Thesis (Ph. D.)--California Institute of Technology, 1972. UM #72-22,605. / Advisor names found in the Acknowledgments pages of the thesis. Title from home page. Viewed 02/12/10. Includes bibliographical references.

No description available.

No description available.

Thesis--Georg-August-Universität zu Göttingen, 1912. / Cover title. Lebenslauf.

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. / Science, Faculty of / Mathematics, Department of / Graduate

Three different constraints are considered in this thesis, namely: the integral electron cusp condition as a constraint; the off-diagonal hyper-virial theorems as constraints; and perturbation-induced constraints. Eleven approximate configuration-interaction wavefunctions for the ground state of helium are used to test the application of the integral electron cusp condition as a constraint. The results indicate that, if the approximate wavefunction is flexible enough, the calculated electron density at the nucleus is improved when the cusp constraint is imposed. However, the expectation values of rˉ ¹and r ˉ² do not change significantly. Further investigation is made on the use of off-diagonal hypervirial theorems as constraints. The transition from the 1¹ S state to the 2¹ P state of helium is chosen as an example. Firstly, it is found that an energy-independent off-diagonal constraint is not useful in improving calculation of transition probabilities. Secondly, when the approximate wavefunction is flexible enough, iteration on the transition energy converges very rapidly. Finally, the study is extended to the isoelectronic species Li⁺ and Be⁺⁺. A five-term approximate configuration-interaction wavefunction for the ground state of helium is used to test the validity of the perturbation-induced constraints scheme. Different constraint operators are constructed for different properties. The properties studied are expectation values of rˉ² , rˉ¹ , r and r⁺² . Two methods of the perturbation-induced constraints are tested: in one, the first-order wavefunction is fixed and constant for all constrained properties; in the other, the first-order wavefunction varies with the constrained properties. It is disappointing to find that for this particular wavefunction chosen, both methods fail to improve the properties studied when one imposes the constraints. / Science, Faculty of / Chemistry, Department of / Graduate

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No description available.

Thesis (Ph.D. 1971) from the Dept. of Organic Chemistry, University of Adelaide.

Thesis (Ph. D.)--University of Florida, 1980. / Description based on print version record. Typescript. Vita. Includes bibliographical references (leaves 100-101).