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3D Numerov method; 2D Numerov method; Nuclear Schrödinger equation; Hydrogen bond classification; Short delocalized hydrogen bonds; Low barrier hydrogen bonds; Chebyshev collocation; DVR
Abstract:
The classification of short hydrogen bonds depends on several factors including the shape and energy spacing between the nuclear eigenstates of the hydrogen.
Here, we describe the NuSol program in which three classes of algorithms were implemented to solve the 1D, 2D and 3D time independent nuclear Schrödinger equation. The Schrödinger equation was solved using the finite differences based Numerov’s method which was extended to higher dimensions, the more accurate pseudo-spectral Chebyshev collocation method and the image discrete variable representation by Colbert and Miller. NuSol can be applied to solve the Schrödinger equation for arbitrary analytical or numerical potentials with focus on nuclei bound by the potential of their molecular environment. We validated the methods against literature values for the 2D Helon-Heiles potential, the 3D linearly coupled sextic oscillators and applied them to study hydrogen bonding in the malonaldehyde derivate 4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione.
With NuSol, the extent of nuclear delocalization in a given molecular potential can directly be calculated without relying on linear reaction coordinates in 3D molecular space.
