Molecular Orbital Theory

Question 1

When do we turn to MO theory?

Answer 1

For more general methods, turn to more fundamental theories (QM based methods) which all in some way involve the molecular orbital approximation

Question 2

Wavefunction

Answer 2

Electrons of a molecule are said to exist collectively in energy-quantized states, each state is described by a multi dimensional wavefunction

Question 3

Born Interpretation of Wavefunction

Answer 3

Function YY or |Y|^2 is a probability density function
Integral from a,b of YY is the probability that electron is between a and b

Question 4

Hamiltonian Operator

Answer 4

Extracts eigenvalue E from eigenfunction Y
Quantized states arise from the Schrodinger equation:
HYn = EnYn

Question 5

Variational Theorem

Answer 5

If a trial wavefunction (Ytrial) is not equal to Ytrue then < E > is always greater than Etrue

< E > = int( Y * (trial) H Y(trial) dT )

Question 6

Variational Principle

Answer 6

One way of approximating Eelec is to guess a Ytrial function containing adjustable parameters and optimize the values of these parameters to minimize < E >

Question 7

Basis Set

Answer 7

The set of AO functions used to build the MO’s
Basis set choice effects final Eelec and Yelec

Question 8

Slater Determinant

Answer 8

Many electron wavefunction
Accommodate electron indistinguishability and wavefunction asymmetry

Question 9

What does the HF-SCF method do?

Answer 9

Uses the variational principle to optimize the parameters within a Slater determinant

Question 10

Characteristics of HF-SCF method

Answer 10

• simplest QM method
• parameter free
• results depend on basis set chosen for LCAO-MO’s
• reduces solving ‘mini’ Schrodinger equations
• iterative (like geometry optimizations) because the MO coefficients are improved until they converge to 6 sig figs in energy

Question 11

What is the time consuming part of HF-SCF?

Answer 11

The large number of electron repulsion integrals (ERI’s)
N basis functions = N^4 ERI’s