1
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Csóka J, Kállay M. Analytic gradients for local density fitting Hartree-Fock and Kohn-Sham methods. J Chem Phys 2023; 158:024110. [PMID: 36641408 DOI: 10.1063/5.0131683] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022] Open
Abstract
We present analytic gradients for local density fitting Hartree-Fock (HF) and hybrid Kohn-Sham (KS) density functional methods. Due to the non-variational nature of the local fitting algorithm, the method of Lagrange multipliers is used to avoid the solution of the coupled perturbed HF and KS equations. We propose efficient algorithms for the solution of the arising Z-vector equations and the gradient calculation that preserve the third-order scaling and low memory requirement of the original local fitting algorithm. In order to demonstrate the speed and accuracy of our implementation, gradient calculations and geometry optimizations are presented for various molecular systems. Our results show that significant speedups can be achieved compared to conventional density fitting calculations without sacrificing accuracy.
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Affiliation(s)
- József Csóka
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Faculty of Chemical Technology and Biotechnology, Budapest University of Technology and Economics, Műegyetem rkp. 3., H-1111 Budapest, Hungary
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2
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Csóka J, Kállay M. Speeding up Hartree-Fock and Kohn-Sham calculations with first-order corrections. J Chem Phys 2021; 154:164114. [PMID: 33940810 DOI: 10.1063/5.0041276] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
Several approaches are presented to improve the efficiency of Hartree-Fock and Kohn-Sham self-consistent field (SCF) calculations relying on a simple first-order energy correction reminiscent of the scheme used in dual-basis SCF methods. The basic idea is to perform an initial SCF calculation computing approximate Fock-matrices and, in the final iteration step, to use a more complete Fock-matrix builder together with the energy correction to diminish the error. The approximation is tested for conventional and local density fitting (DF) SCF approaches combining various auxiliary basis sets, fitting metrics, and Fock-matrix construction algorithms in the initial and final iterations as well as for seminumerical SCF methods combining integration grids of different qualities. We also report the implementation of the occupied orbital resolution of identity exchange construction algorithm with local DF approximations. Benchmark calculations are presented for total energies, reaction energies, and molecular geometries. Our results show that speedups of up to 80% can be expected utilizing the new approaches without significant loss of accuracy.
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Affiliation(s)
- József Csóka
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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3
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Veccham SP, Lee J, Mao Y, Horn PR, Head-Gordon M. A non-perturbative pairwise-additive analysis of charge transfer contributions to intermolecular interaction energies. Phys Chem Chem Phys 2021; 23:928-943. [DOI: 10.1039/d0cp05852a] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A non-perturbative scheme for complete decomposition of energy and charge associated with charge transfer interaction into pairwise additive components.
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Affiliation(s)
| | - Joonho Lee
- Department of Chemistry
- University of California
- Berkeley
- USA
- Chemical Sciences Division
| | - Yuezhi Mao
- Department of Chemistry
- University of California
- Berkeley
- USA
- Chemical Sciences Division
| | - Paul R. Horn
- Department of Chemistry
- University of California
- Berkeley
- USA
- Chemical Sciences Division
| | - Martin Head-Gordon
- Department of Chemistry
- University of California
- Berkeley
- USA
- Chemical Sciences Division
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4
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Lüder J, Manzhos S. Nonparametric Local Pseudopotentials with Machine Learning: A Tin Pseudopotential Built Using Gaussian Process Regression. J Phys Chem A 2020; 124:11111-11124. [DOI: 10.1021/acs.jpca.0c05723] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Johann Lüder
- Department of Materials and Optoelectronic Science, National Sun Yat-sen University, 80424, No. 70, Lien-Hai Road, Kaohsiung, Taiwan, R.O.C
- Center for Crystal Research, National Sun Yat-sen University, 70 Lien-Hai Road, Kaohsiung 80424, Taiwan, R.O.C
| | - Sergei Manzhos
- Centre Énergie Matériaux Télécommunications, Institut National de la Recherche Scientifique, 1650 boulevard Lionel-Boulet, Varennes QC J3X1S2, Canada
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5
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Otero-de-la-Roza A, DiLabio GA. Improved Basis-Set Incompleteness Potentials for Accurate Density-Functional Theory Calculations in Large Systems. J Chem Theory Comput 2020; 16:4176-4191. [PMID: 32470304 DOI: 10.1021/acs.jctc.0c00102] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The accurate calculation of chemical properties using density-functional theory (DFT) requires the use of a nearly complete basis set. In chemical systems involving hundreds to thousands of atoms, the cost of the calculations place practical limitations on the number of basis functions that can be used. Therefore, in most practical applications of DFT to large systems, there exists a basis-set incompleteness error (BSIE). In this article, we present the next iteration of the basis-set incompleteness potentials (BSIPs), one-electron potentials designed to correct for basis-set incompleteness error. The ultimate goal associated with the development of BSIPs is to allow the calculation of molecular properties using DFT with near-complete-basis-set results at a computational cost that is similar to a small basis set calculation. In this work, we develop BSIPs for 10 atoms in the first and second rows (H, B-F, Si-Cl) and 15 common basis sets of the Pople, Dunning, Karlsruhe, and Huzinaga types. Our new BSIPs are constructed to minimize BSIE in the calculation of reaction energies, barrier heights, noncovalent binding energies, and intermolecular distances. The BSIPs were obtained using a training set of 15 944 data points. The fitting approach employed a regularized linear least-squares method with variable selection (the LASSO method), which results in a much better fit to the training data than our previous BSIPs while, at the same time, reducing the computational cost of BSIP development. The proposed BSIPs are tested on various benchmark sets and demonstrate excellent performance in practice. Our new BSIPs are also transferable; i.e., they can be used to correct BSIE in calculations that employ density functionals other than the one used in the BSIP development (B3LYP). Finally, BSIPs can be used in any quantum chemistry program that have implemented effective-core potentials without changes to the software.
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Affiliation(s)
- A Otero-de-la-Roza
- Departamento de Quı́mica Fı́sica y Analítica and MALTA-Consolider Team, Facultad de Quı́mica, Universidad de Oviedo, 33006 Oviedo, Spain
| | - Gino A DiLabio
- Department of Chemistry, University of British Columbia, Okanagan, 3247 University Way, Kelowna, British Columbia V1V 1V7, Canada.,Faculty of Management, University of British Columbia, Okanagan, 1137 Alumni Avenue, Kelowna, British Columbia V1V 1V7, Canada
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6
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Claudino D, Mayhall NJ. Simple and Efficient Truncation of Virtual Spaces in Embedded Wave Functions via Concentric Localization. J Chem Theory Comput 2019; 15:6085-6096. [DOI: 10.1021/acs.jctc.9b00682] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Affiliation(s)
- Daniel Claudino
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
| | - Nicholas J. Mayhall
- Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24060, United States
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7
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Kearns FL, Warrensford L, Boresch S, Woodcock HL. The Good, the Bad, and the Ugly: "HiPen", a New Dataset for Validating (S)QM/MM Free Energy Simulations. Molecules 2019; 24:E681. [PMID: 30769826 PMCID: PMC6413162 DOI: 10.3390/molecules24040681] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2018] [Revised: 01/28/2019] [Accepted: 01/29/2019] [Indexed: 11/25/2022] Open
Abstract
Indirect (S)QM/MM free energy simulations (FES) are vital to efficiently incorporating sufficient sampling and accurate (QM) energetic evaluations when estimating free energies of practical/experimental interest. Connecting between levels of theory, i.e., calculating Δ A l o w → h i g h , remains to be the most challenging step within an indirect FES protocol. To improve calculations of Δ A l o w → h i g h , we must: (1) compare the performance of all FES methods currently available; and (2) compile and maintain datasets of Δ A l o w → h i g h calculated for a wide-variety of molecules so that future practitioners may replicate or improve upon the current state-of-the-art. Towards these two aims, we introduce a new dataset, "HiPen", which tabulates Δ A g a s M M → 3 o b (the free energy associated with switching from an M M to an S C C - D F T B molecular description using the 3ob parameter set in gas phase), calculated for 22 drug-like small molecules. We compare the calculation of this value using free energy perturbation, Bennett's acceptance ratio, Jarzynski's equation, and Crooks' equation. We also predict the reliability of each calculated Δ A g a s M M → 3 o b by evaluating several convergence criteria including sample size hysteresis, overlap statistics, and bias metric ( Π ). Within the total dataset, three distinct categories of molecules emerge: the "good" molecules, for which we can obtain converged Δ A g a s M M → 3 o b using Jarzynski's equation; "bad" molecules which require Crooks' equation to obtain a converged Δ A g a s M M → 3 o b ; and "ugly" molecules for which we cannot obtain reliably converged Δ A g a s M M → 3 o b with either Jarzynski's or Crooks' equations. We discuss, in depth, results from several example molecules in each of these categories and describe how dihedral discrepancies between levels of theory cause convergence failures even for these gas phase free energy simulations.
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Affiliation(s)
- Fiona L Kearns
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
| | - Luke Warrensford
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
| | - Stefan Boresch
- Department of Computational Biological Chemistry, Faculty of Chemistry, University of Vienna, Waehringerstrasse 17, A-1090 Vienna, Austria.
| | - H Lee Woodcock
- Department of Chemistry, University of South Florida, 4202 E. Fowler Avenue, Tampa, FL 33620, USA.
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8
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Nikšić-Franjić I, Ljubić I. Comparing the performances of various density functionals for modelling the mechanisms and kinetics of bimolecular free radical reactions in aqueous solution. Phys Chem Chem Phys 2019; 21:23425-23440. [DOI: 10.1039/c9cp04688g] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
We systematically tested the performances of 18 density functionals for the mechanisms and kinetics of reactions of the α-hydroxyisopropyl radical with 9 organic substrates.
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Affiliation(s)
| | - Ivan Ljubić
- Department of Physical Chemistry
- Ruđer Bošković Institute
- Zagreb
- Croatia
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9
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Schütt O, VandeVondele J. Machine Learning Adaptive Basis Sets for Efficient Large Scale Density Functional Theory Simulation. J Chem Theory Comput 2018; 14:4168-4175. [PMID: 29957943 PMCID: PMC6096449 DOI: 10.1021/acs.jctc.8b00378] [Citation(s) in RCA: 26] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
It is chemically intuitive that an optimal atom centered basis set must adapt to its atomic environment, for example by polarizing toward nearby atoms. Adaptive basis sets of small size can be significantly more accurate than traditional atom centered basis sets of the same size. The small size and well conditioned nature of these basis sets leads to large saving in computational cost, in particular in a linear scaling framework. Here, it is shown that machine learning can be used to predict such adaptive basis sets using local geometrical information only. As a result, various properties of standard DFT calculations can be easily obtained at much lower costs, including nuclear gradients. In our approach, a rotationally invariant parametrization of the basis is obtained by employing a potential anchored on neighboring atoms to ultimately construct a rotation matrix that turns a traditional atom centered basis set into a suitable adaptive basis set. The method is demonstrated using MD simulations of liquid water, where it is shown that minimal basis sets yield structural properties in fair agreement with basis set converged results, while reducing the computational cost in the best case by a factor of 200 and the required flops by 4 orders of magnitude. Already a very small training set yields satisfactory results as the variational nature of the method provides robustness.
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Affiliation(s)
- Ole Schütt
- Department of Materials , ETH Zürich , 8093 Zürich , Switzerland
| | - Joost VandeVondele
- Department of Materials , ETH Zürich , 8093 Zürich , Switzerland.,Swiss National Supercomputing Centre (CSCS) , 6900 Lugano , Switzerland
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10
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Hégely B, Nagy PR, Kállay M. Dual Basis Set Approach for Density Functional and Wave Function Embedding Schemes. J Chem Theory Comput 2018; 14:4600-4615. [DOI: 10.1021/acs.jctc.8b00350] [Citation(s) in RCA: 25] [Impact Index Per Article: 4.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/03/2023]
Affiliation(s)
- Bence Hégely
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Péter R. Nagy
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
| | - Mihály Kállay
- MTA-BME Lendület Quantum Chemistry Research Group, Department of Physical Chemistry and Materials Science, Budapest University of Technology and Economics, P.O. Box 91, H-1521 Budapest, Hungary
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11
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Albaugh A, Boateng HA, Bradshaw RT, Demerdash ON, Dziedzic J, Mao Y, Margul DT, Swails J, Zeng Q, Case DA, Eastman P, Wang LP, Essex JW, Head-Gordon M, Pande VS, Ponder JW, Shao Y, Skylaris CK, Todorov IT, Tuckerman ME, Head-Gordon T. Advanced Potential Energy Surfaces for Molecular Simulation. J Phys Chem B 2018; 120:9811-32. [PMID: 27513316 DOI: 10.1021/acs.jpcb.6b06414] [Citation(s) in RCA: 66] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/29/2023]
Abstract
Advanced potential energy surfaces are defined as theoretical models that explicitly include many-body effects that transcend the standard fixed-charge, pairwise-additive paradigm typically used in molecular simulation. However, several factors relating to their software implementation have precluded their widespread use in condensed-phase simulations: the computational cost of the theoretical models, a paucity of approximate models and algorithmic improvements that can ameliorate their cost, underdeveloped interfaces and limited dissemination in computational code bases that are widely used in the computational chemistry community, and software implementations that have not kept pace with modern high-performance computing (HPC) architectures, such as multicore CPUs and modern graphics processing units (GPUs). In this Feature Article we review recent progress made in these areas, including well-defined polarization approximations and new multipole electrostatic formulations, novel methods for solving the mutual polarization equations and increasing the MD time step, combining linear-scaling electronic structure methods with new QM/MM methods that account for mutual polarization between the two regions, and the greatly improved software deployment of these models and methods onto GPU and CPU hardware platforms. We have now approached an era where multipole-based polarizable force fields can be routinely used to obtain computational results comparable to state-of-the-art density functional theory while reaching sampling statistics that are acceptable when compared to that obtained from simpler fixed partial charge force fields.
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Affiliation(s)
| | - Henry A Boateng
- Department of Mathematics, Bates College , 2 Andrews Road, Lewiston, Maine 04240, United States
| | - Richard T Bradshaw
- School of Chemistry, University of Southampton , Highfield, Southampton SO17 1BJ, United Kingdom
| | | | - Jacek Dziedzic
- School of Chemistry, University of Southampton , Highfield, Southampton SO17 1BJ, United Kingdom.,Faculty of Applied Physics and Mathematics, Gdansk University of Technology , 80-223 Gdansk, Poland
| | | | | | - Jason Swails
- Department of Chemistry and Chemical Biology, Rutgers University , Piscataway, New Jersey 08854-8066, United States
| | - Qiao Zeng
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health , Bethesda, Maryland 20892, United States
| | - David A Case
- Department of Chemistry and Chemical Biology, Rutgers University , Piscataway, New Jersey 08854-8066, United States
| | - Peter Eastman
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Lee-Ping Wang
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Jonathan W Essex
- School of Chemistry, University of Southampton , Highfield, Southampton SO17 1BJ, United Kingdom
| | | | - Vijay S Pande
- Department of Chemistry, Stanford University , Stanford, California 94305, United States
| | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis , St. Louis, Missouri 63130, United States
| | - Yihan Shao
- Q-Chem Inc. , 6601 Owens Drive, Suite 105, Pleasanton, California 94588, United States
| | - Chris-Kriton Skylaris
- School of Chemistry, University of Southampton , Highfield, Southampton SO17 1BJ, United Kingdom
| | - Ilian T Todorov
- STFC Daresbury Laboratory , Keckwick Lane, Daresbury, Warrington WA4 4AD, United Kingdom
| | - Mark E Tuckerman
- NYU-ECNU, Center for Computational Chemistry at NYU, Shanghai , Shanghai 200062, China
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12
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Otero-de-la-Roza A, DiLabio GA. Transferable Atom-Centered Potentials for the Correction of Basis Set Incompleteness Errors in Density-Functional Theory. J Chem Theory Comput 2017. [DOI: 10.1021/acs.jctc.7b00300] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- A. Otero-de-la-Roza
- Department
of Chemistry and ‡Faculty of Management, University of British Columbia, Okanagan, 3247
University Way, Kelowna, British Columbia, Canada V1V 1V7
| | - Gino A. DiLabio
- Department
of Chemistry and ‡Faculty of Management, University of British Columbia, Okanagan, 3247
University Way, Kelowna, British Columbia, Canada V1V 1V7
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13
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Witte J, Neaton JB, Head-Gordon M. Effective empirical corrections for basis set superposition error in the def2-SVPD basis: gCP and DFT-C. J Chem Phys 2017. [DOI: 10.1063/1.4986962] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/27/2023] Open
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