A quasi-degenerate perturbation theory QDPT is presented that is based on quasi-complete active space self-consistent field QCAS-SCF reference functions. The perturbation method shown here is an extension of a previously proposed QDPT with CAS-SCF reference functions CAS-QDPT but is a more compact perturbation method that can employ a much smaller reference configuration space with the same number of active electrons and orbitals as the CAS case. A computational scheme to second-order using a diagrammatic approach is described. The second-order effective Hamiltonian consists of the contribution from external excitations, which involve core or/and virtual orbitals, and internal excitations, which involve only active orbitals. The importance of the internal excitation contribution is emphasized. The method is tested on the potential energy curves of the LiF molecule, the Rydberg excitation energies of furan, and the transition state barrier height of the reaction, H 2 CO→H 2 CO. The results are in very good agreement with the corresponding CAS-SCF reference QDPT results and available experimental data. The deviations from the CAS-QDPT values in the energy are less than 0.1 eV on the average for the excitation energies of furan and less than 1 kcal for the barrier height of the reaction, H 2 CO→H 2 CO. The deviation from the experimental values is 0.11 eV at most for the excitation energies, and 1.2 kcal/mol, which is within the twice the experimental uncertainty, for the barrier height. © 2001 American Institute of Physics.