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QUANTUM CHEMISTRY COMPUTATIONS IN MOMENTUM SPACE 149
3.3. SEMI-ANALYTICAL TECHNIQUE
The method presented here allows, starting with trial gaussian functions, a partial
analytical treatment which we have used to improve the LCAO-GTO orbitals (trial
functions) essentially obtained from all ab initio quantum chemistry programs. As in r-
representation, trial functions (Eq. 21) are conveniently expressed as linear
combinations of functions themselves written as linear combinations of
gaussian functions (LCAO-GTO approximation)
and
where is a normalized gaussian function expressed in momentum space. As
belong to the Sobolev space direct Fourier transformation leads to a
set that fulfills the criterion about the convergence of the energy and wave
function (the completeness of the orbital bases is not sufficient
to guarantee the convergence of the energy and wave function in the norm of ; to
ensure this convergence the set must be complete in . The expression
for the first iterate based on trial functions expressed as LCAO-GTO
expansions is thus :
The various quantities entering Eq. 24 are deduced when the trial orbitals are
expressed as linear combinations of Gaussian functions, they are expressible in terms of
