1
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Yu J, Su NQ, Yang W. Describing Chemical Reactivity with Frontier Molecular Orbitalets. JACS AU 2022; 2:1383-1394. [PMID: 35783161 PMCID: PMC9241161 DOI: 10.1021/jacsau.2c00085] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 02/11/2022] [Revised: 04/07/2022] [Accepted: 04/19/2022] [Indexed: 06/15/2023]
Abstract
Locality in physical space is critical in understanding chemical reactivity in the analysis of various phenomena and processes in chemistry, biology, and materials science, as exemplified in the concepts of reactive functional groups and active sites. Frontier molecular orbitals (FMOs) pinpoint the locality of chemical bonds that are chemically reactive because of the associated orbital energies and thus have achieved great success in describing chemical reactivity, mainly for small systems. For large systems, however, the delocalization nature of canonical molecular orbitals makes it difficult for FMOs to highlight the locality of the chemical reactivity. To obtain localized molecular orbitals that also reflect the frontier nature of the chemical processes, we develop the concept of frontier molecular orbitalets (FMOLs) for describing the reactivity of large systems. The concept of orbitalets was developed recently in the localized orbital scaling correction method, which aims for eliminating the delocalization error in common density functional approximations. Orbitalets are localized in both physical and energy spaces and thus contain both orbital locality and energy information. The FMOLs are thus the orbitalets with energies highest among occupied orbitalets and lowest among unoccupied ones. The applications of FMOLs to hexadeca-1,3,5,7,9,11,13,15-octaene in its equilibrium geometry, inter- and intra-molecular charge-transfer systems, and two transition states of a bifurcating reaction demonstrate that FMOLs can connect quantum mechanical treatments of chemical systems and chemical reactivities by locating the reactive region of large chemical systems. Therefore, FMOLs extend the role of FMOs for small systems and describe the chemical reactivity of large systems with energy and locality insight, with potentially broad applications.
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Affiliation(s)
- Jincheng Yu
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Taishan
College, Shandong University, Jinan 250100, China
| | - Neil Qiang Su
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department
of Chemistry, Key Laboratory of Advanced Energy Materials Chemistry
(Ministry of Education) and Renewable Energy Conversion and Storage
Center (RECAST), Nankai University, Tianjin 300071, China
| | - Weitao Yang
- Department
of Chemistry, Duke University, Durham, North Carolina 27708, United States
- Department
of Physics, Duke University, Durham, North Carolina 27708, United States
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2
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Peng L, Peng D, Gu FL, Yang W. Regularized Localized Molecular Orbitals in a Divide-and-Conquer Approach for Linear Scaling Calculations. J Chem Theory Comput 2022; 18:2975-2982. [PMID: 35416665 PMCID: PMC9972215 DOI: 10.1021/acs.jctc.2c00142] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
Non-orthogonal localized molecular orbitals (NOLMOs) have been employed as building blocks for the divide-and-conquer (DC) linear scaling method. The NOLMOs are calculated from subsystems and used for constructing the density matrix (DM) of the entire system, instead of the subsystem DM in the original DC approach. Also, unlike the original DC method, the inverse electronic temperature parameter β is not needed anymore. Furthermore, a new regularized localization approach for NOLMOs has been developed, in which the localization cost function is a sum of the spatial spread function, as in the Boys method, and the kinetic energy, as a regularization measure to limit the oscillation of the NOLMOs. The optimal weight of the kinetic energy can be determined by optimization with analytical gradients. The resulting regularized NOLMOs have enhanced smoothness and better transferability because of reduced kinetic energies. Compared with the original DC, while NOLMO-DC has a similar computational linear scaling cost, the accuracy of NOLMO-DC is better by several orders of magnitude for large conjugated systems and by about 1 order of magnitude for other systems. The NOLMO-DC method is thus a promising development of the DC approach for linear scaling calculations.
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Affiliation(s)
- Liang Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Daoling Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Feng Long Gu
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education; School of Environment, South China Normal University, Guangzhou 510006, People’s Republic of China
| | - Weitao Yang
- Department of Chemistry, Duke University, Durham, North Carolina 27708-0346, United States
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3
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Luo Z, Khaliullin RZ. Variable-Metric Localization of Occupied and Virtual Orbitals. J Chem Theory Comput 2021; 17:5568-5581. [PMID: 34370474 DOI: 10.1021/acs.jctc.1c00379] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The key idea of the variable-metric approach to orbital localization is to allow nonorthogonality between orbitals while, at the same time, preventing them from becoming linearly dependent. The variable-metric localization has been shown to improve the locality of occupied nonorthogonal orbitals relative to their orthogonal counterparts. In this work, numerous localization algorithms are designed and tested to exploit the conceptual simplicity of the variable-metric approach with the goal of creating a straightforward and reliable localization procedure for virtual orbitals. The implemented algorithms include the steepest descent, conjugate gradient (CG), limited-memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS), and hybrid procedures as well as trust-region (TR) methods based on the CG and Cauchy-point subproblem solvers. Comparative analysis shows that the CG-based TR algorithm is the best overall method to obtain nonorthogonal localized molecular orbitals (NLMOs), occupied or virtual. The L-BFGS and CG algorithms can also be used to obtain NLMOs reliably but often at higher computational cost. Extensive tests demonstrate that the implemented methods allow us to obtain well-localized Boys-Foster (i.e., maximally localized Wannier functions) and Pipek-Mezey, orthogonal and nonorthogonal, and occupied and virtual orbitals for a variety of gas-phase molecules and periodic materials. The tests also show that virtual NLMOs, which have not been described before, are, on average, 13% (Boys-Foster) and 18% (Pipek-Mezey) more localized than their orthogonal counterparts.
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Affiliation(s)
- Ziling Luo
- Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal QC H3A 0B8, Canada
| | - Rustam Z Khaliullin
- Department of Chemistry, McGill University, 801 Sherbrooke St. West, Montreal QC H3A 0B8, Canada
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4
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Luo Z, Khaliullin RZ. Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals. J Chem Theory Comput 2020; 16:3558-3566. [PMID: 32320232 DOI: 10.1021/acs.jctc.9b01286] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Spatially localized one-electron orbitals, orthogonal and non-orthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the existing localization methods either constrain orbital transformations to be unitary, that is, metric preserving, or, in the case of variable-metric methods, fix the centers of non-orthogonal localized orbitals. Here, we developed a different approach to orbital localization, in which these constraints are replaced with a single restriction that specifies the maximum allowed deviation from the orthogonality for the final set of localized orbitals. This reformulation, which can be viewed as a generalization of existing localization methods, enables one to choose the desired balance between the orthogonality and locality of the orbitals. Furthermore, the approach is conceptually and practically simple as it obviates the necessity in unitary transformations and allows one to determine optimal positions of the centers of non-orthogonal orbitals in an unconstrained and straightforward minimization procedure. It is demonstrated to produce well-localized orthogonal and non-orthogonal orbitals with the Berghold and Pipek--Mezey localization functions for a variety of molecules and periodic materials including large systems with nontrivial bonding.
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Affiliation(s)
- Ziling Luo
- Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec QC H3A 0B8, Canada
| | - Rustam Z Khaliullin
- Department of Chemistry, McGill University, 801 Sherbrooke Street West, Montreal, Quebec QC H3A 0B8, Canada
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5
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A local perspective on the conjugation of double bonds in acyclic polyenes. MONATSHEFTE FUR CHEMIE 2020. [DOI: 10.1007/s00706-020-02626-1] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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6
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Hansen AS, Baardsen G, Rebolini E, Maschio L, Pedersen TB. Representation of the virtual space in extended systems – a correlation energy convergence study. Mol Phys 2020. [DOI: 10.1080/00268976.2020.1733118] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
Affiliation(s)
- A. S. Hansen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - G. Baardsen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
| | - E. Rebolini
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
- Institut Laue Langevin, Grenoble, France
| | - L. Maschio
- Dipartimento di Chimica, Universitá di Torino, Torino, Italy
| | - T. B. Pedersen
- Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, Oslo, Norway
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7
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Zhu T, de Silva P, Van Voorhis T. Self-Attractive Hartree Decomposition: Partitioning Electron Density into Smooth Localized Fragments. J Chem Theory Comput 2017; 14:92-103. [DOI: 10.1021/acs.jctc.7b00931] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Tianyu Zhu
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Piotr de Silva
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
| | - Troy Van Voorhis
- Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139, United States
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8
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Li H, Liu W, Suo B. Localization of open-shell molecular orbitals via least change from fragments to molecule. J Chem Phys 2017; 146:104104. [DOI: 10.1063/1.4977929] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Hongyang Li
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Bingbing Suo
- Institute of Modern Physics, Northwest University, Xi’an 710069, People’s Republic of China
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9
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Høyvik IM, Olsen J, Jørgensen P. Generalising localisation schemes of orthogonal orbitals to the localisation of non-orthogonal orbitals. Mol Phys 2016. [DOI: 10.1080/00268976.2016.1173733] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Ida-Marie Høyvik
- Department of Chemistry, The Norwegian University of Science and Technology, Trondheim, Norway
| | - Jeppe Olsen
- Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Aarhus, Denmark
| | - Poul Jørgensen
- Department of Chemistry, qLEAP Center for Theoretical Chemistry, Aarhus University, Aarhus, Denmark
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10
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Høyvik IM, Jørgensen P. Characterization and Generation of Local Occupied and Virtual Hartree–Fock Orbitals. Chem Rev 2016; 116:3306-27. [DOI: 10.1021/acs.chemrev.5b00492] [Citation(s) in RCA: 37] [Impact Index Per Article: 4.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Ida-Marie Høyvik
- Department
of Chemistry, The Norwegian University of Science and Technology, Høgskoleringen 5, 7491 Trondheim, Norway
| | - Poul Jørgensen
- qLEAP
Center for Theoretical Chemistry, Department of Chemistry, Aarhus University, Langelandsgade 140, 8000 Aarhus C, Denmark
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11
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Zhang C, Li S. An efficient localization procedure for large systems using a sequential transformation strategy. J Chem Phys 2014; 141:244106. [DOI: 10.1063/1.4904292] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Chenyang Zhang
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People’s Republic of China
| | - Shuhua Li
- Key Laboratory of Mesoscopic Chemistry of Ministry of Education, School of Chemistry and Chemical Engineering, Institute of Theoretical and Computational Chemistry, Nanjing University, Nanjing 210093, People’s Republic of China
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12
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Li Z, Li H, Suo B, Liu W. Localization of molecular orbitals: from fragments to molecule. Acc Chem Res 2014; 47:2758-67. [PMID: 25019464 DOI: 10.1021/ar500082t] [Citation(s) in RCA: 33] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Conspectus Localized molecular orbitals (LMO) not only serve as an important bridge between chemical intuition and molecular wave functions but also can be employed to reduce the computational cost of many-body methods for electron correlation and excitation. Therefore, how to localize the usually completely delocalized canonical molecular orbitals (CMO) into confined physical spaces has long been an important topic: It has a long history but still remains active to date. While the known LMOs can be classified into (exact) orthonormal and nonorthogonal, as well as (approximate) absolutely localized MOs, the ways for achieving these can be classified into two categories, a posteriori top-down and a priori bottom-up, depending on whether they invoke the global CMOs (or equivalently the molecular density matrix). While the top-down approaches have to face heavy tasks of minimizing or maximizing a given localization functional typically of many adjacent local extrema, the bottom-up ones have to invoke some tedious procedures for first generating a local basis composed of well-defined occupied and unoccupied subsets and then maintaining or resuming the locality when solving the Hartree-Fock/Kohn-Sham (HF/KS) optimization condition. It is shown here that the good of these kinds of approaches can be combined together to form a very efficient hybrid approach that can generate the desired LMOs for any kind of gapped molecules. Specifically, a top-down localization functional, applied to individual small subsystems only, is minimized to generate an orthonormal local basis composed of functions centered on the preset chemical fragments. The familiar notion for atomic cores, lone pairs, and chemical bonds emerges here automatically. Such a local basis is then employed in the global HF/KS calculation, after which a least action is taken toward the final orthonormal localized molecular orbitals (LMO), both occupied and virtual. This last step is very cheap, implying that, after the CMOs, the LMOs can be obtained essentially for free. Because molecular fragments are taken as the basic elements, the approach is in the spirit of "from fragments to molecule". Two representatives of highly conjugated molecules, that is, C12H2 and C60, are taken as showcases for demonstrating the success of the proposed approach. The use of the so-obtained LMOs will lead naturally to low-order scaling post-HF/KS methods for electron correlation or excitation. In addition, the underlying fragment picture allows for easy and pictorial interpretations of the correlation/excitation dynamics.
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Affiliation(s)
- Zhendong Li
- Beijing
National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Hongyang Li
- Beijing
National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Bingbing Suo
- Beijing
National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
| | - Wenjian Liu
- Beijing
National Laboratory
for Molecular Sciences, Institute of Theoretical and Computational
Chemistry, State Key Laboratory of Rare Earth Materials Chemistry
and Applications, College of Chemistry and Molecular Engineering,
and Center for Computational Science and Engineering, Peking University, Beijing 100871, People’s Republic of China
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13
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Peng L, Gu FL, Yang W. Effective preconditioning for ab initio ground state energy minimization with non-orthogonal localized molecular orbitals. Phys Chem Chem Phys 2014; 15:15518-27. [PMID: 23943010 DOI: 10.1039/c3cp52989d] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
The non-orthogonal localized molecular orbital (NOLMO) is the most localized representation of electronic degrees of freedom. As such, NOLMOs are thus potentially the most efficient for linear-scaling calculations of electronic structures for large systems. However, direct ab initio calculations with NOLMO have not been fully implemented and widely used, partly because of the slow convergence issue in the optimization of NOLMO. Towards realizing the potential of NOLMO for large systems, we applied an energy minimum variational principle for carrying out ab initio self-consistent-field (SCF) calculations with NOLMOs. We developed an effective preconditioning approach using the diagonal part of the second order derivatives and show that the convergence of the energy optimization is significantly improved. The speed of convergence of the energy and density are comparable with that of the conventional SCF approach, thus paving the way for the optimization of NOLMO in linear scaling calculations for large systems.
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Affiliation(s)
- Liang Peng
- Key Laboratory of Theoretical Chemistry of Environment, Ministry of Education, School of Chemistry and Environment, South China Normal University, Guangzhou 510006, China.
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14
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Lehtola S, Jónsson H. Unitary Optimization of Localized Molecular Orbitals. J Chem Theory Comput 2013; 9:5365-72. [DOI: 10.1021/ct400793q] [Citation(s) in RCA: 58] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Susi Lehtola
- COMP Centre of Excellence, Department of
Applied Physics, School of Science, Aalto University, P.O.
Box 11000, FI-00076 Aalto, Espoo, Finland
| | - Hannes Jónsson
- COMP Centre of Excellence, Department of
Applied Physics, School of Science, Aalto University, P.O.
Box 11000, FI-00076 Aalto, Espoo, Finland
- Faculty of Physical Sciences, University of Iceland, 101 Reykjavík, Iceland
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15
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Bowler DR, Miyazaki T. O(N) methods in electronic structure calculations. REPORTS ON PROGRESS IN PHYSICS. PHYSICAL SOCIETY (GREAT BRITAIN) 2012; 75:036503. [PMID: 22790422 DOI: 10.1088/0034-4885/75/3/036503] [Citation(s) in RCA: 210] [Impact Index Per Article: 17.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/21/2023]
Abstract
Linear-scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical properties of systems to be modelled, along with a survey of recent developments in real-space methods which are important for efficient use of high-performance computers. The linear-scaling methods proposed to date can be divided into seven different areas, and the applicability, efficiency and advantages of the methods proposed in these areas are then discussed. The applications of linear-scaling methods, as well as the implementations available as computer programs, are considered. Finally, the prospects for and the challenges facing linear-scaling methods are discussed.
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Affiliation(s)
- D R Bowler
- London Centre for Nanotechnology, UCL, 17-19 Gordon St, London WC1H 0AH, UK.
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16
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Affiliation(s)
- Brian M. Austin
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - Dmitry Yu. Zubarev
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
| | - William A. Lester
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
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17
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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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18
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Cui G, Fang W, Yang W. Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals. Phys Chem Chem Phys 2010; 12:416-21. [DOI: 10.1039/b916688b] [Citation(s) in RCA: 25] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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19
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Gygi F. Compact representations of Kohn-Sham invariant subspaces. PHYSICAL REVIEW LETTERS 2009; 102:166406. [PMID: 19518735 DOI: 10.1103/physrevlett.102.166406] [Citation(s) in RCA: 22] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/02/2008] [Indexed: 05/27/2023]
Abstract
We present a method to compute a hierarchical approximate representation of the solutions of the Kohn-Sham equations. The method is based on a recursive bisection algorithm and yields one-particle wave functions localized on subdomains of varying sizes. The accuracy of the representation is set a priori by specifying the highest acceptable error in 2-norm for any solution. Applications to large systems are used to illustrate the achievable reduction in data size. Implications for the development of linear-scaling methods and for the acceleration of conventional iterative methods are discussed.
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Affiliation(s)
- François Gygi
- Department of Applied Science, University of California Davis, Davis, California 95616, USA
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20
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Ferenczy GG, Adams WH. Optimization of selected molecular orbitals in group basis sets. J Chem Phys 2009; 130:134108. [DOI: 10.1063/1.3096690] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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21
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Hollett JW, Poirier RA. SEST: Simulated Electronic Structure Theory. J Chem Theory Comput 2009; 5:126-35. [PMID: 26609826 DOI: 10.1021/ct800433r] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A novel approach to empirically modeling the electronic structure of molecules is introduced. The theory is based on relationships between molecular orbital energy components and the average distance between electrons and electrons and nuclei. The electron-electron and electron-nucleus distances are subsequently related to interatomic distances which provides a means for modeling the electronic structure of molecules. The general energy expression for a simulated electronic structure theory is defined, along with the functional form of the interatomic distance dependent energy functions. The theory is used to model the hydrogen molecule, the first-row hydrides, and ethane. The models, which have the correct RHF/6-31G(d) optimized geometries, also fit the RHF/6-31G(d) energy at equilibrium and the UHF/6-31G(d) energy at the bond dissociation limit as well as some vibrational frequencies.
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Affiliation(s)
- Joshua W Hollett
- Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland A1B 3X7, Canada
| | - Raymond A Poirier
- Department of Chemistry, Memorial University of Newfoundland, St. John's, Newfoundland A1B 3X7, Canada
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22
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Jansík B, Høst S, Johansson MP, Olsen J, Jørgensen P, Helgaker T. A stepwise atomic, valence-molecular, and full-molecular optimisation of the Hartree–Fock/Kohn–Sham energy. Phys Chem Chem Phys 2009; 11:5805-13. [DOI: 10.1039/b901987a] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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23
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Burger SK, Yang W. Linear-scaling quantum calculations using non-orthogonal localized molecular orbitals. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2008; 20:294209. [PMID: 25076813 PMCID: PMC4112540 DOI: 10.1088/0953-8984/20/29/294209] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/05/2023]
Abstract
An absolute energy minimum variational principle is used for carrying out linear scaling calculations with non-orthogonal localized orbitals. Compared with results based on orthogonal localized molecular orbitals, the method is shown to give significantly more accurate results when the localized molecular orbitals are allowed to be non-orthogonal. This is made possible by introducing a second minimization for approximating the inverse overlap matrix. We also show how an exact line search may be used efficiently with the conjugate gradient method for minimizing the energy functional.
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Affiliation(s)
- Steven K Burger
- Department of Chemistry, McMaster University, 1280 Main St. West, Hamilton, ON, Canada
| | - Weitao Yang
- Department of Chemistry, Duke University, Box 90346, Durham, NC 27708-0346, USA
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24
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Weber V, Hutter J. A smooth ℓ1-norm sparseness function for orbital based linear scaling total energy minimization. J Chem Phys 2008; 128:064107. [DOI: 10.1063/1.2828507] [Citation(s) in RCA: 13] [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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25
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Lee HS, Tuckerman ME. Ab initio molecular dynamics with discrete variable representation basis sets: techniques and application to liquid water. J Phys Chem A 2007; 110:5549-60. [PMID: 16623489 DOI: 10.1021/jp0570770] [Citation(s) in RCA: 40] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Finite temperature ab initio molecular dynamics (AIMD), in which forces are obtained from "on-the-fly" electronic structure calculations, is a widely used technique for studying structural and dynamical properties of chemically active systems. Recently, we introduced an AIMD scheme based on discrete variable representation (DVR) basis sets, which was shown to have improved convergence properties over the conventional plane wave (PW) basis set [Liu,Y.; et al. Phys. Rev. B 2003, 68, 125110]. In the present work, the numerical algorithms for the DVR based AIMD scheme (DVR/AIMD) are provided in detail, and the latest developments of the approach are presented. The accuracy and stability of the current implementation of the DVR/AIMD scheme are tested by performing a simulation of liquid water at ambient conditions. The structural information obtained from the present work is in good agreement with the result of recent AIMD simulations with a PW basis set (PW/AIMD). Advantages of using the DVR/AIMD scheme over the PW/AIMD method are discussed. In particular, it is shown that a DVR/AIMD simulation of liquid water in the complete basis set limit is possible with a relatively small number of grid points.
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Affiliation(s)
- Hee-Seung Lee
- Department of Chemistry, New York University, New York, New York 10003, USA
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Collins MA. Molecular potential energy surfaces constructed from interpolation of systematic fragment surfaces. J Chem Phys 2007; 127:024104. [PMID: 17640116 DOI: 10.1063/1.2746025] [Citation(s) in RCA: 53] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments has previously been presented. Here it is shown that this approach provides a feasible, systematic method for constructing a global molecular potential energy surface (PES) for reactions of a moderate-sized molecule from the corresponding surfaces for small molecular fragments. The method is demonstrated by construction of PESs for the reactions of a hydrogen atom with propane and n-pentane.
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Affiliation(s)
- Michael A Collins
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia.
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Liu S. Steric effect: A quantitative description from density functional theory. J Chem Phys 2007; 126:244103. [PMID: 17614533 DOI: 10.1063/1.2747247] [Citation(s) in RCA: 181] [Impact Index Per Article: 10.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The concepts of steric energy, steric potential, and steric charge are introduced within the density functional theory framework. The steric energy, representing a hypothetical state with all electrons packed into the lowest orbital and other effects entirely excluded, is a measure of the intrinsic space occupied by an electronic system. It is exclusive, repulsive, and extensive, and it vanishes for homogeneous electron gas. When Bader's zero-flux boundary condition is adopted, atoms in molecules are found to achieve balanced steric repulsion among one another with vanished steric energy density interfaces. A few molecular systems involving conformation changes and chemical reactions have been investigated to examine the relative contribution of the steric and other effects, providing insights for a few controversial topics from a different perspective.
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Affiliation(s)
- Shubin Liu
- The Renaissance Computing Institute (RENCI), University of North Carolina, Chapel Hill, North Corolina 27599-3420, USA.
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Anikin NA, Anisimov VM, Bugaenko VL, Bobrikov VV, Andreyev AM. LocalSCF method for semiempirical quantum-chemical calculation of ultralarge biomolecules. J Chem Phys 2007; 121:1266-70. [PMID: 15260667 DOI: 10.1063/1.1764496] [Citation(s) in RCA: 38] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/02/2023] Open
Abstract
A linear-scaling semiempirical method, LocalSCF, has been proposed for the quantum-chemical calculations of ultralarge molecular systems by treating the large-scale molecular task as a variational problem. The method resolves the self-consistent field task through the finite atomic expansion of weakly nonorthogonal localized molecular orbitals. The inverse overlap matrix arising from the nonorthogonality of the localized orbitals is approximated by preserving the first-order perturbation term and applying the second-order correction by means of a penalty function. This allows for the separation of the orbital expansion procedure from the self-consistent field optimization of linear coefficients, thereby maintaining the localized molecular orbital size unchanged during the refinement of linear coefficients. Orbital normalization is preserved analytically by the variation of virtual degrees of freedom, which are orthogonal to the initial orbitals. Optimization of linear coefficients of localized orbitals is performed by a gradient procedure. The computer program running on a commodity personal computer was applied to the GroEL-GroES chaperonin complex containing 119,273 atoms.
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Affiliation(s)
- N A Anikin
- Quantum Biochemistry Group, Konstantina Fedina-3/24, 105215 Moscow, Russian Federation
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Collins MA, Deev VA. Accuracy and efficiency of electronic energies from systematic molecular fragmentation. J Chem Phys 2006; 125:104104. [PMID: 16999512 DOI: 10.1063/1.2347710] [Citation(s) in RCA: 143] [Impact Index Per Article: 7.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
A systematic method for approximating the ab initio electronic energy of molecules from the energies of molecular fragments is tested on a large sample of typical organic molecular structures. The detailed methods, including some additional refinements for molecular rings and long range interactions, are described. The accuracy and computational efficiency of the systematic hierarchy of methods are reported.
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Affiliation(s)
- Michael A Collins
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia.
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Dipole Correlation of the Electronic Structures of theConformations of Water Molecule Evolving Through theNormal Modes of Vibrations Between Angular (C2v) to Linear(D∝h) Shapes. Int J Mol Sci 2006. [DOI: 10.3390/i7030071] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/28/2023] Open
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31
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Nonorthogonal ultralocalized functions and fitted Wannier functions for local electron correlation methods for solids. Theor Chem Acc 2005. [DOI: 10.1007/s00214-005-0685-5] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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32
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Deev V, Collins MA. Approximateab initioenergies by systematic molecular fragmentation. J Chem Phys 2005; 122:154102. [PMID: 15945620 DOI: 10.1063/1.1879792] [Citation(s) in RCA: 225] [Impact Index Per Article: 11.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A scheme is introduced for generating a hierarchy of molecular fragmentations by which the total electronic energy can be approximated from the energies of the fragments. Higher levels in the hierarchy produce molecular fragments of larger size and approximate the total electronic energy more reliably. A correction to account for nonbonded interactions is also presented. The accuracy of the approach is tested for a number of examples, and shown to be essentially independent of the level of ab initio theory employed. The computational cost increases linearly with the size of the molecule.
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Affiliation(s)
- Vitali Deev
- Research School of Chemistry, Australian National University, Canberra ACT 0200, Australia
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Aspuru-Guzik A, Salomón-Ferrer R, Austin B, Lester WA. A sparse algorithm for the evaluation of the local energy in quantum Monte Carlo. J Comput Chem 2005; 26:708-15. [PMID: 15761862 DOI: 10.1002/jcc.20205] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
A new algorithm is presented for the sparse representation and evaluation of Slater determinants in the quantum Monte Carlo (QMC) method. The approach, combined with the use of localized orbitals in a Slater-type orbital basis set, significantly extends the size molecule that can be treated with the QMC method. Application of the algorithm to systems containing up to 390 electrons confirms that the cost of evaluating the Slater determinant scales linearly with system size.
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Affiliation(s)
- Alán Aspuru-Guzik
- Kenneth S. Pitzer Center for Theoretical Chemistry, Department of Chemistry, University of California at Berkeley, Berkeley, California 94720-1460, USA.
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Feng H, Bian J, Li L, Yang W. An efficient method for constructing nonorthogonal localized molecular orbitals. J Chem Phys 2004; 120:9458-66. [PMID: 15267957 DOI: 10.1063/1.1691396] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
A new method for constructing nonorthogonal localized molecular orbitals (NOLMOs) is presented. The set of highly localized NOLMOs is obtained by minimization of the spread functional starting from an initial set of canonical orthogonal molecular orbitals. To enhance the stability and efficiency, the centroids of the NOLMOs are constrained to be those of the corresponding orthogonal localized molecular orbitals (OLMOs), which are obtained with the Boys criterion in advance. In particular, these centroid constraints make the optimization for each NOLMO independent of the others, which is an attractive feature for application to large systems. The minimization with the constraints incorporated through the multiplier-penalty function method is stable and efficient in convergence. While exhibiting the classical bonding pattern in chemistry and sharing a spatial distribution similar to that of the corresponding OLMOs, the obtained NOLMOs are more compact than the corresponding OLMOs with about 10%-28% reduction in the value of the spread functional and devoid of the troublesome "orthogonalization tails."
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Affiliation(s)
- Huasheng Feng
- State Key Laboratory of Rare Earth Materials Chemistry and Applications, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, People's Republic of China
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Iftimie R, Thomas JW, Tuckerman ME. On-the-fly localization of electronic orbitals in Car–Parrinello molecular dynamics. J Chem Phys 2004; 120:2169-81. [PMID: 15268355 DOI: 10.1063/1.1636697] [Citation(s) in RCA: 32] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The ab initio molecular-dynamics formalism of Car and Parrinello is extended to preserve the locality of the orbitals. The supplementary term in the Lagrangian does not affect the nuclear dynamics, but ensures "on the fly" localization of the electronic orbitals within a periodic supercell in the Gamma-point approximation. The relationship between the resulting equations of motion and the formation of a gauge-invariant Lagrangian combined with a gauge-fixing procedure is briefly discussed. The equations of motion can be used to generate a very stable and easy to implement numerical integration algorithm. It is demonstrated that this algorithm can be used to compute the trajectory of the maximally localized orbitals, known as Wannier orbitals, in ab initio molecular dynamics with only a modest increase in the overall computer time. In the present paper, the new method is implemented within the generalized gradient approximation to Kohn-Sham density-functional theory employing plane wave basis sets and atomic pseudopotentials. In the course of the presentation, we briefly discuss how the present approach can be combined with localized basis sets to design fast linear scaling ab initio molecular-dynamics methods.
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Affiliation(s)
- Radu Iftimie
- Department of Chemistry, New York University, New York, New York 10003, USA
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Paulus B, Rościszewski K, Stoll H, Birkenheuer U. Ab initio incremental correlation treatment with non-orthogonal localized orbitals. Phys Chem Chem Phys 2003. [DOI: 10.1039/b308870g] [Citation(s) in RCA: 24] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
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Ferré N, Assfeld X, Rivail JL. Specific force field parameters determination for the hybrid ab initio QM/MM LSCF method. J Comput Chem 2002; 23:610-24. [PMID: 11939595 DOI: 10.1002/jcc.10058] [Citation(s) in RCA: 117] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
The pure quantum mechanics method, called Local Self-Consistent Field (LSCF), that allows to optimize a wave function within the constraint that some predefined spinorbitals are kept frozen, is discussed. These spinorbitals can be of any shape, and their occupation numbers can be 0 or 1. Any post-Hartree-Fock method, based on the restricted or unrestricted Hartree-Fock Slater determinant, and Kohn-Sham-based DFT method are available. The LSCF method is easily applied to hybrid quantum mechanics/molecular mechanics (QM/MM) procedure where the quantum and the classical parts are covalently bonded. The complete methodology of our hybrid QM/MM scheme is detailed for studies of macromolecular systems. Not only the energy but also the gradients are derived; thus, the full geometry optimization of the whole system is feasible. We show that only specific force field parameters are needed for a correct description of the molecule, they are given for some general chemical bonds. A careful analysis of the errors induced by the use of molecular mechanics in hybrid computation show that a general procedure can be derived to obtain accurate results at low computation effort. The methodology is applied to the structure determination of the crambin protein and to Menshutkin reactions between primary amines and chloromethane.
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Affiliation(s)
- Nicolas Ferré
- Equipe de Chimie et Biochimie théoriques, UMR Université Henri Poincaré, CNRS No. 7565, Vandoeuvre-lès-Nancy, France
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