This Letter proposes a scheme to incorporate electron-electron (e-e) correlation for the explicitly correlated Gaussian-nuclear orbital plus molecular orbital (ECG-NOMO) theory, which offers accurate descriptions for electronic and nuclear states. The second order Moller-Plesset perturbation theory and coupled-cluster theory with singles and doubles in the ECG-NOMO framework are adopted for evaluating the e-e correlation. Illustrative applications for dihydrogen, trihydrogen cation molecules, and their isotopomers confirm significant improvement for the total energies and zero-point energies. (C) 2012 Elsevier B. V. All rights reserved.