A Tour of the Foundations of
Computational Chemistry and Material Science
Lecture 1: ab initio Methods



The Hartree-Fock Self-Consistent Field Method

One starts with the independent particle (IP) approximation. Let the wave function
tex2html_wrap_inline979 where tex2html_wrap_inline981 can be expressed as a Slater determinant,

equation81

Now apply the variational procedure to such a function as a trial function. In addition, we require that the single particle functions tex2html_wrap_inline983 be orthonormalized, i.e.,

equation98

Then we can write the variational principle as,

equation108

This gives a set of non-linear integro-differential equations known as the Dirac-Fock SCF equations. (See the next chapter for more details on the variational procedure)



Author: Dr. Warren Perger and Ken Flurchick