Evaluation of electron repulsion integral of the explicitly correlated Gaussian-nuclear orbital plus molecular orbital theory

This Letter proposes two schemes for the efficient evaluation of electron repulsion integrals required for the explicitly correlated Gaussian-nuclear orbital plus molecular orbital (ECG-NOMO) theory, which offers accurate descriptions for electrons and nuclei. Two schemes, i.e., fully analytical and hybrid schemes for analytical and numerical integrations, for the ECG-NOMO/Hartree–Fock theory are assessed. Illustrative applications of these schemes to two-electron diatomic molecules demonstrate that the ECG-NOMO/HF theory provides significantly accurate zero-point energies within 123.5 cm−1 deviation when compared with the experimental data.