Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz

Blunt, Nick S.; Neuscamman, Eric

doi:10.1021/acs.jctc.8b00879

Title: Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz

Journal Article · 07 December 2018 · Journal of Chemical Theory and Computation

DOI: https://doi.org/10.1021/acs.jctc.8b00879 · OSTI ID:1543632

^[1];

^[2]

Univ. Chemical Lab, Cambridge (United Kingdom)
Univ. of California, Berkeley, CA (United States); Lawrence Berkeley National Lab. (LBNL), Berkeley, CA (United States)

We perform excited-state variational Monte Carlo and diffusion Monte Carlo calculations using a simple and efficient wave function ansatz. This ansatz follows the recent variation-after-response formalism, accurately approximating a configuration interaction singles wave function as a sum of only two nonorthogonal Slater determinants and further including important orbital relaxation. The ansatz is used to perform diffusion Monte Carlo calculations with large augmented basis sets, comparing to benchmarks from near-exact quantum chemical methods. Here, the significance of orbital optimization in excited-state diffusion Monte Carlo is demonstrated, and the excited-state optimization procedure is discussed in detail. Diffuse excited states in water and formaldehyde are studied, in addition to the formaldimine and benzonitrile molecules.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing; Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States). National Energy Research Scientific Computing Center (NERSC); Univ. of California, Oakland, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES) (SC-22)

Grant/Contract Number:: AC02-05CH11231

OSTI ID:: 1543632

Journal Information:: Journal of Chemical Theory and Computation, Journal Name: Journal of Chemical Theory and Computation Journal Issue: 1 Vol. 15; ISSN 1549-9618

Publisher:: American Chemical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (64)

General atomic and molecular electronic structure system Schmidt, Michael W.; Baldridge, Kim K.; Boatz, Jerry A. Journal of Computational Chemistry, Vol. 14, Issue 11, p. 1347-1363 https://doi.org/10.1002/jcc.540141112	journal	November 1993
P y SCF: the Python-based simulations of chemistry framework : The PySCF program Sun, Qiming; Berkelbach, Timothy C.; Blunt, Nick S. Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 8, Issue 1 https://doi.org/10.1002/wcms.1340	journal	September 2017
Multiconfiguration second-order perturbation theory approach to strong electron correlation in chemistry and photochemistry: Multiconfiguration second-order perturbation theory Roca-Sanjuán, Daniel; Aquilante, Francesco; Lindh, Roland Wiley Interdisciplinary Reviews: Computational Molecular Science, Vol. 2, Issue 4 https://doi.org/10.1002/wcms.97	journal	November 2011
Individualized configuration selection in CI calculations with subsequent energy extrapolation Buenker, Robert J.; Peyerimhoff, Sigrid D. Theoretica Chimica Acta, Vol. 35, Issue 1 https://doi.org/10.1007/BF02394557	journal	August 1974
Electric properties of the low-lying excited states of benzonitrile: geometry relaxation and solvent effects Medveď, Miroslav; Budzák, Šimon; Pluta, Tadeusz Theoretical Chemistry Accounts, Vol. 134, Issue 6 https://doi.org/10.1007/s00214-015-1678-7	journal	May 2015
Convergence of an improved CIPSI algorithm Evangelisti, Stefano; Daudey, Jean-Pierre; Malrieu, Jean-Paul Chemical Physics, Vol. 75, Issue 1 https://doi.org/10.1016/0301-0104(83)85011-3	journal	February 1983
An extension of the coupled cluster formalism to excited states (I) Emrich, K. Nuclear Physics A, Vol. 351, Issue 3 https://doi.org/10.1016/0375-9474(81)90179-2	journal	January 1981
Water VUV electronic state spectroscopy by synchrotron radiation Mota, R.; Parafita, R.; Giuliani, A. Chemical Physics Letters, Vol. 416, Issue 1-3 https://doi.org/10.1016/j.cplett.2005.09.073	journal	November 2005
Heat-Bath Configuration Interaction: An Efficient Selected Configuration Interaction Algorithm Inspired by Heat-Bath Sampling Holmes, Adam A.; Tubman, Norm M.; Umrigar, C. J. Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00407	journal	August 2016
An Efficient Variational Principle for the Direct Optimization of Excited States Zhao, Luning; Neuscamman, Eric Journal of Chemical Theory and Computation, Vol. 12, Issue 8 https://doi.org/10.1021/acs.jctc.6b00508	journal	July 2016
Semistochastic Heat-Bath Configuration Interaction Method: Selected Configuration Interaction with Semistochastic Perturbation Theory Sharma, Sandeep; Holmes, Adam A.; Jeanmairet, Guillaume Journal of Chemical Theory and Computation, Vol. 13, Issue 4 https://doi.org/10.1021/acs.jctc.6b01028	journal	March 2017
Suppressing Ionic Terms with Number-Counting Jastrow Factors in Real Space Goetz, Brett Van Der; Neuscamman, Eric Journal of Chemical Theory and Computation, Vol. 13, Issue 5 https://doi.org/10.1021/acs.jctc.7b00158	journal	April 2017
Optimizing the Energy with Quantum Monte Carlo: A Lower Numerical Scaling for Jastrow–Slater Expansions Assaraf, Roland; Moroni, S.; Filippi, Claudia Journal of Chemical Theory and Computation, Vol. 13, Issue 11 https://doi.org/10.1021/acs.jctc.7b00648	journal	October 2017
Size Consistent Excited States via Algorithmic Transformations between Variational Principles Shea, Jacqueline A. R.; Neuscamman, Eric Journal of Chemical Theory and Computation, Vol. 13, Issue 12 https://doi.org/10.1021/acs.jctc.7b00923	journal	November 2017
Deterministic Construction of Nodal Surfaces within Quantum Monte Carlo: The Case of FeS Scemama, Anthony; Garniron, Yann; Caffarel, Michel Journal of Chemical Theory and Computation, Vol. 14, Issue 3 https://doi.org/10.1021/acs.jctc.7b01250	journal	January 2018
A Mountaineering Strategy to Excited States: Highly Accurate Reference Energies and Benchmarks Loos, Pierre-François; Scemama, Anthony; Blondel, Aymeric Journal of Chemical Theory and Computation, Vol. 14, Issue 8 https://doi.org/10.1021/acs.jctc.8b00406	journal	June 2018
Intramolecular Charge-Transfer Excited-State Processes in 4-( N , N -Dimethylamino)benzonitrile: The Role of Twisting and the πσ* State Georgieva, Ivelina; Aquino, Adélia J. A.; Plasser, Felix The Journal of Physical Chemistry A, Vol. 119, Issue 24 https://doi.org/10.1021/acs.jpca.5b03282	journal	May 2015
Excited States of Methylene, Polyenes, and Ozone from Heat-Bath Configuration Interaction Chien, Alan D.; Holmes, Adam A.; Otten, Matthew The Journal of Physical Chemistry A, Vol. 122, Issue 10 https://doi.org/10.1021/acs.jpca.8b01554	journal	February 2018
Multiconfiguration Self-Consistent Field and Multireference Configuration Interaction Methods and Applications Szalay, Péter G.; Müller, Thomas; Gidofalvi, Gergely Chemical Reviews, Vol. 112, Issue 1 https://doi.org/10.1021/cr200137a	journal	December 2011
Structural Changes Accompanying Intramolecular Electron Transfer: Focus on Twisted Intramolecular Charge-Transfer States and Structures Grabowski, Zbigniew R.; Rotkiewicz, Krystyna; Rettig, Wolfgang Chemical Reviews, Vol. 103, Issue 10 https://doi.org/10.1021/cr940745l	journal	October 2003
Absorption Spectrum of the Green Fluorescent Protein Chromophore: A Difficult Case for ab Initio Methods? Filippi, Claudia; Zaccheddu, Maurizio; Buda, Francesco Journal of Chemical Theory and Computation, Vol. 5, Issue 8 https://doi.org/10.1021/ct900227j	journal	July 2009
Long-range charge-transfer excited states in time-dependent density functional theory require non-local exchange Dreuw, Andreas; Weisman, Jennifer L.; Head-Gordon, Martin The Journal of Chemical Physics, Vol. 119, Issue 6 https://doi.org/10.1063/1.1590951	journal	August 2003
Iterative perturbation calculations of ground and excited state energies from multiconfigurational zeroth‐order wavefunctions Huron, B.; Malrieu, J. P.; Rancurel, P. The Journal of Chemical Physics, Vol. 58, Issue 12 https://doi.org/10.1063/1.1679199	journal	June 1973
Optimized Jastrow–Slater wave functions for ground and excited states: Application to the lowest states of ethene Schautz, Friedemann; Filippi, Claudia The Journal of Chemical Physics, Vol. 120, Issue 23 https://doi.org/10.1063/1.1752881	journal	June 2004
Excitations in photoactive molecules from quantum Monte Carlo Schautz, Friedemann; Buda, Francesco; Filippi, Claudia The Journal of Chemical Physics, Vol. 121, Issue 12 https://doi.org/10.1063/1.1777212	journal	September 2004
Correlated geminal wave function for molecules: An efficient resonating valence bond approach Casula, Michele; Attaccalite, Claudio; Sorella, Sandro The Journal of Chemical Physics, Vol. 121, Issue 15 https://doi.org/10.1063/1.1794632	journal	October 2004
Energy-consistent pseudopotentials for quantum Monte Carlo calculations Burkatzki, M.; Filippi, C.; Dolg, M. The Journal of Chemical Physics, Vol. 126, Issue 23 https://doi.org/10.1063/1.2741534	journal	June 2007
Excited states of the water molecule: Analysis of the valence and Rydberg character Rubio, Mercedes; Serrano-Andrés, Luis; Merchán, Manuela The Journal of Chemical Physics, Vol. 128, Issue 10 https://doi.org/10.1063/1.2837827	journal	March 2008
Fermion Monte Carlo without fixed nodes: A game of life, death, and annihilation in Slater determinant space Booth, George H.; Thom, Alex J. W.; Alavi, Ali The Journal of Chemical Physics, Vol. 131, Issue 5 https://doi.org/10.1063/1.3193710	journal	January 2009
Resonating valence bond wave function with molecular orbitals: Application to first-row molecules Marchi, Mariapia; Azadi, Sam; Casula, Michele The Journal of Chemical Physics, Vol. 131, Issue 15 https://doi.org/10.1063/1.3249966	journal	October 2009
Communications: Survival of the fittest: Accelerating convergence in full configuration-interaction quantum Monte Carlo Cleland, Deidre; Booth, George H.; Alavi, Ali The Journal of Chemical Physics, Vol. 132, Issue 4 https://doi.org/10.1063/1.3302277	journal	January 2010
Communication: Configuration interaction singles has a large systematic bias against charge-transfer states Subotnik, Joseph E. The Journal of Chemical Physics, Vol. 135, Issue 7 https://doi.org/10.1063/1.3627152	journal	August 2011
Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm Clark, Bryan K.; Morales, Miguel A.; McMinis, Jeremy The Journal of Chemical Physics, Vol. 135, Issue 24 https://doi.org/10.1063/1.3665391	journal	December 2011
Electron‐impact excitation of H ₂ O and D ₂ O at various scattering angles and impact energies in the energy‐loss range 4.2–12 eV Chutjian, A.; Hall, R. I.; Trajmar, S. The Journal of Chemical Physics, Vol. 63, Issue 2 https://doi.org/10.1063/1.431370	journal	July 1975
A random‐walk simulation of the Schrödinger equation: H ⁺ ₃ Anderson, James B. The Journal of Chemical Physics, Vol. 63, Issue 4 https://doi.org/10.1063/1.431514	journal	August 1975
Molecular Rydberg states. VII. Water Wang, H. -t.; Felps, W. S.; McGlynn, S. P. The Journal of Chemical Physics, Vol. 67, Issue 6 https://doi.org/10.1063/1.435173	journal	January 1977
Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen Dunning, Thom H. The Journal of Chemical Physics, Vol. 90, Issue 2 https://doi.org/10.1063/1.456153	journal	January 1989
Electron affinities of the first‐row atoms revisited. Systematic basis sets and wave functions Kendall, Rick A.; Dunning, Thom H.; Harrison, Robert J. The Journal of Chemical Physics, Vol. 96, Issue 9 https://doi.org/10.1063/1.462569	journal	May 1992
The equation of motion coupled‐cluster method. A systematic biorthogonal approach to molecular excitation energies, transition probabilities, and excited state properties Stanton, John F.; Bartlett, Rodney J. The Journal of Chemical Physics, Vol. 98, Issue 9 https://doi.org/10.1063/1.464746	journal	May 1993
A diffusion Monte Carlo algorithm with very small time‐step errors Umrigar, C. J.; Nightingale, M. P.; Runge, K. J. The Journal of Chemical Physics, Vol. 99, Issue 4 https://doi.org/10.1063/1.465195	journal	August 1993
Communication: Adjusting charge transfer state energies for configuration interaction singles: Without any parameterization and with minimal cost Liu, Xinle; Fatehi, Shervin; Shao, Yihan The Journal of Chemical Physics, Vol. 136, Issue 16 https://doi.org/10.1063/1.4705757	journal	April 2012
Accuracy of electronic wave functions in quantum Monte Carlo: The effect of high-order correlations Huang, Chien-Jung; Umrigar, C. J.; Nightingale, M. P. The Journal of Chemical Physics, Vol. 107, Issue 8 https://doi.org/10.1063/1.474658	journal	August 1997
Benzonitrile: Electron affinity, excited states, and anion solvation Dixon, Andrew R.; Khuseynov, Dmitry; Sanov, Andrei The Journal of Chemical Physics, Vol. 143, Issue 13 https://doi.org/10.1063/1.4931985	journal	October 2015
Simple formalism for efficient derivatives and multi-determinant expansions in quantum Monte Carlo Filippi, Claudia; Assaraf, Roland; Moroni, Saverio The Journal of Chemical Physics, Vol. 144, Issue 19 https://doi.org/10.1063/1.4948778	journal	May 2016
Communication: Variation after response in quantum Monte Carlo Neuscamman, Eric The Journal of Chemical Physics, Vol. 145, Issue 8 https://doi.org/10.1063/1.4961686	journal	August 2016
Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo Blunt, N. S.; Neuscamman, Eric The Journal of Chemical Physics, Vol. 147, Issue 19 https://doi.org/10.1063/1.4998197	journal	November 2017
Delayed Slater determinant update algorithms for high efficiency quantum Monte Carlo McDaniel, T.; D’Azevedo, E. F.; Li, Y. W. The Journal of Chemical Physics, Vol. 147, Issue 17 https://doi.org/10.1063/1.4998616	journal	November 2017
Fate of the open-shell singlet ground state in the experimentally accessible acenes: A quantum Monte Carlo study Dupuy, Nicolas; Casula, Michele The Journal of Chemical Physics, Vol. 148, Issue 13 https://doi.org/10.1063/1.5016494	journal	April 2018
Communication: An efficient and accurate perturbative correction to initiator full configuration interaction quantum Monte Carlo Blunt, Nick S. The Journal of Chemical Physics, Vol. 148, Issue 22 https://doi.org/10.1063/1.5037923	journal	June 2018
Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes Scemama, Anthony; Benali, Anouar; Jacquemin, Denis The Journal of Chemical Physics, Vol. 149, Issue 3 https://doi.org/10.1063/1.5041327	journal	July 2018
Communication: A mean field platform for excited state quantum chemistry Shea, Jacqueline A. R.; Neuscamman, Eric The Journal of Chemical Physics, Vol. 149, Issue 8 https://doi.org/10.1063/1.5045056	journal	August 2018
`QMCPACK` : an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids Kim, Jeongnim; Baczewski, Andrew D.; Beaudet, Todd D. Journal of Physics: Condensed Matter, Vol. 30, Issue 19 https://doi.org/10.1088/1361-648X/aab9c3	journal	April 2018
Diffusion quantum Monte Carlo calculations of the excited states of silicon Williamson, A. J.; Hood, Randolph Q.; Needs, R. J. Physical Review B, Vol. 57, Issue 19 https://doi.org/10.1103/PhysRevB.57.12140	journal	May 1998
Generalized Lanczos algorithm for variational quantum Monte Carlo Sorella, Sandro Physical Review B, Vol. 64, Issue 2 https://doi.org/10.1103/PhysRevB.64.024512	journal	June 2001
Beyond the locality approximation in the standard diffusion Monte Carlo method Casula, Michele Physical Review B, Vol. 74, Issue 16 https://doi.org/10.1103/PhysRevB.74.161102	journal	October 2006
Nonlinear biases, stochastically sampled effective Hamiltonians, and spectral functions in quantum Monte Carlo methods Blunt, Nick S.; Alavi, Ali; Booth, George H. Physical Review B, Vol. 98, Issue 8 https://doi.org/10.1103/PhysRevB.98.085118	journal	August 2018
Projector Quantum Monte Carlo Method for Nonlinear Wave Functions Schwarz, Lauretta R.; Alavi, A.; Booth, George H. Physical Review Letters, Vol. 118, Issue 17 https://doi.org/10.1103/PhysRevLett.118.176403	journal	April 2017
Density-Functional Theory for Time-Dependent Systems Runge, Erich; Gross, E. K. U. Physical Review Letters, Vol. 52, Issue 12 https://doi.org/10.1103/PhysRevLett.52.997	journal	March 1984
Optimized trial wave functions for quantum Monte Carlo calculations Umrigar, C. J.; Wilson, K. G.; Wilkins, J. W. Physical Review Letters, Vol. 60, Issue 17 https://doi.org/10.1103/PhysRevLett.60.1719	journal	April 1988
Energy and Variance Optimization of Many-Body Wave Functions Umrigar, C. J.; Filippi, Claudia Physical Review Letters, Vol. 94, Issue 15 https://doi.org/10.1103/PhysRevLett.94.150201	journal	April 2005
Alleviation of the Fermion-Sign Problem by Optimization of Many-Body Wave Functions Umrigar, C. J.; Toulouse, Julien; Filippi, Claudia Physical Review Letters, Vol. 98, Issue 11 https://doi.org/10.1103/PhysRevLett.98.110201	journal	March 2007
Quantum Monte Carlo simulations of solids Foulkes, W. M. C.; Mitas, L.; Needs, R. J. Reviews of Modern Physics, Vol. 73, Issue 1 https://doi.org/10.1103/RevModPhys.73.33	journal	January 2001
Using perturbatively selected configuration interaction in quantum Monte Carlo calculations Giner, Emmanuel; Scemama, Anthony; Caffarel, Michel Canadian Journal of Chemistry, Vol. 91, Issue 9 https://doi.org/10.1139/cjc-2013-0017	journal	September 2013
Equation-of-Motion Coupled-Cluster Methods for Open-Shell and Electronically Excited Species: The Hitchhiker's Guide to Fock Space Krylov, Anna I. Annual Review of Physical Chemistry, Vol. 59, Issue 1 https://doi.org/10.1146/annurev.physchem.59.032607.093602	journal	May 2008

Cited By (6)

Excited states with selected CI-QMC: chemically accurate excitation energies and geometries Dash, Monika; Feldt, Jonas; Moroni, Saverio arXiv https://doi.org/10.48550/arxiv.1905.06737	text	January 2019
Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo Otis, Leon; Neuscamman, Eric Physical Chemistry Chemical Physics, Vol. 21, Issue 27 https://doi.org/10.1039/c9cp02269d	journal	January 2019
Singlet–triplet gaps in diradicals obtained with diffusion quantum Monte Carlo using a Slater–Jastrow trial wavefunction with a minimum number of determinants Zhou, Xiaojun; Wang, Fan Physical Chemistry Chemical Physics, Vol. 21, Issue 36 https://doi.org/10.1039/c9cp03045j	journal	January 2019
Diffusion quantum Monte Carlo calculations with a recent generation of effective core potentials for ionization potentials and electron affinities Zhou, Xiaojun; Zhao, Hewang; Wang, Ting Physical Review A, Vol. 100, Issue 6 https://doi.org/10.1103/physreva.100.062502	journal	December 2019
Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory Zhao, Luning; Neuscamman, Eric Physical Review Letters, Vol. 123, Issue 3 https://doi.org/10.1103/physrevlett.123.036402	journal	July 2019
Structural, electronic, and magnetic properties of bulk and epitaxial LaCoO 3 through diffusion Monte Carlo Saritas, Kayahan; Krogel, Jaron T.; Okamoto, Satoshi Physical Review Materials, Vol. 3, Issue 12 https://doi.org/10.1103/physrevmaterials.3.124414	journal	December 2019

Similar Records

Charge-transfer excited states: Seeking a balanced and efficient wave function ansatz in variational Monte Carlo

Journal Article · 2017 · Journal of Chemical Physics · OSTI ID:1409183

Blunt, Nick S.; Neuscamman, Eric

Non-orthogonal determinants in multi-Slater-Jastrow trial wave functions for fixed-node diffusion Monte Carlo

Journal Article · 2018 · Journal of Chemical Physics · OSTI ID:1611136

Pathak, Shivesh; Wagner, Lucas K.

Computing the energy of a water molecule using multideterminants: A simple, efficient algorithm

Journal Article · 2011 · Journal of Chemical Physics · OSTI ID:1386340

Clark, Bryan K.; Morales, Miguel A.; McMinis, Jeremy; +2 more

Related Subjects

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY
Chemistry
Physics

Title: Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz

Citation Formats

References (64)

Cited By (6)

Similar Records

Related Subjects