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

In this paper we present results of ab initio calculations for the beryllium dimer with a 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. We have developed STO basis sets, ranging in quality from double to sextuple $\zeta$, which are used in these computations. Principles of their construction are discussed and several atomic benchmarks are presented. Relativistic effects of order ${\alpha }^2$ 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 electronic binding energy of the beryllium dimer is determined to be $929.0\pm 1.9{\text{cm}}^{-1}$, in a very good agreement with the recent experimental value.

Figure 1

Quality of the extrapolation towards the CBS for the beryllium dimer using results from basis sets A-ETCC-$L$ with $L=2,...,6$ based on the theoretical expression (4). The dashed line denotes the estimated limit.

Figure 2

Contribution of the inner-shell effects to the interaction energy, denoted shortly $D_e^{\mathrm{core}}$, calculated by using ATC-ETCC-$L$ basis sets. Black dots are the CCSD(T) results and the black line is the CCSD(T)/CBS extrapolation curve. Analogously, red dots are the MP4 results and the red line is the corresponding CBS extrapolation. Blue squares are the available CCSDT results, for $L=2$, 3, 4.