1
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Alcoba DR, Lain L, Torre A, Ayala TR, Oña OB, Massaccesi GE, Peralta JE, Melo JI. Generalized Spin in the Variance-Based Wave Function Optimization Method within the Doubly Occupied Configuration Interaction Framework. J Phys Chem A 2024; 128:7277-7283. [PMID: 39140833 DOI: 10.1021/acs.jpca.4c02742] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 08/15/2024]
Abstract
In this work, we implement a generalized spin formulation of the doubly occupied configuration interaction methodology using the energy variance of the N-electron Hamiltonian. We perform the optimization of the N-electron wave functions and calculate their corresponding energies, using a unified variational treatment for ground and excited states based on the energy variance, which allows us to describe the entire energy spectra on an equal footing. We analyze the effects produced by the breakdown of the Ŝ2 and Ŝz symmetries in the spectra of model hydrogenic clusters in terms of energies and spin-related quantities, arising from the restricted, unrestricted, and generalized spin methods. The results are compared with other related methods as well as full configuration interaction.
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Affiliation(s)
- Diego R Alcoba
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET─Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Luis Lain
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Alicia Torre
- Departamento de Química Física, Facultad de Ciencia y Tecnología, Universidad del País Vasco, Apdo. 644, E-48080 Bilbao, Spain
| | - Tomás R Ayala
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Ofelia B Oña
- Instituto de Investigaciones Fisicoquímicas Teóricas y Aplicadas, Universidad Nacional de La Plata, Consejo Nacional de Investigaciones Científicas y Técnicas, Diag. 113 y 64 (S/N), Sucursal 4, CC 16, 1900 La Plata, Argentina
| | - Gustavo E Massaccesi
- Departamento de Ciencias Exactas, Ciclo Básico Común, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- Instituto de Investigaciones Matemáticas "Luis A. Santaló" (IMAS), Consejo Nacional de Investigaciones Científicas y Técnicas, Universidad de Buenos Aires, Ciudad Universitaria, 1428 Buenos Aires, Argentina
| | - Juan E Peralta
- Department of Physics, Central Michigan University, Mount Pleasant, Michigan 48859, United States
| | - Juan I Melo
- Universidad de Buenos Aires, Facultad de Ciencias Exactas y Naturales, Departamento de Física, Ciudad Universitaria, 1428 Buenos Aires, Argentina
- CONICET─Universidad de Buenos Aires, Instituto de Física de Buenos Aires (IFIBA), Ciudad Universitaria, 1428 Buenos Aires, Argentina
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2
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Filip MA. Fighting Noise with Noise: A Stochastic Projective Quantum Eigensolver. J Chem Theory Comput 2024; 20:5964-5981. [PMID: 38954827 PMCID: PMC11270749 DOI: 10.1021/acs.jctc.4c00295] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2024] [Revised: 06/13/2024] [Accepted: 06/14/2024] [Indexed: 07/04/2024]
Abstract
In the current noisy intermediate scale quantum era of quantum computation, available hardware is severely limited by both qubit count and noise levels, precluding the application of many current hybrid quantum-classical algorithms to nontrivial quantum chemistry problems. In this paper we propose applying some of the fundamental ideas of conventional Quantum Monte Carlo algorithms─stochastic sampling of both the wave function and the Hamiltonian─to quantum algorithms in order to significantly decrease quantum resource costs. In the context of an imaginary-time propagation based projective quantum eigensolver, we present a novel approach to estimating physical observables which can lead to an order of magnitude reduction in the required sampling of the quantum state to converge the ground state energy of a system relative to current state-of-the-art eigensolvers. The method can be equally applied to excited-state calculations and, combined with stochastic approximations of the system Hamiltonian, provides a promising near-term approach to Hamiltonian simulation for general chemistry on quantum devices.
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Affiliation(s)
- Maria-Andreea Filip
- Yusuf Hamied Department of
Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K.
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3
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Marie A, Burton HGA. Excited States, Symmetry Breaking, and Unphysical Solutions in State-Specific CASSCF Theory. J Phys Chem A 2023; 127:4538-4552. [PMID: 37141564 DOI: 10.1021/acs.jpca.3c00603] [Citation(s) in RCA: 8] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/06/2023]
Abstract
State-specific electronic structure theory provides a route toward balanced excited-state wave functions by exploiting higher-energy stationary points of the electronic energy. Multiconfigurational wave function approximations can describe both closed- and open-shell excited states and avoid the issues associated with state-averaged approaches. We investigate the existence of higher-energy solutions in complete active space self-consistent field (CASSCF) theory and characterize their topological properties. We demonstrate that state-specific approximations can provide accurate higher-energy excited states in H2 (6-31G) with more compact active spaces than would be required in a state-averaged formalism. We then elucidate the unphysical stationary points, demonstrating that they arise from redundant orbitals when the active space is too large or symmetry breaking when the active space is too small. Furthermore, we investigate the singlet-triplet crossing in CH2 (6-31G) and the avoided crossing in LiF (6-31G), revealing the severity of root flipping and demonstrating that state-specific solutions can behave quasi-diabatically or adiabatically. These results elucidate the complexity of the CASSCF energy landscape, highlighting the advantages and challenges of practical state-specific calculations.
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Affiliation(s)
- Antoine Marie
- Physical and Theoretical Chemical Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, U.K
| | - Hugh G A Burton
- Physical and Theoretical Chemical Laboratory, Department of Chemistry, University of Oxford, Oxford OX1 3QZ, U.K
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4
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Wheeler WA, Pathak S, Kleiner KG, Yuan S, Rodrigues JNB, Lorsung C, Krongchon K, Chang Y, Zhou Y, Busemeyer B, Williams KT, Muñoz A, Chow CY, Wagner LK. PyQMC: An all-Python real-space quantum Monte Carlo module in PySCF. J Chem Phys 2023; 158:114801. [PMID: 36948839 DOI: 10.1063/5.0139024] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/19/2023] Open
Abstract
We describe a new open-source Python-based package for high accuracy correlated electron calculations using quantum Monte Carlo (QMC) in real space: PyQMC. PyQMC implements modern versions of QMC algorithms in an accessible format, enabling algorithmic development and easy implementation of complex workflows. Tight integration with the PySCF environment allows for a simple comparison between QMC calculations and other many-body wave function techniques, as well as access to high accuracy trial wave functions.
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Affiliation(s)
- William A Wheeler
- Department of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shivesh Pathak
- Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - Kevin G Kleiner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Shunyue Yuan
- Department of Applied Physics and Materials Science, California Institute of Technology, Pasadena, California 91125, USA
| | - João N B Rodrigues
- Centro de Ciências Naturais e Humanas, Universidade Federal do ABC-UFABC, Santo André, São Paulo 09210-580, Brazil
| | - Cooper Lorsung
- Department of Mechanical Engineering, Carnegie Mellon University, Pittsburgh, Pennsylvania 15213, USA
| | - Kittithat Krongchon
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Yueqing Chang
- Department of Physics and Astronomy, Rutgers University, Piscataway, New Jersey 08854, USA
| | - Yiqing Zhou
- Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
| | | | | | - Alexander Muñoz
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Chun Yu Chow
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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5
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Otis L, Neuscamman E. Optimization Stability in Excited-State-Specific Variational Monte Carlo. J Chem Theory Comput 2023; 19:767-782. [PMID: 36662538 DOI: 10.1021/acs.jctc.2c00642] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
We investigate the issue of optimization stability in variance-based state-specific variational Monte Carlo, discussing the roles of the objective function, the complexity of wave function ansatz, the amount of sampling effort, and the choice of minimization algorithm. Using a small cyanine dye molecule as a test case, we systematically perform minimizations using variants of the linear method as both a standalone algorithm and in a hybrid combination with accelerated descent. We demonstrate that adaptive step control is crucial for maintaining the linear method's stability when optimizing complicated wave functions and that the hybrid method enjoys both greater stability and minimization performance.
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Affiliation(s)
- Leon Otis
- Department of Physics, University of California Berkeley, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California Berkeley, Berkeley, California 94720, United States.,Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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6
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Otis L, Neuscamman E. A promising intersection of excited‐state‐specific methods from quantum chemistry and quantum Monte Carlo. WIRES COMPUTATIONAL MOLECULAR SCIENCE 2023. [DOI: 10.1002/wcms.1659] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 02/11/2023]
Affiliation(s)
- Leon Otis
- Department of Physics University of California Berkeley Berkeley California USA
| | - Eric Neuscamman
- Department of Chemistry University of California Berkeley Berkeley California USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory Berkeley California USA
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7
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Entwistle MT, Schätzle Z, Erdman PA, Hermann J, Noé F. Electronic excited states in deep variational Monte Carlo. Nat Commun 2023; 14:274. [PMID: 36650151 PMCID: PMC9845370 DOI: 10.1038/s41467-022-35534-5] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2022] [Accepted: 12/08/2022] [Indexed: 01/19/2023] Open
Abstract
Obtaining accurate ground and low-lying excited states of electronic systems is crucial in a multitude of important applications. One ab initio method for solving the Schrödinger equation that scales favorably for large systems is variational quantum Monte Carlo (QMC). The recently introduced deep QMC approach uses ansatzes represented by deep neural networks and generates nearly exact ground-state solutions for molecules containing up to a few dozen electrons, with the potential to scale to much larger systems where other highly accurate methods are not feasible. In this paper, we extend one such ansatz (PauliNet) to compute electronic excited states. We demonstrate our method on various small atoms and molecules and consistently achieve high accuracy for low-lying states. To highlight the method's potential, we compute the first excited state of the much larger benzene molecule, as well as the conical intersection of ethylene, with PauliNet matching results of more expensive high-level methods.
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Affiliation(s)
- M T Entwistle
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - Z Schätzle
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - P A Erdman
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany
| | - J Hermann
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
| | - F Noé
- Department of Mathematics and Computer Science, FU Berlin, Arnimallee 12, 14195, Berlin, Germany.
- Microsoft Research AI4Science, Berlin, Germany.
- Department of Physics, FU Berlin, Arnimallee 14, 14195, Berlin, Germany.
- Department of Chemistry, Rice University, Houston, TX, 77005, USA.
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8
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Shepard S, Panadés-Barrueta RL, Moroni S, Scemama A, Filippi C. Double Excitation Energies from Quantum Monte Carlo Using State-Specific Energy Optimization. J Chem Theory Comput 2022; 18:6722-6731. [DOI: 10.1021/acs.jctc.2c00769] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
Affiliation(s)
- Stuart Shepard
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
| | | | - Saverio Moroni
- CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali and SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 31062 Toulouse, France
| | - Claudia Filippi
- MESA+ Institute for Nanotechnology, University of Twente, 7500 AE Enschede, The Netherlands
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9
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Burton HGA. Energy Landscape of State-Specific Electronic Structure Theory. J Chem Theory Comput 2022; 18:1512-1526. [PMID: 35179023 PMCID: PMC9082508 DOI: 10.1021/acs.jctc.1c01089] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2021] [Indexed: 11/29/2022]
Abstract
State-specific approximations can provide a more accurate representation of challenging electronic excitations by enabling relaxation of the electron density. While state-specific wave functions are known to be local minima or saddle points of the approximate energy, the global structure of the exact electronic energy remains largely unexplored. In this contribution, a geometric perspective on the exact electronic energy landscape is introduced. On the exact energy landscape, ground and excited states form stationary points constrained to the surface of a hypersphere, and the corresponding Hessian index increases at each excitation level. The connectivity between exact stationary points is investigated, and the square-magnitude of the exact energy gradient is shown to be directly proportional to the Hamiltonian variance. The minimal basis Hartree-Fock and excited-state mean-field representations of singlet H2 (STO-3G) are then used to explore how the exact energy landscape controls the existence and properties of state-specific approximations. In particular, approximate excited states correspond to constrained stationary points on the exact energy landscape, and their Hessian index also increases for higher energies. Finally, the properties of the exact energy are used to derive the structure of the variance optimization landscape and elucidate the challenges faced by variance optimization algorithms, including the presence of unphysical saddle points or maxima of the variance.
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Affiliation(s)
- Hugh G. A. Burton
- Physical and Theoretical
Chemistry Laboratory, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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10
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11
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Pathak S, Busemeyer B, Rodrigues JNB, Wagner LK. Excited states in variational Monte Carlo using a penalty method. J Chem Phys 2021; 154:034101. [DOI: 10.1063/5.0030949] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Shivesh Pathak
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Brian Busemeyer
- Center for Computational Quantum Physics, Flatiron Institute, York, New York 10010, USA
| | | | - Lucas K. Wagner
- University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
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12
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Otis L, Craig I, Neuscamman E. A hybrid approach to excited-state-specific variational Monte Carlo and doubly excited states. J Chem Phys 2020; 153:234105. [PMID: 33353344 DOI: 10.1063/5.0024572] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/19/2023] Open
Abstract
We extend our hybrid linear-method/accelerated-descent variational Monte Carlo optimization approach to excited states and investigate its efficacy in double excitations. In addition to showing a superior statistical efficiency when compared to the linear method, our tests on small molecules show good energetic agreement with benchmark methods. We also demonstrate the ability to treat double excitations in systems that are too large for a full treatment by using selected configuration interaction methods via an application to 4-aminobenzonitrile. Finally, we investigate the stability of state-specific variance optimization against collapse to other states' variance minima and find that symmetry, Ansatz quality, and sample size all have roles to play in achieving stability.
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Affiliation(s)
- Leon Otis
- Department of Physics, University of California, Berkeley, Berkeley, California 94720, USA
| | - Isabel Craig
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, USA
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13
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Garner SM, Neuscamman E. A variational Monte Carlo approach for core excitations. J Chem Phys 2020; 153:144108. [DOI: 10.1063/5.0020310] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/22/2022] Open
Affiliation(s)
- Scott M. Garner
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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14
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Dong X, Mahler AD, Kempfer-Robertson EM, Thompson LM. Global Elucidation of Self-Consistent Field Solution Space Using Basin Hopping. J Chem Theory Comput 2020; 16:5635-5644. [DOI: 10.1021/acs.jctc.0c00488] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Xinju Dong
- Department of Chemistry, University of Louisville, Louisville, Kentucky 40205, United States
| | - Andrew D. Mahler
- Department of Chemistry, University of Louisville, Louisville, Kentucky 40205, United States
| | | | - Lee M. Thompson
- Department of Chemistry, University of Louisville, Louisville, Kentucky 40205, United States
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15
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Cuzzocrea A, Scemama A, Briels WJ, Moroni S, Filippi C. Variational Principles in Quantum Monte Carlo: The Troubled Story of Variance Minimization. J Chem Theory Comput 2020; 16:4203-4212. [PMID: 32419451 PMCID: PMC7365558 DOI: 10.1021/acs.jctc.0c00147] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
![]()
We
investigate the use of different variational principles in quantum
Monte Carlo, namely, energy and variance minimization, prompted by
the interest in the robust and accurate estimation of electronic excited
states. For two prototypical, challenging molecules, we readily reach
the accuracy of the best available reference excitation energies using
energy minimization in a state-specific or state-average fashion for
states of different or equal symmetry, respectively. On the other
hand, in variance minimization, where the use of suitable functionals
is expected to target specific states regardless of the symmetry,
we encounter severe problems for a variety of wave functions: as the
variance converges, the energy drifts away from that of the selected
state. This unexpected behavior is sometimes observed even when the
target is the ground state and generally prevents the robust estimation
of total and excitation energies. We analyze this problem using a
very simple wave function and infer that the optimization finds little
or no barrier to escape from a local minimum or local plateau, eventually
converging to a lower-variance state instead of the target state.
For the increasingly complex systems becoming in reach of quantum
Monte Carlo simulations, variance minimization with current functionals
appears to be an impractical route.
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Affiliation(s)
- Alice Cuzzocrea
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, 118 route de Narbonne, 31062 Toulouse Cedex 09, France
| | - Wim J Briels
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
| | - Saverio Moroni
- CNR-IOM DEMOCRITOS, Istituto Officina dei Materiali, Via Bonomea 265, I-34136 Trieste, Italy.,SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy
| | - Claudia Filippi
- MESA+ Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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16
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Zhao L, Neuscamman E. Excited state mean-field theory without automatic differentiation. J Chem Phys 2020; 152:204112. [DOI: 10.1063/5.0003438] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023] Open
Affiliation(s)
- Luning Zhao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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17
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Kent PRC, Annaberdiyev A, Benali A, Bennett MC, Landinez Borda EJ, Doak P, Hao H, Jordan KD, Krogel JT, Kylänpää I, Lee J, Luo Y, Malone FD, Melton CA, Mitas L, Morales MA, Neuscamman E, Reboredo FA, Rubenstein B, Saritas K, Upadhyay S, Wang G, Zhang S, Zhao L. QMCPACK: Advances in the development, efficiency, and application of auxiliary field and real-space variational and diffusion quantum Monte Carlo. J Chem Phys 2020; 152:174105. [DOI: 10.1063/5.0004860] [Citation(s) in RCA: 43] [Impact Index Per Article: 10.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- P. R. C. Kent
- Center for Nanophase Materials Sciences Division and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Abdulgani Annaberdiyev
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | - M. Chandler Bennett
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Edgar Josué Landinez Borda
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Peter Doak
- Center for Nanophase Materials Sciences Division and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Hongxia Hao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Ilkka Kylänpää
- Computational Physics Laboratory, Tampere University, P.O. Box 692, 33014 Tampere, Finland
| | - Joonho Lee
- Department of Chemistry, Columbia University, New York, New York 10027, USA
| | - Ye Luo
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | - Fionn D. Malone
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Cody A. Melton
- Sandia National Laboratories, Albuquerque, New Mexico 87123, USA
| | - Lubos Mitas
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Miguel A. Morales
- Quantum Simulations Group, Lawrence Livermore National Laboratory, 7000 East Avenue, Livermore, California 94551, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
| | - Fernando A. Reboredo
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Brenda Rubenstein
- Department of Chemistry, Brown University, Providence, Rhode Island 02912, USA
| | - Kayahan Saritas
- Department of Applied Physics, Yale University, New Haven, Connecticut 06520, USA
| | - Shiv Upadhyay
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, USA
| | - Guangming Wang
- Department of Physics, North Carolina State University, Raleigh, North Carolina 27695-8202, USA
| | - Shuai Zhang
- Laboratory for Laser Energetics, University of Rochester, 250 E River Rd., Rochester, New York 14623, USA
| | - Luning Zhao
- Department of Chemistry, University of Washington, Seattle, Washington 98195, USA
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18
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Shea JAR, Gwin E, Neuscamman E. A Generalized Variational Principle with Applications to Excited State Mean Field Theory. J Chem Theory Comput 2020; 16:1526-1540. [DOI: 10.1021/acs.jctc.9b01105] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Jacqueline A. R. Shea
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Elise Gwin
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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19
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Tran LN, Shea JAR, Neuscamman E. Tracking Excited States in Wave Function Optimization Using Density Matrices and Variational Principles. J Chem Theory Comput 2019; 15:4790-4803. [DOI: 10.1021/acs.jctc.9b00351] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Lan Nguyen Tran
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Ho Chi Minh City Institute of Physics, VAST, Ho Chi Minh City 700000, Vietnam
| | - Jacqueline A. R. Shea
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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20
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Zhao L, Neuscamman E. Variational Excitations in Real Solids: Optical Gaps and Insights into Many-Body Perturbation Theory. PHYSICAL REVIEW LETTERS 2019; 123:036402. [PMID: 31386452 DOI: 10.1103/physrevlett.123.036402] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/25/2018] [Revised: 02/26/2019] [Indexed: 06/10/2023]
Abstract
We present an approach to studying optical band gaps in real solids in which quantum Monte Carlo methods allow for the application of a rigorous variational principle to both ground and excited state wave functions. In tests that include small, medium, and large band gap materials, optical gaps are predicted with a mean absolute deviation of 3.5% against experiment, less than half the equivalent errors for typical many-body perturbation theories. The approach is designed to be insensitive to the choice of density functional, a property we exploit in order to provide insight into how far different functionals are from satisfying the assumptions of many-body perturbation theory. We explore this question most deeply in the challenging case of ZnO, where we show that, although many commonly used functionals have shortcomings, there does exist a one-particle basis in which perturbation theory's zeroth-order picture is sound. Insights of this nature should be useful in guiding the future application and improvement of these widely used techniques.
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Affiliation(s)
- Luning Zhao
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Lawrence Berkeley National Laboratory, Chemical Sciences Division, Berkeley, California 94720, USA
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21
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Ye HZ, Van Voorhis T. Half-Projected σ Self-Consistent Field For Electronic Excited States. J Chem Theory Comput 2019; 15:2954-2965. [PMID: 30995060 DOI: 10.1021/acs.jctc.8b01224] [Citation(s) in RCA: 22] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Fully self-consistent mean-field solutions of electronic excited states have been much less accessible compared to ground state solutions (e.g., Hartree-Fock). The main reason for this is that most excited states are energy saddle points, and hence energy-based optimization methods such as Δ-SCF often collapse to the ground state. Recently, our research group has developed a new method, σ-SCF [ J. Chem. Phys. 2017 , 147 , 214104 ], that successfully solves the "variational collapse" problem of energy-based methods. Despite the success, σ-SCF solutions are often spin-contaminated for open-shell states due to the single-determinant nature; unphysical behaviors such as disappearing solutions and discontinuous first-order energy derivatives are also observed along with the spontaneous breaking of spin or spatial symmetries. In this work, we tackle these problems by partially restoring the broken spin-symmetry of a σ-SCF solution through an approximate spin-projection scheme called half-projection. Orbitals of the projected wave function are optimized in a variation-after-projection (VAP) manner. The resulting theory, which we term half-projected (HP) σ-SCF, brings substantial improvement to the description of singlet and triplet excitations of the original σ-SCF method. Numerical simulations on small molecules suggest that HP σ-SCF delivers high-quality excited-state solutions that exist in a wide range of geometries with smooth potential energy surfaces. We also show that local excitations in HP σ-SCF can be size-intensive.
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Affiliation(s)
- Hong-Zhou Ye
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
| | - Troy Van Voorhis
- Department of Chemistry , Massachusetts Institute of Technology , Cambridge , Massachusetts 02139 , United States
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22
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Pineda Flores SD, Neuscamman E. Excited State Specific Multi-Slater Jastrow Wave Functions. J Phys Chem A 2019; 123:1487-1497. [DOI: 10.1021/acs.jpca.8b10671] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Sergio D. Pineda Flores
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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23
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Van Der Goetz BW, Otis L, Neuscamman E. Clean and Convenient Tessellations for Number Counting Jastrow Factors. J Chem Theory Comput 2019; 15:1102-1121. [DOI: 10.1021/acs.jctc.8b01139] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
| | - Leon Otis
- Department of Chemistry, University of California, Berkeley, California 94720, United States
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Science Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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24
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Otis L, Neuscamman E. Complementary first and second derivative methods for ansatz optimization in variational Monte Carlo. Phys Chem Chem Phys 2019; 21:14491-14510. [DOI: 10.1039/c9cp02269d] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
This Perspective contrasts first and second derivative methods in variational Monte Carlo and presents a hybrid optimization approach that combines their advantages.
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Affiliation(s)
- Leon Otis
- Department of Physics
- University of California
- Berkeley
- USA
| | - Eric Neuscamman
- Department of Chemistry
- University of California
- Berkeley
- USA
- Chemical Sciences Division
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25
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Influence of pseudopotentials on excitation energies from selected configuration interaction and diffusion Monte Carlo. RESULTS IN CHEMISTRY 2019. [DOI: 10.1016/j.rechem.2019.100002] [Citation(s) in RCA: 16] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
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26
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Blunt NS, Neuscamman E. Excited-State Diffusion Monte Carlo Calculations: A Simple and Efficient Two-Determinant Ansatz. J Chem Theory Comput 2018; 15:178-189. [DOI: 10.1021/acs.jctc.8b00879] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Nick S. Blunt
- University Chemical
Laboratory, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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27
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Wei H, Neuscamman E. Reduced scaling Hilbert space variational Monte Carlo. J Chem Phys 2018; 149:184106. [DOI: 10.1063/1.5047207] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Haochuan Wei
- Department of Chemistry, University of California, Berkeley, California 94720, USA
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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28
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Shea JAR, Neuscamman E. Communication: A mean field platform for excited state quantum chemistry. J Chem Phys 2018; 149:081101. [DOI: 10.1063/1.5045056] [Citation(s) in RCA: 33] [Impact Index Per Article: 5.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
| | - Eric Neuscamman
- Department of Chemistry, University of California, Berkeley, California 94720, USA
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, USA
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29
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Scemama A, Benali A, Jacquemin D, Caffarel M, Loos PF. Excitation energies from diffusion Monte Carlo using selected configuration interaction nodes. J Chem Phys 2018; 149:034108. [DOI: 10.1063/1.5041327] [Citation(s) in RCA: 44] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Anthony Scemama
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Anouar Benali
- Computational Science Division, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Denis Jacquemin
- Laboratoire CEISAM—UMR CNRS 6230, Université de Nantes, 2 Rue de la Houssinière, BP 92208, 44322 Nantes Cedex 3, France
| | - Michel Caffarel
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
| | - Pierre-François Loos
- Laboratoire de Chimie et Physique Quantiques, Université de Toulouse, CNRS, UPS, Toulouse, France
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30
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Kim J, Baczewski AT, Beaudet TD, Benali A, Bennett MC, Berrill MA, Blunt NS, Borda EJL, Casula M, Ceperley DM, Chiesa S, Clark BK, Clay RC, Delaney KT, Dewing M, Esler KP, Hao H, Heinonen O, Kent PRC, Krogel JT, Kylänpää I, Li YW, Lopez MG, Luo Y, Malone FD, Martin RM, Mathuriya A, McMinis J, Melton CA, Mitas L, Morales MA, Neuscamman E, Parker WD, Pineda Flores SD, Romero NA, Rubenstein BM, Shea JAR, Shin H, Shulenburger L, Tillack AF, Townsend JP, Tubman NM, Van Der Goetz B, Vincent JE, Yang DC, Yang Y, Zhang S, Zhao L. QMCPACK: an open source ab initio quantum Monte Carlo package for the electronic structure of atoms, molecules and solids. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2018; 30:195901. [PMID: 29582782 DOI: 10.1088/1361-648x/aab9c3] [Citation(s) in RCA: 74] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/28/2023]
Abstract
QMCPACK is an open source quantum Monte Carlo package for ab initio electronic structure calculations. It supports calculations of metallic and insulating solids, molecules, atoms, and some model Hamiltonians. Implemented real space quantum Monte Carlo algorithms include variational, diffusion, and reptation Monte Carlo. QMCPACK uses Slater-Jastrow type trial wavefunctions in conjunction with a sophisticated optimizer capable of optimizing tens of thousands of parameters. The orbital space auxiliary-field quantum Monte Carlo method is also implemented, enabling cross validation between different highly accurate methods. The code is specifically optimized for calculations with large numbers of electrons on the latest high performance computing architectures, including multicore central processing unit and graphical processing unit systems. We detail the program's capabilities, outline its structure, and give examples of its use in current research calculations. The package is available at http://qmcpack.org.
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Affiliation(s)
- Jeongnim Kim
- Intel Corporation, Hillsboro, OR 987124, United States of America
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