The translation- and rotation-free nuclear orbital plus molecular orbital (TRF-NOMO) theory was developed in order to accurately determine the nonadiabatic nuclear and electronic wave functions without Born-Oppenheimer approximation. This study presents a hybrid method combining the TRF-NOMO theory with the generator coordinate method (GCM). The TRF-NOMO/GCM treatment is capable of giving the vibrational excited states with high accuracy, as well as improving the ground-state description by inclusion of the many-body effect. Numerical applications of the TRF-NOMO/GCM calculations to an HF molecule confirm its reliability and usefulness.
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