TY - JOUR

T1 - Many-Electron Integrals over Gaussian Basis Functions. I. Recurrence Relations for Three-Electron Integrals

AU - Barca, Giuseppe M.J.

AU - Loos, Pierre François

AU - Gill, Peter M.W.

N1 - Publisher Copyright:
© 2016 American Chemical Society.

PY - 2016/4/12

Y1 - 2016/4/12

N2 - Explicitly correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations and can often achieve chemical accuracy with relatively small Gaussian basis sets. In most calculations, the many three- and four-electron integrals that formally appear in the theory are avoided through judicious use of resolutions of the identity (RI). However, for the intrinsic accuracy of the F12 wave function to not be jeopardized, the associated RI auxiliary basis set must be large. Here, inspired by the Head-Gordon-Pople and PRISM algorithms for two-electron integrals, we present an algorithm to directly compute three-electron integrals over Gaussian basis functions and a very general class of three-electron operators without invoking RI approximations. A general methodology to derive vertical, transfer, and horizontal recurrence relations is also presented.

AB - Explicitly correlated F12 methods are becoming the first choice for high-accuracy molecular orbital calculations and can often achieve chemical accuracy with relatively small Gaussian basis sets. In most calculations, the many three- and four-electron integrals that formally appear in the theory are avoided through judicious use of resolutions of the identity (RI). However, for the intrinsic accuracy of the F12 wave function to not be jeopardized, the associated RI auxiliary basis set must be large. Here, inspired by the Head-Gordon-Pople and PRISM algorithms for two-electron integrals, we present an algorithm to directly compute three-electron integrals over Gaussian basis functions and a very general class of three-electron operators without invoking RI approximations. A general methodology to derive vertical, transfer, and horizontal recurrence relations is also presented.

UR - http://www.scopus.com/inward/record.url?scp=84964425505&partnerID=8YFLogxK

U2 - 10.1021/acs.jctc.6b00130

DO - 10.1021/acs.jctc.6b00130

M3 - Article

SN - 1549-9618

VL - 12

SP - 1735

EP - 1740

JO - Journal of Chemical Theory and Computation

JF - Journal of Chemical Theory and Computation

IS - 4

ER -