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Chen S, Zhang S. A structural optimization algorithm with stochastic forces and stresses. NATURE COMPUTATIONAL SCIENCE 2022; 2:736-744. [PMID: 38177372 DOI: 10.1038/s43588-022-00350-w] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/07/2022] [Accepted: 10/07/2022] [Indexed: 01/06/2024]
Abstract
We propose an algorithm for optimizations in which the gradients contain stochastic noise. This arises, for example, in structural optimizations when computations of forces and stresses rely on methods involving Monte Carlo sampling, such as quantum Monte Carlo or neural network states, or are performed on quantum devices that have intrinsic noise. Our proposed algorithm is based on the combination of two ingredients: an update rule derived from the steepest-descent method, and a staged scheduling of the targeted statistical error and step size, with position averaging. We compare it with commonly applied algorithms, including some of the latest machine learning optimization methods, and show that the algorithm consistently performs efficiently and robustly under realistic conditions. Applying this algorithm, we achieve full-degree optimizations in solids using ab initio many-body computations, by auxiliary-field quantum Monte Carlo with plane waves and pseudopotentials. A potential metastable structure in Si is discovered using density-functional calculations with synthetic noisy forces.
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Affiliation(s)
- Siyuan Chen
- Department of Physics, College of William & Mary, Williamsburg, VA, USA.
| | - Shiwei Zhang
- Center for Computational Quantum Physics, Flatiron Institute, New York, NY, USA
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2
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Tiihonen J, Kent PRC, Krogel JT. Surrogate Hessian accelerated structural optimization for stochastic electronic structure theories. J Chem Phys 2022; 156:054104. [DOI: 10.1063/5.0079046] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Juha Tiihonen
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Paul R. C. Kent
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Tennessee 37831, USA
| | - Jaron T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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3
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Liu YYF, Andrews B, Conduit GJ. Direct evaluation of the force constant matrix in quantum Monte Carlo. J Chem Phys 2019; 150:034104. [DOI: 10.1063/1.5070138] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Y. Y. F. Liu
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - B. Andrews
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
| | - G. J. Conduit
- Theory of Condensed Matter Group, Cavendish Laboratory, J. J. Thomson Avenue, Cambridge CB3 0HE, United Kingdom
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4
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Archibald R, Krogel JT, Kent PRC. Gaussian process based optimization of molecular geometries using statistically sampled energy surfaces from quantum Monte Carlo. J Chem Phys 2018; 149:164116. [DOI: 10.1063/1.5040584] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Affiliation(s)
- R. Archibald
- Computer Science and Mathematics Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - J. T. Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - P. R. C. Kent
- Center for Nanophase Materials Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
- Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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5
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Barborini M, Guidoni L. Geometries of low spin states of multi-centre transition metal complexes through extended broken symmetry variational Monte Carlo. J Chem Phys 2016; 145:124107. [DOI: 10.1063/1.4963015] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Matteo Barborini
- Dipartimento di Ingegneria, Scienze dell’Informazione e Matematica, Università degli studi dell’Aquila, Via Vetoio 2, 67100 Coppito, L’Aquila, Italy
- Dipartimento di Scienze Fisiche e Chimiche, Università degli studi dell’Aquila, Via Vetoio 2, 67100 Coppito, L’Aquila, Italy
| | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli studi dell’Aquila, Via Vetoio 2, 67100 Coppito, L’Aquila, Italy
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6
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Wagner LK, Ceperley DM. Discovering correlated fermions using quantum Monte Carlo. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2016; 79:094501. [PMID: 27518859 DOI: 10.1088/0034-4885/79/9/094501] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/06/2023]
Abstract
It has become increasingly feasible to use quantum Monte Carlo (QMC) methods to study correlated fermion systems for realistic Hamiltonians. We give a summary of these techniques targeted at researchers in the field of correlated electrons, focusing on the fundamentals, capabilities, and current status of this technique. The QMC methods often offer the highest accuracy solutions available for systems in the continuum, and, since they address the many-body problem directly, the simulations can be analyzed to obtain insight into the nature of correlated quantum behavior.
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Affiliation(s)
- Lucas K Wagner
- Department of Physics, University of Illinois at Urbana-Champaign, Champaign, IL, USA
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Barborini M, Guidoni L. Ground State Geometries of Polyacetylene Chains from Many-Particle Quantum Mechanics. J Chem Theory Comput 2015; 11:4109-18. [PMID: 26405437 PMCID: PMC4570661 DOI: 10.1021/acs.jctc.5b00427] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/08/2015] [Indexed: 11/28/2022]
Abstract
Due to the crucial role played by electron correlation, the accurate determination of ground state geometries of π-conjugated molecules is still a challenge for many quantum chemistry methods. Because of the high parallelism of the algorithms and their explicit treatment of electron correlation effects, Quantum Monte Carlo calculations can offer an accurate and reliable description of the electronic states and of the geometries of such systems, competing with traditional quantum chemistry approaches. Here, we report the structural properties of polyacetylene chains H-(C₂H₂)(N)-H up to N = 12 acetylene units, by means of Variational Monte Carlo (VMC) calculations based on the multi-determinant Jastrow Antisymmetrized Geminal Power (JAGP) wave function. This compact ansatz can provide for such systems an accurate description of the dynamical electronic correlation as recently detailed for the 1,3-butadiene molecule [J. Chem. Theory Comput. 2015 11 (2), 508-517]. The calculated Bond Length Alternation (BLA), namely the difference between the single and double carbon bonds, extrapolates, for N → ∞, to a value of 0.0910(7) Å, compatible with the experimental data. An accurate analysis was able to distinguish between the influence of the multi-determinantal AGP expansion and of the Jastrow factor on the geometrical properties of the fragments. Our size-extensive and self-interaction-free results provide new and accurate ab initio references for the structures of the ground state of polyenes.
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Affiliation(s)
- Matteo Barborini
- Dipartimento
di Ingegneria e Scienze dell’Informazione e Matematica, Università degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
- Dipartimento
di Scienze Fisiche e Chimiche, Università
degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
| | - Leonardo Guidoni
- Dipartimento
di Scienze Fisiche e Chimiche, Università
degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
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8
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Cazorla C. The role of density functional theory methods in the prediction of nanostructured gas-adsorbent materials. Coord Chem Rev 2015. [DOI: 10.1016/j.ccr.2015.05.002] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
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9
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Moroni S, Saccani S, Filippi C. Practical Schemes for Accurate Forces in Quantum Monte Carlo. J Chem Theory Comput 2014; 10:4823-9. [DOI: 10.1021/ct500780r] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023]
Affiliation(s)
- S. Moroni
- CNR-IOM DEMOCRITOS,
Istituto Officina dei Materiali, and SISSA Scuola Internazionale Superiore
di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy
| | - S. Saccani
- SISSA Scuola Internazionale Superiore di Studi Avanzati, Via Bonomea 265, I-34136 Trieste, Italy
| | - C. Filippi
- MESA+
Institute for Nanotechnology, University of Twente, P.O. Box 217, 7500 AE Enschede, The Netherlands
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Varsano D, Barborini M, Guidoni L. Kohn-Sham orbitals and potentials from quantum Monte Carlo molecular densities. J Chem Phys 2014; 140:054102. [DOI: 10.1063/1.4863213] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Zen A, Luo Y, Sorella S, Guidoni L. Molecular Properties by Quantum Monte Carlo: An Investigation on the Role of the Wave Function Ansatz and the Basis Set in the Water Molecule. J Chem Theory Comput 2013; 9:4332-4350. [PMID: 24526929 PMCID: PMC3920371 DOI: 10.1021/ct400382m] [Citation(s) in RCA: 35] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Quantum Monte Carlo methods are accurate and promising many body techniques for electronic structure calculations which, in the last years, are encountering a growing interest thanks to their favorable scaling with the system size and their efficient parallelization, particularly suited for the modern high performance computing facilities. The ansatz of the wave function and its variational flexibility are crucial points for both the accurate description of molecular properties and the capabilities of the method to tackle large systems. In this paper, we extensively analyze, using different variational ansatzes, several properties of the water molecule, namely, the total energy, the dipole and quadrupole momenta, the ionization and atomization energies, the equilibrium configuration, and the harmonic and fundamental frequencies of vibration. The investigation mainly focuses on variational Monte Carlo calculations, although several lattice regularized diffusion Monte Carlo calculations are also reported. Through a systematic study, we provide a useful guide to the choice of the wave function, the pseudopotential, and the basis set for QMC calculations. We also introduce a new method for the computation of forces with finite variance on open systems and a new strategy for the definition of the atomic orbitals involved in the Jastrow-Antisymmetrised Geminal power wave function, in order to drastically reduce the number of variational parameters. This scheme significantly improves the efficiency of QMC energy minimization in case of large basis sets.
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Affiliation(s)
- Andrea Zen
- Dipartimento di Fisica, La Sapienza—Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Ye Luo
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy
| | - Sandro Sorella
- Scuola Internazionale Superiore di Studi Avanzati (SISSA), via Bonomea 265, 34136 Trieste, Italy
| | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli studi de L’Aquila, Via Vetoio, 67100 Coppito, L’Aquila, Italy
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12
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Saccani S, Filippi C, Moroni S. Minimum energy pathways via quantum Monte Carlo. J Chem Phys 2013; 138:084109. [DOI: 10.1063/1.4792717] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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13
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Barborini M, Guidoni L. Reaction pathways by quantum Monte Carlo: insight on the torsion barrier of 1,3-butadiene, and the conrotatory ring opening of cyclobutene. J Chem Phys 2012; 137:224309. [PMID: 23249005 PMCID: PMC3925821 DOI: 10.1063/1.4769791] [Citation(s) in RCA: 32] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum Monte Carlo (QMC) methods are used to investigate the intramolecular reaction pathways of 1,3-butadiene. The ground state geometries of the three conformers s-trans, s-cis, and gauche, as well as the cyclobutene structure are fully optimised at the variational Monte Carlo (VMC) level, obtaining an excellent agreement with the experimental results and other quantum chemistry high level calculations. Transition state geometries are also estimated at the VMC level for the s-trans to gauche torsion barrier of 1,3-butadiene and for the conrotatory ring opening of cyclobutene to the gauche-1,3-butadiene conformer. The energies of the conformers and the reaction barriers are calculated at both variational and diffusional Monte Carlo levels providing a precise picture of the potential energy surface of 1,3-butadiene and supporting one of the two model profiles recently obtained by Raman spectroscopy [Boopalachandran et al., J. Phys. Chem. A 115, 8920 (2011)]. Considering the good scaling of QMC techniques with the system's size, our results also demonstrate how variational Monte Carlo calculations can be applied in the future to properly investigate the reaction pathways of large and correlated molecular systems.
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Affiliation(s)
- Matteo Barborini
- Dipartimento di Matematica Pura ed Applicata, Università degli studi dell'Aquila, via Vetoio (Coppito 2), 67100 L'Aquila, Italy
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14
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Zen A, Zhelyazov D, Guidoni L. Optimized Structure and Vibrational Properties by Error Affected Potential Energy Surfaces. J Chem Theory Comput 2012; 8:4204-4215. [PMID: 24093004 DOI: 10.1021/ct300576n] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The precise theoretical determination of the geometrical parameters of molecules at the minima of their potential energy surface and of the corresponding vibrational properties are of fundamental importance for the interpretation of vibrational spectroscopy experiments. Quantum Monte Carlo techniques are correlated electronic structure methods promising for large molecules, which are intrinsically affected by stochastic errors on both energy and force calculations, making the mentioned calculations more challenging with respect to other more traditional quantum chemistry tools. To circumvent this drawback in the present work, we formulate the general problem of evaluating the molecular equilibrium structures, the harmonic frequencies, and the anharmonic coefficients of an error affected potential energy surface. The proposed approach, based on a multidimensional fitting procedure, is illustrated together with a critical evaluation of systematic and statistical errors. We observe that the use of forces instead of energies in the fitting procedure reduces the statistical uncertainty of the vibrational parameters by 1 order of magnitude. Preliminary results based on variational Monte Carlo calculations on the water molecule demonstrate the possibility to evaluate geometrical parameters and harmonic and anharmonic coefficients at this level of theory with an affordable computational cost and a small stochastic uncertainty (<0.07% for geometries and <0.7% for vibrational properties).
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Affiliation(s)
- Andrea Zen
- Dipartimento di Fisica, La Sapienza-Università di Roma, P.le Aldo Moro 2, 00185 Roma, Italy
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15
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Affiliation(s)
- Brian M. Austin
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - Dmitry Yu. Zubarev
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - William A. Lester
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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