Roothan-Hartree-Fock energy

The Hamiltonian, Hea, which is called the Hartree-Fock-Roothan operator is a 1-electron operator whose application yields the energy of an electron moving in the average field of the other electrons and nuclei. In principle an SCF theory approach will lead to a well-defined expression for Hett for closed and open shell systems (188, 189), and with the aid of modern computers Hm integrals can be evaluated numerically even for transition metal complexes. This type of ab initio calculation has been reported for a reasonable number of organometallic complexes of first-row transition elements by Hillier, Veillard, and their co-workers (48, 49, 102, 103, 111-115 58, 68, 70, 187, 228, 229). 

Sum Over States (SOS). This method computes molecular orbitals, from which values for transition fi equencies may be calculated. First the electronic ground state of the molecular system is determined, after which one may apply either the Hartree-Fock-Roothan method or the LCAO (hnear combination of atomic orbitals) approximation. Then one accoimts for correlations by configuration interaction calculations to form the lowest-energy excited states and transition dipole moments of the molecule. Finally transition frequencies and dipole moments are employed along with the formulas for the hyperpolarizabilities. The SOS method needs as input, energies and transition moments for excited states. It yields Pico) directly (eq. 1) identification of contributing excited states is important. 

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