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Datar A, Matthews DA. Robust Tensor Hypercontraction of the Particle-Particle Ladder Term in Equation-of-Motion Coupled Cluster Theory. J Chem Theory Comput 2024; 20:708-720. [PMID: 38198505 DOI: 10.1021/acs.jctc.3c00892] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2024]
Abstract
One method of representing a high-rank tensor as a (hyper-)product of lower-rank tensors is the tensor hypercontraction (THC) method of Hohenstein et al. This strategy has been found to be useful for reducing the polynomial scaling of coupled-cluster methods by representation of a four-dimensional tensor of electron-repulsion integrals in terms of five two-dimensional matrices. Pierce et al. have already shown that the application of a robust form of THC to the particle-particle ladder (PPL) term reduces the cost of this term in couple-cluster singles and doubles (CCSD) from O ( N 6 ) to O ( N 5 ) with negligible errors in energy with respect to the density-fitted variant. In this work, we have implemented the least-squares variant of THC (LS-THC) which does not require a nonlinear tensor factorization, including the robust form (R-LS-THC), for the calculation of the excitation and electron attachment energies using equation-of-motion coupled cluster methods EOMEE-CCSD and EOMEA-CCSD, respectively. We have benchmarked the effect of the R-LS-THC-PPL approximation on excitation energies using the comprehensive QUEST database and the accuracy of electron attachment energies using the NAB22 database. We find that errors on the order of 1 meV are achievable with a reduction in total calculation time of approximately 5 ×.
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Affiliation(s)
- Avdhoot Datar
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
| | - Devin A Matthews
- Department of Chemistry, Southern Methodist University, Dallas, Texas 75275, United States
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2
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Pierce K, Rishi V, Valeev EF. Robust Approximation of Tensor Networks: Application to Grid-Free Tensor Factorization of the Coulomb Interaction. J Chem Theory Comput 2021; 17:2217-2230. [PMID: 33780616 DOI: 10.1021/acs.jctc.0c01310] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Approximation of a tensor network by approximating (e.g., factorizing) one or more of its constituent tensors can be improved by canceling the leading-order error due to the constituents' approximation. The utility of such robust approximation is demonstrated for robust canonical polyadic (CP) approximation of a (density-fitting) factorized two-particle Coulomb interaction tensor. The resulting algebraic (grid-free) approximation for the Coulomb tensor, closely related to the factorization appearing in pseudospectral and tensor hypercontraction approaches, is efficient and accurate, with significantly reduced rank compared to the naive (nonrobust) approximation. Application of the robust approximation to the particle-particle ladder term in the coupled-cluster singles and doubles reduces the size complexity from O (N6) to O (N5) with robustness ensuring negligible errors in chemically relevant energy differences using CP ranks approximately equal to the size of the density-fitting basis.
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Affiliation(s)
- Karl Pierce
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Varun Rishi
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
| | - Edward F Valeev
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, United States
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3
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Le HA, Shiozaki T. Occupied-Orbital Fast Multipole Method for Efficient Exact Exchange Evaluation. J Chem Theory Comput 2018; 14:1228-1234. [DOI: 10.1021/acs.jctc.7b00880] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Hai-Anh Le
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
| | - Toru Shiozaki
- Department of Chemistry, Northwestern University, 2145 Sheridan Road, Evanston, Illinois 60208, United States
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Koh KJ, Nguyen-Beck TS, Parkhill J. Accelerating Realtime TDDFT with Block-Orthogonalized Manby–Miller Embedding Theory. J Chem Theory Comput 2017; 13:4173-4178. [DOI: 10.1021/acs.jctc.7b00494] [Citation(s) in RCA: 15] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Kevin J. Koh
- Department of Chemistry and
Biochemistry, The University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
| | - Triet S. Nguyen-Beck
- Department of Chemistry and
Biochemistry, The University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
| | - John Parkhill
- Department of Chemistry and
Biochemistry, The University of Notre Dame, 251 Nieuwland Science Hall, Notre Dame, Indiana 46556, United States
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Williams-Young D, Goings JJ, Li X. Accelerating Real-Time Time-Dependent Density Functional Theory with a Nonrecursive Chebyshev Expansion of the Quantum Propagator. J Chem Theory Comput 2016; 12:5333-5338. [DOI: 10.1021/acs.jctc.6b00693] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- David Williams-Young
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Joshua J. Goings
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Xiaosong Li
- Department
of Chemistry, University of Washington, Seattle, Washington 98195, United States
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6
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Toivanen EA, Losilla SA, Sundholm D. The grid-based fast multipole method – a massively parallel numerical scheme for calculating two-electron interaction energies. Phys Chem Chem Phys 2015; 17:31480-90. [DOI: 10.1039/c5cp01173f] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A grid-based fast multipole method has been developed for calculating two-electron interaction energies for non-overlapping charge densities.
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Affiliation(s)
| | | | - Dage Sundholm
- Department of Chemistry
- University of Helsinki
- Finland
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Kuźniarowicz P, Liu K, Aoki Y, Gu FL, Stachowicz A, Korchowiec J. Intermediate electrostatic field for the elongation method. J Mol Model 2014; 20:2277. [PMID: 24878802 PMCID: PMC4072069 DOI: 10.1007/s00894-014-2277-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/29/2013] [Accepted: 04/25/2014] [Indexed: 11/25/2022]
Abstract
A simple way to improve the accuracy of the fragmentation methods is proposed. The formalism was applied to the elongation (ELG) method at restricted open-shell Hartree-Fock (ROHF) level of theory. The α-helix conformer of polyglycine was taken as a model system. The modified ELG method includes a simplified electrostatic field resulting from point-charge distribution of the system's environment. In this way the long-distance polarization is approximately taken into account. The field attenuates during the ELG process to eventually disappear when the final structure is reached. The point-charge distributions for each ELG step are obtained from charge sensitivity analysis (CSA) in force-field atoms resolution. The presence of the intermediate field improves the accuracy of ELG calculations. The errors in total energy and its kinetic and potential contributions are reduced by at least one-order of magnitude. In addition the SCF convergence of ROHF scheme is improved.
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Affiliation(s)
- Piotr Kuźniarowicz
- Department of Molecular and Material Sciences, Interdisciplinary Graduate School of Engineering Sciences, Kyushu University, 6-1 Kasuga-Park, Fukuoka, 816-8580 Japan
| | - Kai Liu
- Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, 816-8580 Japan
| | - Yuriko Aoki
- Department of Material Sciences, Faculty of Engineering Sciences, Kyushu University, Kasuga, Fukuoka, 816-8580 Japan
| | - Feng Long Gu
- MOE Key Laboratory of Theoretical Chemistry of Environment; School of Chemistry and Environment, South China Normal University, Guangzhou, 510631 China
| | - Anna Stachowicz
- K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland
| | - Jacek Korchowiec
- K. Gumiński Department of Theoretical Chemistry, Faculty of Chemistry, Jagiellonian University, Ingardena 3, 30-060 Krakow, Poland
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García-Risueño P, Alberdi-Rodriguez J, Oliveira MJT, Andrade X, Pippig M, Muguerza J, Arruabarrena A, Rubio A. A survey of the parallel performance and accuracy of Poisson solvers for electronic structure calculations. J Comput Chem 2013; 35:427-44. [DOI: 10.1002/jcc.23487] [Citation(s) in RCA: 21] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/20/2013] [Revised: 10/13/2013] [Accepted: 10/13/2013] [Indexed: 11/06/2022]
Affiliation(s)
- Pablo García-Risueño
- Institut für Physik; Humboldt Universität zu Berlin; Zum grossen Windkanal 6 12489 Berlin Germany
- Institute for Biocomputation and Physics of Complex Systems BIFI; Universidad de Zaragoza C/ Mariano Esquillor; 50018 Zaragoza Spain
- Instituto de Química Física Rocasolano (CSIC); C/ Serrano 119 28006 Madrid Spain
| | - Joseba Alberdi-Rodriguez
- Department of Computer Architecture and Technology; University of the Basque Country UPV/EHU; M. Lardizabal, 1 20018 Donostia/San Sebastián Spain
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility; Spanish node; University of the Basque Country UPV/EHU; Edif. Joxe Mari Korta, Av. Tolosa 72 20018 Donostia/San Sebastián Spain
| | - Micael J. T. Oliveira
- Center for Computational Physics; University of Coimbra; Rua Larga 3004-516 Coimbra Portugal
| | - Xavier Andrade
- Department of Chemistry and Chemical Biology; Harvard University; 12 Oxford Street Cambridge Massachusetts 02138
| | - Michael Pippig
- Department of Mathematics; Technische Universität Chemnitz; 09107 Chemnitz Germany
| | - Javier Muguerza
- Department of Computer Architecture and Technology; University of the Basque Country UPV/EHU; M. Lardizabal, 1 20018 Donostia/San Sebastián Spain
| | - Agustin Arruabarrena
- Department of Computer Architecture and Technology; University of the Basque Country UPV/EHU; M. Lardizabal, 1 20018 Donostia/San Sebastián Spain
| | - Angel Rubio
- Nano-Bio Spectroscopy Group and European Theoretical Spectroscopy Facility; Spanish node; University of the Basque Country UPV/EHU; Edif. Joxe Mari Korta, Av. Tolosa 72 20018 Donostia/San Sebastián Spain
- Centro de Física de Materiales, CSIC-UPV/EHU-MPC and DIPC; 20018 Donostia/San Sebastián Spain
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10
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Liang W, Chapman CT, Li X. Efficient first-principles electronic dynamics. J Chem Phys 2011; 134:184102. [DOI: 10.1063/1.3589144] [Citation(s) in RCA: 54] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Rubensson EH, Rudberg E, Salek P. Methods for Hartree-Fock and Density Functional Theory Electronic Structure Calculations with Linearly Scaling Processor Time and Memory Usage. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2011. [DOI: 10.1007/978-90-481-2853-2_12] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
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12
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Density Matrix Methods in Linear Scaling Electronic Structure Theory. CHALLENGES AND ADVANCES IN COMPUTATIONAL CHEMISTRY AND PHYSICS 2011. [DOI: 10.1007/978-90-481-2853-2_16] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/30/2022]
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Rudberg E, Rubensson EH, Sałek P. Kohn−Sham Density Functional Theory Electronic Structure Calculations with Linearly Scaling Computational Time and Memory Usage. J Chem Theory Comput 2010; 7:340-50. [DOI: 10.1021/ct100611z] [Citation(s) in RCA: 82] [Impact Index Per Article: 5.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Elias Rudberg
- Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden, and PS Consulting, ul. Zaporoska 8/4, 30-389 Kraków, Poland
| | - Emanuel H. Rubensson
- Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden, and PS Consulting, ul. Zaporoska 8/4, 30-389 Kraków, Poland
| | - Paweł Sałek
- Division of Scientific Computing, Department of Information Technology, Uppsala University, Box 337, SE-751 05 Uppsala, Sweden, and PS Consulting, ul. Zaporoska 8/4, 30-389 Kraków, Poland
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Umeda H, Inadomi Y, Watanabe T, Yagi T, Ishimoto T, Ikegami T, Tadano H, Sakurai T, Nagashima U. Parallel Fock matrix construction with distributed shared memory model for the FMO-MO method. J Comput Chem 2010; 31:2381-8. [DOI: 10.1002/jcc.21531] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
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Molnar LF, He X, Wang B, Merz KM. Further analysis and comparative study of intermolecular interactions using dimers from the S22 database. J Chem Phys 2009; 131:065102. [PMID: 19691412 PMCID: PMC2738737 DOI: 10.1063/1.3173809] [Citation(s) in RCA: 70] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/19/2009] [Accepted: 06/18/2009] [Indexed: 12/25/2022] Open
Abstract
Accurate MP2 and CCSD(T) complete basis set (CBS) interaction energy curves (14 points for each curve) have been obtained for 20 of the dimers reported in the S22 set and analytical Morse curves have been fitted that can be used in developing updated density functional theory (DFT) and force field models. The magnitude and the effect of the basis set superposition error (BSSE) were carefully investigated. We found that going up to aug-cc-pVDZ and aug-cc-pVTZ basis sets is enough to obtain accurate CBS MP2 energies when BSSE corrected values are used but aug-cc-pVTZ and aug-cc-pVQZ basis sets are needed when the BSSE uncorrected total energies are used in CBS extrapolations. MP2 interaction energies with smaller basis sets such as 6-31G* are found to have very little dispersion energy and that the true source of dispersion attributed attractive interactions is almost entirely due to BSSE. MP2 and CCSD(T) CBS interaction energies are found to be very close to one another if aromatic systems are not involved. Comparative analyses have been performed with semiempirical and ab initio methods utilizing the moderate in size but affordable 6-31G* basis set both of which can be readily applied to macromolecular systems. The new M06-2X and M06-L DFT functionals were found to be more accurate than all methods tested herein. Interaction energy curves using the SG1 grid showed discontinuities for several of the dimer systems but this problem disappeared when finer DFT numerical grids were used.
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Affiliation(s)
- Laszlo Fusti Molnar
- Department of Chemistry and the Quantum Theory Project, 2328 New Physics Building, P.O. Box 118435, University of Florida, Gainesville, Florida 32611-8435, USA
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16
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Rudberg E, Rubensson EH, Sałek P. Automatic Selection of Integral Thresholds by Extrapolation in Coulomb and Exchange Matrix Constructions. J Chem Theory Comput 2008; 5:80-5. [DOI: 10.1021/ct8002145] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Elias Rudberg
- Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
| | - Emanuel H. Rubensson
- Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
| | - Paweł Sałek
- Department of Theoretical Chemistry, School of Biotechnology, Royal Institute of Technology, SE-10691 Stockholm, Sweden
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Giese TJ, York DM. Extension of adaptive tree code and fast multipole methods to high angular momentum particle charge densities. J Comput Chem 2008; 29:1895-904. [PMID: 18432622 PMCID: PMC2716046 DOI: 10.1002/jcc.20946] [Citation(s) in RCA: 15] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/06/2022]
Abstract
The development and implementation of a tree code (TC) and fast multipole method (FMM) for the efficient, linear-scaling calculation of long-range electrostatic interactions of particle distributions with variable shape and multipole character are described. The target application of these methods are stochastic boundary molecular simulations with polarizable force fields and/or combined quantum mechanical/molecular mechanical potentials. Linear-scaling is accomplished through the adaptive decomposition of the system into a hierarchy of interacting particle sets. Two methods for effecting this decomposition are evaluated: fluc-splitting and box-splitting, for which the latter is demonstrated to be generally more accurate. In addition, a generalized termination criterion is developed that delivers optimal performance at fixed error tolerance that, in the case of quadrupole-represented Drude water, effects a speed-up by a factor of 2-3 relative to a multipole-independent termination criteria. The FMM is shown to be approximately 2-3 times faster than the TC, independent of the system size and multipole order of the particles. The TC and FMM are tested for a variety of static and polarizable water systems, and for the the 70S ribosome functional complex containing an assembly of transfer and messenger RNAs.
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Affiliation(s)
- Timothy J. Giese
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA
| | - Darrin M. York
- Department of Chemistry, University of Minnesota, Minneapolis, Minnesota 55455, USA
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Rudberg E, Rubensson EH, Sałek P. Hartree–Fock calculations with linearly scaling memory usage. J Chem Phys 2008; 128:184106. [DOI: 10.1063/1.2918357] [Citation(s) in RCA: 35] [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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Bondesson L, Rudberg E, Luo Y, Sałek P. Basis set dependence of solute-solvent interaction energy of benzene in water: A HF/DFT study. J Comput Chem 2008; 29:1725-32. [DOI: 10.1002/jcc.20930] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/08/2022]
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Rubensson EH, Rudberg E, Sałek P. Density matrix purification with rigorous error control. J Chem Phys 2008; 128:074106. [DOI: 10.1063/1.2826343] [Citation(s) in RCA: 37] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Bondesson L, Rudberg E, Luo Y, Sałek P. A Linear Scaling Study of Solvent−Solute Interaction Energy of Drug Molecules in Aqua Solution. J Phys Chem B 2007; 111:10320-8. [PMID: 17676891 DOI: 10.1021/jp072621l] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Abstract
Solvent-solute interaction energies for three well-known drug molecules in water solution are computed at the Hartree-Fock and B3LYP density functional theory levels using a linear scaling technique, which allows one to explicitly include in the model water molecules up to 14 A away from the solute molecule. The dependence of calculated interaction energies on the amount of included solvent has been examined. It is found that it is necessary to account for water molecules within an 8 A radius around the drug molecule to reach the saturated solvent interaction level. Effects of electron correlation and basis set on solvent-solute interaction energies are discussed.
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Affiliation(s)
- Laban Bondesson
- Department of Theoretical Chemistry, Royal Institute of Technology, SE-10691 Stockholm, Sweden
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