Development of the explicitly correlated Gaussian-nuclear orbital plus molecular orbital theory: Incorporation of electron-electron correlation

► ECG-NOMO is a rigorous non-Born-Oppenheimer theory. ► The electron-electron correlation is important for ECG-NOMO. ► We propose the correlation methodologies for the ECG-NOMO theory. ► The ECG-NOMO zero-point energies are close to the experimental results.