Multiconfiguration self-consistent-field study of the importance of triply and quadruply excited electronic configurations in the water molecule

The importance of triple excitations, configurations differing by three electrons from the Hartree–Fock reference configuration, is of considerable interest in electronic structure theory. A simple double zeta basis set O(9s 5p/4s 2p), H(4s/2s) has been used to address this problem for the water molecule. Configuration interaction (CI) and multiconfiguration self-consistent-field (MCSCF) wave functions including up to all single, double, triple, and quadruple (SDTQ) excitations (a total of 17 678 1A1 configurations) have been obtained for this purpose. An interesting result is that the MCSCF wave function including only single excitations yields 52.3% of the comparable correlation energy obtained with all single and double excitations. Using canonical SCF orbitals, triple excitations are found to contribute only 0.8% of the correlation energy. However, the MCSCF procedure increases this correlation energy fraction by more than a factor of 5. The MCSCF energies for the wave functions including SD and SDTQ excitations are less than 0.001 hartree lower than the comparable straight CI energies.