# Combining Slater-type orbitals and effective core potentials

## TL;DR

This paper introduces a new methodology for evaluating matrix elements of effective core potentials using Slater-type orbitals, enabling more accurate quantum chemical calculations involving core electrons.

## Contribution

It develops a general recursive and numerical scheme for matrix element evaluation of ECPs with STOs, including core polarization and spin-orbit effects, and validates it with atomic and molecular data.

## Key findings

- Accurately calculated excitation energies and polarizabilities for alkaline earth metals.
- Predicted molecular properties of barium and strontium hydrides consistent with experimental data.
- Demonstrated the effectiveness of the method for complex quantum chemical calculations.

## 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.