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Esquivel RO, Carrera E. The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules. Chemphyschem 2024; 25:e202400030. [PMID: 38646938 DOI: 10.1002/cphc.202400030] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/12/2024] [Revised: 04/19/2024] [Accepted: 04/22/2024] [Indexed: 04/25/2024]
Abstract
Even though molecules are fundamentally quantum entities, the concept of a molecule retains certain classical attributes concerning its constituents. This includes the empirical separability of a molecule into its three-dimensional, rigid structure in Euclidean space, a framework often obtained through experimental methods like X-Ray crystallography. In this work, we delve into the mathematical implications of partitioning a molecule into its constituent parts using the widely recognized Atoms-In-Molecules (AIM) schemes, aiming to establish their validity within the framework of Information Theory concepts. We have uncovered information-theoretical justifications for employing some of the most prevalent AIM schemes in the field of Chemistry, including Hirshfeld (stockholder partitioning), Bader's (topological dissection), and the quantum approach (Hilbert's space definition). In the first approach we have applied the generalized principle of minimum relative entropy derived from the Sharma-Mittal two-parameter functional, avoiding the need for an arbitrary selection of reference promolecular atoms. Within the ambit of topological-information partitioning, we have demonstrated that the Fisher information of Bader's atoms conform to a comprehensive theory based on the Principle of Extreme Physical Information avoiding the need of employing the Schwinger's principle, which has been proven to be problematic. For the quantum approach we have presented information-theoretic justifications for conducting Löwdin symmetric transformations on the density matrix to form atomic Hilbert spaces generating orthonormal atomic orbitals with maximum occupancy for a given wavefunction.
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Affiliation(s)
- Rodolfo O Esquivel
- Departamento de Química, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Av. Ferrocarril San Rafael Atlixco, Núm. 186, Col. Leyes de Reforma 1 A Sección, Alcaldía Iztapalapa, C.P., 09310, Ciudad de México, Mexico
- Instituto "Carlos I" de Física Teórica y Computacional, Universidad de Granada, Calle Dr. Severo Ochoa, 18071, Granada, Spain
| | - Edmundo Carrera
- Departamento de Química, Universidad Autónoma Metropolitana, Unidad Iztapalapa, Av. Ferrocarril San Rafael Atlixco, Núm. 186, Col. Leyes de Reforma 1 A Sección, Alcaldía Iztapalapa, C.P., 09310, Ciudad de México, Mexico
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Zhao D, Zhao Y, Xu E, Liu W, Ayers PW, Liu S, Chen D. Fragment-Based Deep Learning for Simultaneous Prediction of Polarizabilities and NMR Shieldings of Macromolecules and Their Aggregates. J Chem Theory Comput 2024; 20:2655-2665. [PMID: 38441881 DOI: 10.1021/acs.jctc.3c01415] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/08/2024]
Abstract
Simultaneous prediction of the molecular response properties, such as polarizability and the NMR shielding constant, at a low computational cost is an unresolved issue. We propose to combine a linear-scaling generalized energy-based fragmentation (GEBF) method and deep learning (DL) with both molecular and atomic information-theoretic approach (ITA) quantities as effective descriptors. In GEBF, the total molecular polarizability can be assembled as a linear combination of the corresponding quantities calculated from a set of small embedded subsystems in GEBF. In the new GEBF-DL(ITA) protocol, one can predict subsystem polarizabilities based on the corresponding molecular wave function (thus electron density and ITA quantities) and DL model rather than calculate them from the computationally intensive coupled-perturbed Hartree-Fock or Kohn-Sham equations and finally obtain the total molecular polarizability via a linear combination equation. As a proof-of-concept application, we predict the molecular polarizabilities of large proteins and protein aggregates. GEBF-DL(ITA) is shown to be as accurate enough as GEBF, with mean absolute percentage error <1%. For the largest protein aggregate (>4000 atoms), GEBF-DL(ITA) gains a speedup ratio of 3 compared with GEBF. It is anticipated that when more advanced electronic structure methods are used, this advantage will be more appealing. Moreover, one can also predict the NMR chemical shieldings of proteins with reasonably good accuracy. Overall, the cost-efficient GEBF-DL(ITA) protocol should be a robust theoretical tool for simultaneously predicting polarizabilities and NMR shieldings of large systems.
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Affiliation(s)
- Dongbo Zhao
- Institute of Biomedical Research, Yunnan University, Kunming, Yunnan 650500, P. R. China
| | - Yilin Zhao
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton ONL8S4M1, Canada
| | - Enhua Xu
- Graduate School of System Informatics, Kobe University, Nada-ku, Kobe, Hyogo 657-8501, Japan
| | - Wenqi Liu
- Institute of Biomedical Research, Yunnan University, Kunming, Yunnan 650500, P. R. China
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton ONL8S4M1, Canada
| | - Shubin Liu
- Research Computing Center, University of North Carolina, Chapel Hill, North Carolina 27599-3420, United States
- Department of Chemistry, University of North Carolina, Chapel Hill, North Carolina 27599-3290, United States
| | - Dahua Chen
- Institute of Biomedical Research, Yunnan University, Kunming, Yunnan 650500, P. R. China
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Tehrani A, Anderson JSM, Chakraborty D, Rodriguez-Hernandez JI, Thompson DC, Verstraelen T, Ayers PW, Heidar-Zadeh F. An information-theoretic approach to basis-set fitting of electron densities and other non-negative functions. J Comput Chem 2023; 44:1998-2015. [PMID: 37526138 DOI: 10.1002/jcc.27170] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/02/2023] [Revised: 05/03/2023] [Accepted: 05/08/2023] [Indexed: 08/02/2023]
Abstract
The numerical ill-conditioning associated with approximating an electron density with a convex sum of Gaussian or Slater-type functions is overcome by using the (extended) Kullback-Leibler divergence to measure the deviation between the target and approximate density. The optimized densities are non-negative and normalized, and they are accurate enough to be used in applications related to molecular similarity, the topology of the electron density, and numerical molecular integration. This robust, efficient, and general approach can be used to fit any non-negative normalized functions (e.g., the kinetic energy density and molecular electron density) to a convex sum of non-negative basis functions. We present a fixed-point iteration method for optimizing the Kullback-Leibler divergence and compare it to conventional gradient-based optimization methods. These algorithms are released through the free and open-source BFit package, which also includes a L2-norm squared optimization routine applicable to any square-integrable scalar function.
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Affiliation(s)
- Alireza Tehrani
- Department of Chemistry, Queen's University, Kingston, Ontario, Canada
| | - James S M Anderson
- Instituto de Química, Universidad Nacional Autónoma de México, Ciudad de México, Mexico
| | - Debajit Chakraborty
- Department of Physics, Wake Forest University, Winston-Salem, North Carolina, USA
- Center for Functional Materials, Wake Forest University, Winston-Salem, North Carolina, USA
| | | | | | - Toon Verstraelen
- Center for Molecular Modeling (CMM), Ghent University, Zwijnaarde, Belgium
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario, Canada
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Pujal L, van Zyl M, Vöhringer-Martinez E, Verstraelen T, Bultinck P, Ayers PW, Heidar-Zadeh F. Constrained iterative Hirshfeld charges: A variational approach. J Chem Phys 2022; 156:194109. [PMID: 35597660 DOI: 10.1063/5.0089466] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We develop a variational procedure for the iterative Hirshfeld (HI) partitioning scheme. The main practical advantage of having a variational framework is that it provides a formal and straightforward approach for imposing constraints (e.g., fixed charges on certain atoms or molecular fragments) when computing HI atoms and their properties. Unlike many other variants of the Hirshfeld partitioning scheme, HI charges do not arise naturally from the information-theoretic framework, but only as a reverse-engineered construction of the objective function. However, the procedure we use is quite general and could be applied to other problems as well. We also prove that there is always at least one solution to the HI equations, but we could not prove that its self-consistent equations would always converge for any given initial pro-atom charges. Our numerical assessment of the constrained iterative Hirshfeld method shows that it satisfies many desirable traits of atoms in molecules and has the potential to surpass existing approaches for adding constraints when computing atomic properties.
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Affiliation(s)
- Leila Pujal
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7N 3N6, Canada
| | - Maximilian van Zyl
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7N 3N6, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico-Química, Facultad de Ciencias Químicas, Universidad de Concepción, Concepción, Chile
| | - Toon Verstraelen
- Center for Molecular Modeling (CMM), Ghent University, Technologiepark-Zwijnaarde 46, B-9052 Zwijnaarde, Belgium
| | - Patrick Bultinck
- Ghent Quantum Chemistry Group, Department of Chemistry, Ghent University, Krijgslaan 281 S3, B-9000 Ghent, Belgium
| | - Paul W Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4L8, Canada
| | - Farnaz Heidar-Zadeh
- Department of Chemistry, Queen's University, 90 Bader Lane, Kingston, Ontario K7N 3N6, Canada
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Abstract
In this work some possibilities for deriving a local electrophilicity are studied. First, we consider the original definition proposed by Chattaraj, Maiti, and Sarkar (J Phys Chem A 107:4973, 2003), in which the local electrophilicity is given by the product of the global electrophilicity, and the Fukui function for charge acceptance is derived by two different approaches, making use of the chain rule for functional derivatives. We also modify the proposals based on the electron density so as to have a definition with the same units of the original definition, which also introduces a dependence in the Fukui function for charge donation. Additionally, we also explore other possibilities using the tools of information theory and the temperature dependent reactivity indices of the density functional theory of chemical reactivity. The poor results obtained from the last two approaches lead us to conjecture that this is due to the fact that the global electrophilicity is not a derivative, like most of the other reactivity indices. The conclusion is that Chattaraj's suggestion seems to be the simplest, but at the same time a very reliable approach to this important property.
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Xu H, Zhu Z, Guo Y, Liu C, Zhang W, Zhu Y, Wang Y, Tang M. A DFT study on N-heterocyclic carbene catalyzed [4+2] annulation reaction with in situ generated heterocyclic ortho-quinodimethane: Mechanism, origin of enantioselectivity and role of catalyst. Tetrahedron 2018. [DOI: 10.1016/j.tet.2018.01.030] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Heidar-Zadeh F, Ayers PW, Bultinck P. Fractional nuclear charge approach to isolated anion densities for Hirshfeld partitioning methods. J Mol Model 2017; 23:348. [DOI: 10.1007/s00894-017-3514-6] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/22/2017] [Accepted: 10/26/2017] [Indexed: 11/30/2022]
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Fias S, Heidar-Zadeh F, Anderson JSM, Ayers PW, Parr RG. A reference-free stockholder partitioning method based on the force on electrons. J Comput Chem 2017; 39:1044-1050. [DOI: 10.1002/jcc.25114] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/21/2017] [Revised: 09/14/2017] [Accepted: 10/06/2017] [Indexed: 11/08/2022]
Affiliation(s)
- Stijn Fias
- Department of Chemistry & Chemical Biology; McMaster University; Hamilton Ontario Canada L8S 4M1
| | - Farnaz Heidar-Zadeh
- Department of Chemistry & Chemical Biology; McMaster University; Hamilton Ontario Canada L8S 4M1
- Center for Molecular Modeling; Ghent University, Technologiepark 903; 9052 Zwijnaarde Belgium
- Department of Inorganic and Physical Chemistry; Ghent University, Krijgslaan 281 (S3); 9000 Gent Belgium
| | | | - Paul W. Ayers
- Department of Chemistry & Chemical Biology; McMaster University; Hamilton Ontario Canada L8S 4M1
| | - Robert G. Parr
- Department of Chemistry; University of North Carolina; Chapel Hill NC USA 27599
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Heidar-Zadeh F, Ayers PW, Verstraelen T, Vinogradov I, Vöhringer-Martinez E, Bultinck P. Information-Theoretic Approaches to Atoms-in-Molecules: Hirshfeld Family of Partitioning Schemes. J Phys Chem A 2017; 122:4219-4245. [DOI: 10.1021/acs.jpca.7b08966] [Citation(s) in RCA: 68] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Farnaz Heidar-Zadeh
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
| | - Paul W. Ayers
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Toon Verstraelen
- Center for Molecular Modeling, Ghent University, Technologiepark 903, 9052 Zwijnaarde, Belgium
| | - Ivan Vinogradov
- Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada
| | - Esteban Vöhringer-Martinez
- Departamento de Físico-Química, Facultad de Ciencias Químicas, Universidad de Concepción, Concepción, Chile
| | - Patrick Bultinck
- Department of Chemistry, Ghent University, Krijgslaan 281 (S3), 9000 Gent, Belgium
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