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Jensen F. Unifying Charge-Flow Polarization Models. J Chem Theory Comput 2023. [PMID: 37365806 DOI: 10.1021/acs.jctc.3c00341] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/28/2023]
Abstract
We show that several models where electric polarization in molecular systems is modeled by charge-flow between atoms can all be considered as different manifestations of a general underlying mathematical structure. The models can be classified according to whether they employ atomic or bond parameters and whether they employ atom/bond hardness or softness. We show that an ab initio calculated charge response kernel can be considered as the inverse screened Coulombic matrix projected onto the zero-charge subspace, and this may provide a method for deriving charge screening functions to be used in force fields. The analysis suggests that some models contain redundancies, and we argue that a parameterization of charge-flow models in terms of bond softness is preferable as it depends on local quantities and decay to zero upon bond dissociation, while bond hardness depends on global quantities and increases toward infinity upon bond dissociation.
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Affiliation(s)
- Frank Jensen
- Department of Chemistry, Aarhus University, Langelandsgade 140, Aarhus DK-8000, Denmark
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2
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Fias S, Ayers PW, De Proft F, Geerlings P. Properties of the density functional response kernels and its implications on chemistry. J Chem Phys 2022; 157:114102. [PMID: 36137804 DOI: 10.1063/5.0094653] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
An overview of mathematical properties of the non-local second order derivatives of the canonical, grand canonical, isomorphic, and grand isomorphic ensembles is given. The significance of their positive or negative semidefiniteness and the implications of these properties for atoms and molecules are discussed. Based on this property, many other interesting properties can be derived, such as the expansion in eigenfunctions, bounds on the diagonal and off-diagonal elements, and the eigenvalues of these kernels. We also prove Kato's theorem for the softness kernel and linear response and the dissociation limit of the linear responses as the sum of the linear responses of the individual fragments when dissociating a system into two non-interacting molecular fragments. Finally, strategies for the practical calculation of these kernels, their eigenfunctions, and their eigenvalues are discussed.
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Affiliation(s)
- Stijn Fias
- McMaster University, 1280 Main St. W, Hamilton, Ontario L8S 4L8, Canada
| | - Paul W Ayers
- McMaster University, 1280 Main St. W, Hamilton, Ontario L8S 4L8, Canada
| | - Frank De Proft
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
| | - Paul Geerlings
- Research Group of General Chemistry (ALGC), Vrije Universiteit Brussel (VUB), Pleinlaan 2, B-1050 Brussels, Belgium
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3
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Chakraborty D, Chattaraj PK. Conceptual density functional theory based electronic structure principles. Chem Sci 2021; 12:6264-6279. [PMID: 34084424 PMCID: PMC8115084 DOI: 10.1039/d0sc07017c] [Citation(s) in RCA: 61] [Impact Index Per Article: 20.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/24/2020] [Accepted: 03/10/2021] [Indexed: 12/20/2022] Open
Abstract
In this review article, we intend to highlight the basic electronic structure principles and various reactivity descriptors as defined within the premise of conceptual density functional theory (CDFT). Over the past several decades, CDFT has proven its worth in providing valuable insights into various static as well as time-dependent physicochemical problems. Herein, having briefly outlined the basics of CDFT, we describe various situations where CDFT based reactivity theory could be employed in order to gain insights into the underlying mechanism of several chemical processes.
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Affiliation(s)
- Debdutta Chakraborty
- Department of Chemistry, KU Leuven Celestijnenlaan 200F-2404 3001 Leuven Belgium
| | - Pratim Kumar Chattaraj
- Department of Chemistry, Indian Institute of Technology Kharagpur 721302 West Bengal India +91 3222 255303 +91 3222 283304
- Department of Chemistry, Indian Institute of Technology Bombay Powai Mumbai 400076 India
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4
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Bhattacharjee R, Verma K, Zhang M, Li T. Locality and strength of intermolecular interactions in organic crystals: using conceptual density functional theory (CDFT) to characterize a highly polymorphic system. Theor Chem Acc 2019. [DOI: 10.1007/s00214-019-2508-0] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
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5
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An Occam’s razor approach to chemical hardness: lex parsimoniae. J Mol Model 2018; 24:332. [DOI: 10.1007/s00894-018-3864-8] [Citation(s) in RCA: 21] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/18/2018] [Accepted: 10/04/2018] [Indexed: 10/27/2022]
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6
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Franco-Pérez M, Polanco-Ramírez CA, Gázquez JL, Ayers PW. Local and nonlocal counterparts of global descriptors: the cases of chemical softness and hardness. J Mol Model 2018; 24:285. [DOI: 10.1007/s00894-018-3823-4] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/07/2018] [Accepted: 09/04/2018] [Indexed: 10/28/2022]
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7
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Franco-Pérez M, Ayers PW, Gázquez JL, Vela A. Thermodynamic responses of electronic systems. J Chem Phys 2017; 147:094105. [DOI: 10.1063/1.4999761] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Marco Franco-Pérez
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Paul W. Ayers
- Department of Chemistry, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - José L. Gázquez
- Departamento de Química, Universidad Autónoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Ciudad de México 09340, Mexico
| | - Alberto Vela
- Departamento de Química, Centro de Investigación y de Estudios Avanzados, Av. Instituto Politécnico Nacional 2508, Ciudad de México 07360, Mexico
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8
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Huang J, Mei Y, König G, Simmonett AC, Pickard FC, Wu Q, Wang LP, MacKerell AD, Brooks BR, Shao Y. An Estimation of Hybrid Quantum Mechanical Molecular Mechanical Polarization Energies for Small Molecules Using Polarizable Force-Field Approaches. J Chem Theory Comput 2017; 13:679-695. [PMID: 28081366 DOI: 10.1021/acs.jctc.6b01125] [Citation(s) in RCA: 14] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In this work, we report two polarizable molecular mechanics (polMM) force field models for estimating the polarization energy in hybrid quantum mechanical molecular mechanical (QM/MM) calculations. These two models, named the potential of atomic charges (PAC) and potential of atomic dipoles (PAD), are formulated from the ab initio quantum mechanical (QM) response kernels for the prediction of the QM density response to an external molecular mechanical (MM) environment (as described by external point charges). The PAC model is similar to fluctuating charge (FQ) models because the energy depends on external electrostatic potential values at QM atomic sites; the PAD energy depends on external electrostatic field values at QM atomic sites, resembling induced dipole (ID) models. To demonstrate their uses, we apply the PAC and PAD models to 12 small molecules, which are solvated by TIP3P water. The PAC model reproduces the QM/MM polarization energy with a R2 value of 0.71 for aniline (in 10,000 TIP3P water configurations) and 0.87 or higher for other 11 solute molecules, while the PAD model has a much better performance with R2 values of 0.98 or higher. The PAC model reproduces reference QM/MM hydration free energies for 12 solute molecules with a RMSD of 0.59 kcal/mol. The PAD model is even more accurate, with a much smaller RMSD of 0.12 kcal/mol, with respect to the reference. This suggests that polarization effects, including both local charge distortion and intramolecular charge transfer, can be well captured by induced dipole type models with proper parametrization.
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Affiliation(s)
- Jing Huang
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland , 20 Penn Street, Baltimore, Maryland 21201, United States.,Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute , 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - Ye Mei
- State Key Laboratory of Precision Spectroscopy, School of Physics and Materials Science, East China Normal University , Shanghai 200062, China.,NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Gerhard König
- Max-Planck-Institut für Kohlenforschung , 45470 Mülheim an der Ruhr, NRW Germany, EU
| | - Andrew C Simmonett
- Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute , 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - Frank C Pickard
- Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute , 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - Qin Wu
- Center for Functional Nanomaterials, Brookhaven National Laboratory , Upton, New York 11973, United States
| | - Lee-Ping Wang
- Department of Chemistry, University of California , 1 Shields Avenue, Davis, California 95616, United States
| | - Alexander D MacKerell
- Department of Pharmaceutical Sciences, School of Pharmacy, University of Maryland , 20 Penn Street, Baltimore, Maryland 21201, United States
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Institutes of Health, National Heart, Lung and Blood Institute , 5635 Fishers Lane, T-900 Suite, Rockville, Maryland 20852, United States
| | - Yihan Shao
- Q-Chem Inc., 6601 Owens Drive, Suite 105, Pleasanton, California 94588, United States.,Department of Chemistry and Biochemistry, University of Oklahoma , Norman, Oklahoma 73019, United States
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9
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Polanco-Ramírez CA, Franco-Pérez M, Carmona-Espíndola J, Gázquez JL, Ayers PW. Revisiting the definition of local hardness and hardness kernel. Phys Chem Chem Phys 2017; 19:12355-12364. [DOI: 10.1039/c7cp00691h] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Local hardness is redefined following similar rules to those of local softness. The new concept describes chemical trends correctly.
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Affiliation(s)
| | - Marco Franco-Pérez
- Departamento de Química
- Universidad Autónoma Metropolitana-Iztapalapa
- México
- Mexico
- Department of Chemistry
| | | | - José L. Gázquez
- Departamento de Química
- Universidad Autónoma Metropolitana-Iztapalapa
- México
- Mexico
| | - Paul W. Ayers
- Department of Chemistry
- McMaster University
- Hamilton
- Canada
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10
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Resolving the nature of the reactive sites of phenylsulfinate ( PhSO2-) with a single general-purpose reactivity indicator. COMPUT THEOR CHEM 2014. [DOI: 10.1016/j.comptc.2014.04.032] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
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11
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Heidar Zadeh F, Fuentealba P, Cárdenas C, Ayers PW. An information-theoretic resolution of the ambiguity in the local hardness. Phys Chem Chem Phys 2014; 16:6019-26. [PMID: 24553911 DOI: 10.1039/c3cp52906a] [Citation(s) in RCA: 26] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A definition of the local hardness, suitable for application in the local hard/soft acid/base principle, is derived by applying information theory.
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Affiliation(s)
| | - Patricio Fuentealba
- Departamento de Física
- Facultad de Ciencias
- Universidad de Chile
- 653-Santiago, Chile
- Centro para el desarrollo de la Nanociencias y Nanotecnologia
| | - Carlos Cárdenas
- Departamento de Física
- Facultad de Ciencias
- Universidad de Chile
- 653-Santiago, Chile
- Centro para el desarrollo de la Nanociencias y Nanotecnologia
| | - Paul W. Ayers
- Dept. of Chemistry & Chemical Biology
- McMaster University
- Hamilton, Canada
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12
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Zhang M, Li T. Intermolecular interactions in organic crystals: gaining insight from electronic structure analysis by density functional theory. CrystEngComm 2014. [DOI: 10.1039/c4ce00411f] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Conceptual density functional theory is exploited to extend the HSAB (hard and soft acids and bases) principle for investigating the locality and regioselectivity of intermolecular interactions in organic crystals.
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Affiliation(s)
- Mingtao Zhang
- Industrial & Physical Pharmacy
- Purdue University
- West Lafayette, USA
| | - Tonglei Li
- Industrial & Physical Pharmacy
- Purdue University
- West Lafayette, USA
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13
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Affiliation(s)
- Siamak Noorizadeh
- Chemistry Department, College of
Science, Shahid Chamran University, Ahvaz,
61357-43169, Iran
| | - Hadi Parsa
- Chemistry Department, College of
Science, Shahid Chamran University, Ahvaz,
61357-43169, Iran
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14
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Fuentealba P, Cárdenas C. On the exponential model for energy with respect to number of electrons. J Mol Model 2012; 19:2849-53. [DOI: 10.1007/s00894-012-1708-5] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2012] [Accepted: 11/21/2012] [Indexed: 11/30/2022]
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15
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Kasende OE, Muya JT, Broeckaert L, Maes G, Geerlings P. Theoretical Study of the Regioselectivity of the Interaction of 3-Methyl-4-pyrimidone and 1-Methyl-2-pyrimidone with Lewis Acids. J Phys Chem A 2012; 116:8608-14. [DOI: 10.1021/jp3038158] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Okuma Emile Kasende
- Faculty of Science, University of Kinshasa, B.P. 190 Kinshasa XI, D. R.
Congo
| | - Jules Tshishimbi Muya
- Faculty of Science, University of Kinshasa, B.P. 190 Kinshasa XI, D. R.
Congo
- Department
of Chemistry, University of Leuven, Celestijnenlaan 200F, 3001 Heverlee, Belgium
| | - Lies Broeckaert
- Department of General Chemistry
(ALGC), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
| | - Guido Maes
- Department
of Chemistry, University of Leuven, Celestijnenlaan 200F, 3001 Heverlee, Belgium
| | - Paul Geerlings
- Department of General Chemistry
(ALGC), Vrije Universiteit Brussel, Pleinlaan 2, 1050 Brussels, Belgium
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16
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