Computation of Large Molecules with the Hartree-Fock Model

Abstract

The usual way to compute Hartree-Fock type functions for molecules is by an expansion of the one-electron functions (molecular orbitals) in a linear combination of analytical functions (LCAO-MO-SCF, linear combination of atomic orbitals—Molecular Orbital—Self Consistent field). The expansion coefficients are obtained variationally. This technique requires the computation of several multicenter two-electron integrals (representing the electron-electron interaction) proportional to the fourth power of the basis set size. There are several types of basis sets; the Gaussian type introduced by S. F. Boys is used herein. Since it requires from a minimum of 10 (or 15) Gaussian-type functions to about 25 (or 30) Gaussian functions to describe a second-row atom in a molecule, the fourth power dependency of the basis set has been the de facto bottleneck of quantum chemical computations in the last decade.

In this paper, the concept is introduced of a “dynamical” basis set, which allows for drastic computational simplifications while retaining full numerical accuracy. Examples are given that show that computational saving in computer time of more than a factor of one hundred is achieved and that large basis sets (up to the order of several hundred Gaussian functions per molecule) can be used routinely.

It is noted that the limitation in the Hartree-Fock energy (correlation energy error) can be easily computed by use of a statistical model introduced by Wigner for solid-state systems in 1934.

Thus, large molecules can now be simulated by computational techniques without reverting to semi-empirical parameterization and without requiring enormous computational time and storage.

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