption. Magnetic
circular dichroism has provedmostuseful inthestudyof theexcitedelectronic
statesof transitionmetal complexes andofcolour centres in crystals; particularly
t
heir symmetry species, angular momenta,electronic splittings and vibrational–
electronic interactions. Magneticoptical activity has alsobeenuseful inthestudy
of organic and biological systems,especiallyfor cyclicπelectronmolecules such
as porphyrins.
Notsurprisingly,t
hereis a magnetic versionof thecircular polarizationoflumi-
nescence(outlinedinSection 1.2)thatis shown by all molecules in a magnetic ﬁeld
parallelto thedirectionof observationof theluminescence. Againthis givesinfor-
mationabo
utexcitedstatemolecular properties, and werefertoRichardson and
Riehl (1977forfurtherdetails.Therearealsomagnetic versionsofﬂuorescence
detected circular dichroism, and circular differential photoacoustic spectroscopy.
1.4Light scatteringfro
moptically activemolecules
Optical rotation and circular dichroism areconcernedwiththepolarization charac-
teristicsoflighttransmittedthrough anoptically activemedium, and aretherefore
associatedwithrefraction. Refractionisoneconsequenc
eofthescatteringoflight
bytheelectrons and nucleiintheconstituentmoleculesof themedium, and can be
accompanied by Rayleigh and Raman scattering in all directions. Rayleigh scat-
tered lighthasthesamefrequency astheincidentlight,whereasthef
requencyof
Raman scattered lightis shiftedfromthatoftheincidentlightby amountscorre-
spondingtomolecular rotational, vibrational andelectronictransitions. Specular
reﬂectionbypolished surfacesofglass and metals, and diffusereﬂ
ectionby,for
example,asheet ofpaper, can alsobeattributedultimatelytomolecular scattering.
Thescattering descriptionofrefraction is subtle, and involvesinterferencebe-
tweentheunscatteredcomponentofthelightwaveandt
henetplanewavefrontin
theforward directionfrom planar arraysofindividual scatterers inthemedium.
This process is discussedindetail in Chapter3.This interferencemodiﬁesthepo-
larizationpropertiesof thelightfrom individual molecular scatterers, sot
helight
refractedthrough anoptically activemedium has differentpolarizationproperties
fromtheRayleigh- and Raman-scattered light(andthereﬂected light).Thus with
linearly polarized lightincidentonisotropicoptically activesample
sattransparent

1.4 Optical activity in light scattering 15
wavelengths,therefracted lightsuffers a rotationof theplaneofpolarizationwith
noellipticityproduced, whereasthescattered lightacquiresanellipticitybutno
rotationof theplaneofpolarization.
Theoriginof thee
llipticity in Rayleigh and Raman scattered lightiseasily
understoodingeneralterms becauseoptically activemoleculesrespond differently
toright- and left-circularly polarized light, which arethereforescatteredtodifferent
extents. Consequently,thec
oherentright- and left-circularly polarizedcomponents
intowhich a linearly polarizedbeam can beresolvedarescattereddifferently, and
arenolongerof equal amplitudeinthescattered light, which isthereforeelliptically
polarized. A dramaticexampleis pr
ovidedbycholesteric liquid crystals which
haveenormousoptical rotatory powers sothatthelightreﬂectedfromthesurface
is almostcompletely circularly polarized (Giesel, 1910).
Insteadofmeasuring anellipticity in Rayleigh and Raman scattered light,adiffer-
enceint
hescatteredintensities in right- and left-circularly polarized incidentlight
(thecircular intensity difference) may bemeasured directly instead. Attransparent
wavelengths,theellipticity(ortheassociateddegree ofcircular polarization)of the
scattered lightandthecircular intensit
ydifferenceprovideequivalentinformation
aboutoptically activemolecules, butsubtledifferences can ariseatabsorbing wave-
lengths. Boththedegree ofcircular polarization andthecircular intensitydifference
aremanifestati
onsofRayleigh and Raman optical activity.
Theﬁrstattemptsto observeRayleigh and Ramanoptical activityconcentrated
onthecircular intensitydifference.Thechequered historyof theseattemptsis
brieﬂy asfollows. Gans (1923onsidered additional contributio
nstoRayleigh
scatteringfromoptically activemolecules, butomitted a crucial interferenceterm
thatgeneratestheellipticity andthecircular intensitydifference;heclaimedto
haveobservedoptical activityeffectsinthedepo
larizationratio,butdeMallemann
(1925ointedoutthatthedepolarizationratioanomaliesoriginatedinoptical
rotationof theincidentand scatteredbeams. Shortly afterthediscoveryof the
Ramaneffect, Bhagavantam and Venkateswaran (1930
found differencesinthe
relativeintensitiesofsomeofthevibrational Raman linesof twooptical isomers
in unpolarized incidentlight,buttheseweresubsequently attributedtoimpurities.
Although hehad noexplicittheory, Kastle
r (1930thoughtthat, sinceoptically
activemoleculesrespond differentlytoright- and left-circularly polarized light,a
differencemightexistinthevibrational Raman spectraof optically activemolecules
in right- and left-circularly polarized incidentlight,butthe
instrumentationatthat
timewasfartooprimitivefor himto observetheeffect.Perrin (1942edto the
existenceofadditional polarizationeffects in lightscatteredfromoptically active
molecules; butitwas notuntilthetheor
etical workofAtkins and Barron (1969
thattheinterferencemechanism (between lightwaves scattered viathemolecular
polarizability andoptical activitypropertytensors) responsiblefortheellipticity

16 Ahistorical review of optical activity
inthescattered lightandthecircular intensitydifferencewas discovered. Barron
and Buckingham (1971equently developedamoredeﬁnitiveversionof the
theory and introducedthefollowing deﬁnitionof thedimensionless Rayleigh and
Raman circular inte
nsitydifference,
←=
I
R
−I
L
I
R
+I
L
, (1.4.1)
whereI
R
andI
L
arethescatteredintensities in right- and left-circularly polar-
ized incidentlight, as an appropriate experimental quantity in Rayleigh and Raman
optical activity.Theﬁrstreportednatural Raman circular intensitydifferencespec-
tra by Bosnich, Moskovits and Ozin (1972 em, Fry and Burow (1973
originatedininstrume
ntal artifacts, butthespectra subsequently reportedinthe
chiral molecules 1-phenylethylamineand 1-phenylethanol, (C
6H5)CH(CH3)(NH2)
and (C
6H5)CH(CH3)(OH on, Bogaard and Buckingham (1973erecon-
ﬁrmed by Huget al.(1975enuine. On accountofexperimental difﬁculties,the
natural Rayleigh circular intensitydifferencehas notyetbeenobserved in small
chiral molecules, buthas beenreported in largebiological structures (Maestre
et al.,
1982;Tinocoand Williams, 1984).
Sinceall molecules can showoptical rotation and circular dichroism in a mag-
netic ﬁeld, itis notsurprisingthatall moleculesinastrong magnetic ﬁeld should
show Rayleigh and Ramanoptical activity (Barron and Buckingham, 1972). More
speciﬁcally,themagnetic ﬁeld mustbeparallelto theincide
ntlightbeamtogenerate
a circular intensitydifference, and parallelto thescattered lightbeamtogenerate
anellipticity.Thesignsof theseobservablesreverseonreversingthemagnetic ﬁeld
direction.Theﬁrstobservat
ionof thiseffectwas intheresonanceRaman spectrum
ofa diluteaqueous solutionof ferrocytochromec, a haemprotein (Barron, 1975a).
Itshould bementioned, however,thatthereis a mucholderphenomenonthatproba-
bly
falls withinthedeﬁnitionofmagneticoptical activity in lightscattering, namely
theKerr magneto-opticeffect(Kerr, 1877). Here, linearly polarized lightbecomes
elliptically polarizedwhenreﬂectedfromthepolishedpoleofane
lectromagnet:
theincidentlightmustbelinearly polarizedeither in,orperpendicularto,theplane
ofincidence,otherwiseelliptical polarizationresultsfrommetallic reﬂection.
Moresurprisingly, althoughtherear
enosimpleelectrical analoguesofmagnetic
optical rotation and circular dichroism (theywould violateparity and reversality, as
discussedinSection 1.9), Rayleigh and Ramanoptical activityshould alsobeshown
by any ﬂuid in a staticelectric ﬁeld perpendiculartoboththeincide
ntand scattered
directions (Buckingham and Raab, 1975). Electric Rayleighoptical activitywas
ﬁrstobserved by Buckingham and Shatwell (1980 eous methyl chloride.
Therehas beeninterestintheinﬂuenceon circular dichroism spectraof the
differential scatteringofright- and left-circularly polarized lightbyturbid
optically

1.5Vibrational optical activity 17
activemedia: lightscatteredoutofthesidesof thesampleremovesanintensity
fromthetransmittedbeam additionalto thatfrom absorption(Tinocoand Williams,
1984). A dramaticexampleoftheeffectis providedbycholesteric liquid crystals
(deGennes and Pr
ost, 1993): an initially linearly polarizedbeam can becomeal-
mostcompletely circularly polarizedafter passingthrough a slabon accountof
thepreferential scattering (reﬂection)of oneofthecoherentcircularly polarized
components.
Themain signiﬁcanceofRayleighop
tical activityisthat,from appropriatemea-
surements in lightscatteredat90
◦
,itprovidesameasureoftheanisotropy inthe
molecularoptical activity using an isotropic samplesuch as a liquidorsolution.
Such information canonly beobtainedfromoptical rotationor circular dichroism
measurements using anoriented samplesuch as a crystal,or a ﬂuid in a s
taticelec-
tric ﬁeld (Tinoco, 1957).Themain signiﬁcanceofRamanoptical activityisthat
itprovidesanalternativemethodtoinfraredoptical rotation and circular dichro-
ismformeasuring vibrationaloptical activity:this is discussedfurtherinthen
ext
section.
1.5 Vibrational optical activity
Ithad been appreciatedforsometimethatthemeasurementofoptical activity asso-
ciatedwithmolecular vibrations could provideawealthofdelicatestereochemical
informat
ion. Butonly sincetheearly 1970s,thanks mainlytodevelopmentsin
optical andelectronictechnology, havetheformidabletechnical difﬁcultiesbeen
overcomeand vibrationaloptical activityspectra beenobserved using bothinfrared
and Ramantechniques.
The
signiﬁcanceofvibrationaloptical activitybecomes apparentwhenitis com-
paredwithconventionalelectronicoptical activityintheformof optical rotation
and circular dichroismofvisibleand near ultravioletradiation.Theseconv
entional
techniqueshaveprovedmostvaluablein stereochemical studies, butsincetheelec-
tronictransitionfrequenciesofmoststructural unitsinamoleculeoccur inthefar
ultraviolet,theyarerestrictedtopr
obing limitedregionsofmolecules, in particular
chromophores andtheir immediateintramolecularenvironments, and cannotbe
usedatall whenamoleculelacks a chromophore(althoughoptical rotationmea-
surementsattransparentf
requencies can still beofvalue). Butsincea vibrational
spectrum, infraredor Raman, contains bandsfrom vibrations associatedwithmost
partsofamolecule,measurementsofsomeformofvibrationaloptical activity
could providemuch mor
einformation.
Theobvious methodofmeasuring vibrationaloptical activityisbyextending
optical rotatory dispersion and circular dichroism into theinfrared. Butin addition
to thetechnical difﬁculties in manipulating polarizedinfrared radiation,thereis a

18 Ahistorical review of optical activity
fundamental physical difﬁculty:optical activityisafunctionof thefrequencyof
theexciting lightand infraredfrequenciesareseveralordersofmagnitudesmaller
than visibleand near ultraviolet frequencies. Ontheother hand,theRamaneffec
t
provides vibrational spectra using visibleexciting light,themolecular vibrational
frequenciesbeing measured as small displacementsfromthefrequencyof thein-
cidentlightinthevisiblespectrumof thescattered light.Consequen
tly,thefunda-
mentalfrequency problemdoesnotariseifvibrationaloptical activityismeasured
by meansof theRaman circular intensitydifference(ordegree ofcircular polar-
ization),outlinedintheprevious section.
Natural infrare
doptical rotation was ﬁrstobservedaslong agoas 1836 by Biot
and Melloni, whopassed linearly polarizedinfrared radiationalongtheoptic axis
ofacolumnofquartz, butthis probablyoriginated mainly in near infraredelec-
tronictransitions. Furtherprogress was slow, and Lowry (1935
oncludedareview
ofinfraredoptical activitywiththeunenthusiastic statement:‘Veryfewmeasure-
mentsofrotatory dispersionhavebeen madeintheinfrared, sincethis phenomenon
shows nopointsof out
standing interest,therotatory powerdecreasing steadily with
increasing wavelength,evenwhen passingthrough an infrared absorption band’.
Anomalous infraredoptical rotatory dispersion in quartz was reportedbyGutowsky
(1951tthis work was challengedbyWest
(1954tzin (1964eanalyzed
theearly near infraredoptical rotatory dispersiondataofLowry and Snow (1930
and concludedthat, whileelectronictransitions weremainly responsible,contri-
butionsfrominfrared vibrationaltransitions werec
ertainly present.Hediger and
G¨unthard (1954eportedtheobservationofanomalousoptical rotatory dispersion
associatedwithanovertoneinthevibrational spectrumof2-butanol, butWyss and
G¨unthard (1966equently ques
tionedtheresults and infurtherexperiments
failedto observeanyeffects.
Schrader and Korte(1972eportedanomalousoptical rotatory dispersioninthe
vibrational spectrumofN-(p-methoxybenzylidene)butylanilineper
turbedinto the
cholesteric mesophasebytheadditionofanoptically activesolute.Soonafterwards,
Dudley, Mason and Peacock (1972eported vibrational circular dichroism in a
similar sample.Thereasonthatvibrationaloptical activityissoreadily accessible
in cholesteric liquid crystals isthatthehelix pitch lengthisof theorderof the
wavelengthof theinfrared radiation.
Theﬁrstrayofhopefor practical chemical applicationsofinfrared vibrational
optical activity camein 1973 when Hsu and Holzwarthrepor
tedwell deﬁned cir-
cular dichroism bands arisingfrom vibrationsofwatermoleculesinoptically ac-
tivecrystals such as nickel sulphate,αNiSO
4·6H2O.This ray intensiﬁedwhen
Holzwarthet al. (1974eported circular dichroism inthe2920 cm
−1
bandof2,2,2-
triﬂuorol-phenylethanol, (C
6H5)C*H(CF 3)(OHetotheC*–H stretching mode.
Thepublication by Naﬁe,Keiderling and Stephens (1976ofvibrational circular

1.5Vibrational optical activity 19
dichroism spectra downtoabout2000 cm
−1
in a numberof typicaloptically active
moleculesservednoticethatinfrared vibrational circular dichroism had becomea
routinetechnique.
Whilethisfrontal attackon vibrationaloptical activitythrough infraredoptical
rotation and circular dichroism was unde
r way,theoutﬂanking manoeuvreinvolv-
ing Ramanoptical activity, describedintheprevious section, was passing rela-
tively unnoticed. InfacttheﬁrstobservationsofRamanoptical activityreported
by Barron, Bogaard and Buckingham (1973entionedpreviously, consti
tuted
theﬁrstobservationsofgenuinenatural vibrationaloptical activityofsmall chiral
moleculesintheliquid phase. High qualityinfrared circular dichroism and Raman
optical activityspectraofchiral molecules may nowbemeasuredroutinely and
areproving increasingly valuablefo
rsolving a widerangeofstereochemical prob-
lems.TheRamanoptical activityspectrumofα-pineneis shown in Fig. 1.8 as
atypicalexampleofa vibrationaloptical activityspectrum.Thefactthatthere
is almostperfectmirror symmetry inthespectraof t
hetwoenantiomers, which
werestudied in microgram quantitiesinthrow-away capillarytubes,emphasizes
theeaseand reliabilityofsuch measurements usingthelatestgenerationofinstru-
ment(Hug, 2003).Typical infrared circular dichroism spectra havea similar gen
eral
appearance,exceptthattheydonotpenetratemuch below 800 cm
−1
duetoboth
technical problems andthefundamentalfrequency problemmentionedabove. Also
thesigns and magnitudesofinfrared circular dichroism bands associatedwith par-
ticular vibrations generally bear norelationto thecorresponding Ramanoptical
activi
ty bands duetothecompletely differentmechanisms responsibleforthetwo
phenomena (seeChapter 7).
Vibrationaloptical activitytechniques, bothinfrared and Raman, havebecome
especially valuablein biochemistry and biophysics,enormous progress having been
madesinceth
epublicationof theﬁrsteditionof this book. Importantmilestones
weretheﬁrstreportsof thevibrationaloptical activityspectraofproteins using
infrared circular dichroism by Keiderling (1986 optical activityby
Barron, Gargaroand Wen (1990 optical ac
tivityspectra mayevenbe
recordedroutinelyonintactliveviruses in aqueous solutiontoprovideinformation
onthestructures and mutual interactionsof theprotein coatandthenucleic acid
core(seeSec
tion 7.6).
Vibrationaloptical activity induced by a magnetic ﬁeld using infrared circular
dichroism was ﬁrstobservedbyKeiderling (1981t,asmentionedinSection
1.4, ithad beenobservedpreviously as a circular intensitydifferencein resonance
Raman scattering. Justas conventional magnetic
optical activity injects additional
structureintoanelectronic spectrum, somagnetic infrared and Ramanoptical
activity injectadditional structureintoa vibrational spectrum,therebyfacilitating
theassignmentofbands,fore
xample. Magnetic vibrational circular dichroism

20 Ahistorical review of optical activity
Fig. 1.8TheRaman (a) and Ramanoptical activity(b,c)spectraof thetwoenan-
tiomersofα-pinenemeasuredasthedegree ofcircular polarization in backscat-
tered light. Adaptedfrom Hug (2003ectrum (b)isalittleless intensethan
(c)becausethe(1S
,5S)-(−) samplehad a slightly lowerenantiomericexcess.
TheabsoluteintensitiesarenotdeﬁnedbuttherelativeRaman and Ramanoptical
activityintensitiesaresigniﬁcant.
is valuableforstudiesofsmall moleculesinthegas phase,whereitcan yield
vibrationalg-valuesfromrotationally resolved bands (Bour,Tam and Keiderling,
1996). Ontheother hand, systems in degenerateground states, mostcommonly
encountered as Kram
ers degeneracyinmoleculeswithanodd numberof electrons,

1.6X-ray optical activity 21
add another dimensiontomagnetic Ramanoptical activitystudies, sincetransitions
betweenthemagnetically splitcomponentsof thedegenerategroundelectronic
level superimposeduponthevibrationaltransition may b
eobserved.This ‘Raman
electron paramagnetic resonance’effectwas ﬁrstobserved by Barron and Meehan
(1979esonancescatteringfrom dilutesolutionsof transitionmetal complexes
such as iridium (IVexachloride, IrCl
6
2−. Ramanelectron paramagnetic resonance
providesinformationaboutthemagnetic structureofground and low-lyingexcited
electronic states, includingthesignof theg-factor and howthemagnetic structure
changeswhenthemolecule
is in anexcited vibrational state.
Therehas alsobeen discussionof optical activity associatedwith purerotational
transitionsofchiral moleculesinthegas phase, includingoptical rotation and
circular dichroism inthemicrowaveregion and Ramanoptical activity (Salzman,
1977; Barr
on and Johnston, 1985; Polavarapu, 1987), buttodatenoexperimental
observations havebeenreported.
1.6 X-ray optical activity
Sincetheappearanceoftheﬁrsteditionof this book,optical activitymeasurements
havebeenextendedtoX-ray waveleng
ths,thankstodevelopmentsintheX-ray syn-
chrotronbeamsthatareessentialfor such measurements.This was ﬁrstachieved
for magnetic ﬁeld induced circular dichroism by Schutzet al.(1987ostud-
ied magnetizediron.Theﬁrstobservationofnatural circular dichroism in chiral
molecules was madeadecadelater by Alagnaet al.(1998 talsofa chiral
neodymium complex. Magnetic X-ray circular dichroism wasobserved ﬁrstbe-
causetheX-ray magnetic dissymmetryfactors can beseveralordersofmagnitude
largerthantheX-ray natural dissymmetryfactors.
Both magnetic and natural X-ray circular dichroismoriginatein n
ear-edgeatomic
absorptions andtheir associatedstructure.Themagneticeffectis now widely used
to explorethemagnetic propertiesofmagneticallyorderedmaterials.Thenatural
effect,studiesofwhich arestill intheir infancy (P
eacock and Stewart, 2001; Goulon
et al., 2003), is sensitivetoabsolutechiralityinthemolecularenvironmentaround
theabsorbing atom. An interesting aspectofnatural X-ray circular dichroism is
thatitrelies mainlyon an unusualelectric dipole–electric quadrupolemechanism,
discussedindetail in later chapters,thatsurvivesonly inoriented samples such
as crystals.Theelectric dipole–magnetic dipolemechanismthatdominates in-
frared, visibleand ultravioletcircular dichroism and which survivesinisotropic
media such as liquids and solutions is small intheX-ray region. Inthis respect
magn
etochiral dichroism, describedinthenextsection, could befavourableforthe
studyofchiral samplesintheX-ray regionbecauseanelectric dipole–electric
quadrupolecontribution survivesinisotropic media, and linearly polarized

22 Ahistorical review of optical activity
synchrotron radiation, which iseasiertogenerate than circularly polarized, could be
employedwiththemeasurementseffectedbyreversingthemagnetic ﬁeld direction.
1.7Magnetochiralphenomena
Shortly aftertheappearanceofthe
ﬁrsteditionof this book, a remarkablenew
classof optical phenomenathatdependontheinterplayofchirality and magnetism
cametoprominence. Wagni`ereand Meier (1982edictedthatastatic magnetic
ﬁeld parallelto thepropagation directio
nofan incidentlightbeam would inducea
small shiftintheabsorptioncoefﬁcientofamedium composedofchiral molecules.
This shiftis independentofthepolarization characteristicsof thelightbeam and
soappearseven in unpolarized light.Theshi
ftchanges signeitheronreplacingthe
chiral moleculeby its mirror imageenantiomeroronreversingtherelativedirections
of themagnetic ﬁeld andthepropagation directionof thelightbeam. Portigal and
Burstein (1971earli
ershown,onthebasisofsymmetry arguments,thatan
extratermexistsinthedielectric constantofa chiral medium which is proportional
tok·B,wherekistheunitpropagationvectorof thelightbeam andBisthe
external s
tatic magnetic ﬁeld; and Baranova and Zeldovich (1979a) had predicted
a shiftintherefractiveindexofa ﬂuid composedofchiral moleculesinastatic
magnetic ﬁeld applied parallelto thedirectionofpropagationofa lightbeam.
Theassociateddifference
in absorptionofa lightbeam parallel(↑↑) and an-
tiparallel(↑↓)to themagnetic ﬁeld was subsequently christenedmagnetochiral
dichroismby Barron and Vrbancich (1984ththecorresponding differencein
refractiveindex calledmagnetochiral birefringence.Themagnetochiral dichroism
experimentis illustrated in Fig. 1.9.Thec
orresponding magnetochiral birefrin-
genceand dichroismobservables,n
↑↑
−n
↑↓
andn
↑↑↑
−n
↑↑↓
,arelinear inthe
B (↑↑
k
(
B (↑
(
n'
↑↑
−n'
↑↓
≠ 0
↑
Fig. 1.9Themagnetochiral dichroismexperiment.Theabsorption indexn
↑
ofa
medium composedofchiral molecules is slightly differentforunpolarizedlight
whenastatic magnetic ﬁeld is applied parallel(↑↑) and antiparallel(↑↓)to the
directionofpropagationof thebeam.

1.8The Kerr and Cotton–Mouton effects 23
magnetic ﬁeld strength justliketheFaradayeffect. Magnetochiral dichroism was
ﬁrstobserved by Rikken and Raupach (1997 europium(IIIomplexin
dimethylsulphoxidesolution, and magnetochiral birefringenceby Kleindienstand
Wagni`ere(1998 organic ﬂuids such as a camphorderivativeand carvone.
Atthetimeofwritingther
earesomeunresolvedproblems withmeasurementsof
magnetochiral birefringence, sincedifferentexperimental strategies appeartogive
quitedifferentresults (Valletet al., 2001).
Itmightappear atﬁrstsightthatmagnetochiral dichroism is simplyth
eresultof
cascademechanisms involving successivenatural circular dichroism and magnetic
circular dichroism steps, andvice versa.Thus natural circular dichroismof the
incoherentright- and left-circularly polarizedcomponentsof equal amplitudeinto
which unpolarized lightmay bedecomposedleadsto theinitially unpolarized light
b
eam acquiring a circular componentas itprogressesthroughthemedium, which
will subsequently beabsorbeddifferently dependingonwhethertheapplied mag-
netic ﬁeld is parallelorantiparallelto thepropagation direction. Equivalently, mag-
netic circular dichroism will induc
ea circular componentintheinitially unpolarized
lightbeam,followedbynatural circular dichroism. Althoughthesecascademech-
anisms may providean initial insightinto thephysicaloriginof thephenomenon,
and will indeedprovidehigher-ordercontributions (Rikken and Raupach, 1998), as
elab
orated in Chapter 6 magnetochiral dichroismoriginates primarily in a single-
step scattering process in whichthechiral and magnetic interactions interfere.
Althoughthemagnetochiraleffectsobservedtodatearevery weak,theyareof
fundamental interest.Forexample,theypr
ovideanewsourceofabsolute enan-
tioselectionviaphotochemical reactions in unpolarized lightin a static magnetic
ﬁeldthatmay besigniﬁcantfortheoriginofbiological homochirality (Rikken and
Raupach, 2000). Also,they mightbeexploitedinnewphenome
naof technological
signiﬁcancein chiral magnetic media such as an anisotropy inelectrical resistance
through a chiral conductorindirections parallel and antiparalleltoastatic magnetic
ﬁeld (Rikken, F¨olling and Wyder, 2001).
1.8 TheKerrand Cotton–Moutoneffects
TheKerr and Cotton–Moutoneffectsreferto the
linear birefringenceinducedin
a ﬂuidoranisotropic solid by a staticelectricor magnetic ﬁeld, respectively,
appliedperpendicularto thepropagation directionofa lightbeam (Kerr, 1875;
Cotton and Mouton, 1907).Theeffectsoriginatemainly in a partialorientat
ionof
themoleculesinthemedium.Thesamplebehaves, infact, likea uniaxial crystal
withtheoptic axis parallelto thedirectionof theﬁeld. Althoughthesephenomena
arenotmanifestationsof optical activit
y(theydonot originatein a differencein
responsetoright- and left-circularly polarized light)wedescribethem brieﬂy since

24 Ahistorical review of optical activity
equationsfortheassociatedpolarization changesemergeautomaticallyfromthe
birefringentscatteringtreatmentpresented in Chapter3.
Ifthelightbeam is linearly polarizedat45
◦
to thedirectionof theappliedﬁeld,
elliptical polarizationisproducedon accountofa phasedifferenceinducedinthe
twocoherentresolvedcomponentsof thelightbeam linearly polarized parallel and
perpendicularto the
static ﬁeld direction. Sincethephasedifferenceis
δ=
2πl
λ
(n −n⊥), (1.8.1)
wheren
andn ⊥aretherefractiveindicesfor lightlinearly polarized parallel and
perpendicularto thestatic ﬁeld direction,theresultingellipticity is simplyδ/2so
that, in radians per unitpathlength,
ψ=
π
λ
(n −n⊥). (1.8.2)
Atabsorbing wavelengths,thetwodifferentrefractiveindicesfor lightlinearly
polarized parallel and perpendicularto thestatic ﬁeld directionareaccompanied
by differentabsorptioncoefﬁcients.This resultsinarotat
ionof themajor axisof
thepolarizationellipsebecauseadifferencein amplitudedevelops betweenthetwo
orthogonal resolvedcomponentsfor which nophasedifferenceexists. Again,this
optical rotationdu
etolinear dichroism is nota manifestationof optical activity.
Thelineshapesforthedispersionoflinear birefringenceand linear dichroism are
thesameasforordinary refraction and absorption. Furtherinformationon linear
dichroism and its applicatio
ns in chemistry may befound inthebooks by Michl
andThulstrup (1986 odger and Nord´en (1997
1.9 Symmetryandoptical activity
Thesubjectofsymmetry andoptical activityreviewedinthis section impactson
many differentareasofscience, rangingfrom classical crystaloptics
to elementary
particlephysics, cosmology andtheoriginoflife.Someofthetopics mentioned
herearerevisitedindetail in Chapter4,butforothersamoredetailed accountis
beyondthescopeofthis book.
1.9.1 Spatial symmetry and optical activity
Fresnel’s analysisof optical rota
tionintermsofdifferentrefractiveindicesforleft-
and right-circularly polarized lightimmediately provided a physical insightinto
thesymmetry requirementsforthestructureofanoptically activemedium. Inthe
wordsofFresnel (1824

1.9Symmetry and optical activity 25
L R
Fig. 1.10A right-handedhelix and itsleft-handed mirror image.
Therearecertain refracting media, such as quartzinthedirectionofits axis,turpentine,
essenceoflemon,etc., which havethepropertyofnot transmitting withthesameveloci
ty
circular vibrationsfrom righttoleftandthosefromleft toright.This may resultfrom
apeculiar constitutionof therefracting mediumorofitsmolecules, which producesa
differencebetweenthedirections righttoleftand left torigh
t; such,for instance,would
beahelicoidal arrangementofthemoleculesof themedium, which would presentinverse
properties according asthesehelicesweredextrogyrate orlaevogyrate.
A ﬁnitecylindrical helix isthearchetypefor all ﬁguresexhibiting whatPasteur
(1848eddissymmetrytodescribeobjects ‘which differonly as an imagein a
mirrordiffersfromtheobjectwhich producesit.’Thus a helix and its mirror image
cannotbesuperposed sincereﬂectionreverse
sthescrewsense, as illustrated in Fig.
1.10. Systems whichexistintwononsuperposablemirror imageforms aresaid
to exhibitenantiomorphism.Dissymmetric ﬁguresarenotnecessarilyasymmetric,
thatis devoidofall symmetryelements, sincethey may possessoneormoreproper
r
otationaxes(theﬁnitecylindrical helix has atwofold rotation axisC 2throughthe
mid pointofthecoil, perpendicularto thelong helix axis). However, dissymmetry
excludes improperrotationaxes,thatis centresofinversion, reﬂection planes and
rotation–reﬂectionaxes. In recenty
earstheword dissymmetry has beenreplacedby
chirality,meaning handedness (fromtheGreekchir=hand), inthemoremodern
literatureofstereochemistry andother branchesofscience. ‘Chirality’ was ﬁrstused
inthis contextby Lord Kelvin, ProfessorofNa
tural Philosophy attheUniversity
ofGlasgow. His completedeﬁnitionisasfollows (Lord Kelvin, 1904):
I call any geometrical ﬁgure,orgroupofpoints,chiral, and saythatithas chiralityifits
imagein a planemirror, ideally realized, cannotbebroughttocoincidewithitself.Two
equal and similar righthands arehomochirally similar. Equal and similar rightand left
hands areheterochirally similaror ‘allochirally’ similar (butheterochirally is better).Th
ese
arealsocalled‘enantiomorphs’, after a usageintroduced,Ibelieve,byGerman writers. Any
chiralobjectand its imagein a planemirrorareheterochirally similar.
Theﬁrstsentenceisessentiallythedeﬁnitionusedtoday. Strictly speaking,the
term ‘enantiomorph’ is usually reservedfor a macroscopicobjectsuch as a crystal,
and ‘enantiomer’foramolecule,butbecauseoftheambiguityofscale
inthecase

26 Ahistorical review of optical activity
(a) (b)
Fig. 1.11(a)Aholohedral hexagonal crystal. (b)Ahemihedral hexagonal crystal
and its mirror image.
ofgeneral physical systemsthesetwoterms areused as synonyms inthis book.
Thegrouptheoretical criterionforanobjecttobechiral isthatitmustnotpos-
sess improperrotation symmetryelements such as a centreofinversion, reﬂec
tion
planesorrotation–reﬂectionaxes and somustbelongto oneofthepointgroups
C
n,Dn,O,TorI.
Directevidencethatthestructureofoptically activematerials is in someway
chiralfollowedfromtheobservation by Hauy in 1801thattheapparenthexagonal
symmetryofquartz crystals was infactreducedbythepresenceofsmall
facets
onalternatecornersof thecrystal.Thesehemihedralfacetsdestroythecentreand
planesofsymmetryof thebasic holohedral hexagonal crystal, and reducethesixfold
principal rotation axis with six perpendiculartwofold rotat
ionaxestoathreefold
principal axis withthreeperpendiculartwofold axes, giving risetotwomirror
imageformsofquartz, as in Fig. 1.11.Thetwoformsofquartz which Biothad
foundtoprovideoppositesensesof optical rotationweresubsequently identiﬁedby
Herschel (1822t
hetwohemihedralformsofquartz.Thisearlyexampleis very
instructivesinceitillustratesafeaturecommonto thegenerationofnaturaloptical
activity in many systems; namely a small chiral perturbationofa basic structure
thatis inhere
ntly symmetric.
Pasteurextendedtheconceptofchiralityfromtherealmof thestructuresof
optically activecrystalsto thatoftheindividual molecules which provideoptically
activeﬂuidsorsolutions. Heworkedwithtartaric acid, which Biot
had shownto
beoptically active, and with paratartaric acid, which was chemically identical but
optically inactive.Thecrystalformsof tartaric acid and mostofits saltsarehemihe-
dral, whereasthoseofparatartaric acid and mostofits saltsareholohedral. Butan
anomaly inthecaseof
sodium ammoniumtartratewas discoveredbyMitscherlich:
thecrystalsofbothactiveand inactiveforms arehemihedral (infactthis wasfor-
tuitous sincesodium ammonium paratartrate only giveshemihedral crystals when
crystallizedbelow26
◦
C). In 1848 Pasteur, infollowing upthis discovery,observed
thatalthough bothwereindeedhemihedral, inthetartrate thehemihedralfacets

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principle. The general with his field-glass sees a weakening in the
enemy’s line and orders a charge; the duelist observes a shortening
of breath or an awkward movement and seizes the opportunity. It is
the weak link in the chain of life that breaks; sins of the lower nature
—sensuality—might not appeal to some who fall an easy victim to
pride, ambition, or covetousness; others who are liberal, honest to
the cent, unassuming, are helpless when tempted in the realm of
lower passions. We are at an incalculable disadvantage when our
enemy is familiar with our vulnerable points.
So long as the heart is unregenerated and unpurified by the
cleansing power of the Holy Ghost, Satan has access to every nook
and corner of our heart life. He enters and discovers every
vulnerable and invulnerable section of the soul’s fortification. The
tempted and fallen are often unable to tell how it was done. “Why
did you go there?” or, “Why did you do it?” Oh, so many, many times
do we hear the answer: “I do not know.” A friend once showed me a
little iron safe in which he kept his valuable papers. This safe had a
very ingenious lock; the combinations were such, and the
mechanism so wonderful, that it was capable of three hundred
thousand combinations.
Why and how are sane men and women overcome? They were met
at a certain place, under peculiar circumstances; met by several—a
word, a smile, an argument, a pressure of the hand. How was it
done? They do not know. Somehow the attack came in a way which
rendered them helpless to resist. One effort failed—a dozen failed;
but as often as it failed the Expert changed the combination, until
the door yielded, and an entrance into the citadel of Mansoul was
effected. Three hundred thousand combinations.
The spy has information from within; and, therefore, the most
dangerous man in the army. Satan, by his supernatural powers
directing his practice and experience for several millenniums, is a
crafty, sagacious spy, acquainted with all the weaknesses and
emotions of the human heart. Who is equal to such an enemy?
Contending alone, no one on this sin-burdened footstool.

XIV
THE QUACK DOCTOR
“Having the form of godliness, but
denying the power thereof: from such
turn away.”—2 Timothy iii. 5.
We do not agree with some late views of the nature of sin—that it is
a physical and mental disorder: the resultant of heredity, food, soil,
climate and social environment. If the root of the difficulty springs
from these primary causes, the whole problem of evil could be wiped
out in one generation by the application of sanitary laws and social
betterment. In the Bible sin is known by several disease terms, but
always such diseases as were incurable by any treatment known in
those days: leprosy, born blind, deadly poison, paralytic, etc. Sin is a
disease, and the whole man, body, mind, and spirit, is more or less
affected therefrom; but it is, in particular, a soul malady, going
deeper than human remedies can reach, whether social or
medicinal.
To cure this soul disease the race has sought eagerly from the day
Cain and Abel built their altars. All the ramifications of civilization
have had one all-absorbing desire: a readjustment of something
fundamentally wrong within. This fight for an atonement with the
Creator has been a long, heart-sore pilgrimage; it has painted the
blackest pages of history and committed the bloodiest crimes. This
human drama has been enacted in tragedy and tears. Why is it so?
Because deeper than any other heart-throb is the consciousness of
personal uncleanness, and the bitter anguish it has caused.
The dead civilizations, on their monuments and mausoleums, have
left behind, carved indelibly, one story—whether on the banks of the

Nile, the Areopagus of Greece, or the land of the Montezumas—it is
the story of feeling in the dark after God. They had the disease and
sought for a remedy. From the days of the astrologers and
soothsayers, anxious souls have been victimized by every fad, fake
and fanaticism in their search for relief. The venders of pulverized
snake skins and lizard tongues, in their day, found as willing a
patronage as the cultured proprietors of sanitariums to-day. The
long-haired man on a goods box can do a flourishing business, if he
has the gift of gab to convince the crowd his stuff will cure.
The quack doctor does not handle a variety of medicine; he knows
just enough of anatomy and materia medica to make his speech
sound scholarly—but his remedy, costing less than the price of one
visit from a physician, will cure all the ills of the human body. Like
De Soto, we are seeking the fountain of perennial youth—the elixir
of life.
Just as the disease of the body and a passion to live open wide the
door to charlatans, fakirs, and “healers” claiming powers direct from
Gabriel to Beelzebub, so the disease of the soul, and a hunger for
eternal life—“deep calling unto deep”—has opened the door of the
heart to the religious doctor with his cure-all prescriptions. Out from
unknown depths comes the yearning for readjustment and
reconciliation with God.
No being, beside the Godhead, is more familiar with the secret
hopes and impulses of the soul—than Satan. The long-haired quack
on the street, bawling his “junk,” is not half so anxious to defraud
the crowd as Satan is to prescribe remedies that will not cure. His
chief aspiration is to flood the land with bogus treatments which not
only fail to cure, but they preempt the disease-infected spots so as
to prevent the introduction of the genuine remedy.
The quack doctor is, no doubt, pleased when an imaginary cure has
been wrought by his wares; but Satan is filled with wrath if some of
his formulas strike deeper than he anticipated, and a soul emerges
from darkness unto light. This, however, does not often occur; he is

too cunning to advertise to a hungry, sin-sick world that which will
bring permanent relief.
The beating of tom-toms by an upper Congo medicine man to drive
away evil spirits has about the same efficacy as much that may be
found in the esthetic circles of the world’s religiosity. “A form of
godliness,” be it ever so beautiful and orderly, which does not seek
and obtain the inner power is just another way of beating tom-toms.
We look with compassion upon the poor benighted heathen woman
who trots around the temple of her god one hundred times on a
moonlight night; but how much improvement over her plan of
salvation do we find in the blaze of twentieth century Christian
enlightenment, if our religion consists of just “doing something,”
rather than having faith in a power that saves through the
impartation of the Holy Ghost? At no time in the history of the
Church have we done so many things as we are doing now—all
good; but observe: the Church and the world go hand in hand. It is
a rare exception when an essential difference can be seen in the life
and business methods of the professor and non-professor. “They will
have a form of godliness,” says Paul, “but deny the power.”
It was not a dream or hallucination which took the rich and poor, in
the long ago, out from the world and caused them to give up even
their lives cheerfully; it was an application of the power. They had
tested the “fountain opened in the house of David for sin and
uncleanness.”
“Oh, that fountain deep and wide,
Flowing from the wounded side,
That was pierced for our redemption, long ago;
In thy ever cleansing wave, there is found all power to save;
It’s the power that healed the nations long ago.”
In the multitude of pretenses, makeshifts: forms, ceremonies,
chantings, genuflections, ordinances, will worship, self-
righteousness, “wondrous works,”—“form of godliness”—who is

responsible? It is the great Quack Doctor that is deceiving the world;
those who will not be dragged into sin and ruin he surfeits their lives
with a “form of godliness, but deny the power” plan of salvation.

XV
THE DEVIL A THEOLOGIAN
“Now the Spirit speaketh expressly, that
in the latter times some shall depart from
the faith, giving heed to seducing spirits,
and doctrines of devils.”—1 Timothy iv. 1.
Theology is defined as “the science which treats of God, His
existence, character, government, and doctrines,” or the science of
religion—a system of truth derived from the Scriptures. The caption
of this article—The Devil a Theologian—jars our spiritual nerve
centres. There are three things necessary to produce a theologian:
experience, information, ability. From every possible view-point the
Devil is preëminently qualified to formulate a system of doctrinal
statements having all the earmarks of genuineness and credentials
of authenticity.
In our discussion of the Devil’s theology we shall not, at the present,
touch upon the theories and vile imaginations of demon-possessed
men, but the finer phases of truth, beautifully presented by his
apostles with a show of orthodox reasonableness. By the term
Devil’s theology—doctrines—we do not mean his beliefs—get the
distinction—but what he wants us to believe. He is every whit
orthodox; he believes the Old Book; he does not indorse the new
theology, or the so-called higher learning, only as it may be turned
to his advantage. The Word of God is a mighty reality to him; he has
met its blazing truths, and has been burned by its power. He has
millions of skeptics and doubters blindly following his delusions, but
he is a believer in the “old school”; he “believes and trembles.”

We call attention to the term “doctrines”—therefore religious beliefs:
reasonable, plausible, satisfying beliefs. What are they? First:
Ritualism is Religion; when we have gone through a certain
proscribed programme—whether it be a chant, reading prayers, or
burning a dim light—there you are. How do we know we are
religious? We have gone the rounds, said the required number of
Ave Maries, counted the rosary, etc., etc., therefore the work is
done. It sounds harsh to place these beautiful ceremonies, which
have doubtless comforted so many hearts, in the enemy’s catalogue;
but the Pharisees were rigid ritualists, yet Christ denounced them as
miserable hypocrites—“whited sepulchres.” Anything he can get us
to adopt, having a semblance of reality, yet does not save—does not
deal directly with the sin question, he shouts over our delusion. He
appropriates Ritualism for Religion and it becomes his doctrine.
A second doctrine: Good Resolution for Regeneration. There has
never been as much strenuous evangelism, of a certain quality, as
we are having to-day. Great cities unite in stupendous revival effort;
no expense is spared; the leading masters of assemblies are called
as workers. The zeal and motives of it all are commendable; but the
bane of such evangelism is this: the work stops at the resolution
period. Men are brought under conviction, and the Devil at once
proposes his compromise. Not until the “big meeting” closes do the
convicted multitudes discover the deception. Herein is the
explanation of the lethargy, depression, and utter indifference which
so often obtain after a “sweeping revival.” Faith is then shaken, and
sometimes permanently, in the truth of a conscious, know-so
salvation. If the Prodigal Son had stopped after passing a good
resolution with himself he would have died at the swine pen without
the knowledge of the father’s love, the kiss, the robe, the ring, and
the fatted calf. A sinner must not only “quit his meanness” but
straighten out his meanness. Regeneration is not by the will of the
flesh, the will of man, not of blood; but it is to be born of God—born
from above—a new creature. Doctrines floating under the banner of
evangelism which do not get believers into the kingdom must be
listed with the enemy.

A third doctrine: Sentiment is Salvation. We are a sentimental
people; esthetic and humanitarian developments of recent years
have done much to soften our barbarian instincts. If sentiment were
salvation, this land would be redeemed. Many think we are rapidly
becoming a saved nation; those who enjoy such reflections should
stand at the entrance of any theatre on Sunday, or a pleasure
garden, or a ball park; then hurry around to the entrance of the
finest, best equipped church in the city for comparison. Sentiment is
educated emotion. Rome used to shout over the bloody scenes in
the amphitheatre; now we can weep over the unfortunate girl who
goes down in spectacular glory behind the footlights. Sentiment
makes us rejoice with those who do rejoice, and weep with those
who weep; it moves us to deeds of charity. Satan then has no
difficulty in persuading us that we are religious—spiritually
redeemed; if we weep over our loved ones, our emotions are very
religious. The most grief we ever witnessed at a funeral was in the
home of a saloon-keeper; the dead wife and mother, a depraved
opium and morphine eater; the home was utterly irreligious, but the
grief was hysterical, explosive. The sacrifices of God are a broken
and a contrite heart—over sins committed, producing a godly
sorrow, and not a sentiment.
Again, the Devil takes great delight in telling the unsaved and
unchurched masses that religion is all selfishness; the poor are made
to feel that the Church is the rich man’s institution. Notwithstanding
the efforts of God’s people to reach and help the lost they are
represented as mean and selfish, pretending a pious fraud, with no
bread for the hungry and no helping hand for the needy. We build
stately temples of worship to gratify our pride and vanity with money
earned by the sweat and toil of the poor man; money that ought to
be given to the poor. Judas protested against breaking the alabaster
box. The church is a place for dress parade; the humble and meanly
clad are not wanted. All such is malicious slander against God, His
Church and His people; but as stereotyped as this may sound, it is
being used effectually everywhere. If a church preaches salvation
from sin, it is the poor man’s best friend; but reference to the church

and the preacher is often hissed in gatherings of toiling men. Unless
there shall come to this land the establishment of the righteousness
of Christ, as taught in His Gospel, we shall see another reign of
terror; the fires of restlessness, hate, and discontent are
smouldering in every shop, factory, and mine. “The Golden Age will
never come until it is brought in by the Golden Rule of Christ.” The
Devil is busy keeping these facts from becoming known. The
doctrine stated: we are in it to serve a selfish end; take away our
hope of advantages, and our faith becomes religious junk.

XVI
THE DEVIL A THEOLOGIAN (Continued)
One of the Devil’s tactics is to make much ado about nothing. It is
astonishing how sane people can be deluded over childish non-
essentials. Think of the doctrine of Abstinence; at certain seasons be
holy with a vengeance. It is a mortal sin to let down during certain
days and moons; no meats, no riotous gormandizing, no wine, no
dancing, no theatre going, when the season is holy. But are we not
so commanded concerning the Sabbath day? The Sabbath day must
be kept holy, but if our moral standard and relationship fall below
during the week what we are supposed to make them on Sabbath,
our piety is a farce.
An incident will illustrate. It was a steamboat excursion; drinking and
dancing were freely indulged in by the hilarious passengers. A
parson was among them; he danced not, neither did he look upon
the wine that was red. He looked sad—it was Lent. One week later
we beheld this same parson in full evening dress gracefully waltzing
with one of the lambs of his flock. Amazing spectacle! Robes of
holiness to-day, with fastings and prayers; to-morrow, broadcloth,
perfume, patent leathers, and arms encircling a maiden in the dizzy
whirl of the dance. Paul saw such times coming and warned against
them.
There are many more, but we shall mention only one more: the
gigantic system of saints’ worship. What does this mean? Anything
that diverts and absorbs the attention away from things fundamental
is surely of evil origin. His fall began when he conceived hatred and
jealousy of Jesus; now if he can get people to pay a part or all of
their homage to Mary, or any one of the many “saints,” just so the
Son of God is robbed of His glory and neglected, his devilish malice

is somewhat gratified. There is a long list of dead worthies who are
reverenced and supplicated unto daily; but high over all is the
“Virgin Mother of God.” After the birth of the Saviour Mary was the
wife of Joseph, and bore children as a natural mother—she was not
a virgin. “Thou shalt have no other gods before me;” “Thou shalt not
make unto thee any graven images—thou shalt not bow down to
them.” “Doctrines of Devils.”
Spiritual minded students of the Bible and human conduct are forced
to the conclusion that the Devil is not only a wise theologian, but he
is a great preacher; and, as we have learned, he has a mighty
gospel which he preaches with effectiveness and power. He has
clearly defined doctrines which he promulgates at such times and
places as will best meet the desired end. But with cunning craftiness
he preaches his dogmas and tenets everywhere: housetops, society
parlours, centres of business, legislatures, court rooms, barrooms,
and bawdy houses, as well as in pulpits. This sounds like a strange
mixture: “the sacred desk” associated with such an array of evil—ad
absurdum. If the pulpit is immune, why Paul’s exhortation? Doctrines
presuppose a preacher, and also an effort to gain an audience
whenever and wherever possible.
Yes, the Devil preaches, and if doors are barred he forces an
entrance: home and foreign missions, slums, emigrants, aristocrats
and sports. He has access to scores of avenues where the Gospel of
Christ never enters; but under the cover of human interests he takes
the field with our Lord Jesus and His ministers, offering a more
beautiful, excellent, easier and successful way. As God’s method of
saving the world is by the foolishness of preaching, what better
agency of opposition could be launched than preaching? Nothing.
Far stronger is the expulsive than the opposing power. The most
dangerous poison in the world is the kind that hides its death in a
cup of sweetness; a child eats a sugar-coated pill and never
recovers. Hell is peopled by the multitudes who have drunk at the
Devil’s fountain of soothing, satisfying poison. He keeps his deluded
patrons from the fountain of cleansing by an easier way to

delectable fountains, the waters of which paralyze with the chill of
death.
We note another very remarkable fact concerning the Devil’s
doctrines and his style of preaching. Christ’s ministers often fail
because of a lack of adaptability; “he overshot his crowd” is the
comment often heard. The genius of this subject does not make this
mistake; he is a past-master at adaptability; to those who have a
feeble, fluttering conscience for spiritual things he has the sincere
milk of the word that soothes and sustains; but for his robust
followers, whom he has bound in chains stronger than those which
bound Prometheus, he gives the meat of diabolism, prepared and
seasoned by a skill of six thousand years’ practice.
Place your ear at the keyhole where his children are conducting a
“revival meeting”—high carnival of sin—and hear the ideas of God,
salvation, preachers, the Church, and the hereafter. This is the
strong gospel referred to; the gospel that fires the masses with hate
and prejudice against the only means of human redemption. Yes, he
preaches, preaches, preaches, and from every nook and corner; ten
messengers to one preaching the Christ; his preachers support
themselves, and touch the highways and byways; his lines are gone
out into all the earth, circumscribing sea and land. The Devil gets an
intelligent hearing. He has a long catalogue of doctrines, but he does
not believe a single one of them. We should be wise enough to
eliminate them from our creed also.

XVII
THE DEVIL’S RIGHTEOUSNESS
“Woe unto them! for they have gone in
the way of Cain.”—Jude 11.
“For they being ignorant of God’s
righteousness, and going about to
establish their own righteousness, have
not submitted themselves unto the
righteousness of God.”—Romans x. 3.
We are becoming, according to the canons of this world, a righteous
nation; the standard of civic and commercial righteousness is
elevated as never before. Sleuth-hounds are scenting every
indication of misrule and running to earth evil-doers, high and low.
Our cities are keeping tab rigidly on sewerage, cesspools, and
outhouses; a persistent war is being waged on flies, mosquitoes,
and germs of all kinds. Private citizens are everywhere organizing to
coöperate with officials for public welfare. Corporation and municipal
rings must answer at the bar of an outraged public conscience.
Righteousness is in the air; it resounds from the pulpit, platform and
press. Chautauqua specialists who have discovered some deflection
in the political and social woof and warp declare, amid salutes of
fluttering handkerchiefs, the righteousness of twentieth century
standards. Preaching on the cardinal doctrines of the Bible has been
displaced by rhetorical messages on altruism: light, ethics, mercy,
cleanness, goodness. “The fatherhood of God and the brotherhood
of man,” with a flavour of intellectualism, is the gospel that is now
being emphasized with much gusto, and never fails to solicit the

indorsement of all denominations. “Be good and do good” is the
multum in parvo of present day righteousness.
Who but a chronic faultfinder could object to this upward move, so
obvious now in all directions? The world is getting kinder, more
sympathetic, more charitable; creed lines are dissolving like snow
under an April sun; sectarian prejudice is dying under the withering
frown of new ideals. Does this not indicate a gradual leavening of
the “whole lump”? The spirit of Christ, they tell us, is being adopted
everywhere. He is mounting the throne of universal empire, and the
time surely is not far distant when the social, political, commercial
and domestic life will be regenerated by His influence. Yes—it would
appear so to be; much that is done bears a Christian label; it comes
in the name of Christ; but, says a writer, “it is the Christ of
Bethlehem and not the Christ of the Cross.” It is the human Christ
and not the sacrificial—the exponent of a blood Atonement.
The righteousness that has the full swing of modern religionists
makes much of Christ’s “example,” His beautiful character and self-
abandonment—“He went about doing good.” Much attention is given
to studying His leadership, His pedagogy, His art of public address,
His humanity. His example and not His sacrifice saves the world;
step by step the human Christ has displaced the Christ of Calvary;
His atonement was misguided zeal. This propaganda, on the surface,
is reasonable and popular; but close scrutiny will reveal a poison as
dangerous as it is subtle. It leaves out the Blood; it is a glorification
of Man. “Count the number of the beast, for it is the number of
man.”
This issue is an old one; it became an entering wedge in the
religious life when the first services were held after the Fall. Cain and
Abel made altars; Cain piled his high with beautiful, luscious fruits of
the field. No festal board ever looked more tempting, loaded with
sweet smelling fruit, having variegated colours, than the altar which
Cain presented to God. They were the results of his own sweat and
toil; he offered them as the “first fruits.” But God rejected the

offering; somehow the very beauty and attractiveness of it all
insulted Him.
Abel’s altar was smeared with blood; on top lay a limp, bleeding
lamb. Nothing attractive about this picture; our esthetic nature
recoils at the gore and cruelty of such an offering. Yet God
graciously accepted this bloody, unsightly offering; and no doubt
rained fire upon it—anyhow, Abel was justified. Why did God reject
the one and accept the other? Cain and Abel alike had been taught
from their infancy that “without the shedding of blood there shall be
no remission of sin.” By transgression man stood as an alien before
God; he had forfeited divine favour. Notwithstanding, Cain boldly
brought before God a bloodless sacrifice, and presumes to force Him
to accept it. Through all the millenniums before Christ every
approach to God must contain in the sacrifices and offerings an
element which reminded God of the coming Atonement. He
declared: “For the life of the flesh is the blood, and I have given it to
you upon the altar to make an atonement for your soul. For it is the
blood that maketh an atonement for the soul” (Lev. xvii. 11).
Coming directly to the point: all this new notion of things, touching
Man’s religion, fast becoming prevalent is the “way of Cain,” with a
twentieth century touch and terminology. What is the essence of this
new righteousness? what does it do? Observe, it sets aside God’s
estimate of man, and ignores the plan of redemption He established
at the beginning in types and shadows, then consummated in the
atoning death of His Son on the Cross. The righteousness of to-day
has much in it to commend; but it utterly disregards the only feature
upon which God places emphasis. The Blood and the Cross, as of
old, is an offense; they have found a more excellent way, but it is
the “way of Cain.” It is offering self-righteousness rather than
seeking the righteousness of God. The bloody offering of Abel
suggested suffering, punishment, death, judgment—but it honoured
God. Modern righteousness scoffs at the Abel offerings by hanging a
wreath of flowers on the Cross, bearing a perfumed tag, “With
sympathy.” It is Cain setting up business in town once more. A

sacrificial propitiation for sin is unnecessary when we have “inherent
goodness.” The modern righteousness contends that each man has
self-redemptive qualities; all he needs is a chance. Salvation is not
internal, but external.
The Cainites are filling the earth; they are preaching the popular
sermons, writing the magazine articles, the poetry, the fiction; they
occupy the chief synagogue seats of seminaries; they are
conspicuous at all chatauquas and baccalaureate occasions.
It is a well-known psychological fact that evil cannot exist apart from
Personality—whether it be bad laws, bad books, bad town, or a bad
house. Whence comes all this audacious, undermining insult to the
whole sweep of God’s plan for saving the world? Whence comes all
this preaching about righteousness which places the crown on man,
and robs the Cross of its glory? The righteousness being sounded in
double diapason and angelus keys is the righteousness of the Devil.
Bear in mind it is Righteousness, and a high type of it, he demands;
he wants the offering of Cain to cover up all the needs of the soul—
cheat the blood of its merit—insult God, and lead the race through a
bowery of flowers, fruits, and music on to its ruin. Anything to cheat
the depositum of the Gospel—that which gives a title to heaven—the
precious Blood. The righteousness that leaves out the Blood is the
“way of Cain”—“the righteousness of the Devil.”

XVIII
THE WORLD’S TEMPTER
“Again, the devil taketh him up into an
exceeding high mountain, and showeth
him all the kingdoms of the world, and
the glory of them; and sayeth unto him,
All these things will I give thee, if thou
wilt fall down and worship me.”—
Matthew iv. 8-9.
Temptation is a seduction: meaning to allure or entice one to evil. It
is submitting a proposition which carries with it inducements of
pleasure or gain. The mind that accedes readily and willingly to an
act is not tempted. A temptation is a clash of wills, one being
superior to the other if the contest results in a yielding. The word
embodies the idea of an elastic—“stretched to the snapping point.” If
there is no response, no struggle against desire—it is not a
temptation. The Master was very man as well as very God; yet
strange as it may seem—He was really tempted, and just as we are.
Our purpose in this discussion is not to analyze the different phases
of our Lord’s temptation—the tests to which He was subjected,—but
we wish to emphasize one thing: He was tempted. The appeals
came from His old time enemy; His rival for supremacy. He was not
taken unawares; the facts were clearly before Him, just who and
what it all meant—yet He was tempted. The diabolical assault did
not cease until His threefold nature was “stretched to the snapping
point.” It came from an inferior being, and for sake of illustration,
had the scheme succeeded, the Sun of righteousness would have
gone down forever. Not only would the great plan of human
redemption have proved abortive, but Satan would have snatched

the sceptre from the hand of the Anointed One and shouted his
victory in the face of God. We are amazed to think of the only
Begotten being near the yielding point in the presence of the fallen
Lucifer, but the Book says He was tempted.
Some may contend that He could not have yielded; all the while He
was conscious of divine security. This conclusion forces another
untenable proposition: If He could not have yielded, His humanity
was not real, but veiled in His divinity; the temptation was only a
shadow. We insist that as a man Jesus was tempted; He could have
called to His aid supernatural intervention, but He did not. The issue
was met as every man must meet it; it was manhood that
conquered. Had He yielded, both manhood and divinity would have
become subservient to the enemy. “Fall down and worship me” was
the proposition.
Now we wish to make a few deductions from our Lord’s temptation.
Whatever includes the greater includes the lesser—a fortiori. Natural
man reached his highest expression in Jesus of Nazareth; He was
God’s exponent of human perfection. There were no weaknesses, no
lack of pose or symmetry; His penetration and judgment of others
were absolutely accurate. From the beginning He had known the Evil
One who faced Him. Now, with all those perfect endowments, the
record says He was tempted. The ingenuity of Satan was sufficient
to bring out all the resources of the Son of God. Here was the
greatest, wisest, purest and strongest man that ever walked upon
the earth—susceptible, influenced, strained to the “snapping point,”
when attacked by the Tempter. What will be the inevitable fate of
you and me, dear reader, whenever he selects us as his victims?
The unmistakable teachings of the Word are that every temptation
to which man is or ever has been subjected came fresh from the
seething caldron of the pit. The student of human conduct has
observed universal adaptability of all temptation. A great sagacious
intelligence seems to be managing personally, through his cohorts,
this campaign of promising propositions. There are some who can be
incited to commit horrible crimes, such as murder, incendiary, born

perhaps with vicious tendencies, but this class is comparatively
small; others are susceptible to deeds of milder character. It would
matter little to an army approaching a fortification where or how the
attack should be made if the walls at every point were weak and
crumbling. No time is spent in reconnoitre and playing for position;
but if the battlements be strong, a faulty place must be located if
there be one. Satan rarely ever blunders in laying his temptations;
he is a most skillful strategist. As the world’s tempter he reveals an
ingenuity that is truly astounding; it should cause the bravest heart
to shudder once the eyes are opened to the source. Knowledge of
his approaches, marches, countermarches, advancings, and retreats
—all with a specific object—ought to be a great breakwater.
A writer gives us a striking word picture of Satan’s methods: “As the
enemy who lays siege to a city finds out the weakest portion of the
wall, or the best spot to batter it, or the lowest and safest place to
scale it, or where the intervening obstacle may be easiest overcome,
or where an advantage may be taken, or where an entrance may be
effected, or when is the best time, or what is the best means to
secure the desired end, so the arch-deceiver and destroyer of souls
goes about, watchful, intent upon ruin, scanning all the powers of
the mind, inspecting all the avenues to the heart and assailing every
unguarded spot. Sometimes he attacks our understanding by
injecting erroneous doctrine; sometimes our affections by excessive
devotion to things we love; sometimes our wills by strengthening
them in wrong directions; sometimes our imaginations by vain,
foolish, trifling thoughts; and sometimes our feelings by too high or
too low excitation.”
Some one has called Satan and his subordinates not omnipresent,
but “shifting imps.” They swarm the air, invisible, because they are
spirit, watching for opportunities to edge their way into the hearts of
mankind. They are shifting position, always to a point of least
resistance. Like a current of electricity, always flowing from a point
of higher potential pressure to one of lower, if points are connected
by a conductor. The metallic substances from which the current

starts and towards which it flows are called “electrodes,” and are
always of different potentiality. The current passes from the one of
higher to the lower. Man in his own strength is the lower, and
unprotected by the Spirit of God cannot resist the evil currents
flowing from Satan continually.

XIX
THE CONFIDENCE MAN
“In whom the god of this world hath
blinded the minds of them which believe
not, lest the light of the glorious gospel
of Christ, who is the image of God,
should shine unto them.”—2 Corinthians
iv. 4.
History is one long, tragic recital of human sorrow and suffering; but
there is far more unwritten history than has ever been recorded on
the printed page. Along the march of civilization all that has come
down to us are the lives and doings of great men; we know little of
the heart agonies of the race—such as cannot be recorded—
language is inadequate. Most of history is a record of man’s
inhumanity to man, but historians deal with these dark pages only
on the higher levels. The greatest suffering, the bitterest cries of
anguish, the deepest wails of despair are in the lowlands of human
life: down where its pathos can never be known. The darkest
tragedies of war are lost by the gallant heroism of some officer; the
blood and carnage are overshadowed and forgotten by the heralds
of victory. The real pathos of war remains unnoticed by the
chroniclers and correspondents; it is found in the heart suffering of
the dying in the trenches; the black pall that settles over the homes
made desolate by the news from the front.
The saddest stories of life will never be told; they are the voiceless
agonies and smothered sobs from victims of human treachery and
deceit. Millions are shambling on their weary way, waiting for the
end, whose hearts are dead and buried in graves of misplaced
confidence. More domestic lights have been extinguished, more love

dreams turned from a sweet phantasy to an horrid nightmare, more
bodies fished from the river, more shocking tragedies have resulted
directly from this cause—misplaced and wrecked confidence—than
from all other causes of human wretchedness.
An illustration from actual life will serve to bring the caption of this
chapter—the Confidence Man—out in bold relief. An honest old
farmer, whose horizon had not extended beyond the obscure Indiana
neighbourhood, sold his little home and started for Kansas, hoping
to enlarge his possessions and give his sons and daughters a larger
sphere of opportunity. That they might see the wonders of a great
city, arrangements were secured for a three days’ stop-over at St.
Louis. The Confidence Man saw them pass through the iron gate into
the lobby. He first noted the train on which they had come to the
city. With great enthusiasm he greeted the old gentleman,
introduced himself, extending a business card of his “firm.” With
cunning palaver, and the guilelessness of the farmer—item after item
of information as to name and where they came from were
obtained. The man who said he thought he recognized the old
gentleman soon became satisfied of it—having an uncle living in the
same county—and “I have often heard him speak of you, etc., etc.”
It required only a short time to not only gain the confidence of the
whole family, but also to get all the facts concerning their business
affairs: how much the little farm brought, and how much they had
left to begin life in the west, and actual cash on hand. There was not
a hitch in the scheme; the new friend (?) loaded them with
kindnesses and courtesies, paid all the bills at lunch and theatre—
took the young people into the mysteries of the great wonderland—
all so new and strange.
It was the last afternoon; father and Mr. Confidence Man were
returning from a tour of sightseeing. They met a man walking in
great haste; looking up he saw the two men, and suddenly laid
violent hands on the “farmer’s friend,” demanding the payment of a
note three days overdue. They quarrelled; all manner of apologies
were made, that he was “entertaining an old friend, etc.,” all of

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Molecular Light Scattering And Optical Activity 2nd Ed Rev And Enl Laurence D Barron

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