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Title: Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction

Abstract

Here, we present a reduced scaling formulation of the state specific complete active space second-order perturbation method (CASPT2) requiring O( N 4) operations and O( N 2) memory for a fixed active space, where N is proportional to system size. Motivated by the properties of the Kronecker sum, we introduce the supporting subspace technique (SST), which decomposes the CASPT2 linear equations into two parts: a single-reference MP2 energy term using dressed orbitals, plus a reduced linear system with dimension scaling as O( N 2). Together with Laplace quadrature, the SST allows us to reformulate CASPT2 using a MP2 energy computation and Fock builds. By further applying the tensor hyper-contraction (THC) approximation, the MP2-like term can be computed with O( N 4) operations, and the remainder can be solved with O( N 3) operations using the preconditioned conjugate gradient method. This is the first application of THC in the context of multi-reference methods. We also developed an efficient implementation of the method by utilizing graphical processing units and exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method against conventional CASPT2 for reactions in the gas phase. We apply the new method to Menshutkin S N2 reactionsmore » in carbon nanotubes, demonstrating the feasibility of CASPT2 calculations with O(100) atoms.« less

Authors:
 [1]; ORCiD logo [1]
  1. Stanford Univ., Stanford, CA (United States); SLAC National Accelerator Lab., Menlo Park, CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Lab., Menlo Park, CA (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1468951
Grant/Contract Number:  
AC02-76SF00515; ACI-1429830; CHE-1565249
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 149; Journal Issue: 4; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
74 ATOMIC AND MOLECULAR PHYSICS

Citation Formats

Song, Chenchen, and Martínez, Todd J. Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction. United States: N. p., 2018. Web. doi:10.1063/1.5037283.
Song, Chenchen, & Martínez, Todd J. Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction. United States. doi:10.1063/1.5037283.
Song, Chenchen, and Martínez, Todd J. Wed . "Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction". United States. doi:10.1063/1.5037283. https://www.osti.gov/servlets/purl/1468951.
@article{osti_1468951,
title = {Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction},
author = {Song, Chenchen and Martínez, Todd J.},
abstractNote = {Here, we present a reduced scaling formulation of the state specific complete active space second-order perturbation method (CASPT2) requiring O(N4) operations and O(N2) memory for a fixed active space, where N is proportional to system size. Motivated by the properties of the Kronecker sum, we introduce the supporting subspace technique (SST), which decomposes the CASPT2 linear equations into two parts: a single-reference MP2 energy term using dressed orbitals, plus a reduced linear system with dimension scaling as O(N2). Together with Laplace quadrature, the SST allows us to reformulate CASPT2 using a MP2 energy computation and Fock builds. By further applying the tensor hyper-contraction (THC) approximation, the MP2-like term can be computed with O(N4) operations, and the remainder can be solved with O(N3) operations using the preconditioned conjugate gradient method. This is the first application of THC in the context of multi-reference methods. We also developed an efficient implementation of the method by utilizing graphical processing units and exploiting spatial sparsity in tensor operations. We benchmark the accuracy of the new method against conventional CASPT2 for reactions in the gas phase. We apply the new method to Menshutkin SN2 reactions in carbon nanotubes, demonstrating the feasibility of CASPT2 calculations with O(100) atoms.},
doi = {10.1063/1.5037283},
journal = {Journal of Chemical Physics},
number = 4,
volume = 149,
place = {United States},
year = {2018},
month = {7}
}

Journal Article:
Free Publicly Available Full Text
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Cited by: 4 works
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Figures / Tables:

FIG. 1 FIG. 1: Illustration of the (a) CASPT2 linear system and (b) the supported leading system. The two squares in the upper panel illustrate the sparsity pattern of the matrices, and the lower two graphs provide more details about the sparsity structure in the off-diagonal blocks (i.e., the gray blocks inmore » the squares). Each circle represents a subspace, denoted by the number of holes (H) and particles (P) as H(nH)P(nP), as well as the corresponding indices (i, j, holes; a, b, particles; K, L, hole-type active orbitals; C, G, particle-type active orbitals; D, active excitations). The circles are colored by the total number of holes and particles (purple, 0; blue, 1; green; 2; orange, 3; red, 4.). Lines connecting the circles represent coupling between subspaces. Blues lines represent coupling through hole indices, and red lines represent coupling through particle indices. The number of parallel lines indicate the form of the coupling (see the legend at top right). Dotted lines are for visual effect.« less

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