Local correlation in the virtual space in multireference singles and doubles configuration interaction

Abstract

We describe a multireference configuration interaction method that takes advantage of local correlation methods in both the internal ͑originally occupied͒ and external ͑originally unoccupied or virtual͒ orbital spaces. In the internal space, implementation of local correlation is trivial and involves neglecting configurations having simultaneous excitations out of widely separated orbitals. In the external space, the method involves restricting the space of allowed correlating orbitals to those localized near the hole orbitals. Of course, this necessitates the use of localized virtual orbitals which in turn requires one to sacrifice the orthogonality of the virtual space. This complicates the formalism substantially, and we discuss the necessary changes to the traditional expressions in detail. The scaling of the method with system size, basis set size, and the average number of allowed virtual orbitals is explored. An examination of systems having up to 8 heavy atoms reveals that the computational costs of the method scales somewhere between the third and fourth power of the size of the system. Furthermore, this reduced scaling method is capable of recovering greater than 97% of the correlation energy. Additionally, we demonstrate that the method can produce smooth potential energy surfaces and recover bond dissociation energies in organic molecules at a fraction of the cost ͑уtenfold less expensive͒ while retaining accuracy. We go on to use this new reduced scaling approach to predict bond energies in several large organic molecules for which no experimental data are available.

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

“…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].…”

“…We assess herein the parallel efficiency of this new integral-direct implementation. Additionally, we discuss how augmenting the existing local approximations [9][10][11][12][13][14] with a Cauchy-Schwarz (CS) prescreening [15][16][17] of integrals on the molecular orbital level is used to reduce the scaling of our MRSDCI implementation.…”

DIESEL‐MP2: A new program to perform large‐scale multireference‐MP2 computations

“…Several modifications have been proposed to improve the computational efficiency like the individually selecting MR-CI, 10,11 CASPT2, 12 MR-MPn, [13][14][15][16] MCCEPA, 17 or internally contracted MR-CI. 1,18 The ansatz of local correlation treatments 2,19 were also developed and implemented for multireference approaches like local MR-CI 2d, 20 and local MR-PT2. 21,22 The computational cost of the latter approaches was reduced to a certain degree, but a reliable estimate on the errors coming along with this approximation has not yet been assessed for reaction paths or for systems with a difficult electronic or a bulky geometrical structure.…”