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Properties of nearly one-electron molecules. I. An iterative Green function approach to calculating the reaction matrix

### Abstract

An *ab initio* -matrix method for determining the molecular reaction matrix of scattering theory is introduced. The method makes use of a principal-value Green function to compute the collision channel wave functions for the scattered electron, in combination with the Kohn variational scheme for the evaluation of -matrix eigenvalues on a spherical boundary surface at short range. This technique permits the size of the bounded volume in the variational calculation to be reduced, making the computations fast and efficient. The reaction matrix is determined in a form that minimizes its energy dependence. Thus the procedure does not require modification or an increase in the computational effort to study the electronic structure and dynamics in Rydberg molecules with extremely polar ion cores. The analysis is specialized to examine the bound-state and free-electron scattering properties of nearly one-electron molecular systems, which are characterized by a Rydberg/scattering electron incident on a closed-shell ion core. However, it is shown that the treatment is compatible with all-electron/*ab initio* representations of open-shell and nonlinear polyatomic ion cores, emphasizing its generality. The introduced approach is used to calculate the electronic spectrum of the calcium monofluoride molecule, which has the extremely polar closed-shell ion-core configuration. The calculation utilizes an effective single-electron potential determined by M. Arif, C. Jungen, and A. L. Roche [J. Chem. Phys.106, 4102 (1997)] previously. Close agreement with experimental data is obtained. The results demonstrate the practical utility of this method as a viable alternative to the standard variational approaches.

© 2005 American Institute of Physics

Received 02 May 2005
Accepted 28 June 2005
Published online 01 September 2005

Acknowledgments:
The computer code for the numerical computations carried out in this work was written in MATHEMATICA 5.1, a product of Wolfram Research. This research was supported by the NSF Grant No. CHE-04050876.

Article outline:

I. INTRODUCTION
II. THEORY
A. Solutions of the zero-order equations
B. Coupled equations
C. Iterative procedure to calculate the matrix
1. Solutions of the zero-order equations
2. Solutions of the coupled equations
3. The reaction matrix
D. The energy dependence of the reaction matrix
1. Alternate pair of basis functions
E. The transformation between and
III. CONCLUSIONS

/content/aip/journal/jcp/123/8/10.1063/1.2005017

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/content/aip/journal/jcp/123/8/10.1063/1.2005017

2005-09-01

2016-04-30

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