Reexamination of the calculation of two-center, two-electron integrals over Slater-type orbitals. III. Case study of the beryllium dimer

Abstract

In this paper we present results of ab-initio calculations for the beryllium dimer with basis set of Slater-type orbitals (STOs). Nonrelativistic interaction energy of the system is determined using the frozen-core full configuration interaction calculations combined with high-level coupled cluster correction for inner-shell effects. Newly developed STOs basis sets, ranging in quality from double to sextuple zeta, are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order α 2 are calculated perturbatively by using the Breit-Pauli Hamiltonian and are found to be significant. We also estimate the leading-order QED effects. Influence of the adiabatic correction is found to be negligible. Finally, the interaction energy of the beryllium dimer is determined to be 929.0 ± 1.9 cm −1 , in a very good agreement with the recent experimental value. The results presented here appear to be the most accurate ab-initio calculations for the beryllium dimer available in the literature up to date and probably also one of the most accurate calculations for molecular systems containing more than four electrons.

Combining Slater-type orbitals and effective core potentials

“…In general, construction of the STOs basis sets for pseudopotential calculations is similar as in the recent paper concerning the beryllium dimer [51]. Therefore, we shall not repeat the minutiae of the procedure and illuminate only the most important differences.…”

“…In fact, the maximal value of 6 for the indices n 1 , n 2 is sufficient to cover the whole known periodic table. Moreover, in accurate calculations with Slater-type orbitals for light systems [51] one typically uses even-tempered sequences of functions with n = l+1. This reduces the necessary values of n 1 , n 2 to 1.…”

“…Interestingly enough, there has been a significant progress on this issue in recent years. In fact, looking at only the past 15 years, there are many notable works of Bouferguene et al [10][11][12][13], Rico et al [14][15][16][17][18][19][20][21][22][23][24], Hoggan et al [25][26][27][28][29][30], Pachucki [31][32][33][34][35], and others [36][37][38][39][40][41][42][43][44][45][46][47][48][49][50][51][52]. In particular, for the diatomic systems STOs can be now used routinely [51].…”

Transition moments between excited electronic states from the Hermitian formulation of the coupled cluster quadratic response function

“…E exp is given as an absolute value and the computed energies are given as deviations from the experimental energy. 29,32,33 the two methods. Table II that Non-physical value.…”

“…Slater-type orbitals (STOs) used in this work were constructed according to the correlationconsistency principle, 28 similarly as by Lesiuk et al 29 for the beryllium atom. The only difference in the procedure is that the exponents ζ were chosen according to the welltempered formula, (ζ il = α l + β l i + γ l i 2 /n + δ l i 3 /n 2 ), where n is the number of basis set functions for a given angular momentum, l. After some numerical experimentation, the value of δ l was set equal to zero for l > 2.…”