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

Abstract

An ab initio R-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 R-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 (Ca+2F-)+e- 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.

A quantum defect model for the s, p, d, and f Rydberg series of CaF

“…26,45,46 The R-matrix approach 47 partitions the computational solution of the Schrödinger equation for the electron/ion system into a dynamically complex region near the ion-core and a long-range region of simpler dynamics. 26,45,46 The R-matrix approach 47 partitions the computational solution of the Schrödinger equation for the electron/ion system into a dynamically complex region near the ion-core and a long-range region of simpler dynamics.…”

Direct detection of Rydberg–Rydberg millimeter-wave transitions in a buffer gas cooled molecular beam

“…[6,[13][14][15] To study the structure and dynamics of the molecular Rydberg states with both high resolution and a fast data acquisition rate, we incorporate two cru- (ii) The BaF molecular beam generated from our buffer gas cooled ablation source is a factor of 1000 brighter and has 10 times slower laboratory frame velocity than a BaF beam generated by our Smalley-type supersonic jet ablation source. Exploitation of the broad bandwidth, multiplexed, FID-detection scheme would have been impractical without the enhanced brightness of the buffer gas cooled ablation source.…”

Electric potential invariants and ions-in-molecules effective potentials for molecular Rydberg states

“…In this paper, we focus on optimizing effective potentials for use in Rydberg R-matrix calculations, 17,104,119 as a faithful representation of charge/molecular-ion interactions, and as a predictive tool for moments and polarizabilities. We have shown in Figure 1 how the origin chosen for a single-center multipole series affects the convergence properties of a multipole series, and the transition from penetrating to non-penetrating in the representation of Rydberg states.…”