NuSol — Numerical solver for the 3D stationary nuclear Schrödinger equation

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• 作者：Timo Graen ; Helmut Grubmü ; ller ; ^{hgrubmu@gwdg.de" class="auth_mail" title="E-mail the corresponding author}
• 关键词：3D Numerov method ; 2D Numerov method ; Nuclear Schrö ; dinger equation ; Hydrogen bond classification ; Short delocalized hydrogen bonds ; Low barrier hydrogen bonds ; Chebyshev collocation ; DVR
• 刊名：Computer Physics Communications
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：198
• 期：Complete
• 页码：169-178
• 全文大小：789 K

文摘

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 method=retrieve&_eid=1-s2.0-S0010465515003203&_mathId=si55.gif&_user=111111111&_pii=S0010465515003203&_rdoc=1&_issn=00104655&md5=e207ea7a5aa74e4cd041938ae9941639" title="Click to view the MathML source">sinc$sinc$ 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 Henon–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.

Program summary

Program title: NuSol

Catalogue identifier: AEXO_v1_0

Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEXO_v1_0.html

Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland

Licensing provisions: GPL 3.0

No. of lines in distributed program, including test data, etc.: 195332

No. of bytes in distributed program, including test data, etc.: 4489808

Distribution format: tar.gz

Programming language: Python 2.7, C.

Computer: PC.

Operating system: Linux.

RAM: 0.1–40 GB

Classification: 16.1.

External routines: FEAST v2.1 [1][2] (included in the distribution file).

Nature of problem: Solving the 3D nuclear Schrödinger Equation

Solution method: Grid solver based on Numerov’s method, Chebyshev collocation and sinc() DVR for 1D/2D/3D potential grids

Running time: System dependent

References:

[1]

E. Polizzi, Density-Matrix-Based Algorithms for Solving Eigenvalue Problems, Phys. Rev. B. Vol. 79, 115112 (2009)

[2]

E. Polizzi, A High-Performance Numerical Library for Solving Eigenvalue Problems: FEAST solver User’s guide, arxiv.org/abs/1203.4031 (2012).