Springer Online Journal Archives 1860-2000
Chemistry and Pharmacology
Abstract We have derived the expressions for the extremum condition of 〈E〉, corresponding to any wave function. These expressions are given as a function of the spin orbitals. We have carried out the derivation considering the spin orbitals as vectors belonging to an orthonormal basis. The corresponding variational equations have been derived introducing the condition that the norm of the wave function is constant, as the only additional constraint. From the expression obtained for the first variation of the matrix elements of H, as a function of the spin orbitals, we have derived the RHF equations for a simple case. In the present procedure, the couplings between orbitals of different shells appear directly, being defined explicitly, and they may be taken as corresponding with the elements of a Hermitian matrix. The calculations that we have carried out show that the coupling operators defined in the paper give results which are variationally correct.
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