Physics & Astronomy ETDs

Publication Date

12-2-1974

Abstract

It has been known for many decades that the B 3Ʃu- state of the oxygen molecule, the upper state of the Schumann-Runge electronic band system, is predissociated. The predissociation has been attributed to the 3Πu state, arising from the ground state, separated atom, manifold of molecular states, by previous investigators with the crossing point of the potential energy curves ranging from somewhere on the inner limb to somewhere on the outer limb of the bound excited B 3Ʃu- state. This research has been undertaken to quantitatively describe the observed predissociation. A model with adjustable parameters was developed and used to fit, in a least squares sense, experimentally derived data. The basic experimental data consisted of rotational line widths and positions which were available in the scientific literature at the time this research was started. The rotational line positions were used to determine vibrational band origins which in turn were used to determine the positions of the rotationless vibrational energy levels. A scheme, using polynomials and rational polynomials, was devised to determine the shifts in these levels due to the interaction between the bound and repulsive states. These vibrational energy level shifts along with the line widths were the data used to determine the parameters in the model. The model was based on the theory of configuration interaction between discrete and continuum states developed by Fano. Up to four repulsive potential curves, each with two parameters and each with a corresponding interaction matrix element function with up to three parameters describing the interaction between the bound and repulsive electronic states, were incorporated into the model. The parameters were adjusted using a variable metric, nonlinear, least squares method devised by Davidon. The necessary expressions for the rotational line widths and rotationless vibrational energy level shifts were evaluated, using numerically determined solutions to the appropriate Schrodinger equations. Based on this model, which accounts for the major interactions among the electronic states involved, two repulsive electronic states were found to describe the main features of the predissociation of the B 3Ʃu- state. One repulsive state intersected the bound state potential energy curve on the inner branch near vibrational level v = 1, while the other intersected the bound state potential energy curve on the outer branch between vibrational levels v = 3 and 4. Two more repulsive electronic states were needed to describe minor features of the rotational line width and shift data. Both of these potential energy curves crossed the outer branch of the B 3Ʃu- potential energy curve, one near vibrational level v = 1 and the other near vibrational level v = 6. The symmetries of these states were assigned by comparison with ab initio theoretical results, that is, by assuming the ordering in energy of the four relevant electronic states found by ab initio calculations was correct. This leads to the following conclusions. The main features of the predissociation of the O2 B 3Ʃu- state are determined by a 3Πu state intersecting on the inner branch near v = 1 and a 5Ʃu- state intersecting on the outer branch between v = 4. Minor features of the predissociation are determined by a 1Πu state intersecting on the outer branch near v = 1 and a 5Ʃu- state intersecting on the outer branch near v = 6. This model is able to quantitatively describe the line widths and only qualitatively describe the level shifts.

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

David Solomon King

Fourth Committee Member

William Whitaker

Language

English

Document Type

Dissertation

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