Combining Slater-type orbitals and effective core potentials

Abstract

We present a general methodology to evaluate matrix elements of the effective core potentials (ECPs) within one-electron basis set of Slater-type orbitals (STOs). The scheme is based on translation of individual STO distributions in the framework of Barnett-Coulson method. We discuss different types of integrals which naturally appear and reduce them to few basic quantities which can be calculated recursively or purely numerically. Additionally, we consider evaluation of the STOs matrix elements involving the core polarisation potentials (CPP) and effective spin-orbit potentials. Construction of the STOs basis sets designed specifically for use with ECPs is discussed and differences in comparison with all-electron basis sets are briefly summarised. We verify the validity of the present approach by calculating excitation energies, static dipole polarisabilities and valence orbital energies for the alkaline earth metals (Ca, Sr, Ba). Finally, we evaluate interaction energies, permanent dipole moments and ionisation energies for barium and strontium hydrides, and compare them with the best available experimental and theoretical data.

Theoretical determination of polarizability and magnetic susceptibility of neon

“…Our final theoretical value of the static polarizability α 0 = 2.66080 (36) has an estimated uncertainty of about one part per 10 4 . The most recent experimental value for this quantity, α 0 = 2.661057 (7), obtained by Gaiser and a after applying the correction for the compressibility Fellmuth [7], lies within our error bars, but is about 50 times more accurate.…”

“…These bases, optimized using the methodology established in Refs. [35,36], are available from authors upon request. Computer codes for the STO integrals, described in Refs.…”

Spin-orbit coupling matrix elements from the explicitly connected expressions of the response functions within the coupled-cluster theory

“…[55] For the Ca, Sr, and Ba atoms we used the STO basis sets specifically designed for the calculations with the effective core potentials. [56] The following Gaussian basis sets were used: for Ca the ECP10MDF pseudopotential [57] together with the [12s12p6d] basis augmented with a set of [1s1p1d] diffuse functions, for Sr [8s8p5d4f 1g] augmented with a set of [1s1p1d1f 3g] diffuse functions [58] and the ECP28MDF pseudopotential, [57,59,60] for Ba the ECP46MDF pseudopotential [57] together with the [9s9p6d4f 2g] Gaussian basis set. [57] To assess the quality of the basis sets, in Tables 2 -4 we present the excitation energies obtained with the EOM-CCSD and EOM-CC3 codes and compare them with the experimental results.…”

“…However, there are significant discrepancies for the 1 D and 3 D states. Within the Gaussian basis set both EOM-CCSD and EOM-CC3 iterations did not converge to the desired states, and within the Slater basis set the [56] revealed that this is an inherent problem of the pseudopotentials used in the calculations. The authors of Ref.…”

“…Lifetimes computed with the XCCSD(G), XCCSD(S), XCC3(G) methods are not available due to the divergence of the CC procedure. [56] It can be seen from Eq. ( 48) that in order to compute all the components that contribute to τ [ 1 D2] we need the EOM-CC procedure to converge to the 1 D, 3 D, 1 P and 3 P states.…”