ABSTRACT:A stochastical algorithm to investigate the real closed-shell HartreeFock problem is proposed. The approach is based on a global optimization method, the generalized simulated annealing. We tested this methodology by determining the Hartree-Fock ground state of the H 2 , LiH, BH, Li 2 , OH Ϫ , FH, CO, N 2 , BeH 2 , CH 2 , H 2 O, NH 3 , HCHO, CH 4 molecular systems using minimal, double-zeta, and triple-zeta bases. The main characteristic of this method is that it enables mapping the electronic hypersurface to find minima with the guarantee of finding the absolute minimum of the functional in focus.

In this paper we propose a stochastic algorithm to investigate the real unrestricted Hartree-Fock problem. The approach is based on a global optimization method, the Generalized Simulated Annealing. The main characteristic of this method is that it enables the mapping of the electronic hyper-surface in such a way as to guarantee that the absolute minimum of the functional in focus will be achieved. We tested this methodology by determining the Hartree-Fock ground-state of the H if E(‫ރ‬C tϩ1 ) Յ E(‫ރ‬ t ), replace ‫ރ‬ t by ‫ރ‬ tϩ1 , if E(‫ރ‬ tϩ1 ) Ͼ E(‫ރ‬ t ), run a random number r ʦ [0, GSA ALGORITHM APPLIED TO ELECTRONIC STRUCTURE II VOL. 106, NO. 13

ABSTRACT:In their original form, the Generalized Simulated Annealing (GSA), proposed by Tsallis and Stariolo, was defined with two independent parameters, q a and q v , used in the definition of the acceptance probability, visitation distribution, and temperature functions. In the posterior applications of this algorithm, however, another independent parameter has been introduced, replacing q v in the definition of the temperature function, becoming more efficient and allowing a convergence with a small number of cycles. Nevertheless, there is no convergence proof of the GSA algorithm to the absolute minimum in this case. In this work it is presented a convergence proof of the GSA method to the absolute minimum, with three independent parameters, q a , q v , and q T , to define the acceptance probability, visitation distribution, and temperature functions, using a modified form of the distribution function, Јg qv,qT , in the formulation of the algorithm.

ABSTRACT:The recently introduced multireference Hartree-Fock configuration interaction (MRHFCI) method has been applied to the calculation of the dipole moment of the LiH, BH, FH, CO, and H 2 O molecules. The results obtained indicate that MRHFCI wave functions, much more compact but of the same quality of the orthogonal full CI ones, can provide better dipole moments than the corresponding full CI wave functions. The value of the dipole moments obtained with the MRHFCI wave functions is quite insensitive to the choice of the HF references but the same is not true for the electronic energy. Therefore, further studies are necessary to develop a criterion for selecting a set of HF references which could provide the best values of energy and dipole moment. Also, it would be important to verify if other one-electron properties can be computed with the same degree of accuracy obtained for the dipole moments.

In this work, the multireference Hartree-Fock configuration interaction method (MRHFCI) was applied to calculate the permanent electrical quadrupole moment of the hydrogen fluoride molecule, using the atomic bases STO-6G and CFG-6G. We have obtained MRHFCI functions, with energies comparable to the full CI ones, providing dipole and quadrupole moments in close agreement with the experimental values and with reduced MRHF basis, that is, with significant lower numbers of configurations.