Approximately size extensive local multireference singles and doubles configuration interaction

Abstract

Multi-reference Configuration Interaction (MRCI) is often used to predict the electronic structures and reaction energetics of small molecules with very high accuracy. Unfortunately, MRCI is inapplicable to large or even medium-sized molecules for two reasons: its computational cost scales poorly with molecule size and MRCI methods are not size extensive, leading to large energy errors. We have developed a new local (L) and approximately size extensive MRCI method that addresses both shortcomings. Truncating long-range electron correlation in a local orbital basis as well as efficient processing of two-electron integrals via Cholesky decomposition (CD) and integral screening reduce the computational cost to O(N(3)) with a small prefactor. A priori and a posteriori size extensivity corrections are both considered. The Multi-reference Averaged Coupled-Pair Functional (MRACPF) provides approximate size extensivity by modifying the energy functional. The very inexpensive Davidson-Silver and Pople a posteriori schemes also produce quite accurate corrections over a large range of molecular size. Employing CD-LMRACPF is slightly more expensive than using a Davidson-type correction, but the former gives superior results. Molecules with up to 50 heavy atoms can be treated with our CD-LMRACPF method thus far.

Density Fitting and Cholesky Decomposition of the Two-Electron Integrals in Local Multireference Configuration Interaction Theory

“…The local electron correlation approximation was first employed by Pulay and Szabo [4][5][6][7][8] and is used in many different local CWs. [9][10][11][12][13][14][15][16][17][18][19][20][21][22][23][24] Other methods have also emerged to remove nonlocal correlations by non-distance metrics. The pair natural orbital (PNO) method, for instance, removes nonlocal correlations by creating a small set of unique, local virtual orbitals for each pair of internal orbitals.…”

Assessment of a semi integral-direct local multi-reference configuration interaction implementation employing shared-memory parallelization

“…By removing a large number of configurations from the wavefunction, this reduces the computational complexity of the CI problem from OðN 6 Þ to OðN 3 Þ or less with N as a measure of the system size [7,18,20]. We solve the CI problem either in a standard MRSDCI or a sizeextensive MRACPF [8] way using a Davidson solver and the symmetric group graphical approach (SGGA) [27,28].…”

“…TigerCI currently is a plugin to either MOLCAS [21] or GAMESS [22][23][24]. As both the algorithms and numerical challenges have been reviewed at length elsewhere [2,8], we focus here on concise discussions of the properties relevant for our integral-direct implementation.…”

“…All algorithms presented in this contribution were implemented in our TigerCI program for Cholesky-decomposed (CD) local multi-reference SDCI/ACPF [2,7,8,13,14,[18][19][20]. TigerCI currently is a plugin to either MOLCAS [21] or GAMESS [22][23][24].…”

“…In this contribution, we discuss our new integral-direct, parallel [6] implementation of Cholesky-decomposed local multi-reference singles and doubles configuration interaction (CD-LMRSDCI [7]) and its size-extensive extension, multi-reference averaged coupled-pair functional (MRACPF) [8] theory within our TigerCI code [2]. Since I/O is intrinsically a process of low parallelism, fewer I/O operations directly translate to reducing bottlenecks in the code.…”