Chapter 2 chemical_bonding_final

very good slides for chemical bonding.

1. Many-electron atoms Hartree proposed that the wave function could be expressed simply as a product of spin orbitals, one for each electron: ψ(1,2,…) = ψ 1 (1)ψ 2 (2)….. ψ(1,2,…) = ψ 1 (1)ψ 2 (2)….. Each orbital may be thought of as being hydrogen-like with an effective nuclear charge. configuration the list of occupied orbitals The orbital approximation allows us to express the electronic structure of an atom in terms of its:

2. He For example, if one disregards the inter-electronic repulsion, the ground state wavefunction of He may be written as ψ(1,2) = (8/ a 3 ) 1/2 e -2r 1 /a (8/ a 3 ) 1/2 e -2r 2 /a corresponding to the configuration 1s 2 with the 1s orbital being somewhat more compact than in H (Nuclear charge being 2).

3. Li Three electrons First two electrons occupy as: 1s 2 with the 1s orbital being more compact than in He (Z=3) Next electron? 1s 3 ? NO!!! Pauli exclusion principle No more than two electrons may occupy a given orbital, and if two electrons do occupy one orbital, then their spins must be paired This principle forms the basis of the electronic structure of atoms, chemical periodicity, and molecular structure.

4. K SHELL COMPLETE! CLOSED SHEEL;[He] Last electron in 2s or 2p?? Three electrons occupy as: 1s 2 2s ? or 1s 2 2p ? The third electron in Li must enter the n = 2 shell, Equivalently written as: [He] 2s ? or [He] 2p ? Are the s and p orbitals degenerate? Degenerate in H Not in many electron systems 2s and 2p orbitals are non-degenerate p electrons are lower in energy, d,…. S electrons are lower in energy than p,… WHY?

5. In a many electron atom, each electron is shielded from the nucleus by the others, and to a first approximation, each electron may be thought of as experiencing an effective nuclear charge . Shielding and Penetration The effective nuclear charge experienced by an electron will be determined by its probability density distribution, and this in turn by its wave function .

6. ‘s’ electron penetrates more than a ‘p’ electron of the same shell ‘s’ electron experiences a greater effective nuclear charge than a ‘p’ electron of the same shell . The ‘p’ electron experienced greater effective nuclear charge than that for a ‘d’ electron in the same shell. In general therefore, in the same shell of a many-electron atom, the order of energies of the orbitals is s < p < d < f. The ground electronic configuration of Li is therefore 1s 2 2s 1 , or [He]2s 1 .

7. Building-up principle ( aufbauprinzip ) Order of occupation of atomic orbitals. Rules: 1s 2s 2p 3s 3p 4s 3d 4p 5s 4d 5p 6s 5d 4f 6p… Each orbital may accommodate up to two electrons (Pauli exclusion principle)

8. 1s 2s 2p 2p 2p C Six electrons First four electrons occupy as: 1s 2 2s 2 Remaining two electrons occupy as: 2p 2 On the basis of electrostatic repulsion as: 2p 1 x 2p 1 y 1s 2 2s 2 2p 1 x 2p 1 y ; [He]2s 2 2p 1 x 2p 1 y

9. Building-up (aufbau) principle Rules: Electrons occupy different orbitals of a given subshell before doubly occupying any one of them. In its ground state, atom adopts configuration with greatest number of unpaired electrons (Hund’s rule of maximum multiplicity). Carbon Friedrich Hund © Emilio segre visual archive

10. Eg ., C 1s 2 2s 2 2p x 1 2p y 1 ; N 1s 2 2s 2 2p x 1 2p y 1 2p z 1 Origin of Hund’s rule: Spin Correlation – Electrons in different orbitals with parallel spins have a quantum mechanical tendency to stay apart. This allows slight shrinkage, leading to greater attraction to nucleus . So using the Building-up principles the configuration of multielectron system can be written and their periodic properties can be explained

11. Chapter 2: Chemical Bonding Scheduled Lectures: 4

12. What is a Chemical Bond? Matter is made up of one or different type of elements. Under normal conditions no other element exists as an independent atom in nature, except noble gases. The combination of atoms leads to the formation of a molecule that has distinct properties different from that of the constituent atoms. Obviously there must be some force which holds these constituent atoms together in the molecules . The attractive force which holds various constituents (atoms, ions, etc.) together in different chemical species is called a chemical bond .

13. Since the formation of chemical compounds takes place as a result of combination of atoms of various elements in different ways, it raises many questions. Why do atoms combine? Why are only certain combinations possible? Why do some combine while certain others do not? Why do molecules possess definite shapes? To answer such questions different theories and concepts have been put forward from time to time. Kössel -Lewis approach Valence Shell Electron Pair Repulsion (VSEPR) Theory Valence Bond (VB) Theory Molecular Orbital (MO) Theory

14. Every system tends to be more stable and bonding is nature’s way of lowering the energy of the system to attain stability. Thus a chemical bond may be visualised as an effect that leads to the decrease in the energy. How do atoms achieve the decrease in energy to form the bond? The answer lies in the electronic configuration. The formation of a bond between two atoms may be visualised in terms of their acquiring stable electronic configurations; they will do so in such a way that they attain an electronic configuration of the nearest noble gas. The stable electronic configuration of the noble gases can be achieved in a number of ways; by losing, gaining or sharing of electrons . Ionic or electrovalent bond Covalent bond Co-ordinate covalent bond

15. Why do atoms combine? Every system tends to be more stable and bonding is nature’s way of lowering the energy of the system to attain stability. Balance of attractive and repulsive forces Consider an instantaneous configuration of two atoms When they are far: Attraction of A and e(1) + B and e(2) When close (R): [Attraction of A and e(1),e(2) + B and e(1), e(2 )] + Repulsion between A,B

16. Potential energy-separation curve: diatomic molecule Low energy: stable state High energy: unstable state Large separation: Energy of isolated atoms Energetic advantage for formation of a molecule

17. How do atoms achieve the decrease in energy to form the bond? By losing, gaining or sharing of electrons. Ionic or electrovalent bond Covalent bond Co-ordinate covalent bond Ionic and covalent bonds are idealized or extreme representations and though one type generally predominates, in most substances the bond type is somewhere between these extreme forms LiCl : considered to be ionic but soluble in alcohol (covalent character)

18. Types of Chemical Bond There are three (important) types of bonding exist among atoms. Metallic bonding Ionic bonding Covalent bonding Covalent CsF F 2 , H 2 Cs, Cu Most of compounds have more than one type of bonding interaction. 18

19. Ionic bond: Transfer of electron(s) from one atom to another, and the consequent attraction between the ions so formed Electropositive element + Electronegative element  Ionic Bond Some examples of ionic bonds and ionic compounds: NaBr - sodium bromide NaF - sodium fluoride KI - potassium iodide KCl - potassium chloride CaCl 2 - calcium chloride KBr - potassium bromide

20. Characteristics of Ionic Compounds Are polar; soluble in polar solvents (H 2 O and NH 3 ) but insoluble in non-polar solvents (CCl 4 and C 6 H 6 ) Are ionisable in solutions or in fused state Solutions of these compounds are good conductors of electricity Possess high melting and boiling points The polar linkages present in ionic compounds are non directional The ion pair “ c + a  ” has a strong residual electric field thereby attracts other ion pairs and a large number of ion pairs arrange within an ionic crystal. The total energy released in this process is called “ lattice energy ”

21. Metallic Bond: Metallic bond  constitutes the electrostatic attractive forces between the delocalized electrons, called  conduction electrons, gathered in an electron cloud and the positively charged metal ions.

22. Melting points and boiling points Metals tend to have high melting and boiling points because of the strength of the metallic bond . Electrical conductivity Metals conduct electricity . The delocalised electrons are free to move throughout the structure in 3-dimensions . Thermal conductivity Metals are good conductors of heat . Heat energy is picked up by the electrons as additional kinetic energy. Malleability and ductility Metals are described as malleable (can be beaten into sheets) and ductile (can be pulled out into wires) . This is because of the ability of the atoms to roll over each other into new positions without breaking the metallic bond. Properties of metals

23. In CY101, we will concentrate on covalent bonding only! Covalent bonding Covalent bond is formed by sharing of the VALENCE ELECTRONS of each atom in a bond. Electrons are divided between core and valence electrons. ATOM core valence Br [ Ar ] 3d 10 4s 2 4p 5 [ Ar ] 3d 10 4s 2 4p 5 Br Br Occurs between two or more electronegative atoms. Covalent bonds are directional in nature.

24. 24 Development of theories to understand covalent bonding Lewis Theory G. N. Lewis Valence bond theory Linus Pauling Molecular Orbital Theory Mulliken Density functional theory Kohn and Pople 1916 1954 1966 1998 VSEPR theory 1957 Several theories were developed to explain shape and electronic structure of covalent molecules.

25. 25 G. N. Lewis 1875 - 1946 Lewis Theory If two electrons are shared between two atoms, it makes a bond and bind the atoms together. Valence electrons are distributed as shared or BOND PAIRS and unshared or LONE PAIRS. Except for H, total no. of valence electrons: #Bond Pairs + #Lone Pairs = 4 pairs or 8 electrons Atoms in a molecule tends to have eight valence electrons to form stable arrangement as in noble gases. This is called as OCTET RULE. •• Cl •• • • shared or bond pair Unshared or lone pair (LP) •• Cl •• • • This is a LEWIS ELECTRON DOT structure.

26. 26 Step 2. Count valence electrons S = 6 3 x O = 3 x 6 = 18 Negative charge = 2 TOTAL = 6 + 18 + 2 = 26 e- or 13 pairs Step 1. Central atom = S 10 pairs of electrons are left. Electron dot structure of Sulfite ion, SO 3 2- Step 3. Form three covalent bonds with three oxygen atoms Step 4: Remaining pairs become lone pairs, first on outside atoms then on central atom. • • O O O S •• •• •• •• •• •• • • • • • • Each atom is surrounded by an octet of electrons.

27. 27 Count valence electrons H = 1 and N = 5 Total = (3 x 1) + 5 = 8 electrons or 4 pairs Electron Dot Structure of NH 3 Ammonia, NH 3 Form a sigma bond between the central atom and surrounding atoms. Remaining electrons form LONE PAIRS to complete octet as needed. H •• H H N 3 BOND PAIRS and 1 LONE PAIR (Central atom = N; surrounding atoms = H)

28. The incomplete octet of the central atom BeH 2 BF 3 F B F F H Be H Limitations of the Octet Rule BF 3 Central atom = B Valence electrons = 3 + 3*7 = 24 (12 electron pairs) The B atom has a share in only 6 electrons (or 3 pairs). B atom is electron deficient.

29. Odd-electron molecules Expanded octet NO N O In a number of compounds there are more than eight valence electrons around the central atom. PF 5 , SF 6 , H 2 SO 4 and a number of coordination compounds. 5 pairs around the S atom

30. Other drawbacks of the octet theory • It is clear that octet rule is based upon the chemical inertness of noble gases. However, some noble gases (for example xenon and krypton) also combine with oxygen and fluorine to form a number of compounds like XeF 2 , KrF 2 , XeOF 2 etc., • It does not explain the relative stability of the molecules, being totally silent about the energy of a molecule. • This theory does not account for the shape of molecules.

31. Sidgwick – Powell Theory In 1940 Sidgwick and Powell suggested that for molecules and ions that contain only single bonds, the approximate shape can be predicted from the number of electron pairs in the outer or valence shell of the central atom. Bond pairs and lone pairs were taken as equivalent All electron pair take up some space All electron pairs repel each other Repulsion is minimized if the electron pairs are oriented in space as far as possible.

32. Predicted molecular shapes from Sidgwick - Powell Theory: No. of electron pairs in outer shell Arrangement of electron pairs Electron-pair geometry Bond angles 2 3 4 5 6 Linear Trigonal Planar Tetrahedral Trigonal bipyramid Octahedral 180 120 109.5 90 , 120 90

33. Valence Shell Electron Pair Repulsion (VSEPR) Theory 33 The theory was suggested by Sidgwick and Powell in 1940 and was developed by Gillespie and Nyholm in 1957. VSEPR theory is based on the idea that the geometry of a molecule or polyatomic ion is determined primarily by repulsion among the pairs of electrons associated with a central atom. The pairs of electrons may be bonding or nonbonding ( lone pairs ). Only valence electrons of the central atom influence the molecular shape in a meaningful way. The shape of the molecule is determined by repulsions between all of the electron pairs present in the valence shell. Trigonal planar Pyramidal

34. A lone pair of electrons takes up more space around the central atom than a bond pair. And hence, lp-lp repulsion > lp-bp repulsion > bp-bp repulsion 34 The bonds around the central atom and hence the shape of molecule depends on number of electron pairs surrounds it. For a given number of electron pairs in the valence shell of the central atom, the preferred arrangement is that which minimizes their repulsion. VSEPR theory may be summarized as: The space occupied by a bond pair electron around the central atom decreases with increase in electronegativity of ligand. Double bond occupy more space around the central atom than single bond, and triple bond occupy more space around central atom than double bond lp belongs to central atom b p belongs to both atoms

35. 35 Effect of lone pair A. Molecules with four electron pairs (steric numbers) CH 4 4 bp lp Tetrahedral 109.5 degree NH 3 3 bp 1 lp Trigonal pyramid 107.3 H 2 O 2 bp 2 lp Bent or angular 104.5

36. 36 Effect of lone pair B . Molecules with five electron pairs (steric numbers) I. PCl 5 (5 bp + 0 lp ) trigonal bipyramidal geometry (all bonds are identical) P Cl Cl Cl Cl Cl 90 ° 120 ° II. SF 4 Valence electron of S = 6 Contribution from each 4F = 4 x 1 Total = 10 VE (4 bp + 1 lp ) There are two possible structure (a) lone pair at equatorial position or (b) lone pair at axial position. S .. F F F F S F F F F .. (a) (b)

37. 37 (a) (b) lp-lp ---- --- Lp-bp 2@120, 2@90 1@180, 3@90 If the angle is >120 , the repulsions have same effect on the structure. So 120 and 180 repulsions have same effect on the structure. Since in structure (a), there are only 2@90 lp-bp repulsions, so it is the preferred structure for SF4. Effect of lone pair II. SF 4 III. ClF 3 (Home work)

38. ClF 3 Lewis model: Shape : T shape Lone pairs occupy equatorial positions of trigonal bipyramid Cl F F F

39. 39 Effect of Electronegativity If the ligand has larger electronegativity, the smaller is the bond angle. If the central atom has larger electronegativity, the larger is the bond angle. NH 3 ; bond angle 106.7 NF 3 ; bond angle 102.2 H 2 O; bond angle 104.5 H 2 S; bond angle 92 The high electronegativity of F pulls the bonding electrons away from N in NF 3 than in NH 3 Thus repulsion between bp-bp is less in NF 3 than in NH 3

40. 40 Effect of Double bond Double bond has very similar effect as that of the lone pair because of the repulsive effect of  electrons . CH 3 C C H CH 3 H 122.2 115.6 Q. Draw all possible structures of the following molecules and explain which one is the preferred structure based on VSEPR theory. (a) SO 2 Cl 2 , (b) ClOF 3

41. Limitations of VSEPR Theory It fails to predict the shapes of several isoelectronic species. Two  isoelectronic species, can differ in geometry despite the fact that they have the same numbers of valence electrons It fails to predict the shapes of transition metal complexes The model does not take relative size of substituents into account. Atomic orbitals overlap cannot be explained by VSEPR theory The theory makes no predictions about the lengths of the bonds, which is another aspect of the shape of a molecule

42. Valence Bond Theory (VBT)- localized quantum mechanical approach Proposed by Heitler and London in 1927 This theory was further developed by Linus Pauling (Nobel Prize 1954) The process of chemical bond formation can be visualized as the overlapping of atomic orbitals of the two atoms as they approach each other. Bond regarded as being formed when electron in an orbital on one atom pairs its spin with that of an electron in an orbital on another atom . The strength of the bond depends on the effectiveness or extent of the overlapping. Greater the overlapping of the orbitals , stronger is the bond formed. Consider the approach of two ground state hydrogen atoms and bond formation in H 2 :  A and  B stand for the 1s orbitals centered on nucleus A and nucleus B respectively. Nucleus A:  A Nucleus B:  B

43. 1 H A 2 H B 2 H A 1 H B Ψ (1,2 ) =  A (1)  B (2 ) Ψ (1,2) =  A (2)  B (1) A linear combination is appropriate: Ψ (1,2) = [C I  A (1)  B (2) +C II  A (2)  B (1)] { (1)(2)- (1) (2)} C I and C II : Mixing coefficients

44. When orbitals of two atoms come close to form bond, their overlap may be positive, negative or zero depending upon the sign (phase) and direction of orientation . Positive overlap : Orbitals forming bond should have same sign (phase) and orientation in space.

45. sigma bonds ( σ bonds ) are formed by head-on overlapping between atomic orbitals. Sigma bonds are cylindrically symmetric about the inter nuclear axis. More overlap and hence the sigma bonds are strongest type of covalent chemical bond. S igma ( σ ) bond 45

46. Pi bonds (π bonds) are formed by sideways overlap of orbitals. Pi bonds have electron density in two lobes, one each side of the bond axis. Pi (π ) bond 46 Overlap of 2 2 p orbitals for the formation of p bond Nodal plane Pi bond has one nodal plane containing the inter-nuclear axis and the sign of the lobe changes across the axis. Pi bond is not as strong as sigma - less overlap.

47. 1s  1s  1 s-1s overlap gives a H – H single bond The 1s-2p overlap gives a H – F single bond F    2 s 2 p   1 s H Non-bonding electrons Three 2p-1s overlaps lead to the formation of three N – H single bonds. N    2 s 2 p  3H  1 s

48. 48 Single bond: must be one sigma bond Double bond: one sigma + one pi bond (ethylene) Triple bond: one sigma + two pi bonds (nitrogen molecule) Sigma bonds and the lone pairs are responsible for shape/geometry of molecule. Pi bond only shorten the bond distance. Multiple bond

49. Limitations Poor prediction of bond angles If the p orbitals are used for bonding in H 2 O and NH 3 then the bond angle should be 90 . Inability to explain the tetra valence of carbon C= 1s 2 2s 2 2p x 1 2p y 1 Promotion and hybridization C= 1s 2 2s 2 2p x 1 2p y 1  C= 1s 2 2s 1 2p x 1 2p y 1 2p z 1 Promotion Driving force : To attain more stability by forming more number of bonds

50. 50 s p 2 sp hybrid orbitals from mixing of a s and a p orbital sp 2 3 sp 2 hybrid orbitals from mixing of a s and 2 p orbital s p 3 4 sp 4 hybrid orbitals from mixing of a s and 3 p orbital sp 3 d 5 sp 3 d hybrid orbitals from mixing of a s and 3 p and a d orbital The valence orbitals (of central atom) undergo hybridization before making chemical bond. Hybridization (A hypothetical concept for bonds) A hybrid animal – Centaur – Greek myth with head, arms and torso of a man united to the body and legs of a horse

51. Consider n atomic orbitals with wave functions ψ 1 …. ψ n mix Mixing : makes linear combination n hybrid orbitals Ψ 1 …. Ψ n are formed Ψ 1 = C 1,1 ψ 1 + C 1,2 ψ 2 ………… + C 1,n ψ n ……………………………………………………… ……………………………………………………… Ψ n = C n,1 ψ 1 + C n,2 ψ 2 ………… + C n,n ψ n How the coefficients are determined? They should be so that directional properties of resultant hybrid orbitals are achieved Constructive and destructive interference of the wave characteristics of the corresponding orbital Square of coefficients should also give proportion of each atomic orbital in the hybrid

52. sp hybrids Ψ sp1 = (1/ 2) ( ψ s + ψ p z ) Ψ sp2 = (1/ 2) ( ψ s – ψ p z ) Hybridization of one s and one p orbitals = 2 sp hybrid orbitals

53. 53 H-C-C-H: three s bonds due to overlapping of 1s H – sp C ; sp C – sp C ; and sp C – 1s H . Two p bonds in HC  CH are due to overlapping of p orbitals results. H H sp hybrid orbitals Two nodal planes of p bonds are perpendicular to each other. in p bond C 2s 2p 2p 2p sp sp 2p 2p H-C  C-H Examples of sp Hybridization

54. The sp 2 Hybrid Orbitals Hybridization of one s and two p orbitals =3 sp 2 hybrid orbitals Ψ 1 = (1/3) 1/2 ψ s + (2/3) 1/2 ψ p x Ψ 2 = (1/3) 1/2 ψ s – (1/6) 1/2 ψ p x  ( 1/2) 1/2 ψ p y Ψ 3 = (1/3) 1/2 ψ s  (1/6) 1/2 ψ p x + ( 1/2) 1/2 ψ p y These lie in a plane and point towards the corners of an equilateral triangle.

55. sp 2 hybrids: Ethene H 2 C =CH 2 Uses the three sp 2 orbitals to form  bonds with 2H atoms and the other C atom. Use the remaining unhybridized 2p orbitals on the two C atoms to form a  bond

56. 56 Compounds involving sp2 hybrid orbitals: BF 3 , CO 3 2– , H 2 CO, H 2 C=CH 2 , NO 3 – , etc examples of sp 2 hybridization Total number of hybrid orbitals = total number of sigma bonds (of central atom) + lone pairs on central atom

57. The sp 3 Hybridized Orbitals The hybridization of a s and three p orbitals lead to 4 sp 3 hybrid orbitals for bonding. Ψ 1 = (½) ( ψ 2s + ψ 2px + ψ 2py + ψ 2pz ) Ψ 2 = (½) ( ψ 2s + ψ 2px - ψ 2py - ψ 2pz ) Ψ 3 = (½) ( ψ 2s - ψ 2px - ψ 2py + ψ 2pz ) Ψ 4 = (½) ( ψ 2s - ψ 2px + ψ 2py - ψ 2pz ) These arrange in a tetrahedral geometry with bond angle 109 .5

58. 58 Compounds involving sp 3 hybrid orbitals: CF 4 , CH 4 , : NH 3 , H 2 O :: , SiO 4 4– , SO 4 2– , ClO 4 – , etc sp 3 hybridization Dr. Saroj L. Samal Department of Chemistry hybridization of s and p x , p y and p z orbitals = 4 sp 3 hybrid orbitals (tetrahedral geometry)

59. 59 hybridization of s and p x , p y , p z and d z2 orbitals = 5 sp 3 d hybrid orbitals (trigonal bipyramid) The sp 3 d Hybridization Some structures due to these type of orbitals are PF5, PClF 4 , TeCl 4 , and BrF 3 .

60. The sp 3 d 2 Hybrid Orbitals Hybridization of one s , three p , and two d orbitals results in 6 sp 3 d 2 hybrid orbitals . The arrangement of these orbitals is an octahedron. Compounds using these type of orbitals are of the type: AX 6 ,   AX 5 E,   AX 4 E 2

61. 61 Bent’s Rule Bent’s rule More electronegative substituents prefer hybrid orbitals having less s- character (small bond angle) and vice versa . sp 3 d hybrid orbitals are combination of two sets of hybrid orbitals. sp x p y hybrids and p z d z2 hybrid orbitals. s p 2 hybrid orbitals are form stronger bond and are shorter than weak axial p z d z2 hybrid orbitals. Empirical rule proposed by H. A. Bent , in the chloroflurides of phosphorous, 1960. PCl 5 has sp 3 d hybridization. When the electronegativities of the substituents on the phosphorous atom differ (PCl 5-x F x ), it has been experimentally observed that the more electronegative substituent occupies axial position. In CH 2 Cl 2 , the H-C-H bond angle is more than 109.5 o indicating more than 25% s character where as the Cl -C- Cl bond angle is less than 109.5 o indicating less than 25% s character

62. 62 Draw backs of VBT Does not tell anything about the excited states of molecule. Because of orbital overlap, the bonding electrons localize in the region between the bonding nuclei 2. Not able to explain paramagnetic nature of O 2 molecule. 3. Can’t explain the delocalized pi-electrons in certain molecules. Ex- benzene. Paramagnetic compound: compounds/elements having unpaired electrons. Diamagnetic compound: All electrons are paired up, no unpaired electron.

63. 63 Molecular Orbital Theory MOT is developed by Robert S. Mulliken (Got nobel prize in 1966). Based on delocalized quantum mechanical approach. Uses symmetry to describe the bonding in molecule. Basic Principles of MOT Describes the electrons in a molecule using wave functions called molecular orbitals . A molecular orbital is a one electron wavefunction which spread over the entire molecule The atomic orbitals of different atoms combine to create molecular orbitals. The symmetry and relative energy of atomic orbitals determine how they interact to form molecular orbital. These molecular orbitals are then filled with available electrons according to the increasing order of energy.

64. 64 VBT MOT Electrons occupy orbitals, localized to overlap region. (localized electron pair concept) Hybridization of A. O.s of same atom to explain the geometry of molecule. Does not tell anything about the excited states of molecule. Electrons in molecular orbitals belong to the molecule as a whole. (Delocalized concept) No concept of hybridization. It does not tell anything about geometry of molecule. Better describe the excited states of molecule. MOT and VBT MO theory more “accurately predict the bonding" than VB theory and also the properties of molecules.

65. 65 Types of Molecular Orbitals Combination of atomic orbitals, gives following molecular orbitals: Bonding molecular orbital Antibonding molecular orbital Nonbonding molecular orbital Bonding molecular orbital When two orbitals with same sign overlaps, then there is increase in electron density in the overlap region and a bonding MO is formed. This is called as constructive interference of atomic orbitals. lower energy than atomic orbital Cyllinderical symmetry. Called  orbital

66. Overlap integral (S) Represent the accumulation of electron density between atoms Probability density Coefficients C – extent to which each AO contributes to the MO  A  B  MO = C A  A + C B  B  2 MO = c A 2  A 2 + 2c A c B  A  B + c B 2  B 2

67. 67 Antibonding molecular orbital Destructive interference leads exclusion of electrons for the region between the nuclei Highest electron density is located on opposite sides of the nuclei higher energy than atomic orbital Types of Molecular Orbitals  MO = C A  A - C B  B  2 MO = c A 2  A 2 - 2c A c B  A  B + c B 2  B 2

68. 68 Nonbonding molecular orbitals have essentially same as that of the atomic orbitals. These may exist in following situations: 1. Combination of atomic orbitals whose symmetry do not match and remain unchanged in the molecule. Ex: interaction of s with p x or p y or d xy or d yz etc 2. When there are three atomic orbitals of the same symmetry and similar energy, three MOs are formed: bonding MO (lower energy), antibonding MO (higher energy), and nonbonding MO (same energy as atomic orbital). Types of Molecular Orbitals Nonbonding molecular orbital

69. 69 Procedure for forming molecular orbitals Identify set of symmetry related atomic orbitals with similar energy. 2. MOs form by linear combinations of the atomic orbitals (LCAO). 3 . For poly atomic molecule, the LCs of ligands combine with the atomic orbitals of central atom to form MOs. Molecular Orbital Theory Application of MOT (a) Homonuclear diatomic molecule (b) Heteronuclear diatomic molecule

70. 70 Molecular orbitals from 1s atomic orbitals MOs may be either sigma ( σ ) or pi ( π ) orbitals. σ MO: MO which are symmetric to rotation about the inter-nuclear axis. π MO: MO which have a nodal plane containing the inter-nuclear axis (not symmetric to rotation about the inter-nuclear axis .) ψ A (1s) = 1s orbital wave function of A ψ B (1s) = 1s orbital wave function of B Molecular orbitals are:  1s = 1/ 2[ ψ A (1s) + ψ B (1s )] (Bonding MO)  * 1s = 1/ 2[ ψ A (1s) − ψ B (1s)] (Antibonding MO) Homonuclear diatomic molecule Note: In homonuclear diatomic molecule, the contribution from each atom to the MO is equal.

71. First period diatomic molecules 1s 2 H Energy H H 2 1s 1s  1s g * 1s Bond order = ½ (bonding electrons – antibonding electrons) Bond order: 1 u MO Diagram of H 2

72. 72 Bond order (strength of bond) Bond order = (no. of bonding e - − no. of antibonding e - ) 2 Single bond: bond order = 1 Double bond: bond order = 2 Triple bond: bond order = 3 Fractional bond orders also exist! In MO Theory, the strength of a covalent bond can be related to its bond order

73. 1s 2 ,  * 1s 2 He Energy He He 2 1s 1s Molecular Orbital theory is powerful because it allows us to predict whether molecules should exist or not and it gives us a clear picture of the electronic structure of any hypothetical molecule that we can imagine. MO diagram of He 2 Bond order: 0  1s * 1s

74. Second period diatomic molecules 1s 2 ,  * 1s 2 , 2s 2 Bond order: 1 Li Energy Li Li 2 1s 1s 2s 2s * 1s  1s  2s * 2 s Bond energy for Li 2 = 110 kJ.mol -1 , Compared to 436 kJ.mol -1 for H 2 .

75. 1s 2 ,  * 1s 2 , 2s 2 ,  * 2s 2 Bond order: 0 Be Energy Be Be 2 1s 1s 2s 2s Diatomic molecules: Homonuclear Molecules of the Second Period  1s * 1s  2 s * 2s

76. 76 Homonuclear diatomic molecule Molecular orbitals from 2p atomic orbitals Combination of 2p orbitals gives two sets of molecular orbitals based on symmetry. If the inter nuclear axis is the z -axis, then the combination of 2p z atomic orbitals [2p z (A) ± 2p z (B)] gives MOs that are symmetric about inter nuclear axis. S hape 2p z 2p z σ *2p z σ 2p z σ 2p z = 2p z (A) − 2p z (B) σ *2p z = 2p z (A) + 2p z (B) + + - − - - + + -

77. 77 Molecular orbitals from 2p atomic orbitals Combination of 2p x atomic orbitals [2p x (A ) ± 2p x (B )] gives molecular orbitals having nodal plane containing internuclear axis. MOs are: Shape + + + - - - 2p x 2p x + + − − Similarly, 2py atomic orbitals combine to give π2 p y and π * 2 p y MOs. π 2p x = 2p x (A ) + 2p x (B ) π *2p x = 2p x (A ) − 2p x (B ) Since the 2p x and 2p y orbitals have identical energy, so the resulting MOs also have same energy. These MOs differ only in spatial orientation.

78. 78 Homonuclear diatomic molecule Molecular orbital diagram An energy level diagram that shows the energy level of molecular orbitals relative to the atomic orbitals from which they’re derived Draw the skeleton MOs Use only the valence electrons of the atoms Follow the aufbau principle Each MO can hold a maximum of 2 electrons Follow Hund’s rule. Keep electrons unpaired until all MO’s having the same energy have one e - .

79. Molecular Orbital Diagram of N₂ 79 Number of valence electrons for two N atoms = 10 B. O. = (8−2)/2 = 3 Magnetic properties: Since all the electrons are paired up, so it is a diamagnetic compound. HOMO LUMO Frontier orbitals

80. 80 Q. Draw the molecular orbital diagram of O2 molecule. Fill the valence electrons and write down the energy order of MOs. Find out the bond order and show that it is paramagnetic in nature. Since there are two unpaired electrons present in π * 2px and π * 2py , so oxygen molecule is paramagnetic in nature.

81. Homonuclear period 2 Diatomics  2s   2s *   2pz   2px =  2py  * 2px  * 2py  2pz *. (O 2 and higher)  2s   2s *   2px =  2py   2pz   * 2px  * 2py  2pz *. (Up to N 2 )

82. Energy levels of first-row homonuclear diatomic Molecules Li 2 , Be 2 , B 2 ,C 2 and N 2 have π (2 p ) lower in energy than σ (2 p ) Molecules O 2 , and F 2 have π (2 p ) higher in energy than σ (2 p ) crossover point

83. 83 Heteronuclear diatomic molecule In heteronuclear diatomic molecule, the atomic orbital have different energy and hence their contribution to MO will be unequal. The AO closer in energy to a MO contribute more to that MO and its coefficient is large.

84. For example, in HF, ψ = c H 1s H + c F 2p zF The bonding orbital has principally F2p z character, and the antibonding orbital, H 1s . The bond will be polar with a partial negative charge on F. Bonding character Antibonding character HF molecule B.O = 1

85. 85 Molecular orbital diagram of CO Total no. of electrons = 14 (isoelectronic to N2) Total valence electrons = 10 So the electronic configuration is: ( σ 2s) 2 ( σ *2s) 2 ( π 2p x ) 2 = ( π 2p y ) 2 ( σ 2 p z ) 2 Oxygen has more electronegativity, so the atomic orbitals are lower lying compared to carbon. B.O = 3

86. 86 Q. Draw the MO diagram for NO. Find out the B.O.? Predict the magnetism in it.