Calculation of multicenter electric field gradient integrals over Slater-type orbitals using unsymmetrical one-range addition theorems

Abstract

The electric field induced within a molecule by its electrons determines a whole series of important physical properties of the molecule. In particular, the values of the gradient of this field at the nuclei determine the interaction of their quadrupole moments with the electrons. Using unsymmetrical one-range addition theorems introduced by one of the authors, the sets of series expansion relations for multicenter electric field gradient integrals over Slater-type orbitals in terms of multicenter charge density expansion coefficients and two-center basic integrals are presented. The convergence of the series is tested by calculating concrete cases for different values of quantum numbers, parameters and locations of orbitals.

Quantum Monte Carlo simulation of carbon monoxide reactivity when adsorbed at metal and oxide catalyst surfaces: Trial wave‐functions with exponential type basis and quasi‐exact three‐body correlation

“…In such a case, the basis remains ortho‐normal and othogonalises a / r α . This eliminates the r 2 term, arising for quadrupole moments when α = −2, thus confirming the very recent numerical observations in the Guseinov group 36. Similarly, it would be expected that α = −1 ETOs would constitute the optimal basis for magnetic dipole integrals of NMR shielding.…”

“…This article records the precedent of electric quadrupole integrals, already published by Guseinov and Seckin Gorgun, where the negative α basis converges as well as (if not better than) the STO36 and recaps a new application to the dipole integrals in the NMR experimental setup. It appears best to use α = −1 ETOs in this case (see above and39).…”

How specific exponential type orbitals recently became a viable basis set choice in NMR shielding tensor calculation

“…In such a case, the basis remains ortho-normal and othogonalises a/r α . This eliminates the r 2 term, arising for quadrupole moments when α = −2, thus confirming the very recent numerical observations in the Guseinov group [107]. Similarly, it would be expected that α = −1 ETOs would constitute the optimal basis for magnetic dipole integrals of NMR shielding.…”

Israfil I. Guseinov: A pioneer of the quantum theory of atomic, molecular, and nuclear systems*

“…In Refs. , by the use of Guseinov's symmetrical and unsymmetrical one‐range addition theorems for integer and noninteger n STOs and complete sets of ‐METOs, one‐ and two‐electron multicenter electron‐repulsion integrals with the arbitrary location of STOs are expressed in terms of overlap integrals. The final results are of a simple structure and are, therefore, especially useful for machine computations.…”

“…, the prepared computer program for Guseinov's CHFR equations can be successfully applied to the study of various properties of atomic, molecular, and nuclear systems. Note that all of the one‐ and two‐electron multicenter integrals over STOs arising in the solution of CHFR equations have been evaluated using Guseinov's symmetrical and unsymmetrical one‐range addition theorems …”