A finite-difference Newton-Raphson solution of the two-center electronic Schrödinger equation

Continuum wavefunctions for one-electron two-centre molecular ions from the Killingbeck - Miller method

“…It is well known that exact solutions are obtainable in prolate spheroidal coordinates (−1 η 1; 1 ξ < ∞; 0 ϕ 2π) in the cases of both bound and continuum states. Various computational methods, generally based on infinite expansions of the wavefunctions in terms of some basis functions, have been developed to determine eigenvalues and eigenfunctions of bound states; such as infinite continued fractions (Baber and Hassé 1935, Bates et al 1953, Bates and Carson 1956, Brown and Steiner 1966, Wilson and Gallup 1966, Power 1973, Abramov and Slavyanov 1978, matrix techniques (Hunter and Pritchard 1967, Hartmann and Helfrich 1968, Helfrich and Hartmann 1970, Helfrich 1971, Aubert et al 1974 or direct use of recurrence relations (Ley-Koo and Cruz 1981, Frantz et al 1989, Hadinger et al 1989, 1990 as well as to determine continuum wavefunctions (Cayford et al 1974, Ponomarev and Somov 1976, Greenland and Greiner 1976, Rankin and Thorson 1979, Abramov et al 1979, Ley-Koo and Cruz 1981, Tergiman 1993.…”

dftatom: A robust and general Schrödinger and Dirac solver for atomic structure calculations

“…Note that the table shows only shooting-type solvers [18], as we discuss in the present work. Other non-shooting type approaches, see, e.g., [19][20][21][22][23][24][25][26] and references therein, have been developed and implemented as well but have not yet found wide adoption in larger-scale electronic structure calculations due in part to robustness issues (e.g., spurious states) which can arise [26]. Note also that the table is intended only as a general guide: in the context of any given feature, "No" should be understood to mean only that we did not find it straightforward to implement in the referenced code.…”