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A Multi-Center Quadrature Scheme for the Molecular Continuum



Barry I. Schneider, Heman Gharibnejad, nicholas douguet, Luca Argenti, Jeppe Olsen


A common way to evaluate electronic integrals for polyatomic molecules is to use Becke's partitioning scheme [\colorblue}J. Chem. Phys. \bf 88}, 2547 (1988)}] in conjunction with multi- center grids of comparable size. Becke's scheme, however, is efficient only for integrands that fall off rapidly at large distances, such as those approximating bound electronic states. Here, we present a modified version of Becke's multi-center quadrature scheme to functions which do not satisfy the above criterion. The present approach is thus applicable to molecular photoionization and electron-molecule scattering. In this modified scheme, the original atomic weights in Becke's partition of unity are smoothly switched off outside the molecular region. The atomic integrals are evaluated on radial grids, centered on each atom, and with a radius of the order of few bond lengths. A central master grid is used to evaluate the residual contribution in the interstitial region and at long range. This method is designed to efficiently evaluate integrals involving continuum electronic wavefunctions required in single and double photoionization processes involving large polyatomic systems. In this study we provide a general description and proof-of-principles of the method.
Computer Physics Communications


multi-center quadrature, molecular scattering, molecular photoionization


Schneider, B. , Gharibnejad, H. , Douguet, N. , Argenti, L. and Olsen, J. (2021), A Multi-Center Quadrature Scheme for the Molecular Continuum, Computer Physics Communications, [online], (Accessed April 23, 2024)
Created June 1, 2021, Updated March 27, 2024