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Constrained Hartree-Fock wave functions for atoms Qureshi, Hilal Ahmed


This thesis deals with the calculation of Hartree-Fock wave functions satisfying an off-diagonal hypervirial relation as a constraint. The constraint in this case implies that the dipole length form and the dipole velocity form of the transition probability give identical values. Mathematically, this is equivalent to forcing the approximate eigenfunctions of the Hamiltonian of the system to satisfy a relation which is true for exact eigenfunctions. The method of constrained variation is used to solve this problem. The constrained Hartree-Fock system of equations is solved numerically. The Z-expansions of radial wave functions, the diagonal and the off-diagonal energy parameters and the parameter of constraint are carried out. The effect of the constraint on the total energy E of the system, defined as the change in the Hartree-Fock total energy due to the constraint, is estimated. The method of constrained variation is then applied to a few two, three and four electron systems to calculate the constrained total energy E of the system and also the oscillator strengths of a few of the transitions of the system. The results indicate that the oscillator strengths can be calculated more accurately, at practically no cost of the total energy E, with the aid of the constrained Hartree-Fock functions than with the standard Hartree-Fock functions in all those cases where the correlation effects are not too strong to invalidate the single configuration approximation.

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