title: Fast, accurate evaluation of exact exchange: The occ-RI-K algorithm.
abstract: Construction of the exact exchange matrix, K, is typically the rate-determining step in hybrid density functional theory, and therefore, new approaches with increased efficiency are highly desirable. We present a framework with potential for greatly improved efficiency by computing a compressed exchange matrix that yields the exact exchange energy, gradient, and direct inversion of the iterative subspace (DIIS) error vector. The compressed exchange matrix is constructed with one index in the compact molecular orbital basis and the other index in the full atomic orbital basis. To illustrate the advantages, we present a practical algorithm that uses this framework in conjunction with the resolution of the identity (RI) approximation. We demonstrate that convergence using this method, referred to hereafter as occupied orbital RI-K (occ-RI-K), in combination with the DIIS algorithm is well-behaved, that the accuracy of computed energetics is excellent (identical to conventional RI-K), and that significant speedups can be obtained over existing integral-direct and RI-K methods. For a 4400 basis function C68H22 hydrogen-terminated graphene fragment, our algorithm yields a 14× speedup over the conventional algorithm and a speedup of 3.3× over RI-K.
authors.affiliation: Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Samuel
authors.initials: S
authors.lastname: Manzer
authors.affiliation: Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Paul R
authors.initials: PR
authors.lastname: Horn
authors.affiliation: Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Narbe
authors.initials: N
authors.lastname: Mardirossian
authors.affiliation: Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California, Berkeley, and Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Head-Gordon
mesh_terms: D000465:Algorithms; D006108:Graphite / Q000737:chemistry; D006859:Hydrogen / Q000737:chemistry; D008956:Models, Chemical; D013997:Time Factors
chemical_list: D006108:Graphite; D006859:Hydrogen