TY - JOUR
T1 - A physically motivated sparse cubature scheme with applications to molecular density-functional theory
AU - Rodriguez, Juan I.
AU - Thompson, David C.
AU - Anderson, James S.M.
AU - Thomson, Jordan W.
AU - Ayers, Paul W.
PY - 2008/7/24
Y1 - 2008/7/24
N2 - We present a novel approach for performing multi-dimensional integration of arbitrary functions. The method starts with Smolyak-type sparse grids as cubature formulae on the unit cube and uses a transformation of coordinates based on the conditional distribution method to adapt those formulae to real space. Our method is tested on integrals in one, two, three and six dimensions. The three dimensional integration formulae are used to evaluate atomic interaction energies via the Gordon-Kim model. The six dimensional integration formulae are tested in conjunction with the nonlocal exchange-correlation energy functional proposed by Lee and Parr. This methodology is versatile and powerful; we contemplate application to frozen-density embedding, next-generation molecular-mechanics force fields, 'kernel-type' exchange-correlation energy functionals and pair-density functional theory.
AB - We present a novel approach for performing multi-dimensional integration of arbitrary functions. The method starts with Smolyak-type sparse grids as cubature formulae on the unit cube and uses a transformation of coordinates based on the conditional distribution method to adapt those formulae to real space. Our method is tested on integrals in one, two, three and six dimensions. The three dimensional integration formulae are used to evaluate atomic interaction energies via the Gordon-Kim model. The six dimensional integration formulae are tested in conjunction with the nonlocal exchange-correlation energy functional proposed by Lee and Parr. This methodology is versatile and powerful; we contemplate application to frozen-density embedding, next-generation molecular-mechanics force fields, 'kernel-type' exchange-correlation energy functionals and pair-density functional theory.
UR - http://www.scopus.com/inward/record.url?scp=54749152446&partnerID=8YFLogxK
U2 - 10.1088/1751-8113/41/36/365202
DO - 10.1088/1751-8113/41/36/365202
M3 - Artículo
SN - 1751-8113
VL - 41
JO - Journal of Physics A: Mathematical and Theoretical
JF - Journal of Physics A: Mathematical and Theoretical
IS - 36
M1 - 365202
ER -