1
|
Thürlemann M, Riniker S. Hybrid classical/machine-learning force fields for the accurate description of molecular condensed-phase systems. Chem Sci 2023; 14:12661-12675. [PMID: 38020395 PMCID: PMC10646964 DOI: 10.1039/d3sc04317g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/17/2023] [Accepted: 10/24/2023] [Indexed: 12/01/2023] Open
Abstract
Electronic structure methods offer in principle accurate predictions of molecular properties, however, their applicability is limited by computational costs. Empirical methods are cheaper, but come with inherent approximations and are dependent on the quality and quantity of training data. The rise of machine learning (ML) force fields (FFs) exacerbates limitations related to training data even further, especially for condensed-phase systems for which the generation of large and high-quality training datasets is difficult. Here, we propose a hybrid ML/classical FF model that is parametrized exclusively on high-quality ab initio data of dimers and monomers in vacuum but is transferable to condensed-phase systems. The proposed hybrid model combines our previous ML-parametrized classical model with ML corrections for situations where classical approximations break down, thus combining the robustness and efficiency of classical FFs with the flexibility of ML. Extensive validation on benchmarking datasets and experimental condensed-phase data, including organic liquids and small-molecule crystal structures, showcases how the proposed approach may promote FF development and unlock the full potential of classical FFs.
Collapse
Affiliation(s)
- Moritz Thürlemann
- Department of Chemistry and Applied Biosciences, ETH Zürich Vladimir-Prelog-Weg 2 Zürich 8093 Switzerland
| | - Sereina Riniker
- Department of Chemistry and Applied Biosciences, ETH Zürich Vladimir-Prelog-Weg 2 Zürich 8093 Switzerland
| |
Collapse
|
2
|
Thürlemann M, Böselt L, Riniker S. Regularized by Physics: Graph Neural Network Parametrized Potentials for the Description of Intermolecular Interactions. J Chem Theory Comput 2023; 19:562-579. [PMID: 36633918 PMCID: PMC9878731 DOI: 10.1021/acs.jctc.2c00661] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/24/2022] [Indexed: 01/13/2023]
Abstract
Simulations of molecular systems using electronic structure methods are still not feasible for many systems of biological importance. As a result, empirical methods such as force fields (FF) have become an established tool for the simulation of large and complex molecular systems. The parametrization of FF is, however, time-consuming and has traditionally been based on experimental data. Recent years have therefore seen increasing efforts to automatize FF parametrization or to replace FF with machine-learning (ML) based potentials. Here, we propose an alternative strategy to parametrize FF, which makes use of ML and gradient-descent based optimization while retaining a functional form founded in physics. Using a predefined functional form is shown to enable interpretability, robustness, and efficient simulations of large systems over long time scales. To demonstrate the strength of the proposed method, a fixed-charge and a polarizable model are trained on ab initio potential-energy surfaces. Given only information about the constituting elements, the molecular topology, and reference potential energies, the models successfully learn to assign atom types and corresponding FF parameters from scratch. The resulting models and parameters are validated on a wide range of experimentally and computationally derived properties of systems including dimers, pure liquids, and molecular crystals.
Collapse
Affiliation(s)
- Moritz Thürlemann
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Lennard Böselt
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| | - Sereina Riniker
- Laboratory of Physical Chemistry, ETH Zürich, Vladimir-Prelog-Weg 2, 8093 Zürich, Switzerland
| |
Collapse
|
3
|
Burnham CJ, English NJ. A New Relatively Simple Approach to Multipole Interactions in Either Spherical Harmonics or Cartesians, Suitable for Implementation into Ewald Sums. Int J Mol Sci 2019; 21:ijms21010277. [PMID: 31906127 PMCID: PMC7017380 DOI: 10.3390/ijms21010277] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/13/2019] [Revised: 12/12/2019] [Accepted: 12/20/2019] [Indexed: 11/16/2022] Open
Abstract
We present a novel derivation of the multipole interaction (energies, forces and fields) in spherical harmonics, which results in an expression that is able to exactly reproduce the results of earlier Cartesian formulations. Our method follows the derivations of Smith (W. Smith, CCP5 Newsletter 1998, 46, 18.) and Lin (D. Lin, J. Chem. Phys. 2015, 143, 114115), who evaluate the Ewald sum for multipoles in Cartesian form, and then shows how the resulting expressions can be converted into spherical harmonics, where the conversion is performed by establishing a relation between an inner product on the space of symmetric traceless Cartesian tensors, and an inner product on the space of harmonic polynomials on the unit sphere. We also introduce a diagrammatic method for keeping track of the terms in the multipole interaction expression, such that the total electrostatic energy can be viewed as a 'sum over diagrams', and where the conversion to spherical harmonics is represented by 'braiding' subsets of Cartesian components together. For multipoles of maximum rank n, our algorithm is found to have scaling of n 3.7 vs. n 4.5 for our most optimised Cartesian implementation.
Collapse
|
4
|
Jing Z, Liu C, Cheng SY, Qi R, Walker BD, Piquemal JP, Ren P. Polarizable Force Fields for Biomolecular Simulations: Recent Advances and Applications. Annu Rev Biophys 2019; 48:371-394. [PMID: 30916997 DOI: 10.1146/annurev-biophys-070317-033349] [Citation(s) in RCA: 222] [Impact Index Per Article: 44.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Abstract
Realistic modeling of biomolecular systems requires an accurate treatment of electrostatics, including electronic polarization. Due to recent advances in physical models, simulation algorithms, and computing hardware, biomolecular simulations with advanced force fields at biologically relevant timescales are becoming increasingly promising. These advancements have not only led to new biophysical insights but also afforded opportunities to advance our understanding of fundamental intermolecular forces. This article describes the recent advances and applications, as well as future directions, of polarizable force fields in biomolecular simulations.
Collapse
Affiliation(s)
- Zhifeng Jing
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Chengwen Liu
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Sara Y Cheng
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Rui Qi
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Brandon D Walker
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| | - Jean-Philip Piquemal
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA; .,Sorbonne Université, CNRS, Laboratoire de Chimie Theórique, 75252 Paris CEDEX 05, France.,Institut Universitaire de France, 75005 Paris, France
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA;
| |
Collapse
|
5
|
Boateng HA. Mesh-free hierarchical clustering methods for fast evaluation of electrostatic interactions of point multipoles. J Chem Phys 2018; 147:164104. [PMID: 29096477 DOI: 10.1063/1.4990552] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
Abstract
Electrostatic interactions involving point multipoles are being increasingly implemented to achieve higher accuracy in molecular simulations. A major drawback of multipolar electrostatics is the increased computational cost. Here we develop and compare two Cartesian tree algorithms which employ Taylor approximations and hierarchical clustering to speed up the evaluation of point multipole interactions. We present results from applying the algorithms to compute the free space Coulomb potential and forces of different sets of interacting point multipoles with different densities. The methods achieve high accuracy and speedup of more than an order of magnitude over direct sum calculations and scale well in parallel.
Collapse
Affiliation(s)
- H A Boateng
- Department of Mathematics, Bates College, 2 Andrews Rd., Lewiston, Maine 04240, USA
| |
Collapse
|
6
|
Simmonett AC, Pickard FC, Ponder JW, Brooks BR. An empirical extrapolation scheme for efficient treatment of induced dipoles. J Chem Phys 2017; 145:164101. [PMID: 27802661 DOI: 10.1063/1.4964866] [Citation(s) in RCA: 24] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Many cutting edge force fields include polarization, to enhance their accuracy and range of applicability. In this work, we develop efficient strategies for the induced dipole polarization method. By fitting various orders of perturbation theory (PT) dipoles to a diverse training set, we arrive at a family of fully analytic methods - whose nth order is referred to OPTn - that span the full spectrum of polarization methods from the fast zeroth-order approach that neglects mutual dipole coupling, approaching the fully variational approach at high order. Our training set contains many difficult cases where the PT series diverges, and we demonstrate that our OPTn methods still deliver excellent results in these cases. Our tests show that the OPTn methods exhibit rapid convergence towards the exact answer with each increasing PT order. The fourth order OPT4 method, whose costs are commensurate with three iterations of the leading conjugate gradient method, is a particularly promising candidate to be used as a drop-in replacement for existing solvers without further parameterization.
Collapse
Affiliation(s)
- Andrew C Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Frank C Pickard
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, USA
| | - Bernard R Brooks
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
| |
Collapse
|
7
|
Elking DM. Torque and atomic forces for Cartesian tensor atomic multipoles with an application to crystal unit cell optimization. J Comput Chem 2016; 37:2067-80. [PMID: 27349179 DOI: 10.1002/jcc.24427] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/22/2016] [Accepted: 05/17/2016] [Indexed: 01/31/2023]
Abstract
New equations for torque and atomic force are derived for use in flexible molecule force fields with atomic multipoles. The expressions are based on Cartesian tensors with arbitrary multipole rank. The standard method for rotating Cartesian tensor multipoles and calculating torque is to first represent the tensor with n indexes and 3(n) redundant components. In this work, new expressions for directly rotating the unique (n + 1)(n + 2)/2 Cartesian tensor multipole components Θpqr are given by introducing Cartesian tensor rotation matrix elements X(R). A polynomial expression and a recursion relation for X(R) are derived. For comparison, the analogous rotation matrix for spherical tensor multipoles are the Wigner functions D(R). The expressions for X(R) are used to derive simple equations for torque and atomic force. The torque and atomic force equations are applied to the geometry optimization of small molecule crystal unit cells. In addition, a discussion of computational efficiency as a function of increasing multipole rank is given for Cartesian tensors. © 2016 Wiley Periodicals, Inc.
Collapse
Affiliation(s)
- Dennis M Elking
- Openeye Scientific Software, Santa Fe, New Mexico, 87508.,Elking Scientific Modeling, Ballwin, Missouri, 63102
| |
Collapse
|