1
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Charry Martinez J, Barborini M, Tkatchenko A. Correlated Wave Functions for Electron-Positron Interactions in Atoms and Molecules. J Chem Theory Comput 2022; 18:2267-2280. [PMID: 35333513 PMCID: PMC9009097 DOI: 10.1021/acs.jctc.1c01193] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2021] [Indexed: 11/29/2022]
Abstract
The positron, as the antiparticle of the electron, can form metastable states with atoms and molecules before its annihilation with an electron. Such metastable matter-positron complexes are stabilized by a variety of mechanisms, which can have both covalent and noncovalent character. Specifically, electron-positron binding often involves strong many-body correlation effects, posing a substantial challenge for quantum-chemical methods based on atomic orbitals. Here we propose an accurate, efficient, and transferable variational ansatz based on a combination of electron-positron geminal orbitals and a Jastrow factor that explicitly includes the electron-positron correlations in the field of the nuclei, which are optimized at the level of variational Monte Carlo (VMC). We apply this approach in combination with diffusion Monte Carlo (DMC) to calculate binding energies for a positron e+ and a positronium Ps (the pseudoatomic electron-positron pair), bound to a set of atomic systems (H-, Li+, Li, Li-, Be+, Be, B-, C-, O- and F-). For PsB, PsC, PsO, and PsF, our VMC and DMC total energies are lower than that from previous calculations; hence, we redefine the state of the art for these systems. To assess our approach for molecules, we study the potential-energy surfaces (PES) of two hydrogen anions H- mediated by a positron (e+H22-), for which we calculate accurate spectroscopic properties by using a dense interpolation of the PES. We demonstrate the reliability and transferability of our correlated wave functions for electron-positron interactions with respect to state-of-the-art calculations reported in the literature.
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Affiliation(s)
| | - Matteo Barborini
- Department of Physics and Materials
Science, University of Luxembourg, L-1511, Luxembourg
City, Luxembourg
| | - Alexandre Tkatchenko
- Department of Physics and Materials
Science, University of Luxembourg, L-1511, Luxembourg
City, Luxembourg
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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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Tiihonen J, Clay RC, Krogel JT. Toward quantum Monte Carlo forces on heavier ions: Scaling properties. J Chem Phys 2021; 154:204111. [PMID: 34241166 DOI: 10.1063/5.0052266] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff 6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff -2, insensitive to model assumptions or the use of the "space warp" variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.
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Affiliation(s)
- Juha Tiihonen
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Raymond C Clay
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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4
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Nakano K, Attaccalite C, Barborini M, Capriotti L, Casula M, Coccia E, Dagrada M, Genovese C, Luo Y, Mazzola G, Zen A, Sorella S. TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo. J Chem Phys 2020; 152:204121. [DOI: 10.1063/5.0005037] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Kousuke Nakano
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Claudio Attaccalite
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | | | - Luca Capriotti
- New York University, Tandon School of Engineering, 6 MetroTech Center, Brooklyn, New York 11201, USA
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Michele Casula
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, IRD UMR 206, MNHN, 4 Place Jussieu, 75252 Paris, France
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - Mario Dagrada
- Forescout Technologies, John F. Kennedylaan 2, 5612AB Eindhoven, The Netherlands
| | - Claudio Genovese
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Ye Luo
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
- Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | | | - Andrea Zen
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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5
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Zen A, Brandenburg JG, Michaelides A, Alfè D. A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: Improving reproducibility and reducing the trial-wave-function bias. J Chem Phys 2019; 151:134105. [DOI: 10.1063/1.5119729] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Andrea Zen
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
- Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom
| | - Jan Gerit Brandenburg
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- Interdisciplinary Center for Scientific Computing, University of Heidelberg, Im Neuenheimer Feld 205A, 69120 Heidelberg, Germany
| | - Angelos Michaelides
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Dario Alfè
- Thomas Young Centre, University College London, London WC1H 0AH, United Kingdom
- London Centre for Nanotechnology, Gordon St., London WC1H 0AH, United Kingdom
- Department of Earth Sciences, University College London, London WC1E 6BT, United Kingdom
- Dipartimento di Fisica Ettore Pancini, Università di Napoli Federico II, Monte S. Angelo, I-80126 Napoli, Italy
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6
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Nakano K, Maezono R, Sorella S. All-Electron Quantum Monte Carlo with Jastrow Single Determinant Ansatz: Application to the Sodium Dimer. J Chem Theory Comput 2019; 15:4044-4055. [DOI: 10.1021/acs.jctc.9b00295] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kousuke Nakano
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Ryo Maezono
- School of Information Science, Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
- Computational Engineering Applications Unit, RIKEN, 2-1 Hirosawa, Wako, Saitama 351-0198, Japan
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136, Trieste, Italy
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7
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Dubecký M, Jurečka P, Mitas L, Ditte M, Fanta R. Toward Accurate Hydrogen Bonds by Scalable Quantum Monte Carlo. J Chem Theory Comput 2019; 15:3552-3557. [DOI: 10.1021/acs.jctc.9b00096] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Matúš Dubecký
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
- ATRI, Slovak University of Technology, Paulínska 16, 917 24 Trnava, Slovakia
| | - Petr Jurečka
- Department of Physical Chemistry, Palackỳ University Olomouc, tř. 17 listopadu 12, 771 46 Olomouc, Czech Republic
| | - Lubos Mitas
- Department of Physics and CHiPS, North Carolina State University, Raleigh, North Carolina 27695, United States
| | - Matej Ditte
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
| | - Roman Fanta
- Department of Physics, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic
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8
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Crawford TD, Kumar A, Bazanté AP, Di Remigio R. Reduced‐scaling coupled cluster response theory: Challenges and opportunities. WILEY INTERDISCIPLINARY REVIEWS-COMPUTATIONAL MOLECULAR SCIENCE 2019. [DOI: 10.1002/wcms.1406] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Affiliation(s)
- T. Daniel Crawford
- Department of Chemistry Virginia Tech, Blacksburg Virginia
- The Molecular Sciences Software Institute Blacksburg Virginia
| | - Ashutosh Kumar
- Department of Chemistry Virginia Tech, Blacksburg Virginia
| | | | - Roberto Di Remigio
- Department of Chemistry Virginia Tech, Blacksburg Virginia
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry University of Tromsø ‐ The Arctic University of Norway Tromsø Norway
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9
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Sorella S, Seki K, Brovko OO, Shirakawa T, Miyakoshi S, Yunoki S, Tosatti E. Correlation-Driven Dimerization and Topological Gap Opening in Isotropically Strained Graphene. PHYSICAL REVIEW LETTERS 2018; 121:066402. [PMID: 30141665 DOI: 10.1103/physrevlett.121.066402] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/09/2018] [Indexed: 06/08/2023]
Abstract
The phase diagram of isotropically expanded graphene cannot be correctly predicted by ignoring either electron correlations, or mobile carbons, or the effect of applied stress, as was done so far. We calculate the ground state enthalpy (not just energy) of strained graphene by an accurate off-lattice quantum Monte Carlo correlated ansatz of great variational flexibility. Following undistorted semimetallic graphene at low strain, multideterminant Heitler-London correlations stabilize between ≃8.5% and ≃15% strain an insulating Kekulé-like dimerized (DIM) state. Closer to a crystallized resonating-valence bond than to a Peierls state, the DIM state prevails over the competing antiferromagnetic insulating state favored by density-functional calculations which we conduct in parallel. The DIM stressed graphene insulator, whose gap is predicted to grow in excess of 1 eV before failure near 15% strain, is topological in nature, implying under certain conditions 1D metallic interface states lying in the bulk energy gap.
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Affiliation(s)
- Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Democritos Simulation Center CNR-IOM Istituto Officina dei Materiali, Via Bonomea 265, 34136 Trieste, Italy
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
| | - Kazuhiro Seki
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
| | - Oleg O Brovko
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
| | - Tomonori Shirakawa
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
- Computational Quantum Matter Research Team, RIKEN, Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
| | - Shohei Miyakoshi
- Computational Quantum Matter Research Team, RIKEN, Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
| | - Seiji Yunoki
- Computational Materials Science Research Team, RIKEN Center for Computational Science (R-CCS), Hyogo 650-0047, Japan
- Computational Condensed Matter Physics Laboratory, RIKEN Cluster for Pioneering Research (CPR), Saitama 351-0198, Japan
- Computational Quantum Matter Research Team, RIKEN, Center for Emergent Matter Science (CEMS), Saitama 351-0198, Japan
| | - Erio Tosatti
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Democritos Simulation Center CNR-IOM Istituto Officina dei Materiali, Via Bonomea 265, 34136 Trieste, Italy
- The Abdus Salam International Centre for Theoretical Physics (ICTP), Strada Costiera 11, 34151 Trieste, Italy
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10
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Coccia E, Varsano D, Guidoni L. Theoretical S1 ← S0 Absorption Energies of the Anionic Forms of Oxyluciferin by Variational Monte Carlo and Many-Body Green’s Function Theory. J Chem Theory Comput 2017; 13:4357-4367. [DOI: 10.1021/acs.jctc.7b00505] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Emanuele Coccia
- S3
Center, CNR Institute of Nanoscience, Via Campi 213/A, 41125 Modena, Italy
| | - Daniele Varsano
- S3
Center, CNR Institute of Nanoscience, Via Campi 213/A, 41125 Modena, Italy
| | - Leonardo Guidoni
- Dipartimento
di Scienze Fisiche e Chimiche, Universitá degli Studi dell’Aquila, via Vetoio, 67100, L’Aquila, Italy
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11
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Al-Hamdani YS, Rossi M, Alfè D, Tsatsoulis T, Ramberger B, Brandenburg JG, Zen A, Kresse G, Grüneis A, Tkatchenko A, Michaelides A. Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy. J Chem Phys 2017; 147:044710. [DOI: 10.1063/1.4985878] [Citation(s) in RCA: 35] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yasmine S. Al-Hamdani
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Mariana Rossi
- Fritz Haber Institute of the Max Planck Society, Faradayweg 4-6, 14195 Berlin, Germany
| | - Dario Alfè
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Theodoros Tsatsoulis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Benjamin Ramberger
- University of Vienna, Faculty of Physics and Center for Computational Materials Sciences, Sensengasse 8/12, 1090 Wien, Austria
| | - Jan Gerit Brandenburg
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Department of Chemistry, University College London, 20 Gordon Street, London WC1H 0AH, United Kingdom
| | - Andrea Zen
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Georg Kresse
- University of Vienna, Faculty of Physics and Center for Computational Materials Sciences, Sensengasse 8/12, 1090 Wien, Austria
| | - Andreas Grüneis
- Max Planck Institute for Solid State Research, Heisenbergstraße 1, D-70569 Stuttgart, Germany
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, L-1511 Luxembourg, Luxembourg
| | - Angelos Michaelides
- Thomas Young Centre and London Centre for Nanotechnology, 17–19 Gordon Street, London WC1H 0AH, United Kingdom
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, United Kingdom
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12
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Krongchon K, Busemeyer B, Wagner LK. Accurate barrier heights using diffusion Monte Carlo. J Chem Phys 2017; 146:124129. [DOI: 10.1063/1.4979059] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Kittithat Krongchon
- Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA
| | - Brian Busemeyer
- 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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13
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Mazzola G, Sorella S. Accelerating ab initio Molecular Dynamics and Probing the Weak Dispersive Forces in Dense Liquid Hydrogen. PHYSICAL REVIEW LETTERS 2017; 118:015703. [PMID: 28106448 DOI: 10.1103/physrevlett.118.015703] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/06/2016] [Indexed: 06/06/2023]
Abstract
We propose an ab initio molecular dynamics method, capable of dramatically reducing the autocorrelation time required for the simulation of classical and quantum particles at finite temperatures. The method is based on an efficient implementation of a first order Langevin dynamics modified by means of a suitable, position dependent acceleration matrix S. Here, we apply this technique to both Lennard-Jones models, to demonstrate the accuracy and speeding-up of the sampling, and within a quantum Monte Carlo based wave function approach, for determining the phase diagram of high-pressure hydrogen with simulations much longer than the autocorrelation time. With the proposed method, we are able to equilibrate in a few hundred steps even close to the liquid-liquid phase transition (LLT). Within our approach, we find that the LLT transition is consistent with recent density functionals predicting a much larger transition pressure when the long range dispersive forces are taken into account.
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Affiliation(s)
| | - Sandro Sorella
- International School for Advanced Studies (SISSA) Via Beirut 2, 4 34014 Trieste, Italy and INFM Democritos National Simulation Center, Via Beirut 2-4, I-34014 Trieste, Italy
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14
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Chu S, Coccia E, Barborini M, Guidoni L. Role of Electron Correlation along the Water Splitting Reaction. J Chem Theory Comput 2016; 12:5803-5810. [DOI: 10.1021/acs.jctc.6b00632] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/31/2023]
Affiliation(s)
- Shibing Chu
- Dipartimento
di Scienze Fisiche e Chimiche, Università degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
| | - Emanuele Coccia
- Dipartimento
di Scienze Fisiche e Chimiche, Università degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
- Sorbonne Universités,
UPMC Univ Paris 06, CNRS, Laboratoire de Chimie Théorique, CC 137-4 place Jussieu, F. 75252 Paris Cedex 05, France
| | | | - Leonardo Guidoni
- Dipartimento
di Scienze Fisiche e Chimiche, Università degli studi dell’Aquila, Via Vetoio (Coppito), 67100 L’Aquila, Italy
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15
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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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16
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Zen A, Coccia E, Gozem S, Olivucci M, Guidoni L. Quantum Monte Carlo Treatment of the Charge Transfer and Diradical Electronic Character in a Retinal Chromophore Minimal Model. J Chem Theory Comput 2016; 11:992-1005. [PMID: 25821414 PMCID: PMC4357234 DOI: 10.1021/ct501122z] [Citation(s) in RCA: 36] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2014] [Indexed: 01/22/2023]
Abstract
![]()
The
penta-2,4-dieniminium cation (PSB3) displays similar ground
state and first excited state potential energy features as those of
the retinal protonated Schiff base (RPSB) chromophore in rhodopsin.
Recently, PSB3 has been used to benchmark several electronic structure
methods, including highly correlated multireference wave function
approaches, highlighting the necessity to accurately describe the
electronic correlation in order to obtain reliable properties even
along the ground state (thermal) isomerization paths. In this work,
we apply two quantum Monte Carlo approaches, the variational Monte
Carlo and the lattice regularized diffusion Monte Carlo, to study
the energetics and electronic properties of PSB3 along representative
minimum energy paths and scans related to its thermal cis–trans isomerization. Quantum Monte Carlo
is used in combination with the Jastrow antisymmetrized geminal power
ansatz, which guarantees an accurate and balanced description of the
static electronic correlation thanks to the multiconfigurational nature
of the antisymmetrized geminal power term, and of the dynamical correlation,
due to the presence of the Jastrow factor explicitly depending on
electron–electron distances. Along the two ground state isomerization
minimum energy paths of PSB3, CASSCF calculations yield wave functions
having either charge transfer or diradical character in proximity
of the two transition state configurations. Here, we observe that
at the quantum Monte Carlo level of theory, only the transition state
with charge transfer character can be located. The conical intersection,
which becomes highly sloped, is observed only if the path connecting
the two original CASSCF transition states is extended beyond the diradical
one, namely by increasing the bond-length-alternation (BLA). These
findings are in good agreement with the results obtained by MRCISD+Q
calculations, and they demonstrate the importance of having an accurate
description of the static and dynamical correlation when studying
isomerization and transition states of conjugated systems.
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17
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Cleland DM, Per MC. Performance of quantum Monte Carlo for calculating molecular bond lengths. J Chem Phys 2016; 144:124108. [DOI: 10.1063/1.4944826] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Deidre M. Cleland
- CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville, Victoria 3052, Australia
| | - Manolo C. Per
- CSIRO Virtual Nanoscience Laboratory, 343 Royal Parade, Parkville, Victoria 3052, Australia
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18
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Sorella S, Devaux N, Dagrada M, Mazzola G, Casula M. Geminal embedding scheme for optimal atomic basis set construction in correlated calculations. J Chem Phys 2015; 143:244112. [DOI: 10.1063/1.4938089] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- S. Sorella
- International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy
| | - N. Devaux
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - M. Dagrada
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
| | - G. Mazzola
- Theoretische Physik, ETH Zurich, 8093 Zurich, Switzerland
| | - M. Casula
- CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, Case 115, 4 Place Jussieu, 75252 Paris Cedex 05, France
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19
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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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20
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Lüchow A, Sturm A, Schulte C, Haghighi Mood K. Generic expansion of the Jastrow correlation factor in polynomials satisfying symmetry and cusp conditions. J Chem Phys 2015; 142:084111. [PMID: 25725716 DOI: 10.1063/1.4909554] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Jastrow correlation factors play an important role in quantum Monte Carlo calculations. Together with an orbital based antisymmetric function, they allow the construction of highly accurate correlation wave functions. In this paper, a generic expansion of the Jastrow correlation function in terms of polynomials that satisfy both the electron exchange symmetry constraint and the cusp conditions is presented. In particular, an expansion of the three-body electron-electron-nucleus contribution in terms of cuspless homogeneous symmetric polynomials is proposed. The polynomials can be expressed in fairly arbitrary scaling function allowing a generic implementation of the Jastrow factor. It is demonstrated with a few examples that the new Jastrow factor achieves 85%-90% of the total correlation energy in a variational quantum Monte Carlo calculation and more than 90% of the diffusion Monte Carlo correlation energy.
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Affiliation(s)
- Arne Lüchow
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Alexander Sturm
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Christoph Schulte
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
| | - Kaveh Haghighi Mood
- Institute of Physical Chemistry, RWTH Aachen University, 52056 Aachen, Germany
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21
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Dupuy N, Bouaouli S, Mauri F, Sorella S, Casula M. Vertical and adiabatic excitations in anthracene from quantum Monte Carlo: Constrained energy minimization for structural and electronic excited-state properties in the JAGP ansatz. J Chem Phys 2015; 142:214109. [DOI: 10.1063/1.4922048] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2022] Open
Affiliation(s)
- Nicolas Dupuy
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Samira Bouaouli
- Laboratoire de Chimie Théorique, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Francesco Mauri
- CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05, France
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Beirut 2-4, 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy
| | - Michele Casula
- CNRS and Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie, Université Pierre et Marie Curie, case 115, 4 place Jussieu, 75252 Paris Cedex 05, France
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22
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Zen A, Luo Y, Mazzola G, Guidoni L, Sorella S. Ab initio molecular dynamics simulation of liquid water by quantum Monte Carlo. J Chem Phys 2015; 142:144111. [PMID: 25877566 DOI: 10.1063/1.4917171] [Citation(s) in RCA: 55] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Although liquid water is ubiquitous in chemical reactions at roots of life and climate on the earth, the prediction of its properties by high-level ab initio molecular dynamics simulations still represents a formidable task for quantum chemistry. In this article, we present a room temperature simulation of liquid water based on the potential energy surface obtained by a many-body wave function through quantum Monte Carlo (QMC) methods. The simulated properties are in good agreement with recent neutron scattering and X-ray experiments, particularly concerning the position of the oxygen-oxygen peak in the radial distribution function, at variance of previous density functional theory attempts. Given the excellent performances of QMC on large scale supercomputers, this work opens new perspectives for predictive and reliable ab initio simulations of complex chemical systems.
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Affiliation(s)
- Andrea Zen
- Dipartimento di Fisica, “La Sapienza” - Università di Roma, piazzale Aldo Moro 5, 00185 Rome, Italy
- London Centre for Nanotechnology, University College London, London WC1E 6BT, United Kingdom
| | - Ye Luo
- SISSA–International School for Advanced Studies, Via Bonomea 26, 34136 Trieste, Italy
- Democritos Simulation Center CNR–IOM Istituto Officina dei Materiali, 34151 Trieste, Italy
| | - Guglielmo Mazzola
- SISSA–International School for Advanced Studies, Via Bonomea 26, 34136 Trieste, Italy
- Democritos Simulation Center CNR–IOM Istituto Officina dei Materiali, 34151 Trieste, Italy
| | - Leonardo Guidoni
- Dipartimento di Fisica, “La Sapienza” - Università di Roma, piazzale Aldo Moro 5, 00185 Rome, Italy
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’ Aquila, via Vetoio, 67100 L’ Aquila, Italy
| | - Sandro Sorella
- SISSA–International School for Advanced Studies, Via Bonomea 26, 34136 Trieste, Italy
- Democritos Simulation Center CNR–IOM Istituto Officina dei Materiali, 34151 Trieste, Italy
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23
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Mazzola G, Sorella S. Distinct metallization and atomization transitions in dense liquid hydrogen. PHYSICAL REVIEW LETTERS 2015; 114:105701. [PMID: 25815949 DOI: 10.1103/physrevlett.114.105701] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 11/20/2014] [Indexed: 06/04/2023]
Abstract
We perform molecular dynamics simulations driven by accurate quantum Monte Carlo forces on dense liquid hydrogen. There is a recent report of a complete atomization transition between a mixed molecular-atomic liquid and a completely dissociated fluid in an almost unaccessible pressure range [Nat. Commun. 5, 3487 (2014)]. Here, instead, we identify a different transition between the fully molecular liquid and the mixed-atomic fluid at ∼400 GPa, i.e., in a much more interesting pressure range. We provide numerical evidence supporting the metallic behavior of this intermediate phase. Therefore, we predict that the metallization at finite temperature occurs in this partially dissociated molecular fluid, well before the complete atomization of the liquid. At high temperature this first-order transition becomes a crossover, in very good agreement with the experimental observation. Several systematic tests supporting the quality of our large scale calculations are also reported.
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Affiliation(s)
- Guglielmo Mazzola
- International School for Advanced Studies (SISSA), and CRS Democritos, CNR-INFM, -Via Bonomea 265, I-34136 Trieste, Italy
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), and CRS Democritos, CNR-INFM, -Via Bonomea 265, I-34136 Trieste, Italy
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24
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Barborini M, Guidoni L. π-Conjugation in trans-1,3-butadiene: static and dynamical electronic correlations described through quantum Monte Carlo. J Chem Theory Comput 2015; 11:508-17. [PMID: 26580909 DOI: 10.1021/ct501157f] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
We investigate the effects of the static and dynamical electronic correlations on the level of conjugation of the trans-1,3-butadiene molecule through Quantum Monte Carlo methods applied to an Antisymmetrized Geminal Power (AGP) wave function, with a Jastrow factor similar to the Gutzwiller ansatz. The degree of conjugation is measured through the convergence of the structural properties of 1,3-butadiene and in particular of the Bond Length Alternation (BLA), that is the difference between the lengths of the single and double carbon bonds. After verifying the different roles of the Fermionic AGP part of our wave function and of the Jastrow factor in recovering electronic correlation, we study the effects of a constrained Active Space AGP (AGPAS), similar to that used in the Complete Active Space (CAS) representation. Through this AGPAS, we are able to identify the effect of the limited active space on the degree of conjugation, showing that in the limit of infinite active space the structural properties converge exactly to those of the atomic AGP, giving a BLA for 1,3-butadiene around 0.1244(5) Å.
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Affiliation(s)
- Matteo Barborini
- Dipartimento di Ingegneria e Scienze dell'Informazione e Matematica, Università degli studi dell'Aquila , L'Aquila, Italy.,Dipartimento di Scienze Fisiche e Chimiche, Università degli studi dell'Aquila , , L'Aquila, Italy
| | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli studi dell'Aquila , , L'Aquila, Italy
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25
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Luo Y, Zen A, Sorella S. Ab initio molecular dynamics with noisy forces: Validating the quantum Monte Carlo approach with benchmark calculations of molecular vibrational properties. J Chem Phys 2014; 141:194112. [DOI: 10.1063/1.4901430] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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26
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Dubecký M, Derian R, Jurečka P, Mitas L, Hobza P, Otyepka M. Quantum Monte Carlo for noncovalent interactions: an efficient protocol attaining benchmark accuracy. Phys Chem Chem Phys 2014; 16:20915-23. [DOI: 10.1039/c4cp02093f] [Citation(s) in RCA: 42] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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27
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Zen A, Trout BL, Guidoni L. Properties of reactive oxygen species by quantum Monte Carlo. J Chem Phys 2014; 141:014305. [DOI: 10.1063/1.4885144] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023] Open
Affiliation(s)
- Andrea Zen
- Dipartimento di Fisica, La Sapienza - Università di Roma, Piazzale Aldo Moro 2, 00185 Rome, Italy
| | - Bernhardt L. Trout
- Department of Chemical Engineering, Massachusetts Institute of Technology, 77 Massachusetts Ave, Cambridge, Massachusetts 02139, USA
| | - 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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28
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Varsano D, Coccia E, Pulci O, Conte AM, Guidoni L. Ground state structures and electronic excitations of biological chromophores at Quantum Monte Carlo/Many Body Green’s Function Theory level. COMPUT THEOR CHEM 2014. [DOI: 10.1016/j.comptc.2014.03.011] [Citation(s) in RCA: 24] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022]
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29
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Dagrada M, Casula M, Saitta AM, Sorella S, Mauri F. Quantum Monte Carlo Study of the Protonated Water Dimer. J Chem Theory Comput 2014; 10:1980-93. [DOI: 10.1021/ct401077x] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Mario Dagrada
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Michele Casula
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Antonino M. Saitta
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
| | - Sandro Sorella
- International School for Advanced Studies (SISSA) Via Beirut 2,4 34014 Trieste, Italy and INFM Democritos National Simulation Center, Trieste, Italy
| | - Francesco Mauri
- Institut
de Minéralogie, de Physique des Matériaux, et de Cosmochimie
(IMPMC), Sorbonne Universités - UPMC Paris 06, UMR CNRS 7590, Muséum
National d’Histoire Naturelle, IRD UMR 206, 4 Place Jussieu, 75005 Paris, France
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30
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Zen A, Coccia E, Luo Y, Sorella S, Guidoni L. Static and Dynamical Correlation in Diradical Molecules by Quantum Monte Carlo Using the Jastrow Antisymmetrized Geminal Power Ansatz. J Chem Theory Comput 2014; 10:1048-61. [DOI: 10.1021/ct401008s] [Citation(s) in RCA: 47] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/23/2023]
Affiliation(s)
- Andrea Zen
- Dipartimento
di Fisica, Sapienza-Università di Roma, Piazzale Aldo Moro
5, 00185 Rome, Italy
| | - Emanuele Coccia
- Dipartimento
di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, Via Vetoio 2, 67010 L’Aquila, Italy
| | - Ye Luo
- Scuola
Internazionale Superiore di Studi Avanzati (SISSA) and Democritos
National Simulation Center, Istituto Officina dei Materiali del CNR, via Bonomea 265, 34136 Trieste, Italy
| | - Sandro Sorella
- Scuola
Internazionale Superiore di Studi Avanzati (SISSA) and Democritos
National Simulation Center, Istituto Officina dei Materiali del CNR, via Bonomea 265, 34136 Trieste, Italy
| | - Leonardo Guidoni
- Dipartimento
di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, Via Vetoio 2, 67010 L’Aquila, Italy
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31
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Coccia E, Varsano D, Guidoni L. Ab Initio Geometry and Bright Excitation of Carotenoids: Quantum Monte Carlo and Many Body Green's Function Theory Calculations on Peridinin. J Chem Theory Comput 2014; 10:501-6. [PMID: 26580027 PMCID: PMC4864508 DOI: 10.1021/ct400943a] [Citation(s) in RCA: 48] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this letter, we report the singlet ground state structure of the full carotenoid peridinin by means of variational Monte Carlo (VMC) calculations. The VMC relaxed geometry has an average bond length alternation of 0.1165(10) Å, larger than the values obtained by DFT (PBE, B3LYP, and CAM-B3LYP) and shorter than that calculated at the Hartree-Fock (HF) level. TDDFT and EOM-CCSD calculations on a reduced peridinin model confirm the HOMO-LUMO major contribution of the Bu(+)-like (S2) bright excited state. Many Body Green's Function Theory (MBGFT) calculations of the vertical excitation energy of the Bu(+)-like state for the VMC structure (VMC/MBGFT) provide an excitation energy of 2.62 eV, in agreement with experimental results in n-hexane (2.72 eV). The dependence of the excitation energy on the bond length alternation in the MBGFT and TDDFT calculations with different functionals is discussed.
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Affiliation(s)
- Emanuele Coccia
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, via Vetoio, 67110 L’Aquila, Italy
| | - Daniele Varsano
- S3 Center, CNR Institute of Nanoscience, Via Campi 213/A, 41125 Modena, Italy
| | - Leonardo Guidoni
- Dipartimento di Scienze Fisiche e Chimiche, Università degli Studi dell’Aquila, via Vetoio, 67110 L’Aquila, Italy
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32
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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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