Analytic coupled-cluster (CC) and many-body perturbation theory (MBPT) energy gradient methods with restricted Hartree-Fock (RHF), unrestricted Hartree-Fock (UHF), restricted open-shell Hartree-Fock (ROHF), and quasi-RHF(QRHF) reference functions are extended to permit dopping core and excited orbitals. By using the canonical property of the semicanonical ROHF orbitals and the RHF orbitals from which the QRHF reference function is constructed, it is shown that a general procedure can be established not only for RHF and UHF, but also for ROHF and QRHF reference functions. The basic theory and implementation are reported. To provide a systematic study of the trends and magnitudes of the effects of dropped molecular orbitals (MOs) on the structures, harmonic frequencies, and ir intensities, we study HCN, C2H2, CO2, HO2, and C2H4 at increasing levels of correlation and basis sets. The effects of the dropped MOs with the largest basis sets are about 0.003 Angstrom and 0.1 degrees in structures and about 1% on harmonic frequencies and ir intensities. The magnitude and the direction of the drop-MO effect tend to be almost constant from MBPT(2) to CCSD(T) methods. The two isomers of S-3 are studied by the drop-MO-method, yielding very accurate results. (C) 1997 American Institute of Physics.