<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>R</mml:mi></mml:math>-matrix implementation giving well-behaved quantum defect matrices of molecular hydrogen

Abstract

The ab initio variational R-matrix method is combined with generalized quantum-defect theory to calculate quantum defect matrices for ${}^{1}{\ensuremath{\Sigma}}_{u}^{+}$ and ${}^{1}{\ensuremath{\Pi}}_{u}$ symmetries of molecular hydrogen. The calculations take account of doubly excited channels and are optimized so as to minimize the dependence of the quantum-defect matrix elements as functions of energy and internuclear distance. The matrices are used to calculate the lowest clamped-nuclei Rydberg potential energy curves as well as doubly excited resonance positions and widths near the first excited state of ${\mathrm{H}}_{2}^{+}.$ The results are in good agreement with previous ab initio results. Owing to their smoothness, the quantum-defect matrices are well suited for rovibronic multichannel quantum-defect applications. This opens up the possibility of a fully ab initio quantitative theoretical description of excited ${\mathrm{H}}_{2},$ including ionization and dissociation.