Abstract
The use of curvilinear coordinates results in kinetic energy operators with singular terms. These singularities can be in the dynamically relevant region. The present work specifically considers 1/sin 2 θ singularities and wavefunctions showing significant amplitude close to θ = 0. It investigates the use of direct product-type discrete variable representations (DVRs) to describe such situations in quantum dynamics calculations and discusses the regularization of such repulsive singularities. A new scheme, the cot-DVR, is developed which can be used to construct well converging direct product DVRs for Hamiltonians showing a 1/sin 2 θ singularity. The cot-DVR is based on the diagonalization of the cot θ-matrix and adds two additional basis function, sin( θ) and sin(2 θ), to the standard basis of Legendre polynomials. It is particularly well suited for multi-configurational time-dependent Hartree calculations which employ one-dimensional (bottom layer) single-particle functions.
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