Explicitly correlated wavefunctions of the ground state and the lowest quintuplet state of the carbon atom

Abstract

Variational, nonrelativisitic energies have been calculated for the ground state (${}^3{P}_g$) and the lowest quintuplet state (${}^5{S}_u$) of the carbon atom, with wavefunctions expressed in the basis of symmetry-projected, explicitly correlated Gaussian (ECG) lobe functions. New exact limits of these energies have been estimated, amounting to $-37.844906(4)$ and $-37.691751(2)$ hartree. With finite nuclear masses and leading, scalar relativistic corrections included, respective experimental excitation energy of ${}^{12}C$ has been reproduced with accuracy of about 7 cm${}^{-1}$.

10 pages, 2 figures, research paper; updated because original version of this paper contained erroneous values of the orbit-orbit term