Using Collocation to Solve the Schro?dinger Equation

Sergei Manzhos

doi:10.1021/acs.jctc.2c01232

Using Collocation to Solve the Schro?dinger Equation

2023-03-08

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DOI：10.1021/acs.jctc.2c01232

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We review the collocation approach to the solution of the Schro''dinger equation and its uses in applications. Interrelations between collocation and other methods are highlighted. We also stress advantages and disadvantages of the rectangular collocation formulation. Using collocation makes it possible to use any, e.g. optimized, coordinates and basis functions, including nonintegrable basis functions, and provides a straightforward way of dealing with singularities in the potential. In addition, we stress that using collocation facilitates tuning the shape of basis functions and the placement of points, both of which can be done with machine-learning methods. Applications to electronic and vibrational problems are reviewed focusing on calculations for molecules on surfaces for which there are few variational calculations. Collocation has advantages when potential energy surfaces are unavailable, in particular, for molecule-surface systems, and for systems for which standard direct product quadrature grids, often used with variational methods, are costly.

Keywords:

ITERATIVE CONFIGURATION-INTERACTION

DISCRETE VARIABLE REPRESENTATION

DISTRIBUTED GAUSSIAN BASES

DENSITY-FUNCTIONAL THEORY

VIBRATIONAL-ENERGY LEVELS

BASIS FUNCTION NETWORKS

HARTREE-FOCK EQUATIONS

WAVE-PACKET DYNAMICS

BASIS-SET

MOLECULAR-DYNAMICS

Using Collocation to Solve the Schro?dinger Equation

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