A Fifth-order Multi-perturbation Derivation of the Energy Coefficients of Polyatomic Molecules

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Issam Abdelraziq
Moh'd Abu-Jafar
Sharif Musameh
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A multiperturbation theory has been developed for molecular systems. In the present paper we extend this theory to fifth order in the energy. The "bare-nucleus" hydrogenic function is chosen as the zero-order wave function rather than the more customary hartree-fock function. With this choice the multiperturbation wave functions are independent of the nuclear charges and of the total number of nuclear centers and electrons for the molecule and are thus completely transferable to other systems. Making the simplest possible choice, we describe an n-electron, m-center polyatomic molecule as n "hydrogenic" electrons on a single center perturbed by electron-electron and electron-nucleus coulomb interactions. With this choice of zero-order Hamiltonian (H0) the first-order wave function for any polyatomic molecule will consist entirely of two-electron, one-center and one-electron, two-center first-order wave functions. These are exactly transferable from calculations on He-like and H2-like systems. To calculate the first-order and second order correction for the wave function of any polyatomic molecule, we need the first-order and second-order correction for a two-electron atomic wave function, the first-order and second-order correction for a one-electron diatomic molecular wave function and some additional mixed second-order corrections. The wave functions necessary will be two-center, one-electron at most. The second-order wave function for a polyatomic molecule contains additional contributions which cannot be obtained from the simple subsystems, but represent multiple perturbation contributions which are two electron diatomic, and one-electron triatomic in character. The expressions for the multiperturbation energy-expansion coefficients through fifth order are derived.