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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.

We introduce a new method for the computation of the transition moments between the excited electronic states based on the expectation value formalism of the coupled cluster theory (XCC) [B. Jeziorski and R. Moszynski, Int. J. Quant. Chem. 48, 161 (1993)]. The working expressions of the new method solely employ the coupled cluster operator T and an auxiliary operator S that is expressed as a finite commutator expansion in terms of T and T † . In the approximation adopted in the present paper the cluster expansion is limited to single, double, and linear triple excitations.The computed dipole transition probabilities for the singlet-singlet and triplet-triplet transitions in alkali earth atoms agree well with the available theoretical and experimental data. In contrast to the existing coupled cluster response theory, the matrix elements obtained by using our approach satisfy the Hermitian symmetry even if the excitations in the cluster operator are truncated, but the operator S is exact. The Hermitian symmetry is slightly broken if the commutator series for the operator S are truncated. As a part of the numerical evidence for the new method, we report calculations of the transition moments between the excited triplet states which have not yet been reported in the literature within the coupled cluster theory. Slater-type basis sets constructed according to the correlation-consistency principle are used in our calculations.

In this work we present a coupled cluster based approach to the computation of the spin orbit coupling matrix elements. The working expressions are derived from the quadratic response function with the coupled cluster parametrization, using the auxiliary excitation operator S. Systematic approximations are proposed with the CCSD and CC3 levels of theory. The new method is tested by computing lifetimes of several electronic states of Ca, Sr and Ba atoms, with Gaussian and Slater basis sets. The results are compared with available theoretical and experimental data.

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