Bonding in C2

1. STUDY OF BONDING IN C
2AND
ANALOGOUS EIGHT VALENCE
SPECIES
SAYANTAN MONDAL
Roll-91/CEM/131027
Reg. No. A01-1112-0634-10
Department of Chemistry
University of Calcutta
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2. DEPARTMENT OF CHEMISTRY
University of Calcutta
UNIVERSITY COLLEGE OF SCIENCE, TECHNOLOGY AND
AGRICULTURE
92 A.P.C. ROAD, KOL-700 009
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3. One Molecule, Two Atoms, Three Views, Four Bonds?**
Sason Shaik,* Henry S. Rzepa,* and Roald Hoffman*
Angewandte
And Finally
Chemical Bonding
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4. Existence of C
2Molecule
Blue Colour of hot hydrocarbon flames (Emission
from excited C
2).
Astrophysical environment (Responsible for the aqua
hue in some Comets).
COMET ISON
Discovered on 21
st
Sept. 2012 (Russia)
4

5. Valence molecular orbitals of C
2 at Ground State
(The energy scale is schematic, 1s combinations are omitted)
Bond Order = 2
E
5

6. Carbon-Carbon Bond lengths
1.54 Å 1.34 Å 1.20 Å
(ethane) (ethelene) (acytelene)
In Diatomic Carbon the equilibrium bond length is
1.243 Å
Ref : “Bond length and bond multiplicity : σ-bonds prevent short π-bonds”
E.D.Jemmis, B.Pathak, R.B.King, H.F. Schaefer; Chem. Comm. 2006(2164-2166)
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7. Possible Causes :
1.The suspended πbonds are shorter than σ+πbonds
2.The antibonding MO (2σ
u) is less antibonding i.eit can
not compensate the bonding effect of the bonding MO
(2σ
g )
If so, The bond order would be close to THREE!
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8. Inverted bond
C
2Molecule
[1.1.1] propellane
Ref : W . Wu, J. Gu, J. Song, S. Shaik, P.C. Hiberty; Angew. Chem. 2009, 121,
(1435-1438)
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9. Ref : R. S. Mulliken, Phys. Rev. 1939, 56, 778 –781.
Mulliken’s Foresight
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10. Ref : R. S. Mulliken, Phys. Rev. 1939, 56, 778 –781.
Mulliken’s Foresight
Diatomic Carbon is Quadruply Bonded in a High Lying Excited State
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11. C-C distances in some extended carbides containing C
2units.
Ref: W. Jeitschko, M. H. Gerss, R. Hoffmann, S. Lee, J. Less-Common Met. 1989, 156, 397 –412.
J. Li, R. Hoffmann, Chem. Mater.. 1989, 1, 83 –101; H.-J. Meyer,R. Hoffmann, Z. Anorg. Allg.
Chem. 1992, 607, 57–71; J.R.
Long, J.-F. Halet, J.-Y. Saillard, R. Hoffmann, H.-J. Meyer, New J. Chem. 1992, 16, 839 –846; H.
Deng, R. Hoffmann, Inorg.
Chem. 1993, 32, 1991 –1996; E. F. Merschrod, S. H. Tang, R. Hoffmann, Z. Naturforsch. B 1998,
53, 322.
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12. Bond lengths in CaC
2in different phases
1.242Å
1.065Å
1.19Å
1.216Å
Space group ‘P 1 21/a1'
Space group 'C 12/c1'
Space Group ‘14/m m m'
Space Group ‘P 1 21/a1'
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13. Calcium Carbide is used to send TIN-CAN ROCKETS !
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14. Molecule Wiberg Bond Order Equilibrium Bond Dist. (Ǻ)
C
2 3.7660 1.26
Si
2 3.1450 2.07
Ge
2 2.0093 2.16
BN 3.0524 1.24
CN
+
3.5889 1.18
BC
-
3.6777 1.39
Wiberg Bond Order Analysis
DFT Calculations (Gaussian 09 outputs)
B3LYP/6-31+G(d,p)
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15. DFT Calculations
B3LYP/6-31+G(d,p)
C
2Singlet Energy = -75.888 a.u
C
2Triplet (first excited) Energy= -75.925 a.u
This level is showing OPEN SHELL diradical structure
Contradicting many previous studies on the same molecule
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16. NEED TO CHECK MULTI-REFERENCE
CHARACTER (IF ANY )
TOOLS :
•Full Configurational Interaction (FCI)
•Complete Active Space Self Consistent Field (CASSCF)
•Multi Reference Configurational Interaction (MRCI)
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17. CASSCF (8/8) Results
Str. No Configuration Coefficcient Weight(%)
1 KK(2σ
g)
2
(2σ
u)
2
(1π
u)
4
0.8525036 72.25
2 KK(2σ
g)
2
(1π
u)
4
(3σ
g)
2
-0.3364305 11.29
3 KK(2σ
g)
2
(2σ
u)
1
(1π
u)
1
(1π
u)
2
(3σ
g)
1
(1π
u)
1
0.1934542 03.74
4 KK(2σ
g)
2
(2σ
u)
1
(1π
u)
2
(1π
u)
1
(3σ
g)
1
(1π
u)
1
-0.1934542 03.74
5 KK(2σ
g)
2
(2σ
u)
2
(1π
u)
2
(1π
u)
2
-0.1224776 01.49
Basis Set : 6-31+G(d,p)
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18. Significant Contributions
Config. 1 Config. 2
Coefficient = 0.8525036 Coefficient = -0.3364305
% Weight = 72.25 % Weight = 11.29
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19. CASSCF Shows ---
Energy of C
2Singlet = -75.60 a.u
Energy of C
2Triplet = -75.58 a.u
Singlet state is more stable than triplet by 0.02 a.u that is,
12.54 Kcal/molenergy
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20. The Ground State of C
2Shows distinct
Multi-Reference Character
Bond Order in between 2 and 3
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21. Is there a fourth bond?
•Dimerisationof C
2to form C
4 (:C=C=C=C:) is exothermic by
~170 Kcal/mol
(Source : NIST webbook)
•If it is a diradical, there should be hardly any barrier to dimerise.
•This fact accounts for another bond !
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22. Calculation using Thermodynamic Data
•Using consecutive BDEs of C-H bonds of Acetylene
The first BDE of HCCH is 130-134 Kcal/mol
(HCCHHCC٠+٠H)
the second BDE is 110-117 Kcal/mol
(HCC٠٠CC٠+٠H)
•BDE of 4
th
Bond (!) = 14-30 Kcal/mol
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23. BDE of the 4
th
bond can be thought of as the
energy required to untangle the singlet pair to the
next triplet
ΔE=12.54 Kcal/mol
C C
C C
Energy of the Fourth Bond in C
2
is ~ 12-17 Kcal/mol
(Full CI result;
Nature Chem. March. 2012, Vol. 4)
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Conclusions:
•C
2has multi reference character in its ground state
and excited states.
•The higher analogues like Si
2and Ge
2 , due to their
larger size can not form multiple bonds (higher
than 3)
•Other first row isoelectronic molecules (including
C
2) may show quadruple bonds. (Full CI must be
done; already reported)

25. Similar quadruple bonding in isoelectronic species
*Ref: S. Shaik, D. Danovich, W. Wu, P. Su, H. S. Rzepa, P. C. Hiberty,
Nat. Chem. 2012, 4, 195 –200.
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Full CI study of analogous eight valence species*

26. References :
[1] J. Chem. Theo. Comput. 2011, 7, 121-130; Bonding Conundrums in the
C
2 Molecule : A Valence Bond Study ;P.Su, J.Wu, J.Gu, Wei Wu, Sason Shaik
and Phillippe C. Hiberty
[2] W. Wu, J. Gu, J. Song, S. Shaik, P. C. Hiberty, Angew. Chem.2009, 121,
1435 –1438;
Angew. Chem. Int. Ed. 2008, 48, 1407 –1410.
[3] R. S. Mulliken. Phys. Rev. 1939, 56, 778-781
[4] Journal of Molecular Structure: THEOCHEM; Symmetry decomposition
of quantum chemical bond orders; Olga V. Sizova *, Leonid V. Skripnikov,
Alexander Yu. Sokolov
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27. [5] Grimme, S. Semiempirical hybrid density functional with perturbative
second order correlation. J. Chem. Phys. 124, 034108 (2006).
[6] Quadruple bonding in C
2and analogous eight-valence electron species :
Sason Shaik*, David Danovich, WeiWu, Peifeng Su, Henry S. Rzepa and Philippe
C. Hiberty, 2012, Nature Chemistry. Vol. 4 (195-200)
[7] R. I. Kaiser, M. Goswami, P. Maksyutenko, F. Zhang, Y. S. Kim, A. Landera, A.
M. Mebel, J. Phys. Chem. A 2011, 115, 10251 –10258.
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28. Project Supervisor
Dr. Ayan Datta
Associate Professor
Department of Spectroscopy
Indian Association for the Cultivation of Science
Jadavpur, Kolkata
Saied Md Pratik
Sarmistha Karmakar
My Teachers and Friends
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