A. The Shape of the Compton Line for Helium and Molecular Hydrogen. B. Bond Formation in Simple Molecules

Citation

Hicks, Bruce Lathan (1939) A. The Shape of the Compton Line for Helium and Molecular Hydrogen. B. Bond Formation in Simple Molecules. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/vmd0-ez38. https://resolver.caltech.edu/CaltechTHESIS:01222025-224500277

Abstract

A. By using variation functions which take into consideration the instantaneous interaction of the electrons, momentum distribution functions and intensity distributions in the Compton line are computed for helium and molecular hydrogen, neglecting small relativity and binding corrections. The half-value breadths are expressed in terms of 1/2 λ* where 1 is the wave-length displacement from the center of the shifted line and 2λ* = (λ₁² + λ_c² - 2λ,λ_c cooX)^1/2 λ₁ and λ_c are the primary and scattered wave-lengths and X the scattering angle. The absolute breadth of the line may therefore be computed for any λ₁ and X. For helium and molecular hydrogen the values of 1/2 λ* at half-maximum are 10.8 and 8.5, respectively.

B. This thesis is a review of the quantum mechanical methods which have been used to compute the dissociation energies and interatomic distances of homonuclear diatomic molecules in the ground state. In comparing the different methods three qualifications for a successful type of treatment are emphasized. First, it must be of as general applicability as possible. Second, the inherent uncertainty attending its application should either be small or of known order of magnitude. Finally, it should provide a simple and general physical picture of bond formation. These three qualifications are discussed in some detail for H₂⁺ up to Li₂.

New calculations for the lithium molecule and for the beryllium molecule-ion, Be₂⁺⁺, are described. In particular a comparison is made between the permissible types of hybridization treatment for Li₂ and Li₂⁺. It is concluded that the complete hybridization of the atomic orbitals in Li₂ is not possible when the K electrons are neglected.

In a section on numerical methods certain improvements in the technique of evaluating some of the two electron integrals are described. The different procedures used in solving secular equations are compared with regard to their accuracy, generality of application, and their amenableness to machine computation. It is shown how the Duncan-Collar-Aitken technique may be extended so that it conforms perfectly to the demands of quantum mechanical calculations.

The problem discussed in this part of the thesis was suggested by Professor Linus Pauling, to whom I am also greatly indebted for advice and guidance during the course of the work. To Dr. Sidney Weinbaum I owe my best thanks for his calculation of the numerical values of most of the integrals.

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