Partitioned R-matrix theory for molecules

Abstract

R-matrix calculations usually require all the eigenvalues and eigenvectors of the inner region Hamiltonian matrix. For molecular problems, particularly when large configuration interaction expansions are used for the target, the Hamiltonian matrix is often too large to be completely diagonalized. Berrington and Ballance (2002 J. Phys. B: At. Mol. Opt. Phys. 35 2275) proposed a partitioned R-matrix theory which only required a proportion of the solutions of the Hamiltonian matrix. This theory was implemented and tested in the atomic R-matrix code. The theory is adapted to the needs of R-matrix calculations on low-energy electron–molecule collisions. A number of alternative procedures are tested. The best is shown to give reliable results with explicit inclusion of only a fraction of the solutions. It is shown that with this revised theory the number of solutions required does not depend on the complexity of the target wavefunction even though this strongly influences the size of the final Hamiltonian matrix. This method will be implemented as part of the UK molecular R-matrix program suite.