Correlation Energies of Ten-Electron Molecular Systems by a United-Atom Many-Body Perturbation Procedure: ${\mathrm{H}}_2$O, N${\mathrm{H}}_3$, and C${\mathrm{H}}_4$

The linked-cluster many-body perturbation theory has been applied to the calculation of the correlation energies of the molecular systems ${\mathrm{H}}_2$O, N${\mathrm{H}}_3$, and C${\mathrm{H}}_4$. The Hartree-Fock and correlation energies are obtained separately by combining the contributions from the pertinent diagrams. The calculated Hartree-Fock energies are in satisfactory agreement with the best previous theoretical results. The correlation energies (in a. u.) that we have obtained are -0.338, -0.317, and -0.312 for ${\mathrm{H}}_2$O, N${\mathrm{H}}_3$, and C${\mathrm{H}}_4$, respectively. These latter energies are utilized for two purposes. One is to combine them with the total Hartree-Fock energies to obtain the total energies to compare with experiment. Secondly, they are subtracted from the "experimental" total energies to obtain reference Hartree-Fock energies with which to compare the energies from theoretical one-electron calculations.