Real-space quadrature: A convenient, efficient representation for multipole expansions
- University of South Florida, 4202 E. Fowler Ave., CHE 205, Tampa, Florida 33620 (United States)
Multipoles are central to the theory and modeling of polarizable and nonpolarizable molecular electrostatics. This has made a representation in terms of point charges a highly sought after goal, since rotation of multipoles is a bottleneck in molecular dynamics implementations. All known point charge representations are orders of magnitude less efficient than spherical harmonics due to either using too many fixed charge locations or due to nonlinear fitting of fewer charge locations. We present the first complete solution to this problem—completely replacing spherical harmonic basis functions by a dramatically simpler set of weights associated to fixed, discrete points on a sphere. This representation is shown to be space optimal. It reduces the spherical harmonic decomposition of Poisson’s operator to pairwise summations over the point set. As a corollary, we also shows exact quadrature-based formulas for contraction over trace-free supersymmetric 3D tensors. Moreover, multiplication of spherical harmonic basis functions translates to a direct product in this representation.
- OSTI ID:
- 22416134
- Journal Information:
- Journal of Chemical Physics, Vol. 142, Issue 7; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0021-9606
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
GENERAL PHYSICS
COMPUTERIZED SIMULATION
DECOMPOSITION
ELECTROSTATICS
EXPANSION
MATHEMATICAL SOLUTIONS
MOLECULAR DYNAMICS METHOD
MULTIPOLES
NONLINEAR PROBLEMS
POINT CHARGE
QUADRATURES
ROTATION
SPACE
SPHERES
SPHERICAL CONFIGURATION
SPHERICAL HARMONICS
SUPERSYMMETRY
TENSORS