Practical Implementation and Examples

Quantum chemistry calculations are currently quite common and we recall the excitement this author experienced when first reading Roberts Notes on Molecular Orbital Theory [2] in the early 1960s. Therefore, we include some modern but simple examples here in the hope that the amazement factor is still possible for undergraduates eager to learn up-to-date material. First we can write down the main Hartree-Fock-Roothaan energy operator and at least interpret the various terms. We have used Slater s derivation [1] of the Roothaan LCAO form of the Hartree-Fock equations but prefer Pople s implementation [3] for computer code. First, the one-electron operator 

We noted above that the answer depends on the answer so Pople defines a population matrix  

This adds meaning to the concept that we stand on the shoulders of intellectual giants We have tried to present an understandable derivation of Roothaan s equation in Appendix B leaning on Slater s short form [1], and there is the final SCF equation (in Pople s notation [3])  

We know how to diagonalize a matrix now but the nonzero S matrix makes this more difficult. 

Note that C is not symmetric and E must be last here when we have S as a nonunit matrix. 

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