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Gallegos M, Vassilev-Galindo V, Poltavsky I, Martín Pendás Á, Tkatchenko A. Explainable chemical artificial intelligence from accurate machine learning of real-space chemical descriptors. Nat Commun 2024; 15:4345. [PMID: 38773090 DOI: 10.1038/s41467-024-48567-9] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/11/2023] [Accepted: 04/24/2024] [Indexed: 05/23/2024] Open
Abstract
Machine-learned computational chemistry has led to a paradoxical situation in which molecular properties can be accurately predicted, but they are difficult to interpret. Explainable AI (XAI) tools can be used to analyze complex models, but they are highly dependent on the AI technique and the origin of the reference data. Alternatively, interpretable real-space tools can be employed directly, but they are often expensive to compute. To address this dilemma between explainability and accuracy, we developed SchNet4AIM, a SchNet-based architecture capable of dealing with local one-body (atomic) and two-body (interatomic) descriptors. The performance of SchNet4AIM is tested by predicting a wide collection of real-space quantities ranging from atomic charges and delocalization indices to pairwise interaction energies. The accuracy and speed of SchNet4AIM breaks the bottleneck that has prevented the use of real-space chemical descriptors in complex systems. We show that the group delocalization indices, arising from our physically rigorous atomistic predictions, provide reliable indicators of supramolecular binding events, thus contributing to the development of Explainable Chemical Artificial Intelligence (XCAI) models.
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Affiliation(s)
- Miguel Gallegos
- Department of Analytical and Physical Chemistry, University of Oviedo, E-33006, Oviedo, Spain
| | | | - Igor Poltavsky
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg
| | - Ángel Martín Pendás
- Department of Analytical and Physical Chemistry, University of Oviedo, E-33006, Oviedo, Spain.
| | - Alexandre Tkatchenko
- Department of Physics and Materials Science, University of Luxembourg, L-1511, Luxembourg City, Luxembourg.
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Non-covalent interactions from a Quantum Chemical Topology perspective. J Mol Model 2022; 28:276. [PMID: 36006513 PMCID: PMC9411098 DOI: 10.1007/s00894-022-05188-7] [Citation(s) in RCA: 16] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/07/2021] [Accepted: 02/07/2022] [Indexed: 11/12/2022]
Abstract
About half a century after its little-known beginnings, the quantum topological approach called QTAIM has grown into a widespread, but still not mainstream, methodology of interpretational quantum chemistry. Although often confused in textbooks with yet another population analysis, be it perhaps an elegant but somewhat esoteric one, QTAIM has been enriched with about a dozen other research areas sharing its main mathematical language, such as Interacting Quantum Atoms (IQA) or Electron Localisation Function (ELF), to form an overarching approach called Quantum Chemical Topology (QCT). Instead of reviewing the latter’s role in understanding non-covalent interactions, we propose a number of ideas emerging from the full consequences of the space-filling nature of topological atoms, and discuss how they (will) impact on interatomic interactions, including non-covalent ones. The architecture of a force field called FFLUX, which is based on these ideas, is outlined. A new method called Relative Energy Gradient (REG) is put forward, which is able, by computation, to detect which fragments of a given molecular assembly govern the energetic behaviour of this whole assembly. This method can offer insight into the typical balance of competing atomic energies both in covalent and non-covalent case studies. A brief discussion on so-called bond critical points is given, highlighting concerns about their meaning, mainly in the arena of non-covalent interactions.
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Townsend J, Vogiatzis KD. Transferable MP2-Based Machine Learning for Accurate Coupled-Cluster Energies. J Chem Theory Comput 2020; 16:7453-7461. [DOI: 10.1021/acs.jctc.0c00927] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022]
Affiliation(s)
- Jacob Townsend
- Department of Chemistry, University of Tennessee, Knoxville, Tennessee 37996, United States
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Vincent MA, Silva AF, Popelier PLA. A Comparison of the Interacting Quantum Atoms (IQA) Analysis of the Two‐Particle Density‐Matrices of MP4SDQ and CCSD. Z Anorg Allg Chem 2020. [DOI: 10.1002/zaac.202000169] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023]
Affiliation(s)
- Mark A. Vincent
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
| | - Arnaldo F. Silva
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology The University of Manchester M1 7DN Manchester UK
- Department of Chemistry The University of Manchester M13 9PL Manchester UK
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An Interacting Quantum Atoms (IQA) and Relative Energy Gradient (REG) Study of the Halogen Bond with Explicit Analysis of Electron Correlation. Molecules 2020; 25:molecules25112674. [PMID: 32526931 PMCID: PMC7321288 DOI: 10.3390/molecules25112674] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/26/2020] [Revised: 06/03/2020] [Accepted: 06/03/2020] [Indexed: 01/18/2023] Open
Abstract
Energy profiles of seven halogen-bonded complexes were analysed with the topological energy partitioning called Interacting Quantum Atoms (IQA) at MP4(SDQ)/6-31+G(2d,2p) level of theory. Explicit interatomic electron correlation energies are included in the analysis. Four complexes combine X2 (X = Cl or F) with HCN or NH3, while the remaining three combine ClF with HCN, NH3 or N2. Each complex was systematically deformed by translating the constituent molecules along its central axis linking X and N, and reoptimising its remaining geometry. The Relative Energy Gradient (REG) method (Theor. Chem. Acc. 2017, 136, 86) then computes which IQA energies most correlate with the total energy during the process of complex formation and further compression beyond the respective equilibrium geometries. It turns out that the covalent energy (i.e., exchange) of the halogen bond, X…N, itself drives the complex formation. When the complexes are compressed from their equilibrium to shorter X…N distance then the intra-atomic energy of N is in charge. When the REG analysis is restricted to electron correlation then the interatomic correlation energy between X and N again drives the complex formation, and the complex compression is best described by the destabilisation of the through-space correlation energy between N and the "outer" halogen.
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Silva AF, Duarte LJ, Popelier PLA. Contributions of IQA electron correlation in understanding the chemical bond and non-covalent interactions. Struct Chem 2020. [DOI: 10.1007/s11224-020-01495-y] [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
AbstractThe quantum topological energy partitioning method Interacting Quantum Atoms (IQA) has been applied for over a decade resulting in an enlightening analysis of a variety of systems. In the last three years we have enriched this analysis by incorporating into IQA the two-particle density matrix obtained from Møller–Plesset (MP) perturbation theory. This work led to a new computational and interpretational tool to generate atomistic electron correlation and thus topologically based dispersion energies. Such an analysis determines the effects of electron correlation within atoms and between atoms, which covers both bonded and non-bonded “through -space” atom–atom interactions within a molecule or molecular complex. A series of papers published by us and other groups shows that the behavior of electron correlation is deeply ingrained in structural chemistry. Some concepts that were shown to be connected to bond correlation are bond order, multiplicity, aromaticity, and hydrogen bonding. Moreover, the concepts of covalency and ionicity were shown not to be mutually excluding but to both contribute to the stability of polar bonds. The correlation energy is considerably easier to predict by machine learning (kriging) than other IQA terms. Regarding the nature of the hydrogen bond, correlation energy presents itself in an almost contradicting way: there is much localized correlation energy in a hydrogen bond system, but its overall effect is null due to internal cancelation. Furthermore, the QTAIM delocalization index has a connection with correlation energy. We also explore the role of electron correlation in protobranching, which provides an explanation for the extra stabilization present in branched alkanes compared to their linear counterparts. We hope to show the importance of understanding the true nature of the correlation energy as the foundation of a modern representation of dispersion forces for ab initio, DFT, and force field calculations.
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Vincent MA, Silva AF, Popelier PLA. Atomic Partitioning of the MPn (n = 2, 3, 4) Dynamic Electron Correlation Energy by the Interacting Quantum Atoms Method: A Fast and Accurate Electrostatic Potential Integral Approach. J Comput Chem 2019; 40:2793-2800. [PMID: 31373709 PMCID: PMC6900022 DOI: 10.1002/jcc.26037] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/01/2019] [Revised: 07/10/2019] [Accepted: 07/11/2019] [Indexed: 11/13/2022]
Abstract
Recently, the quantum topological energy partitioning method called interacting quantum atoms (IQA) has been extended to MPn (n = 2, 3, 4) wave functions. This enables the extraction of chemical insight related to dynamic electron correlation. The large computational expense of the IQA-MPn approach is compensated by the advantages that IQA offers compared to older nontopological energy decomposition schemes. This expense is problematic in the construction of a machine learning training set to create kriging models for topological atoms. However, the algorithm presented here markedly accelerates the calculation of atomically partitioned electron correlation energies. Then again, the algorithm cannot calculate pairwise interatomic energies because it applies analytical integrals over whole space (rather than over atomic volumes). However, these pairwise energies are not needed in the quantum topological force field FFLUX, which only uses the energy of an atom interacting with all remaining atoms of the system that it is part of. Thus, it is now feasible to generate accurate and sizeable training sets at MPn level of theory. © 2019 The Authors. Journal of Computational Chemistry published by Wiley Periodicals, Inc.
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Affiliation(s)
- Mark A. Vincent
- Manchester Institute of BiotechnologyThe University of ManchesterManchesterM1 7DNUK
- School of ChemistryThe University of ManchesterManchesterM13 9PLUK
| | - Arnaldo F. Silva
- Manchester Institute of BiotechnologyThe University of ManchesterManchesterM1 7DNUK
- School of ChemistryThe University of ManchesterManchesterM13 9PLUK
| | - Paul L. A. Popelier
- Manchester Institute of BiotechnologyThe University of ManchesterManchesterM1 7DNUK
- School of ChemistryThe University of ManchesterManchesterM13 9PLUK
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McDonagh JL, Shkurti A, Bray DJ, Anderson RL, Pyzer-Knapp EO. Utilizing Machine Learning for Efficient Parameterization of Coarse Grained Molecular Force Fields. J Chem Inf Model 2019; 59:4278-4288. [PMID: 31549507 DOI: 10.1021/acs.jcim.9b00646] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
We present a machine learning approach to automated force field development in dissipative particle dynamics (DPD). The approach employs Bayesian optimization to parametrize a DPD force field against experimentally determined partition coefficients. The optimization process covers a discrete space of over 40 000 000 points, where each point represents the set of potentials that jointly forms a force field. We find that Bayesian optimization is capable of reaching a force field of comparable performance to the current state-of-the-art within 40 iterations. The best iteration during the optimization achieves an R2 of 0.78 and an RMSE of 0.63 log units on the training set of data, these metrics are maintained when a validation set is included, giving R2 of 0.8 and an RMSE of 0.65 log units. This work hence provides a proof-of-concept, expounding the utility of coupling automated and efficient global optimization with a top down data driven approach to force field parametrization. Compared to commonly employed alternative methods, Bayesian optimization offers global parameter searching and a low time to solution.
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Affiliation(s)
- James L McDonagh
- IBM Research U.K. , Hartree Centre, Daresbury WA4 4AD , United Kingdom
| | - Ardita Shkurti
- STFC Daresbury Laboratories , Daresbury WA4 4AD , United Kingdom
| | - David J Bray
- STFC Daresbury Laboratories , Daresbury WA4 4AD , United Kingdom
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Mó O, Montero‐Campillo MM, Alkorta I, Elguero J, Yáñez M. Ternary Complexes Stabilized by Chalcogen and Alkaline‐Earth Bonds: Crucial Role of Cooperativity and Secondary Noncovalent Interactions. Chemistry 2019; 25:11688-11695. [DOI: 10.1002/chem.201901641] [Citation(s) in RCA: 15] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2019] [Revised: 05/31/2019] [Indexed: 01/20/2023]
Affiliation(s)
- Otilia Mó
- Departamento de Química, Módulo 13 Facultad de Ciencias and Institute of, Advanced Chemical Sciences (IadChem) Universidad Autónoma de Madrid Campus de Excelencia UAM-CSIC Cantoblanco 28049 Madrid Spain
| | - M. Merced Montero‐Campillo
- Departamento de Química, Módulo 13 Facultad de Ciencias and Institute of, Advanced Chemical Sciences (IadChem) Universidad Autónoma de Madrid Campus de Excelencia UAM-CSIC Cantoblanco 28049 Madrid Spain
| | - Ibon Alkorta
- Instituto de Química Médica, IQM-CSIC Juan de la Cierva, 3 E-28006 Madrid Spain
| | - José Elguero
- Instituto de Química Médica, IQM-CSIC Juan de la Cierva, 3 E-28006 Madrid Spain
| | - Manuel Yáñez
- Departamento de Química, Módulo 13 Facultad de Ciencias and Institute of, Advanced Chemical Sciences (IadChem) Universidad Autónoma de Madrid Campus de Excelencia UAM-CSIC Cantoblanco 28049 Madrid Spain
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Tognetti V, Silva AF, Vincent MA, Joubert L, Popelier PLA. Decomposition of Møller–Plesset Energies within the Quantum Theory of Atoms-in-Molecules. J Phys Chem A 2018; 122:7748-7756. [DOI: 10.1021/acs.jpca.8b05357] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/10/2023]
Affiliation(s)
- Vincent Tognetti
- Normandy University, COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont St Aignan, Cedex, France
| | - Arnaldo F. Silva
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain
- School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| | - Mark A. Vincent
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain
- School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| | - Laurent Joubert
- Normandy University, COBRA UMR 6014 & FR 3038, Université de Rouen, INSA Rouen, CNRS, 1 rue Tesniére, 76821 Mont St Aignan, Cedex, France
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain
- School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
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Silva AF, Popelier PLA. MP2-IQA: upscaling the analysis of topologically partitioned electron correlation. J Mol Model 2018; 24:201. [PMID: 29995194 PMCID: PMC6061063 DOI: 10.1007/s00894-018-3717-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/16/2018] [Accepted: 06/12/2018] [Indexed: 11/01/2022]
Abstract
When electronic correlation energy is partitioned topologically, a detailed picture of its distribution emerges, both within atoms and between any two atoms. This methodology allows one to study dispersion beyond its more narrow definition in long-range Rayleigh-Schrödinger perturbation theory. The interacting quantum atoms (IQA) method was applied to MP2/6-31G(d,p) (uncontracted) wave functions of a wide variety of systems: glycine…water (hydration), the ethene dimer (π-π interactions), benzene (aromaticity), cyclobutadiene (antiaromaticity), and NH3BH3 (dative bond). Through the study of molecular complexes it turns out that dispersion energy is either important to a system's stabilization (for the C2H4 dimer) or not important (for Gly…H2O). We have also discovered that the delocalization in benzene lowers the strength of Coulomb repulsion in the bonds, which has been quantified for the first time through IQA. Finally, we showed that the nature of the dative bond is much different from that of a regular covalent bond as it is not destabilized by electronic correlation. Finally, the conclusions obtained for these archetypical systems have implications for the future of the quantum topological force field FFLUX in the simulation of larger systems. Graphical abstract Atomic and bond dynamic correlation energies are now available thanks to IQA. Larger molecules can now be accessed to include resonance and solvation of FFLUX force field.
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Affiliation(s)
- Arnaldo F Silva
- Instituto de Química, Universidade Estadual de Campinas, Campinas, SP, 13083-970, Brazil.
| | - Paul L A Popelier
- Manchester Institute of Biotechnology, the University of Manchester, 131 Princess Street, Manchester, M1 7DN, Great Britain.,School of Chemistry, the University of Manchester, Oxford Road, Manchester, M13 9PL, Great Britain
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Di Pasquale N, Davie SJ, Popelier PLA. The accuracy of ab initio calculations without ab initio calculations for charged systems: Kriging predictions of atomistic properties for ions in aqueous solutions. J Chem Phys 2018; 148:241724. [DOI: 10.1063/1.5022174] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Affiliation(s)
- Nicodemo Di Pasquale
- Manchester Institute of Biotechnology (MIB), 131 Princess
Street, Manchester M1 7DN, United Kingdom and School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL,
United Kingdom
| | - Stuart J. Davie
- Manchester Institute of Biotechnology (MIB), 131 Princess
Street, Manchester M1 7DN, United Kingdom and School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL,
United Kingdom
| | - Paul L. A. Popelier
- Manchester Institute of Biotechnology (MIB), 131 Princess
Street, Manchester M1 7DN, United Kingdom and School of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL,
United Kingdom
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McDonagh JL, Silva AF, Vincent MA, Popelier PLA. Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms. J Chem Theory Comput 2017; 14:216-224. [PMID: 29211469 DOI: 10.1021/acs.jctc.7b01157] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/26/2023]
Abstract
We present an innovative method for predicting the dynamic electron correlation energy of an atom or a bond in a molecule utilizing topological atoms. Our approach uses the machine learning method Kriging (Gaussian Process Regression with a non-zero mean function) to predict these dynamic electron correlation energy contributions. The true energy values are calculated by partitioning the MP2 two-particle density-matrix via the Interacting Quantum Atoms (IQA) procedure. To our knowledge, this is the first time such energies have been predicted by a machine learning technique. We present here three important proof-of-concept cases: the water monomer, the water dimer, and the van der Waals complex H2···He. These cases represent the final step toward the design of a full IQA potential for molecular simulation. This final piece will enable us to consider situations in which dispersion is the dominant intermolecular interaction. The results from these examples suggest a new method by which dispersion potentials for molecular simulation can be generated.
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Affiliation(s)
- James L McDonagh
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain
| | - Arnaldo F Silva
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain
| | - Mark A Vincent
- School of Chemistry, The University of Manchester , Oxford Road, Manchester M13 9PL, Great Britain
| | - Paul L A Popelier
- Manchester Institute of Biotechnology, The University of Manchester , 131 Princess Street, Manchester M1 7DN, Great Britain.,School of Chemistry, The University of Manchester , Oxford Road, Manchester M13 9PL, Great Britain
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