Molecular orbital theories for removing the basis set superposition error in the molecular interaction energy and the application to the study on the molecular clusters

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1) Without the orthogonal constraint, the high-spin restricted Hartree-Fock equation is derived By imposing the to of the occupied molecular orbitals on each molecule which constitutes a molecular cluster, the variational condition for the locally projected restricted Hartree-Fock is obtained. The computer code was developed. The cede for the closed shell duster was improved.2) The 3rd and 4th order perturbation theory within the single excitations is developed, and the method was tested The interaction energy evaluated by the 3rd order single excitation perturbation (3^<rd> SPT) is very close to that of the counterpoise corrected Hartree-Fock, if the excited molecular orbitals are properly chosen.3) A new type of neutral duster having an excess electron was computationally herd. The dusters M(HF)_n(M=Li,Na,K) are studied with UHF MP2/6-311++G(d,p) level of theory. For n□3, an electron is ejected from the metal atom and is trapped under the electrostatic field created by HF molecules. This is a typical example that an excess electron is caught under the multiple dipole moments. The duster Main might be a candidate of the molecular unit of a new electride.