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A General Drude Polarizable Force Field with Spherical Charge Density Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1793 Alexandria: A General Drude Polarizable Force Field with Spherical Charge Density MOHAMMAD MEHDI GHAHREMANPOUR ACTA UNIVERSITATIS UPSALIENSIS ISSN 1651-6214 ISBN 978-91-513-0624-7 UPPSALA urn:nbn:se:uu:diva-380687 2019 Dissertation presented at Uppsala University to be publicly examined in Room B21, Uppsala Biomedical Centre, Husargatan 3, Uppsala, Monday, 27 May 2019 at 09:15 for the degree of Doctor of Philosophy. The examination will be conducted in English. Faculty examiner: Professor Kresten Lindorff-Larsen (Department of Biology, University of Copenhagen). Abstract Ghahremanpour, M. M. 2019. Alexandria: A General Drude Polarizable Force Field with Spherical Charge Density. Digital Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 1793. 69 pp. Uppsala: Acta Universitatis Upsaliensis. ISBN 978-91-513-0624-7. Molecular-mechanical (MM) force fields are mathematical functions that map the geometry of a molecule to its associated energy. MM force fields have been extensively used for an atomistic view into the dynamic and thermodynamics of large molecular systems in their condensed phase. Nevertheless, the grand challenge in force field development—which remains to be addressed —is to predict properties of materials with different chemistries and in all their physical phases. Force fields are, in principle, derived through supervised machine learning methods. Therefore, the first step toward more accurate force fields is to provide high-quality reference data from which the force fields can learn. Thus, we benchmarked quantum-mechanical methods—at different levels of theory—in predicting of molecular energetics and electrostatic properties. As the result, the Alexandria library was released as an open access database of molecular properties. The second step is to use potential functions describing interactions between molecules accurately. For this, we incorporated electronic polarization and charge penetration effects into the Alexandria force field. The Drude model was used for the explicit inclusion of electronic polarization. The distribution of the atomic charges was described by either a 1s-Gaussian or an ns-Slater density function to account for charge penetration effects. Moreover, the 12-6 Lennard-Jones (LJ) potential function, commonly used in force fields, was replaced by the Wang-Buckingham (WBK) function to describe the interaction of two particles at very short distances. In contrast to the 12-6 LJ function, the WBK function is well behaved at short distances because it has a finite limit as the distance between two particles approaches zero. The third step is free and open source software (FOSS) for systematic optimization of the built-in force field parameters. For this, we developed the Alexandria chemistry toolkit that is currently part of the GROMACS software package. With these three steps, the Alexandria force field was developed for alkali halides and for organic compounds consisting of (H, C, N, O, S, P) and halogens (F, Cl, Br, I). We demonstrated that the Alexandria force field described alkali halides in gas, liquid, and solid phases with an overall performance better than the benchmarked reference force fields. We also showed that the Alexandria force field predicted the electrostatics of isolated molecules and molecular complexes in agreement with the density functional theory at the B3LYP/aug-cc-pVTZ level of theory. Keywords: Molecular mechanics, Force field, Drude oscillator model, Alexandria library, GROMACS Mohammad Mehdi Ghahremanpour, Department of Cell and Molecular Biology, Box 596, Uppsala University, SE-75124 Uppsala, Sweden. © Mohammad Mehdi Ghahremanpour 2019 ISSN 1651-6214 ISBN 978-91-513-0624-7 urn:nbn:se:uu:diva-380687 (http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-380687) To Rezvan List of papers This thesis is based on the following papers, which are referred to in the text by their Roman numerals. I Ghahremanpour, M. M., van Maaren, P. J., Ditz, J., Lindh, R., Van der Spoel, D. (2016) Large-Scale Calculations of Gas Phase Thermochemistry: Enthalpy of Formation, Standard Entropy and Heat Capacity. J. Chem. Phys., 145, 114305. II Ghahremanpour, M. M., van Maaren, P. J., Van der Spoel, D. (2018) The Alexandria Library: A Quantum Chemical Database of Molecular Properties for Force Field Development. Sci. Data, 5, 180062. III Ghahremanpour, M. M., van Maaren, P. J., Caleman, C., Hutchison, G. R., Van der Spoel, D. (2018) Polarizable Drude Model with s-type Gaussian or Slater Charge Density for General Molecular Mechanics Force Fields. J. Chem. Theory Comput. 14, 5553-5566. IV Walz, M. M., Ghahremanpour, M. M., van Maaren, P. J., Van der Spoel, D. (2018) Phase-Transferable Force Field for Alkali Halides. J. Chem. Theory Comput., 14, 5933-5948. V Van der Spoel, D., Ghahremanpour, M. M., Lemkul, J. (2018) Small Molecule Thermochemistry: A Tool for Empirical Force Field Development. J. Phys. Chem. A, 122, 8982-8988. VI Ghahremanpour, M. M., van Maaren, P. J., Van der Spoel, D. Efficient Physics-Based Polarizable Charges: from Organic Compounds to Proteins. Manuscript. Reprints were made with permission from the publishers. Contents 1 Introduction ................................................................................................ 11 1.1 Quantum-Mechanical Models ....................................................... 12 1.1.1 Wave function theory ...................................................... 12 1.1.2 Density functional theory ................................................ 15 1.2 Molecular-Mechanical Models ..................................................... 17 2 Alexandria Library .................................................................................... 22 2.1 Data Availability ............................................................................ 22 2.2 Properties in the Alexandria Library ............................................. 23 2.2.1 Molecular thermochemistry ............................................ 23 2.2.2 Molecular electrostatics .................................................. 26 2.3 Computational details .................................................................... 29 2.4 Technical validation ....................................................................... 29 3 Intermolecular Potential Energy Function ............................................... 31 3.1 Quantum mechanical approximations for intermolecular energies ........................................................................................... 31 3.2 Alexandria force field approximations for intermolecular energies ........................................................................................... 34 3.2.1 Electrostatic and Charge Penetration ............................. 34 3.2.2 Electronic Polarization .................................................... 36 3.2.3 Repulsion and Dispersion ............................................... 38 4 Generation of Polarizable Atomic Charges ............................................. 42 4.1 Electrostatic Potential (ESP)-fitting with Drude Model .............. 42 4.2 Alexandria Charge Model .............................................................. 44 5 Parameterization ........................................................................................ 47 5.1 Linear Fitting .................................................................................. 47 5.1.1 Singular value decomposition ......................................... 47 5.1.2 Bootstrapping ................................................................... 48 5.2 Nonlinear Fitting ............................................................................ 48 5.2.1 Bayesian inference .......................................................... 48 5.2.2 Bayesian computation ..................................................... 50 5.2.3 Simulated annealing ........................................................ 52 6 Alexandria Chemistry Toolkit .................................................................. 53 6.1 Extracting Quantum Chemistry Data ............................................ 53 6.2 Generation of Force Field Atom Types ........................................ 53 6.3 Optimization of Force Field Parameters ....................................... 53 6.4 Generation of Molecular Topology and Atomic Charges ............ 54 6.5 Coulomb Integrals for Distributed Charge Densities ................... 55 6.6 Parallelization ................................................................................. 55 6.7 License ............................................................................................ 55 7 Summary of papers .................................................................................... 56 7.1 Paper I ............................................................................................. 56 7.2 Paper II ............................................................................................ 56 7.3 Paper III .......................................................................................... 57 7.4 Paper IV .......................................................................................... 57 7.5 Paper V ........................................................................................... 58 7.6 Paper VI .......................................................................................... 59 8 Populärvetenskaplig
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