Page 168 - Strategies and Applications in Quantum Chemistry From Molecular Astrophysics to Molecular Engineer

QUANTUM CHEMISTRY COMPUTATIONS IN MOMENTUM SPACE 153
converges to results close to HF limit, but obviously it cannot approach it completely
because the fit is based on a limited number of gaussian functions.

4. Results and advantages

In Tab. 1 are given the various results obtained in our group ; the precision of the method
used for the resolution as well as the main interest of these results are summarized. When
results have been obtained numerically (section 3.1) the method is denoted num-SCF or
num-MCSCF according to the level of theory used ; when an analytical treatment (section
3.2) has been performed, the denotation is analyt-gauss if the trial functions were
expressed as linear combinations of gaussian functions or analyt-Slater if the trial
functions were expressed as linear combinations of Slater functions. Finally when a
semi-analytical treatment (section 3.3) has been done the method is called analyt-gauss*.
Results fall into three categories : the first one corresponds to pure numerical results on
which have demonstrated the feasibility of numerical
calculations. They have also provided momentum wavefunctions for physical quantities
such as Compton profiles [17], (e,2e) cross-sections [26]. In the second category we
have investigated the possibilities of using a variation-iteration procedure defined in
momentum space to improve the one-electron states for various chemical systems
expressed as linear combinations of gaussian functions. Significant improvements in
energy quantities and properties sensitive to the shape of the wave function (Compton
profile, momentum distribution, etc.) were indeed noted. In particular, the first iteration
transforms the trial wave function expressed as linear combinations of gaussian functions
in an expression which involves Dawson functions. An asymptotic analysis carried on
the first iterate discloses a behavior quite close to the exact one. In the third category, the
semi-numerical approach is used to provide physical quantities. Similarly to the position
space approach it is based on the variation principle which guides the changes of the
wavefunction : the closer the energy E to the nearer the trial wave function the
ground state In LCAO-SCF-MO schemes however, the function obtained by
minimizing the total energy does not necessarily give a good description of properties
such as multipole moments, while in momentum space due to the capacity of the method
to improve the quality of a wavefunction significant improvements have been obtained
e.g. for the dipole moment of the hydrogen fluoride [38].