Physics & Astronomy ETDs

Publication Date

1-18-1971

Abstract

The object of this dissertation was the investigation of the influence on the delta G curve for H2 of polarization, enhancement of charge between the nuclei, and variation of the screening parameter. A better understanding of the influence of these factors could lead to progress in estimating more accurately the dissociation energies of diatomic molecules. Also to be investigated was the correlation between these factors and the vibrational and rotational spectroscopic constants, particularly Bv.

The Heitler-London combination of atomic orbitals (referred to as phi 1) was used in every wave function The atomic orbital 2pz was used in phi 2 (polarization) and phi 3 (charge enhancement). In each of these functions the screening parameter alpha was either set equal to 1 or was varied. The method of linear variation functions (phi 1, phi 2, phi 3 being the functions) was used to solve for the electronic energy in the Born-Oppenheimer approximation. The sum of the electronic energy and the energy of repulsion of the nuclei served as a model for examination of vibration and rotation of the nuclei. Eight models were studied. The integrals were formulated in closed form after the fashion of Rosen and of Hirschfelder and Linnett. Rotationless vibrational levels and Bv values were obtained for each model by applying the Cooley numerical integration procedure to each energy function. The Dunham formulation or a fit to the levels was applied to obtain various spectroscopic constants. Rotational levels were obtained by treating the centrifugal reaction term as a perturbation of the pure vibration.

The values of Re (classical internuclear equilibrium separation) for o< = 1 were all too large by about 0. 25 atomic units. For alpha variable they were close to the experimental value, but the lowest energy minimum was 0.7 e.v. above experiment. Beyond R = 10 a.u. in cases which included polarization nearly all the energy was of the R-6 form. Examination of numerical values of the square of the wave function supported the expectation that phi 2 would be associated with polarization for large values of R, that inclusion of phi 3 would lead to an increase of charge between the nuclei, and that variation of alpha would affect the charge distribution significantly.

The delta G and Bv curves for the four models for which alpha = 1 had negative curvature at small v, but the curves for the four models for which alpha. was varied exhibited a positive curvature instead. The effect of polarization upon the curves was not obvious until the Cooley computations were carried out for increased reduced masses of the molecule (such as 81 times the normal reduced mass of H2). For these, the delta G and Bv curves exhibited a positive curvature near the dissociation limit when polarization was included but not otherwise. Attempts were carried out to stretch the delta G and B curves parallel to both coordinate axes by using the experimental values of delta G1\2 and B0 to obtain multipliers for stretching parallel to one axis and of delta G3/2 and B1 (essentially) to obtain multipliers for stretching the theoretical curves parallel to the remaining axis. These attempts were unsatisfactory in the case of alpha= 1 but much more successful for alpha variable. In the case of the Wang model the stretched Hang delta G and Bv curves fell very close to the experimental ones. This is a further instance in which a correlation between the delta G and Bv curves was found.

Degree Name

Physics

Level of Degree

Doctoral

Department Name

Physics & Astronomy

First Committee Member (Chair)

Charles Leroy Beckel

Second Committee Member

Christopher Pratt Leavitt

Third Committee Member

Christopher Dean

Language

English

Document Type

Dissertation

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