Analytical gradients for Singer's multicenter n‐electron explicitly correlated Gaussians

Abstract

ABSTRACT:Analytical gradients for Singer's basis of n-electron multicenter explicitly correlated Gaussian functions are derived and implemented to variationally optimize the energy and wave function of molecular systems within the Born-Oppenheimer approximation. Wave functions are optimized with respect to ( 1 2 n(n + 1) + 3n) nonlinear variational parameters and one linear coefficient per term in the basis set. Preliminary results for the ground states of H 3 + and H 3 suggest that the method can be more flexible and can achieve lower energies than previously reported calculations.

Nonadiabatic Calculations of the Dipole Moments of LiH and LiD

“…Thus while we formally say that we calculate the ith component of the dipole moment, we really calculate only one value, the observable dipole moment. The integrals and gradients needed to solve (8) and (9) are similar to those presented in [6], and will be presented explicitly in a future paper. Optimization was carried out by supplying the function and energy gradients to the optimization routine TN [12], which was downloaded from the World Wide Web [13].…”

“…For fermions, the projection operators are simply Young operators, derived from the appropriate Young tableau, as shown in the previous work [6]. Thus the final form of the basis function iŝ…”

“…This basis has been used for calculations invoking the BO approximation (see [6] and the references cited therein, also [7]). This work represents the first application of this basis to non-BO calculations.…”

Non-Born–Oppenheimer calculations of the polarizability of LiH in a basis of explicitly correlated Gaussian functions

“…Most of the integrals used in this work are similar to those presented in the previous work, 20 and will in fact be quoted rather than derived. A slight difference in the kinetic energy integral will be shown.…”

Non-Born–Oppenheimer molecular structure and one-particle densities for H2D+

“…The optimization was based on the Newton-type algorithm involving analytical gradients with respect to all three groups of variational parameters. 14 In Table I we present the total energies and the average nuclear distances obtained in the calculations. The geometrical parameters reported in Table I include the distance from the nucleus at the origin of the coordinate system ͑d͒ to the proton ͑r pd ͒, as well the distance between the two "loose" nuclei ͑r pp ͒.…”