P.G Department of Chemistry Govt. P.G College Rajouri Chemical Bonding Molecular Orbital Theory (MOT) Valence Bond Theory (VBT) Dr. Naseem Ahmed Assistant Professor P.G Department of Chemistry Govt. P.G College Rajouri

Molecular Orbital Theory Chemical Bonding Two existing theories, Molecular Orbital Theory (MOT) Valence Bond Theory (VBT) Molecular Orbital Theory MOT starts with the idea that the quantum mechanical principles applied to atoms may be applied equally well to the molecules.

H-CC-H

Simplest possible molecule: H2+ : 2 nuclei and 1 electron. Let the two nuclei be labeled as A and B & wave functions as A & B. Since the complete MO has characteristics separately possessed by A and B,  = CAA + CBB or  = N(A + B)  = CB/CA, and N - normalization constant

This method is known as Linear Combination of Atomic Orbitals or LCAO A and B are same atomic orbitals except for their different origin. By symmetry A and B must appear with equal weight and we can therefore write 2 = 1, or  = ±1 Therefore, the two allowed MO’s are  = A± B

For A+ B we can now calculate the energy From Variation Theorem we can write the energy function as E = A+B H A+B/A+B A+B

Looking at the numerator: E = A+B H A+B/A+B A+B A+B H  A+B = A H A + B H B + A H B + B H A = A H  A + B H B +2AH B

ground state energy of a hydrogen atom. let us call this as EA = A H  A + B H B + 2AH B ground state energy of a hydrogen atom. let us call this as EA A H  B = B H A =   = resonance integral  Numerator = 2EA + 2 

Looking at the denominator: E = A+B H A+B/A+B A+B A+B A+B = A A + B B + A B + B A = A A + B B + 2A B

A B = B A = S, S = Overlap integral. = A A + B B + 2A B A and B are normalized, so A A = B B = 1 A B = B A = S, S = Overlap integral.  Denominator = 2(1 + S)

E = A+B H A+B/A+B A+B Summing Up . . . E = A+B H A+B/A+B A+B Numerator = 2EA + 2  Denominator = 2(1 + S) E+ = (EA + )/ (1 + S) Also E- = (EA - )/ (1 – S) E± = EA ±  S is very small  Neglect S

Energy level diagram EA -  EA +  B A 

Linear combination of atomic orbitals Rules for linear combination 1. Atomic orbitals must be roughly of the same energy. 2. The orbital must overlap one another as much as possible- atoms must be close enough for effective overlap. 3. In order to produce bonding and antibonding MOs, either the symmetry of two atomic orbital must remain unchanged when rotated about the internuclear line or both atomic orbitals must change symmetry in identical manner.

Rules for the use of MOs * When two AOs mix, two MOs will be produced * Each orbital can have a total of two electrons (Pauli principle) * Lowest energy orbitals are filled first (Aufbau principle) * Unpaired electrons have parallel spin (Hund’s rule) Bond order = ½ (bonding electrons – antibonding electrons)

Linear Combination of Atomic Orbitals (LCAO) The wave function for the molecular orbitals can be approximated by taking linear combinations of atomic orbitals. A B AB = N(cA A + cBB) c – extent to which each AO contributes to the MO 2AB = (cA2 A2 + 2cAcB A B + cB2 B 2) Overlap integral Probability density

Amplitudes of wave functions added Constructive interference g bonding cA = cB = 1 Amplitudes of wave functions added g = N [A + B]

2AB = (cA2 A2 + 2cAcB A B + cB2 B 2) density between atoms electron density on original atoms,

The accumulation of electron density between the nuclei put the electron in a position where it interacts strongly with both nuclei. Nuclei are shielded from each other The energy of the molecule is lower

Amplitudes of wave functions subtracted. node antibonding u = N [A - B] cA = +1, cB = -1 u + - Destructive interference Nodal plane perpendicular to the H-H bond axis (en density = 0) Energy of the en in this orbital is higher. Amplitudes of wave functions subtracted. A-B

The electron is excluded from internuclear region  destabilizing Antibonding

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