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

## TL;DR

This paper calculates highly accurate nonrelativistic energies for the ground and lowest quintuplet states of the carbon atom using explicitly correlated Gaussian functions, achieving results close to experimental values.

## Contribution

It introduces a new approach using symmetry-projected, explicitly correlated Gaussian functions to compute precise energies of carbon atom states, including relativistic corrections.

## Key findings

- Estimated energy limits: -37.844906(4) and -37.691751(2) hartree.
- Reproduced experimental excitation energy within about 7 cm$^{-1}$.
- Achieved highly accurate nonrelativistic energy calculations.

## Abstract

Variational, nonrelativisitic energies have been calculated for the ground state ($^3P_g$) and the lowest quintuplet state ($^5S_u$) 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$^{-1}$.