TY - JOUR
T1 - Resolutions of the Coulomb operator
T2 - IV. the spherical bessel quasi-resolution
AU - Limpanuparb, Taweetham
AU - Gilbert, Andrew T.B.
AU - Gill, Peter M.W.
PY - 2011/4/12
Y1 - 2011/4/12
N2 - We show that the Coulomb operator can be resolved as r12-1 = Σnlm φnlm(r1) φ nlm(r2) where φnlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r1 + r2 < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C84H64.
AB - We show that the Coulomb operator can be resolved as r12-1 = Σnlm φnlm(r1) φ nlm(r2) where φnlm(r) is proportional to the product of a spherical Bessel function and a spherical harmonic, provided that r1 + r2 < 2π. The resolution reduces Coulomb matrix elements to Cholesky-like sums of products of auxiliary integrals. We find that these sums converge rapidly for four prototypical electron densities. To demonstrate its viability in large-scale quantum chemical calculations, we also use a truncated resolution to calculate the Coulomb energy of the nanodiamond crystallite C84H64.
UR - http://www.scopus.com/inward/record.url?scp=79954462623&partnerID=8YFLogxK
U2 - 10.1021/ct200115t
DO - 10.1021/ct200115t
M3 - Article
SN - 1549-9618
VL - 7
SP - 830
EP - 833
JO - Journal of Chemical Theory and Computation
JF - Journal of Chemical Theory and Computation
IS - 4
ER -