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Zhou X, Huang Z, He X. Diffusion Monte Carlo method for barrier heights of multiple proton exchanges and complexation energies in small water, ammonia, and hydrogen fluoride clusters. J Chem Phys 2024; 160:054103. [PMID: 38310472 DOI: 10.1063/5.0182164] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/18/2023] [Accepted: 01/09/2024] [Indexed: 02/05/2024] Open
Abstract
Proton exchange reactions are of key importance in many processes in water. However, it is nontrivial to achieve reliable barrier heights for multiple proton exchanges and complexation energies in hydrogen-bonded systems theoretically. Performance of the fixed-node diffusion quantum Monte Carlo (FN-DMC) with the single-Slater-Jastrow trial wavefunction on total energies, barrier heights of multiple proton exchanges, and complexation energies of small water, ammonia, and hydrogen fluoride clusters is investigated in this study. Effects of basis sets and those of locality approximation (LA), T-move approximation (T-move), and determinant localization approximation (DLA) schemes in dealing with the nonlocal part of pseudopotentials on FN-DMC results are evaluated. According to our results, diffuse basis functions are important in achieving reliable barrier heights and complexation energies with FN-DMC, although the cardinal number of the basis set is more important than diffuse basis functions on total energies of these systems. Our results also show that the time step bias with DLA and LA is smaller than T-move; however, the time step bias of DMC energies with respect to time steps using the T-move is roughly linear up to 0.06 a.u., while this is not the case with LA and DLA. Barrier heights and complexation energies with FN-DMC using these three schemes are always within chemical accuracy. Taking into account the fact that T-move and DLA are typically more stable than LA, FN-DMC calculations with the T-move or DLA scheme and basis sets containing diffuse basis functions are suggested for barrier heights of multiple proton exchanges and complexation energies of hydrogen-bonded clusters.
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Affiliation(s)
- Xiaojun Zhou
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, People's Republic of China
- School of Physics & Information Science, Shaanxi University of Science and Technology, Xi'an 710021, People's Republic of China
| | - Zhiru Huang
- Institute of Atomic and Molecular Physics, Key Laboratory of High Energy Density Physics and Technology, Ministry of Education, Sichuan University, Chengdu, People's Republic of China
| | - Xiao He
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, People's Republic of China
- Chongqing Key Laboratory of Precision Optics, Chongqing Institute of East China Normal University, Chongqing 401120, People's Republic of China
- New York University-East China Normal University Center for Computational Chemistry, New York University Shanghai, Shanghai 200062, People's Republic of China
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2
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Ren W, Fu W, Wu X, Chen J. Towards the ground state of molecules via diffusion Monte Carlo on neural networks. Nat Commun 2023; 14:1860. [PMID: 37012248 PMCID: PMC10070323 DOI: 10.1038/s41467-023-37609-3] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/24/2022] [Accepted: 03/20/2023] [Indexed: 04/05/2023] Open
Abstract
Diffusion Monte Carlo (DMC) based on fixed-node approximation has enjoyed significant developments in the past decades and become one of the go-to methods when accurate ground state energy of molecules and materials is needed. However, the inaccurate nodal structure hinders the application of DMC for more challenging electronic correlation problems. In this work, we apply the neural-network based trial wavefunction in fixed-node DMC, which allows accurate calculations of a broad range of atomic and molecular systems of different electronic characteristics. Our method is superior in both accuracy and efficiency compared to state-of-the-art neural network methods using variational Monte Carlo (VMC). We also introduce an extrapolation scheme based on the empirical linearity between VMC and DMC energies, and significantly improve our binding energy calculation. Overall, this computational framework provides a benchmark for accurate solutions of correlated electronic wavefunction and also sheds light on the chemical understanding of molecules.
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Affiliation(s)
- Weiluo Ren
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China.
| | - Weizhong Fu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
- School of Physics, Peking University, 100871, Beijing, People's Republic of China
| | - Xiaojie Wu
- ByteDance Research, Zhonghang Plaza, No. 43, North 3rd Ring West Road, Haidian District, Beijing, People's Republic of China
| | - Ji Chen
- School of Physics, Peking University, 100871, Beijing, People's Republic of China.
- Interdisciplinary Institute of Light-Element Quantum Materials, Frontiers Science Center for Nano-Optoelectronics, Peking University, 100871, Beijing, People's Republic of China.
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Herman KM, Aprà E, Xantheas SS. A critical comparison of CH⋯π versus π⋯π interactions in the benzene dimer: obtaining benchmarks at the CCSD(T) level and assessing the accuracy of lower scaling methods. Phys Chem Chem Phys 2023; 25:4824-4838. [PMID: 36692338 DOI: 10.1039/d2cp04335a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/03/2022]
Abstract
We have established CCSD(T)/CBS (Complete Basis Set) limits for 3 stationary points on the benzene dimer potential energy surface, corresponding to the π⋯π (parallel displaced or PD(C2h), minimum) and CH⋯π (T-shaped or T(C2v), transition state) and tilted T-shaped (or TT(Cs), minimum) bonding scenarios considering both the structure and binding energy. The CCSD(T)/CBS binding energies are -2.65 ± 0.02 (PD), -2.74 ± 0.03 (T), and -2.83 ± 0.01 kcal mol-1 (TT). To this end, the CH⋯π is ∼0.2 kcal mol-1 stronger than the π⋯π interaction, whereas the tilting of the CH donating benzene molecule with respect to the other benzene is worth 0.1 kcal mol-1. As previously discussed in the literature, the MP2 level of theory does not provide a close match for either the energy or structure, yet the SCS-MP2 yields structures in excellent agreement with respect to the CCSD(T) result. It is found that the SCS-MI-MP2 also gives optimized structures very close to SCS-MP2 (within ∼0.01 Å of the benchmark). Despite the closer match in structure, the spin-biased MP2 methods (SCS-, SCS-MI-, and SOS-MP2) incorrectly predict the relative stabilities of the isomers. That said, none of the spin biased MP2 methods offers a good compromise between energy and structure for the systems examined. Finally, the CCSD(T)/CBS benchmarks were used to assess the performance of 13 DFT functionals selected from different rungs of Jacob's ladder. Several functionals such as TPSS-D3, B3LYP-D3, B97-D, B97-D3, and B2PLYP-D3 provided a good description of the binding energies for both CH⋯π and π⋯π interactions, yielding values within 6% of the CCSD(T)/CBS benchmark values. Unlike the MP2 methods, these functionals correctly predict the relative stability of the PD(C2h) and T(C2v) dimers. Further, we find that there is no systematic improvement as Jacob's ladder is ascended (increased complexity of functional). The best functionals that result in a good compromise between structure and energy accuracy are B97-D3 and B2PLYP-D3 for both the CH⋯π and π⋯π interaction. Despite the impressive performance of these functionals, a challenge that remains is ensuring the transferability of these density functionals in accurately describing the interaction between dimers of larger aromatic molecules, the latter requiring high-level benchmarks for these systems.
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Affiliation(s)
- Kristina M Herman
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA.
| | - Edoardo Aprà
- Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, P.O. Box 999, Richland, Washington 99352, USA
| | - Sotiris S Xantheas
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA. .,Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, WA, 99352, USA
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4
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Interactions between large molecules pose a puzzle for reference quantum mechanical methods. Nat Commun 2021; 12:3927. [PMID: 34168142 PMCID: PMC8225865 DOI: 10.1038/s41467-021-24119-3] [Citation(s) in RCA: 45] [Impact Index Per Article: 15.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/20/2020] [Accepted: 06/02/2021] [Indexed: 02/05/2023] Open
Abstract
Quantum-mechanical methods are used for understanding molecular interactions throughout the natural sciences. Quantum diffusion Monte Carlo (DMC) and coupled cluster with single, double, and perturbative triple excitations [CCSD(T)] are state-of-the-art trusted wavefunction methods that have been shown to yield accurate interaction energies for small organic molecules. These methods provide valuable reference information for widely-used semi-empirical and machine learning potentials, especially where experimental information is scarce. However, agreement for systems beyond small molecules is a crucial remaining milestone for cementing the benchmark accuracy of these methods. We show that CCSD(T) and DMC interaction energies are not consistent for a set of polarizable supramolecules. Whilst there is agreement for some of the complexes, in a few key systems disagreements of up to 8 kcal mol-1 remain. These findings thus indicate that more caution is required when aiming at reproducible non-covalent interactions between extended molecules.
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Genovese C, Shirakawa T, Nakano K, Sorella S. General Correlated Geminal Ansatz for Electronic Structure Calculations: Exploiting Pfaffians in Place of Determinants. J Chem Theory Comput 2020; 16:6114-6131. [PMID: 32804497 PMCID: PMC8011928 DOI: 10.1021/acs.jctc.0c00165] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/18/2020] [Indexed: 11/29/2022]
Abstract
We propose here a single Pfaffian correlated variational ansatz that dramatically improves the accuracy with respect to the single determinant one, while remaining at a similar computational cost. A much larger correlation energy is indeed determined by the most general two electron pairing function, including both singlet and triplet channels, combined with a many-body Jastrow factor, including all possible spin-spin, spin-density, and density-density terms. The main technical ingredient to exploit this accuracy is the use of the Pfaffian for antisymmetrizing a highly correlated pairing function, thus recovering the Fermi statistics for electrons with an affordable computational cost. Moreover, the application of the diffusion Monte Carlo, within the fixed node approximation, allows us to obtain very accurate binding energies for the first preliminary calculations reported in this study: C2, N2, and O2 and the benzene molecule. This is promising and remarkable, considering that they represent extremely difficult molecules even for computationally demanding multideterminant approaches, and opens therefore the way for realistic and accurate electronic simulations with an algorithm scaling at most as the fourth power of the number of electrons.
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Affiliation(s)
- Claudio Genovese
- SISSA,
International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
| | - Tomonori Shirakawa
- Computational
Materials Science Research Team, RIKEN Center
for Computational Science (R-CCS), Kobe, Hyogo 650-0047, Japan
| | - Kousuke Nakano
- SISSA,
International School for Advanced Studies, 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
| | - Sandro Sorella
- SISSA,
International School for Advanced Studies, Via Bonomea 265, 34136 Trieste, Italy
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Yang DC, Kim DY, Kim KS. Quantum Monte Carlo Study of the Water Dimer Binding Energy and Halogen-π Interactions. J Phys Chem A 2019; 123:7785-7791. [PMID: 31418568 DOI: 10.1021/acs.jpca.9b04072] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Halogen-π systems are involved with competition between halogen bonding and π-interaction. Using the diffusion quantum Monte Carlo (DMC) method, we compare the interaction of benzene with diatomic halogens (X2: Cl2/Br2) with the typical hydrogen bonding in the water dimer, taking into account explicit correlations of up to three bodies. The benzene-Cl2/Br2 binding energies (13.07 ± 0.42/16.62 ± 0.02 kJ/mol) attributed to both halogen bonding and dispersion are smaller than but comparable to the typical hydrogen bonding in the water dimer binding energy (20.88 ± 0.27 kJ/mol). All of the above values are in good agreement with those from the coupled-cluster with single, double, and noniterative triple excitations (CCSD(T)) results at the complete basis set limit (benzene-Cl2/Br2: 12.78/16.17 kJ/mol; water dimer: 21.0 kJ/mol).
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Affiliation(s)
- D ChangMo Yang
- Center for Superfunctional Materials, Department of Chemistry , Ulsan National Institute of Science and Technology , Ulsan 44919 , Republic of Korea
| | - Dong Yeon Kim
- Center for Superfunctional Materials, Department of Chemistry , Ulsan National Institute of Science and Technology , Ulsan 44919 , Republic of Korea
| | - Kwang S Kim
- Center for Superfunctional Materials, Department of Chemistry , Ulsan National Institute of Science and Technology , Ulsan 44919 , Republic of Korea
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Hongo K, Maezono R. A Computational Scheme To Evaluate Hamaker Constants of Molecules with Practical Size and Anisotropy. J Chem Theory Comput 2017; 13:5217-5230. [PMID: 28981266 DOI: 10.1021/acs.jctc.6b01159] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We propose a computational scheme to evaluate Hamaker constants, A, of molecules with practical sizes and anisotropies. Upon the increasing feasibility of diffusion Monte Carlo (DMC) methods to evaluate binding curves for such molecules to extract the constants, we discussed how to treat the averaging over anisotropy and how to correct the bias due to the nonadditivity. We have developed a computational procedure for dealing with the anisotropy and reducing statistical errors and biases in DMC evaluations, based on possible validations on predicted A. We applied the scheme to cyclohexasilane molecule, Si6H12, used in "printed electronics" fabrications, getting A ≈ 105 ± 2 zJ, being in plausible range supported even by other possible extrapolations. The scheme provided here would open a way to use handy ab initio evaluations to predict wettabilities as in the form of materials informatics over broader molecules.
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Affiliation(s)
- Kenta Hongo
- Research Center for Advanced Computing Infrastructure, JAIST , Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan.,Center for Materials Research by Information Integration, Research and Services Division of Materials Data and Integrated System, National Institute for Materials Science , Tsukuba 305-0047, Japan.,PRESTO, Japan Science and Technology Agency (JST) , Kawaguchi, Saitama 332-0012, Japan
| | - Ryo Maezono
- School of Information Science, JAIST , Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
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Dubecký M. Noncovalent Interactions by Fixed-Node Diffusion Monte Carlo: Convergence of Nodes and Energy Differences vs Gaussian Basis-Set Size. J Chem Theory Comput 2017; 13:3626-3635. [DOI: 10.1021/acs.jctc.7b00537] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Matúš Dubecký
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701
03 Ostrava, Czech Republic
- ATRI, Faculty of Materials
Science and Technology, Slovak University of Technology, Paulínska
16, 917 24 Trnava, Slovakia
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9
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Dubecký M. Bias cancellation in one-determinant fixed-node diffusion Monte Carlo: Insights from fermionic occupation numbers. Phys Rev E 2017; 95:033308. [PMID: 28415179 DOI: 10.1103/physreve.95.033308] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/07/2016] [Indexed: 06/07/2023]
Abstract
The accuracy of the fixed-node diffusion Monte Carlo (FNDMC) depends on the node location of the supplied trial state Ψ_{T}. The practical FNDMC approaches available for large systems rely on compact yet effective Ψ_{T}, most often containing an explicitly correlated single Slater determinant (SD). However, SD nodes may be better suited to one system than to another, which may possibly lead to inaccurate FNDMC energy differences. It remains a challenge how to estimate nonequivalence or appropriateness of SDs. Here we use the differences of a measure based on the Euclidean distance between the natural orbital occupation number (NOON) vector of the SD and the exact solution in the NOON vector space, which can be viewed as a measure of SD nonequivalence and as a qualitative measure of the expected degree of nondynamic-correlation-related bias in FNDMC energy differences. This is explored on a set of small noncovalent complexes and covalent bond breaking of Si_{2} vs N_{2}. It turns out that NOON-based measures well reflect the magnitude and sign of the bias present in the data available, thus providing insights into the nature of bias cancellation in SD FNDMC energy differences.
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Affiliation(s)
- Matúš Dubecký
- Department of Physics, Faculty of Science, University of Ostrava, 30. dubna 22, 701 03 Ostrava, Czech Republic and ATRI, Faculty of Materials Science and Technology, Slovak University of Technology, Paulínska 16, 917 24 Trnava, Slovakia
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10
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Azadi S, Kühne TD. High-pressure hydrogen sulfide by diffusion quantum Monte Carlo. J Chem Phys 2017; 146:084503. [DOI: 10.1063/1.4976836] [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)
- Sam Azadi
- Department of Materials Science, Royal School of Mines, Thomas Young Center, London Centre for Nanotechnology, Imperial College London, London SW7 2AZ, United Kingdom
| | - Thomas D. Kühne
- Dynamics of Condensed Matter, Department of Chemistry, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany and Paderborn Center for Parallel Computing and Institute for Lightweight Design with Hybrid Systems, University of Paderborn, Warburger Strasse 100, D-33098 Paderborn, Germany
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11
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Azadi S, Ackland GJ. The role of van der Waals and exchange interactions in high-pressure solid hydrogen. Phys Chem Chem Phys 2017; 19:21829-21839. [DOI: 10.1039/c7cp03729e] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Our study of the van der Waals interactions in solid molecular hydrogen structures indicates two candidates for phase III.
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Affiliation(s)
- Sam Azadi
- Royal School of Mines and the Thomas Young Centre
- Imperial College London
- SW7 2AZ London
- UK
- School of Physics and Centre for Science at Extreme Conditions
| | - Graeme J. Ackland
- School of Physics and Centre for Science at Extreme Conditions
- University of Edinburgh
- Edinburgh EH9 3JZ
- UK
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12
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Chiu CC, Hung CC, Cheng PY. Ultrafast Charge Recombination Dynamics in Ternary Electron Donor–Acceptor Complexes: (Benzene)2-Tetracyanoethylene Complexes. J Phys Chem B 2016; 120:12390-12403. [DOI: 10.1021/acs.jpcb.6b10593] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/23/2022]
Affiliation(s)
- Chih-Chung Chiu
- Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan 30043, R. O. C
| | - Chih-Chang Hung
- Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan 30043, R. O. C
| | - Po-Yuan Cheng
- Department of Chemistry, National Tsing Hua University, Hsinchu, Taiwan 30043, R. O. C
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13
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Azadi S, Cohen RE. Low-pressure phase diagram of crystalline benzene from quantum Monte Carlo. J Chem Phys 2016. [DOI: 10.1063/1.4960434] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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14
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Affiliation(s)
- Matúš Dubecký
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký 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
| | - Petr Jurečka
- Regional
Centre of Advanced Technologies and Materials, Department of Physical
Chemistry, Faculty of Science, Palacký University Olomouc, tř.
17 listopadu 12, 771 46 Olomouc, Czech Republic
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Gasperich K, Jordan KD. Diffusion Monte Carlo Study of the Parallel Displaced Form of the Benzene Dimer. ACS SYMPOSIUM SERIES 2016. [DOI: 10.1021/bk-2016-1234.ch007] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/05/2022]
Affiliation(s)
- Kevin Gasperich
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
| | - Kenneth D. Jordan
- Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States
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