Configuration Interaction Study of the $^3{\rm P}$ Ground State of the Carbon Atom

TL;DR

This study uses configuration interaction calculations with optimized computational techniques to accurately determine the ground state energy of the carbon atom, exploring configuration importance and efficiency improvements.

Contribution

It introduces an efficient, partially-parallelized CI computational method with optimized exponents for small basis sets to accurately compute atomic ground states.

Findings

Achieved millihartree accuracy in ground state energy

Optimized configuration selection improves computational efficiency

Demonstrated the effectiveness of parallelized CI calculations

Abstract

Configuration Interaction (CI) calculations on the ground state of the C atom are carried out using a small basis set of Slater orbitals [7s6p5d4f3g]. The configurations are selected according to their contribution to the total energy. One set of exponents is optimized for the whole expansion. Using some computational techniques to increase efficiency, our computer program is able to perform partially-parallelized runs of 1000 configuration term functions within a few minutes. With the optimized computer programme we were able to test a large number of configuration types and chose the most important ones. The energy of the $^3{\rm P}$ ground state of carbon atom with a wave function of angular momentum L=1 and M$_{\rm L}$=0 and spin eigenfunction with S=1 and M$_{\rm S}$=0 leads to -37.83526523 h, which is millihartree accurate. We discuss the state of the art in the determination of the ground state of the carbon atom and give an outlook about the complex spectra of this atom and its low-lying states.