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Title: Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method

Abstract

We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [3]
+ Show Author Affiliations
  1. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)
  2. Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States); Kavli Energy NanoScience Inst. of Berkeley, Berkeley, CA (United States)
  3. SLAC National Accelerator Lab., Menlo Park, CA (United States). Photon Ultrafast Laser Science and Engineering Inst. (PULSE); Stanford Univ., CA (United States)
Publication Date:
Research Org.:
SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); University of California, Berkeley, CA (United States); Stanford Univ., CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR). Scientific Discovery through Advanced Computing (SciDAC)
OSTI Identifier:
1767927
Alternate Identifier(s):
OSTI ID: 1755455
Grant/Contract Number:  
AC02-76SF00515; AC02-05CH11231; SciDAC
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 154; Journal Issue: 1; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY

Citation Formats

Song, Chenchen, Neaton, Jeffrey B., and Martínez, Todd J. Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method. United States: N. p., 2021. Web. doi:10.1063/5.0035233.
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Song, Chenchen, Neaton, Jeffrey B., & Martínez, Todd J. Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method. United States. https://doi.org/10.1063/5.0035233
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Song, Chenchen, Neaton, Jeffrey B., and Martínez, Todd J. Thu . "Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method". United States. https://doi.org/10.1063/5.0035233. https://www.osti.gov/servlets/purl/1767927.
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@article{osti_1767927,
title = {Reduced scaling formulation of CASPT2 analytical gradients using the supporting subspace method},
author = {Song, Chenchen and Neaton, Jeffrey B. and Martínez, Todd J.},
abstractNote = {We present a reduced scaling and exact reformulation of state specific complete active space second-order perturbation (CASPT2) analytical gradients in terms of the MP2 and Fock derivatives using the supporting subspace method. This work follows naturally from the supporting subspace formulation of the CASPT2 energy in terms of the MP2 energy using dressed orbitals and Fock builds. For a given active space configuration, the terms corresponding to the MP2-gradient can be evaluated with O(N5) operations, while the rest of the calculations can be computed with O(N3) operations using Fock builds, Fock gradients, and linear algebra. When tensor-hyper-contraction is applied simultaneously, the computational cost can be further reduced to O(N4) for a fixed active space size. The new formulation enables efficient implementation of CASPT2 analytical gradients by leveraging the existing graphical processing unit (GPU)-based MP2 and Fock routines. We present benchmark results that demonstrate the accuracy and performance of the new method. Example applications of the new method in ab initio molecular dynamics simulation and constrained geometry optimization are given.},
doi = {10.1063/5.0035233},
journal = {Journal of Chemical Physics},
number = 1,
volume = 154,
place = {United States},
year = {Thu Jan 07 00:00:00 EST 2021},
month = {Thu Jan 07 00:00:00 EST 2021}
}
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Works referenced in this record:

Analytic first derivatives of floating occupation molecular orbital-complete active space configuration interaction on graphical processing units
journal, July 2015

  • Hohenstein, Edward G.; Bouduban, Marine E. F.; Song, Chenchen
  • The Journal of Chemical Physics, Vol. 143, Issue 1
  • DOI: 10.1063/1.4923259

Classification of configurations and the determination of interacting and noninteracting spaces in configuration interaction
journal, February 1973

  • McLean, A. D.; Liu, B.
  • The Journal of Chemical Physics, Vol. 58, Issue 3
  • DOI: 10.1063/1.1679288

Analytic gradients for the single-reference driven similarity renormalization group second-order perturbation theory
journal, July 2019

  • Wang, Shuhe; Li, Chenyang; Evangelista, Francesco A.
  • The Journal of Chemical Physics, Vol. 151, Issue 4
  • DOI: 10.1063/1.5100175

Multiconfigurational perturbation theory with level shift — the Cr2 potential revisited
journal, October 1995

Tensor hypercontraction density fitting. I. Quartic scaling second- and third-order Møller-Plesset perturbation theory
journal, July 2012

  • Hohenstein, Edward G.; Parrish, Robert M.; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 137, Issue 4
  • DOI: 10.1063/1.4732310

A simple method for the evaluation of the second-order-perturbation energy from external double-excitations with a CASSCF reference wavefunction
journal, April 1982

An atomic orbital-based formulation of the complete active space self-consistent field method on graphical processing units
journal, June 2015

  • Hohenstein, Edward G.; Luehr, Nathan; Ufimtsev, Ivan S.
  • The Journal of Chemical Physics, Vol. 142, Issue 22
  • DOI: 10.1063/1.4921956

Tensor Hypercontraction Second-Order Møller–Plesset Perturbation Theory: Grid Optimization and Reaction Energies
journal, June 2015

  • Kokkila Schumacher, Sara I. L.; Hohenstein, Edward G.; Parrish, Robert M.
  • Journal of Chemical Theory and Computation, Vol. 11, Issue 7
  • DOI: 10.1021/acs.jctc.5b00272

Tensor hypercontraction. II. Least-squares renormalization
journal, December 2012

  • Parrish, Robert M.; Hohenstein, Edward G.; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 137, Issue 22
  • DOI: 10.1063/1.4768233

Quantum Chemistry on Graphical Processing Units. 1. Strategies for Two-Electron Integral Evaluation
journal, January 2008

  • Ufimtsev, Ivan S.; Martínez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 4, Issue 2
  • DOI: 10.1021/ct700268q

Direct configuration interaction with a reference state composed of many reference configurations
journal, November 1980

  • Siegbahn, Per E. M.
  • International Journal of Quantum Chemistry, Vol. 18, Issue 5
  • DOI: 10.1002/qua.560180510

Analytical Derivative Coupling for Multistate CASPT2 Theory
journal, May 2017

  • Park, Jae Woo; Shiozaki, Toru
  • Journal of Chemical Theory and Computation, Vol. 13, Issue 6
  • DOI: 10.1021/acs.jctc.7b00018

A perspective on the CASPT2 method
journal, April 2011

  • Pulay, Peter
  • International Journal of Quantum Chemistry, Vol. 111, Issue 13
  • DOI: 10.1002/qua.23052

Reduced scaling CASPT2 using supporting subspaces and tensor hyper-contraction
journal, July 2018

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 149, Issue 4
  • DOI: 10.1063/1.5037283

Linear scaling geometry optimisation and transition state search in hybrid delocalised internal coordinates
journal, January 2000

  • Billeter, Salomon R.; Turner, Alexander J.; Thiel, Walter
  • Physical Chemistry Chemical Physics, Vol. 2, Issue 10
  • DOI: 10.1039/a909486e

Use of approximate integrals in ab initio theory. An application in MP2 energy calculations
journal, June 1993

  • Feyereisen, Martin; Fitzgerald, George; Komornicki, Andrew
  • Chemical Physics Letters, Vol. 208, Issue 5-6
  • DOI: 10.1016/0009-2614(93)87156-w

Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen
journal, January 1989

  • Dunning, Thom H.
  • The Journal of Chemical Physics, Vol. 90, Issue 2
  • DOI: 10.1063/1.456153

Second‐order perturbation theory with a complete active space self‐consistent field reference function
journal, January 1992

  • Andersson, Kerstin; Malmqvist, Per‐Åke; Roos, Björn O.
  • The Journal of Chemical Physics, Vol. 96, Issue 2
  • DOI: 10.1063/1.462209

An efficient internally contracted multiconfiguration–reference configuration interaction method
journal, November 1988

  • Werner, Hans‐Joachim; Knowles, Peter J.
  • The Journal of Chemical Physics, Vol. 89, Issue 9
  • DOI: 10.1063/1.455556

Coulombic potential energy integrals and approximations
journal, May 1973

  • Whitten, J. L.
  • The Journal of Chemical Physics, Vol. 58, Issue 10
  • DOI: 10.1063/1.1679012

Molecular gradients for the second-order generalized Van Vleck variant of multireference perturbation theory
journal, July 2003

  • Dudley, Timothy J.; Khait, Yuriy G.; Hoffmann, Mark R.
  • The Journal of Chemical Physics, Vol. 119, Issue 2
  • DOI: 10.1063/1.1579467

A modified definition of the zeroth-order Hamiltonian in multiconfigurational perturbation theory (CASPT2)
journal, September 2004

A direct MP2 gradient method
journal, February 1990

GVVPT2 energy gradient using a Lagrangian formulation
journal, July 2011

  • Theis, Daniel; Khait, Yuriy G.; Hoffmann, Mark R.
  • The Journal of Chemical Physics, Vol. 135, Issue 4
  • DOI: 10.1063/1.3611049

A direct-compatible formulation of the coupled perturbed complete active space self-consistent field equations on graphical processing units
journal, May 2017

  • Snyder, James W.; Fales, B. Scott; Hohenstein, Edward G.
  • The Journal of Chemical Physics, Vol. 146, Issue 17
  • DOI: 10.1063/1.4979844

Laplace transform techniques in Mo/ller–Plesset perturbation theory
journal, January 1992

  • Häser, Marco; Almlöf, Jan
  • The Journal of Chemical Physics, Vol. 96, Issue 1
  • DOI: 10.1063/1.462485

Construction of open shell perturbation theory invariant with respect to orbital degeneracy
journal, August 1994

A climbing image nudged elastic band method for finding saddle points and minimum energy paths
journal, December 2000

  • Henkelman, Graeme; Uberuaga, Blas P.; Jónsson, Hannes
  • The Journal of Chemical Physics, Vol. 113, Issue 22, p. 9901-9904
  • DOI: 10.1063/1.1329672

Geometry optimization of atomic microclusters using inverse‐power distance coordinates
journal, December 1996

  • Baker, Jon; Pulay, Peter
  • The Journal of Chemical Physics, Vol. 105, Issue 24
  • DOI: 10.1063/1.472911

Generalized Møller—Plesset perturbation theory applied to general MCSCF reference wave functions
journal, September 1991

Discovering chemistry with an ab initio nanoreactor
journal, November 2014

  • Wang, Lee-Ping; Titov, Alexey; McGibbon, Robert
  • Nature Chemistry, Vol. 6, Issue 12
  • DOI: 10.1038/nchem.2099

Nuclear Energy Gradients for Internally Contracted Complete Active Space Second-Order Perturbation Theory: Multistate Extensions
journal, July 2016

  • Vlaisavljevich, Bess; Shiozaki, Toru
  • Journal of Chemical Theory and Computation, Vol. 12, Issue 8
  • DOI: 10.1021/acs.jctc.6b00572

Pressure-Dependent Kinetics of Initial Reactions in Iso-octane Pyrolysis
journal, April 2015

  • Ning, HongBo; Gong, ChunMing; Li, ZeRong
  • The Journal of Physical Chemistry A, Vol. 119, Issue 18
  • DOI: 10.1021/acs.jpca.5b02013

An efficient method for the evaluation of coupling coefficients in configuration interaction calculations
journal, April 1988

Ab initio molecular dynamics: basic concepts, current trends and novel applications
journal, December 2002

Geometry optimization made simple with translation and rotation coordinates
journal, June 2016

  • Wang, Lee-Ping; Song, Chenchen
  • The Journal of Chemical Physics, Vol. 144, Issue 21
  • DOI: 10.1063/1.4952956

Extended multi-configuration quasi-degenerate perturbation theory: The new approach to multi-state multi-reference perturbation theory
journal, June 2011

  • Granovsky, Alexander A.
  • The Journal of Chemical Physics, Vol. 134, Issue 21
  • DOI: 10.1063/1.3596699

Communication: Extended multi-state complete active space second-order perturbation theory: Energy and nuclear gradients
journal, August 2011

  • Shiozaki, Toru; Győrffy, Werner; Celani, Paolo
  • The Journal of Chemical Physics, Vol. 135, Issue 8
  • DOI: 10.1063/1.3633329

A complete active space SCF method (CASSCF) using a density matrix formulated super-CI approach
journal, May 1980

Partitioning technique, perturbation theory, and rational approximations: PARTITIONING TECHNIQUE
journal, January 1982

  • Löwdin, Per-Olov
  • International Journal of Quantum Chemistry, Vol. 21, Issue 1
  • DOI: 10.1002/qua.560210105

Multireference perturbation theory for large restricted and selected active space reference wave functions
journal, April 2000

  • Celani, Paolo; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 112, Issue 13
  • DOI: 10.1063/1.481132

A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency
journal, August 2002

  • Weigend, Florian
  • Physical Chemistry Chemical Physics, Vol. 4, Issue 18
  • DOI: 10.1039/b204199p

Quantum Chemistry on Graphical Processing Units. 3. Analytical Energy Gradients, Geometry Optimization, and First Principles Molecular Dynamics
journal, August 2009

  • Ufimtsev, Ivan S.; Martinez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 10
  • DOI: 10.1021/ct9003004

Analytic energy gradients for multiconfigurational self-consistent field second-order quasidegenerate perturbation theory (MC-QDPT)
journal, April 1998

  • Nakano, Haruyuki; Hirao, Kimihiko; Gordon, Mark S.
  • The Journal of Chemical Physics, Vol. 108, Issue 14
  • DOI: 10.1063/1.475975

Semi-direct algorithms for the MP2 energy and gradient
journal, February 1990

Analytical energy gradients for internally contracted second-order multireference perturbation theory
journal, September 2003

  • Celani, Paolo; Werner, Hans-Joachim
  • The Journal of Chemical Physics, Vol. 119, Issue 10
  • DOI: 10.1063/1.1597672

State-specific multireference perturbation theory: development and present status: State-specific multireference perturbation theory
journal, February 2016

  • Chattopadhyay, Sudip; Chaudhuri, Rajat K.; Mahapatra, Uttam Sinha
  • Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 6, Issue 3
  • DOI: 10.1002/wcms.1248

Imaginary Shift in CASPT2 Nuclear Gradient and Derivative Coupling Theory
journal, May 2019

  • Park, Jae Woo; Al-Saadon, Rachael; Strand, Nils E.
  • Journal of Chemical Theory and Computation, Vol. 15, Issue 7
  • DOI: 10.1021/acs.jctc.9b00368

Analytical gradients for tensor hyper-contracted MP2 and SOS-MP2 on graphical processing units
journal, October 2017

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 147, Issue 16
  • DOI: 10.1063/1.4997997

Communication: Automatic code generation enables nuclear gradient computations for fully internally contracted multireference theory
journal, February 2015

  • MacLeod, Matthew K.; Shiozaki, Toru
  • The Journal of Chemical Physics, Vol. 142, Issue 5
  • DOI: 10.1063/1.4907717

Analytic energy derivatives for coupled-cluster methods describing excited states: General formulas and comparison of computational costs
journal, July 1995

  • Szalay, P�ter G.
  • International Journal of Quantum Chemistry, Vol. 55, Issue 2
  • DOI: 10.1002/qua.560550210

Second-order perturbation theory with a CASSCF reference function
journal, July 1990

  • Andersson, Kerstin.; Malmqvist, Per Aake.; Roos, Bjoern O.
  • The Journal of Physical Chemistry, Vol. 94, Issue 14
  • DOI: 10.1021/j100377a012

Analytical energy gradients for second-order multireference perturbation theory using density fitting
journal, March 2013

  • Győrffy, Werner; Shiozaki, Toru; Knizia, Gerald
  • The Journal of Chemical Physics, Vol. 138, Issue 10
  • DOI: 10.1063/1.4793737

Quantum Chemistry on Graphical Processing Units. 2. Direct Self-Consistent-Field Implementation
journal, March 2009

  • Ufimtsev, Ivan S.; Martinez, Todd J.
  • Journal of Chemical Theory and Computation, Vol. 5, Issue 4
  • DOI: 10.1021/ct800526s

Multireference Møller—Plesset method
journal, March 1992

Analytical Gradient Theory for Quasidegenerate N -Electron Valence State Perturbation Theory (QD-NEVPT2)
journal, November 2019

Atomic orbital-based SOS-MP2 with tensor hypercontraction. I. GPU-based tensor construction and exploiting sparsity
journal, May 2016

  • Song, Chenchen; Martínez, Todd J.
  • The Journal of Chemical Physics, Vol. 144, Issue 17
  • DOI: 10.1063/1.4948438

Toward an Understanding of Diamond sp 2 -Defects with Unsaturated Diamondoid Oligomer Models
journal, May 2015

  • Zhuk, Tatyana S.; Koso, Tatyana; Pashenko, Alexander E.
  • Journal of the American Chemical Society, Vol. 137, Issue 20
  • DOI: 10.1021/jacs.5b01555
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