NuSol - Solving the Schrödinger Equation for Atomic (Protein) Nuclei

Molecular dynamics simulations as well as most quantum classical QM/MM simulations treat the nuclei of the protein atoms as classical particles. Under physiological conditions (room temperature), quantum effects of the atomic nuclei can largely be neglected. It is only under special conditions, that these effects become important and have to be considered beyond the classical nuclei approximation.

A prominent example in which room temperature nuclear quantum effects become important are molecules with very short hydrogen bonds. Malondialdehyde is one such molecule, through a series of mutations malondialdehyde can be chemically modified (4-cyano-2,2,6,6-tetramethyl-3,5-heptanedione) to consistently produce very short hydrogen bonds.

NuSol is a program, which can be used to calculate the nuclear equilibrium densities for a proton, or deuteron, involved in the short hydrogen bonding. However, also larger nuclei and more than one atom can be solved. To this end, NuSol provides an interface for three different numerical solving strategies for the stationary one, two, and three dimensional Schrödinger equation. The first is a generalized Numerov solver, which we extended to the three dimensional case. The program further includes a Chebyshev polynomial and sinc-DVR solver.

In addition to the application of NuSol to short hydrogen bonds, NuSol also solves analytical text book and model potentials like the 2D Henon–Heiles potential, the 3D linearly coupled sextic oscillators, or the simple quantum harmonic and quantum anharmonic oscillators to high accuracy.


Graen, T.; Grubmüller, H.: NuSol: Numerical solver for the 3D stationary nuclear Schrödinger equation. Computer Physics Communications 198, pp. 169 - 178 (2016)
Graen, T.; Inhester, L.; Clemens, M.; Grubmüller, H.; Groenhof, G.: The low barrier hydrogen bond in the photoactive yellow protein: A vacuum artifact absent in the crystal and solution. Journal of the American Chemical Society 138 (51), pp. 16620 - 16631 (2016)
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