1
|
Devereux M, Boittier ED, Meuwly M. Systematic improvement of empirical energy functions in the era of machine learning. J Comput Chem 2024; 45:1899-1913. [PMID: 38695412 DOI: 10.1002/jcc.27367] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2023] [Revised: 02/13/2024] [Accepted: 02/21/2024] [Indexed: 07/05/2024]
Abstract
The impact of targeted replacement of individual terms in empirical force fields is quantitatively assessed for pure water, dichloromethane (CH 2 Cl 2 ), and solvated K + and Cl - ions. For the electrostatic interactions, point charges (PCs) and machine learning (ML)-based minimally distributed charges (MDCM) fitted to the molecular electrostatic potential are evaluated together with electrostatics based on the Coulomb integral. The impact of explicitly including second-order terms is investigated by adding a fragment molecular orbital (FMO)-derived polarization energy to an existing force field, in this case CHARMM. It is demonstrated that anisotropic electrostatics reduce the RMSE for water (by 1.4 kcal/mol), CH 2 Cl 2 (by 0.8 kcal/mol) and for solvated Cl - clusters (by 0.4 kcal/mol). An additional polarization term can be neglected for CH 2 Cl 2 but further improves the models for pure water (by ∼ 1.0 kcal/mol) and hydrated Cl - (by 0.4 kcal/mol), and is key for solvated K + , reducing the RMSE by 2.3 kcal/mol. A 12-6 Lennard-Jones functional form performs satisfactorily with PC and MDCM electrostatics, but is not appropriate for descriptions that account for the electrostatic penetration energy. The importance of many-body contributions is assessed by comparing a strictly 2-body approach with self-consistent reference data. Two-body interactions suffice for CH 2 Cl 2 whereas water and solvated K + and Cl - ions require explicit many-body corrections. Finally, a many-body-corrected dimer potential energy surface exceeds the accuracy attained using a conventional empirical force field, potentially reaching that of an FMO calculation. The present work systematically quantifies which terms improve the performance of an existing force field and what reference data to use for parametrizing these terms in a tractable fashion for ML fitting of pure and heterogeneous systems.
Collapse
Affiliation(s)
- Mike Devereux
- Department of Chemistry, University of Basel, Basel, Switzerland
| | - Eric D Boittier
- Department of Chemistry, University of Basel, Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Basel, Switzerland
| |
Collapse
|
2
|
Chen G, Jaffrelot Inizan T, Plé T, Lagardère L, Piquemal JP, Maday Y. Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach. J Chem Theory Comput 2024; 20:5558-5569. [PMID: 38875012 DOI: 10.1021/acs.jctc.3c01421] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/16/2024]
Abstract
Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.
Collapse
Affiliation(s)
- Gong Chen
- Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions (LJLL), UMR 7598 CNRS, 75005 Paris, France
| | - Théo Jaffrelot Inizan
- Sorbonne Université, Laboratoire de Chimie Théorique (LCT), UMR 7616 CNRS, 75005 Paris, France
| | - Thomas Plé
- Sorbonne Université, Laboratoire de Chimie Théorique (LCT), UMR 7616 CNRS, 75005 Paris, France
| | - Louis Lagardère
- Sorbonne Université, Laboratoire de Chimie Théorique (LCT), UMR 7616 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, Laboratoire de Chimie Théorique (LCT), UMR 7616 CNRS, 75005 Paris, France
| | - Yvon Maday
- Sorbonne Université, CNRS, Université Paris Cité, Laboratoire Jacques-Louis Lions (LJLL), UMR 7598 CNRS, 75005 Paris, France
| |
Collapse
|
3
|
Brown ML, Isamura BK, Skelton JM, Popelier PLA. Incorporating Noncovalent Interactions in Transfer Learning Gaussian Process Regression Models for Molecular Simulations. J Chem Theory Comput 2024. [PMID: 38981081 DOI: 10.1021/acs.jctc.4c00402] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 07/11/2024]
Abstract
FFLUX is a quantum chemical topology-based multipolar force field that uses Gaussian process regression machine learning models to predict atomic energies and multipole moments on the fly for fast and accurate molecular dynamics simulations. These models have previously been trained on monomers, meaning that many-body effects, for example, intermolecular charge transfer, are missed in simulations. Moreover, dispersion and repulsion have been modeled using Lennard-Jones potentials, necessitating careful parametrization. In this work, we take an important step toward addressing these shortcomings and show that models trained on clusters, in this case, a dimer, can be used in FFLUX simulations by preparing and benchmarking a formamide dimer model. To mitigate the computational costs associated with training higher-dimensional models, we rely on the transfer of hyperparameters from a smaller source model to a larger target model, enabling an order of magnitude faster training than with a direct learning approach. The dimer model allows for simulations that account for two-body effects, including intermolecular polarization and charge penetration, and that do not require nonbonded potentials. We show that addressing these limitations allows for simulations that are closer to quantum mechanics than previously possible with the monomeric models.
Collapse
Affiliation(s)
- Matthew L Brown
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Bienfait K Isamura
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Jonathan M Skelton
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| | - Paul L A Popelier
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom
| |
Collapse
|
4
|
Sami S, LaCour RA, Heindel JP, Head-Gordon T. Simple and Accurate One-Body Energy and Dipole Moment Surfaces for Water and Beyond. J Phys Chem Lett 2024; 15:6712-6721. [PMID: 38900596 PMCID: PMC11229074 DOI: 10.1021/acs.jpclett.4c00587] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/23/2024] [Revised: 06/07/2024] [Accepted: 06/13/2024] [Indexed: 06/22/2024]
Abstract
Water is often the testing ground for new, advanced force fields. While advanced functional forms for intermolecular interactions have been integral to the development of accurate water models, less attention has been paid to a transferable model for intramolecular valence terms. In this work, we present a one-body energy and dipole moment surface model, named 1B-UCB, that is simple yet accurate and can be feasibly adapted for both standard and advanced potentials. 1B-UCB for water is comparable in accuracy to those with much more complex functional forms, despite having drastically fewer parameters. The parametrization protocol has been implemented as part of the Q-Force automated workflow and requires only a quantum mechanical Hessian calculation as reference data, hence allowing it to be easily extended to a variety of molecular systems beyond water, which we demonstrate on a selection of small molecules with different symmetries.
Collapse
Affiliation(s)
- Selim Sami
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
| | - R. Allen LaCour
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Joseph P. Heindel
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Kenneth
S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, Berkeley, California 94720, United States
- Chemical
Sciences Division, Lawrence Berkeley National
Laboratory, Berkeley, California 94720, United States
- Departments
of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, Berkeley, California 94720, United States
| |
Collapse
|
5
|
Hartke B. On the brink of self-hydration: the water heptadecamer. Phys Chem Chem Phys 2024; 26:15445-15451. [PMID: 38747364 DOI: 10.1039/d4cp00816b] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/30/2024]
Abstract
For pure, neutral, isolated molecular clusters, (H2O)17 marks the transition from structures with all water molecules on the cluster surface to water self-hydration, i.e., cluster structures around one central water molecule. Getting this right with water model potentials turns out to be challenging. Even the best water potentials currently available, which reproduce collective properties very well, still deliver contradicting results for (H2O)17, when different low-energy isomers from global structure optimizations are examined. Interestingly, ab initio quantum chemistry also struggles with the only seemingly simple question if (H2O)17 is all-surface or water-centered. Hence, although the long history of water potential development may be entering its final phase, it is not quite finished yet.
Collapse
Affiliation(s)
- Bernd Hartke
- Institute for Physical Chemistry, Kiel University, 24118 Kiel, Germany.
| |
Collapse
|
6
|
Mikkelsen JES, Jensen F. Ambiguities in Decomposing Molecular Polarizability into Atomic Charge Flow and Induced Dipole Contributions. J Phys Chem A 2024; 128:4168-4175. [PMID: 38743593 DOI: 10.1021/acs.jpca.4c01890] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/16/2024]
Abstract
The molecular dipole polarizability can be decomposed into components corresponding to the charge flow between atoms and changes in atomic dipole moments. Such decompositions are recognized to depend on how atoms are defined within a molecule, as, for example, by Hirshfeld, iterative Stockholder, or quantum topology partitioning of the electron density. For some of these, however, there are significant differences between the numerical results obtained by analytical response methods and finite field calculations. We show that this difference is due to analytical response methods accounting for (only) the change in electron density by a perturbation, while finite field methods may also include a component corresponding to a perturbation-dependent change in the definition of an atom within a molecule. For some atom-in-molecule definitions, such as the iterative Hirshfeld, iterative Stockholder, and quantum topology methods, the latter effect significantly increases the charge flow component. The decomposition of molecular polarizability into atomic charge flow and induced dipole components thus depends on whether the atom-in-molecule definition is taken to be perturbation-dependent.
Collapse
Affiliation(s)
- Jonas E S Mikkelsen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark
| | - Frank Jensen
- Department of Chemistry, Aarhus University, Langelandsgade 140, DK-8000 Aarhus, Denmark
| |
Collapse
|
7
|
Chung MKJ, Ponder JW. Beyond isotropic repulsion: Classical anisotropic repulsion by inclusion of p orbitals. J Chem Phys 2024; 160:174118. [PMID: 38748037 PMCID: PMC11078554 DOI: 10.1063/5.0203678] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 04/15/2024] [Indexed: 05/19/2024] Open
Abstract
Accurate modeling of intermolecular repulsion is an integral component in force field development. Although repulsion can be explicitly calculated by applying the Pauli exclusion principle, this approach is computationally viable only for systems of limited sizes. Instead, it has previously been shown that repulsion can be reformulated in a "classical" picture: the Pauli exclusion principle prohibits electrons from occupying the same state, leading to a depletion of electronic charge between atoms, giving rise to an enhanced nuclear-nuclear electrostatic repulsion. This classical picture is called the isotropic S2/R approximation, where S is the overlap and R is the interatomic distance. This approximation accurately captures the repulsion of isotropic atoms such as noble gas dimers; however, a key deficiency is that it fails to capture the angular dependence of the repulsion of anisotropic molecules. To include directionality, the wave function must at least be a linear combination of s and p orbitals. We derive a new anisotropic S2/R repulsion model through the inclusion of the anisotropic p orbital term in the total wave function. Because repulsion is pairwise and decays rapidly, it can be truncated at a short range, making it amenable for efficient calculation of energy and forces in complex biomolecular systems. We present a parameterization of the S101 dimer database against the ab initio benchmark symmetry-adapted perturbation theory, which yields an rms error of only 0.9 kcal/mol. The importance of the anisotropic term is demonstrated through angular scans of water-water dimers and dimers involving halobenzene. Simulation of liquid water shows that the model can be computed efficiently for realistic system sizes.
Collapse
Affiliation(s)
| | - Jay W. Ponder
- Author to whom correspondence should be addressed: . Tel.: 314-935-4275
| |
Collapse
|
8
|
Heinz F, Proksch J, Schmidt RF, Gradzielski M, Koksch B, Keller BG. How Chromophore Labels Shape the Structure and Dynamics of a Peptide Hydrogel. Biomacromolecules 2024; 25:1262-1273. [PMID: 38288602 PMCID: PMC10865361 DOI: 10.1021/acs.biomac.3c01225] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/07/2023] [Revised: 01/11/2024] [Accepted: 01/11/2024] [Indexed: 02/13/2024]
Abstract
Biocompatible and functionalizable hydrogels have a wide range of (potential) medicinal applications. The hydrogelation process, particularly for systems with very low polymer weight percentages (<1 wt %), remains poorly understood, making it challenging to predict the self-assembly of a given molecular building block into a hydrogel. This severely hinders the rational design of self-assembled hydrogels. In this study, we demonstrate the impact of an N-terminal group on the self-assembly and rheology of the peptide hydrogel hFF03 (hydrogelating, fibril forming peptide 03) using molecular dynamics simulations, oscillatory shear rheology, and circular dichroism spectroscopy. We find that the chromophore and even its specific regioisomers have a significant influence on the microscopic structure and dynamics of the self-assembled fibril, and on the macroscopic mechanical properties. This is because the chromophore influences the possible salt bridges, which form and stabilize the fibril formation. Furthermore, we find that the solvation shell fibrils by itself cannot explain the viscoelasticity of hFF03 hydrogels. Our atomistic model of the hFF03 fibril formation enables a more rational design of these hydrogels. In particular, altering the N-terminal chromophore emerges as a design strategy to tune the mechanic properties of these self-assembled peptide hydrogels.
Collapse
Affiliation(s)
- Frederick Heinz
- Department
of Biology, Chemistry and Pharmacy, Freie
Universität Berlin, Arnimallee 22, Berlin 14195, Germany
| | - Jonas Proksch
- Department
of Biology, Chemistry and Pharmacy, Freie
Universität Berlin, Arnimallee 22, Berlin 14195, Germany
| | - Robert F. Schmidt
- Stranski-Laboratorium
für Physikalische und Theoretische Chemie, Institut für
Chemie, Technische Universität Berlin, Straße des 17. Juni 124, Berlin 10623, Germany
| | - Michael Gradzielski
- Stranski-Laboratorium
für Physikalische und Theoretische Chemie, Institut für
Chemie, Technische Universität Berlin, Straße des 17. Juni 124, Berlin 10623, Germany
| | - Beate Koksch
- Department
of Biology, Chemistry and Pharmacy, Freie
Universität Berlin, Arnimallee 22, Berlin 14195, Germany
| | - Bettina G. Keller
- Department
of Biology, Chemistry and Pharmacy, Freie
Universität Berlin, Arnimallee 22, Berlin 14195, Germany
| |
Collapse
|
9
|
Valle JVL, Mendonça BHS, Barbosa MC, Chacham H, de Moraes EE. Accuracy of TIP4P/2005 and SPC/Fw Water Models. J Phys Chem B 2024; 128:1091-1097. [PMID: 38253517 DOI: 10.1021/acs.jpcb.3c07044] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/24/2024]
Abstract
Water is used as the main solvent in model systems containing bioorganic molecules. Choosing the right water model is an important step in the study of the biophysical and biochemical processes that occur in cells. In the present work, we perform molecular dynamics simulations using two distinct force fields for water: the rigid model TIP4P/2005, where only intermolecular interactions are considered, and the flexible model SPC/Fw, where intramolecular interactions are also taken into account. The simulations aim to determine the effect of the inclusion of intramolecular interactions on the accuracy of calculated properties of bulk water (density and thermal expansion coefficient, self-diffusion coefficients, shear viscosity, radial distribution functions, and dielectric constant), as compared to experimental results, over a temperature range between 250 and 370 K. We find that the results of the rigid model present the smallest deviations relative to experiments for most of the calculated quantities, except for the shear viscosity of supercooled water and the water dielectric constant, where the flexible model presents better agreement with experiments.
Collapse
Affiliation(s)
- João V L Valle
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário de Ondina, Salvador 40210-340, BA, Brazil
| | - Bruno H S Mendonça
- Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, Belo Horizonte 30123-970, MG, Brazil
| | - Marcia C Barbosa
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre 91501-970, RS, Brazil
| | - Helio Chacham
- Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, 30123-970 Belo Horizonte, MG, Brazil
| | - Elizane E de Moraes
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário de Ondina, Salvador 40210-340, BA, Brazil
| |
Collapse
|
10
|
Ćeranić K, Milovanović B, Petković M. Density functional theory study of crown ether-magnesium complexes: from a solvated ion to an ion trap. Phys Chem Chem Phys 2023; 25:32656-32665. [PMID: 38010878 DOI: 10.1039/d3cp03991a] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2023]
Abstract
Metal ion detection rests on host-guest recognition. We propose a theoretical protocol for designing an optimal trap for a desired metal cation. A host for magnesium ions was sought for among derivatives of crown ethers 12-crown-4, 15-crown-5, and 18-crown-6. Mg-crown complexes and their hydrated counterparts with water molecules bound to the cation were optimized using density functional theory. Based on specific geometric criteria, Interacting quantum atoms analysis and density functional theory-based molecular dynamics of Mg-crown complexes immersed in water, crown ethers for optimal accommodation of Mg2+ in aqueous solution were identified. Selectivity of the chosen crowns towards Na+, K+, and Ca2+ ions is addressed.
Collapse
Affiliation(s)
- Katarina Ćeranić
- Innovative Centre of the Faculty of Chemistry, Studentski trg 12-16, 11158 Belgrade, Serbia
- University of Belgrade - Faculty of Physical Chemistry, Studentski trg 12-16, 11158 Belgrade, Serbia.
| | - Branislav Milovanović
- University of Belgrade - Faculty of Physical Chemistry, Studentski trg 12-16, 11158 Belgrade, Serbia.
| | - Milena Petković
- University of Belgrade - Faculty of Physical Chemistry, Studentski trg 12-16, 11158 Belgrade, Serbia.
| |
Collapse
|
11
|
Brown M, Skelton JM, Popelier PLA. Application of the FFLUX Force Field to Molecular Crystals: A Study of Formamide. J Chem Theory Comput 2023; 19:7946-7959. [PMID: 37847867 PMCID: PMC10653110 DOI: 10.1021/acs.jctc.3c00578] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/30/2023] [Indexed: 10/19/2023]
Abstract
In this work, we present the first application of the quantum chemical topology force field FFLUX to the solid state. FFLUX utilizes Gaussian process regression machine learning models trained on data from the interacting quantum atom partitioning scheme to predict atomic energies and flexible multipole moments that change with geometry. Here, the ambient (α) and high-pressure (β) polymorphs of formamide are used as test systems and optimized using FFLUX. Optimizing the structures with increasing multipolar ranks indicates that the lattice parameters of the α phase differ by less than 5% to the experimental structure when multipole moments up to the quadrupole are used. These differences are found to be in line with the dispersion-corrected density functional theory. Lattice dynamics calculations are also found to be possible using FFLUX, yielding harmonic phonon spectra comparable to dispersion-corrected DFT while enabling larger supercells to be considered than is typically possible with first-principles calculations. These promising results indicate that FFLUX can be used to accurately determine properties of molecular solids that are difficult to access using DFT, including the structural dynamics, free energies, and properties at finite temperature.
Collapse
Affiliation(s)
- Matthew
L. Brown
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, Britain
| | - Jonathan M. Skelton
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, Britain
| | - Paul L. A. Popelier
- Department of Chemistry, The University of Manchester, Oxford Road, Manchester M13 9PL, Britain
| |
Collapse
|
12
|
Zhu JY, Liu Q, Jiang XN, Zheng XH, Wang L, Hao Q, Wang CS. From bonds to interactions: comprehensive molecular characterization via polarizable bond-dipole approach. Phys Chem Chem Phys 2023; 25:29867-29880. [PMID: 37888898 DOI: 10.1039/d3cp04060g] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2023]
Abstract
Accurately characterizing molecular interactions stands as a pivotal requirement for ensuring the reliability of molecular dynamics simulations. In line with our bond-dipole-based interaction model proposed by Gao et al. [X.-C. Gao, Q. Hao and C.-S. Wang, J. Chem. Theory Comput., 2017, 13, 2730-2741.], we have implemented an efficient and concise approach to compute electrostatic potential. This methodology capitalizes on the polarizable nature of chemical bond dipoles, resulting in a model of remarkable simplicity. In this study, we have revised the polarizable bond-dipole-based force field (PBFF) through the meticulous curation of quantum chemical data sets. These data sets encompass a comprehensive collection of 40 000 conformations, including those of water, methylamine, methanol, and N-methylacetamide. Additionally, we incorporate 520 hydrogen-bonded dimers into our data sets. In pursuit of enhanced accuracy in molecular dynamics simulations and a more faithful representation of potential energy landscapes, we undertook the re-optimization of the nonbonded parameters within the PBFF framework. Concurrently, we intricately fine-tuned the bonded parameters. The results of our comprehensive evaluation denote that this newly optimized force field method adeptly and efficiently computes structural characteristics, harmonic frequencies, and interaction energies. Overall, this study provides further validation for the applicability of PBFF in molecular dynamics simulations.
Collapse
Affiliation(s)
- Jia-Yi Zhu
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Qi Liu
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Xiao-Nan Jiang
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Xiao-Han Zheng
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Lei Wang
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Qiang Hao
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| | - Chang-Sheng Wang
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, China.
| |
Collapse
|
13
|
Polonius S, Zhuravel O, Bachmair B, Mai S. LVC/MM: A Hybrid Linear Vibronic Coupling/Molecular Mechanics Model with Distributed Multipole-Based Electrostatic Embedding for Highly Efficient Surface Hopping Dynamics in Solution. J Chem Theory Comput 2023; 19:7171-7186. [PMID: 37788824 PMCID: PMC10601485 DOI: 10.1021/acs.jctc.3c00805] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2023] [Indexed: 10/05/2023]
Abstract
We present a theoretical framework for a hybrid linear vibronic coupling model electrostatically embedded into a molecular mechanics environment, termed the linear vibronic coupling/molecular mechanics (LVC/MM) method, for the surface hopping including arbitrary coupling (SHARC) molecular dynamics package. Electrostatic embedding is realized through the computation of interactions between environment point charges and distributed multipole expansions (DMEs, up to quadrupoles) that represent each electronic state and transition densities in the diabatic basis. The DME parameters are obtained through a restrained electrostatic potential (RESP) fit, which we extended to yield higher-order multipoles. We also implemented in SHARC a scheme for achieving roto-translational invariance of LVC models as well as a general quantum mechanics/molecular mechanics (QM/MM) interface, an OpenMM interface, and restraining potentials for simulating liquid droplets. Using thioformaldehyde in water as a test case, we demonstrate that LVC/MM can accurately reproduce the solvation structure and energetics of rigid solutes, with errors on the order of 1-2 kcal/mol compared to a BP86/MM reference. The implementation in SHARC is shown to be very efficient, enabling the simulation of trajectories on the nanosecond time scale in a matter of days.
Collapse
Affiliation(s)
- Severin Polonius
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
- Vienna
Doctoral School in Chemistry (DoSChem), University of Vienna, Währinger Str. 42, 1090 Vienna, Austria
| | - Oleksandra Zhuravel
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - Brigitta Bachmair
- Vienna
Doctoral School in Chemistry (DoSChem), University of Vienna, Währinger Str. 42, 1090 Vienna, Austria
- Research
Platform on Accelerating Photoreaction Discovery (ViRAPID), University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| | - Sebastian Mai
- Institute
of Theoretical Chemistry, Faculty of Chemistry, University of Vienna, Währinger Str. 17, 1090 Vienna, Austria
| |
Collapse
|
14
|
Mendonça BHS, de Moraes EE, Kirch A, Batista RJC, de Oliveira AB, Barbosa MC, Chacham H. Flow through Deformed Carbon Nanotubes Predicted by Rigid and Flexible Water Models. J Phys Chem B 2023; 127:8634-8643. [PMID: 37754781 DOI: 10.1021/acs.jpcb.3c02889] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/28/2023]
Abstract
In this study, using nonequilibrium molecular dynamics simulation, the flow of water in deformed carbon nanotubes is studied for two water models TIP4P/2005 and simple point charge/FH (SPC/FH). The results demonstrated a nonuniform dependence of the flow on the tube deformation and the flexibility imposed on the water molecules, leading to an unexpected increase in the flow in some cases. The effects of the tube diameter and pressure gradient are investigated to explain the abnormal flow behavior with different degrees of structural deformation.
Collapse
Affiliation(s)
- Bruno H S Mendonça
- Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, Belo Horizonte 30123-970, MG, Brazil
| | - Elizane E de Moraes
- Instituto de Física, Universidade Federal da Bahia, Campus Universitário de Ondina, Salvador 40210-340, BA, Brazil
| | - Alexsandro Kirch
- Instituto de Física, Universidade de São Paulo, CP 66318, São Paulo 05315-970, SP, Brazil
| | - Ronaldo J C Batista
- Departamento de Física, Universidade Federal de Ouro Preto, Campus Morro do Cruzeiro, Ouro Preto 35400-000, MG, Brazil
| | - Alan B de Oliveira
- Departamento de Física, Universidade Federal de Ouro Preto, Campus Morro do Cruzeiro, Ouro Preto 35400-000, MG, Brazil
| | - Marcia C Barbosa
- Instituto de Física, Universidade Federal do Rio Grande do Sul, Porto Alegre 91501-970, RS, Brazil
| | - Hélio Chacham
- Departamento de Física, ICEX, Universidade Federal de Minas Gerais, CP 702, Belo Horizonte 30123-970, MG, Brazil
| |
Collapse
|
15
|
Herman KM, Stone AJ, Xantheas SS. Accurate Calculation of Many-Body Energies in Water Clusters Using a Classical Geometry-Dependent Induction Model. J Chem Theory Comput 2023; 19:6805-6815. [PMID: 37703063 DOI: 10.1021/acs.jctc.3c00575] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/14/2023]
Abstract
We incorporate geometry-dependent distributed multipole and polarizability surfaces into an induction model that is used to describe the 3- and 4-body terms of the interaction between water molecules. The moment expansion is carried out up to the hexadecapole with the multipoles distributed on the atom sites. Dipole-dipole, dipole-quadrupole, and quadrupole-quadrupole distributed polarizabilities are used to represent the response of the multipoles to an electric field. We compare the model against two large databases consisting of 43,844 3-body terms and 3,603 4-body terms obtained from high level ab initio calculations previously used to fit the MB-pol and q-AQUA classical interaction potentials for water. The classical induction model with no adjustable parameters reproduces the ab initio 3-/4-body terms contained in these two databases with a root-mean-square error (RMSE) of 0.104/0.058 and a mean-absolute error (MAE) of 0.054/0.026 kcal/mol, respectively. These results are on par with the ones obtained by fitting the same data using over 14,000 (for the 3-body) and 200 (for the 4-body) parameters via Permutationally Invariant Polynomials (PIPs). This demonstrates the accuracy of this physically motivated model in describing the 3- and 4-body terms in the interactions between water molecules with no adjustable parameters. The triple-dipole-dispersion energy, included in the calculation of the 3-body energy, was found to be small but not quite negligible. The model represents a practical, efficient, and transferable approach for obtaining accurate nonadditive interactions for multicomponent systems without the need to perform tens of thousands of high level electronic structure calculations and fitting them with PIPs.
Collapse
Affiliation(s)
- Kristina M Herman
- Department of Chemistry, University of Washington, Seattle, Washington 98185, United States
| | - Anthony J Stone
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge CB2 1EW, U.K
| | - Sotiris S Xantheas
- Department of Chemistry, University of Washington, Seattle, Washington 98185, United States
- Advanced Computing Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MSIN J7-10, Richland, Washington 99352, United States
| |
Collapse
|
16
|
Han B, Isborn CM, Shi L. Incorporating Polarization and Charge Transfer into a Point-Charge Model for Water Using Machine Learning. J Phys Chem Lett 2023; 14:3869-3877. [PMID: 37067482 DOI: 10.1021/acs.jpclett.3c00036] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/19/2023]
Abstract
Rigid nonpolarizable water models with fixed point charges have been widely employed in molecular dynamics simulations due to their efficiency and reasonable accuracy for the potential energy surface. However, the dipole moment surface of water is not necessarily well-described by the same fixed charges, leading to failure in reproducing dipole-related properties. Here, we developed a machine-learning model trained against electronic structure data to assign point charges for water, and the resulting dipole moment surface significantly improved the predictions of the dielectric constant and the low-frequency IR spectrum of liquid water. Our analysis reveals that within our atom-centered point-charge description of the dipole moment surface, the intermolecular charge transfer is the major source of the peak intensity at 200 cm-1, whereas the intramolecular polarization controls the enhancement of the dielectric constant. The effects of exact Hartree-Fock exchange in the hybrid density functional on these properties are also discussed.
Collapse
Affiliation(s)
- Bowen Han
- Chemistry and Biochemistry, University of California, Merced, California 95343, United States
| | - Christine M Isborn
- Chemistry and Biochemistry, University of California, Merced, California 95343, United States
| | - Liang Shi
- Chemistry and Biochemistry, University of California, Merced, California 95343, United States
| |
Collapse
|
17
|
Hercigonja M, Milovanović B, Etinski M, Petković M. Decorated crown ethers as selective ion traps: Solvent’s role in crown’s preference towards a specific ion. J Mol Liq 2023. [DOI: 10.1016/j.molliq.2023.121791] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/08/2023]
|
18
|
Plé T, Mauger N, Adjoua O, Inizan TJ, Lagardère L, Huppert S, Piquemal JP. Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials. J Chem Theory Comput 2023; 19:1432-1445. [PMID: 36856658 DOI: 10.1021/acs.jctc.2c01233] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/02/2023]
Abstract
We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.
Collapse
Affiliation(s)
- Thomas Plé
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Nastasia Mauger
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Olivier Adjoua
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | | | - Louis Lagardère
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Simon Huppert
- Institut des Nanosciences de Paris (INSP), CNRS UMR 7588, and Sorbonne Université, F-75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France.,Institut Universitaire de France, 75005 Paris, France.,Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
19
|
Herman KM, Xantheas SS. An extensive assessment of the performance of pairwise and many-body interaction potentials in reproducing ab initio benchmark binding energies for water clusters n = 2-25. Phys Chem Chem Phys 2023; 25:7120-7143. [PMID: 36853239 DOI: 10.1039/d2cp03241d] [Citation(s) in RCA: 10] [Impact Index Per Article: 10.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We assess the performance of 7 pairwise additive (TIP3P, TIP4P, TIP4P-ice, TIP5P, OPC, SPC, SPC/E) and 8 families of many-body potentials (q-AQUA, HIPPO, AMOEBA, EFP, TTM, WHBB, MB-pol, MB-UCB) in reproducing high-level ab initio benchmark values, CCSD(T) or MP2 at the complete basis set (CBS) limit for the binding energy and the many-body expansion (MBE) of water clusters n = 2-11, 16-17, 20, 25. By including a large range of cluster sizes having dissimilar hydrogen bonding networks, we obtain an understanding of how these potentials perform for different hydrogen bonding arrangements that are mostly outside of their parameterization range. While it is appropriate to compare the results of ab initio based many-body potentials directly to the electronic binding energies (De's), the pairwise additive ones are compared to the enthalpies at T = 298 K, ΔH(298 K), as the latter class of force fields are parametrized to reproduce enthalpies (implicitly accounting for zero-point energy corrections) rather than binding energies. We find that all pairwise additive potentials considered overestimate the reference ΔH values for the n = 2-25 clusters by >13%. For the water dimer (n = 2) in particular, the errors are in the range 83-119% for the pairwise additive potentials studied since these are based on an effective rather than the true 2-body interaction specifically designed as a means of partially accounting for the missing many-body terms. This stronger 2-body interaction is achieved by an enhanced monomer dipole moment that mimics its increase from the gas phase monomer to the condensed phase value. Indeed, for cluster sizes n ≥ 4 the percent deviations become slightly smaller (albeit all exceeding 13%). In contrast, we find that the many-body potentials perform more accurately in reproducing the electronic binding energies (De's) throughout the entire cluster range (n = 2-25), all reproducing the ab initio benchmark binding energies within ±7% of the respective CBS values. We further assess the ability of a subset of the many-body potentials (MB-UCB, q-AQUA, MB-pol, and TTM2.1-F) to also reproduce the magnitude of the ab initio many-body energy terms for water cluster sizes n = 7, 10, 16 and 17. The potentials show an overall good agreement with the available benchmark values. However, we identify characteristic differences upon comparing the many-body terms at both the ab initio-optimized geometries and the respective potential-optimized geometries to the reference ab initio values. Additionally, by applying this analysis to a wide range of cluster sizes, trends in the MBE of the potentials with increasing cluster size can be identified. Finally, in an attempt to draw a parallel between the pairwise additive and many-body potentials, we report the analysis of the individual molecular dipole moments for water clusters with 1 to ∼4 solvation shells with the TTM2.1-F potential. We find that the internally solvated water molecules have in general a larger molecular dipole moment ranging from 2.6-3.0 D. This justifies the use of an enhanced, with respect to the gas-phase value, molecular dipole moment for the pairwise additive potentials, which is intended to fold in the many body terms into an effective (enhanced) pairwise interaction through the choice of the charges. These results have important implications for the development of future generations of efficient, transferable, and highly accurate classical interaction potentials in both the pairwise additive and many-body categories.
Collapse
Affiliation(s)
- Kristina M Herman
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA.
| | - Sotiris S Xantheas
- Department of Chemistry, University of Washington, Seattle, WA 98195, USA. .,Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, 902 Battelle Boulevard, P.O. Box 999, MS K1-83, WA, 99352, USA.
| |
Collapse
|
20
|
Li XL, Li CM, Zhu JY, Zhou Z, Hao Q, Wang CS. A scheme for rapid evaluation of the intermolecular three-body polarization effect in water clusters. J Comput Chem 2023; 44:677-686. [PMID: 36408852 DOI: 10.1002/jcc.27032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 09/22/2022] [Accepted: 10/24/2022] [Indexed: 11/22/2022]
Abstract
The ability to accurately and rapidly evaluate the intermolecular many-body polarization effect of the water system is very important for computer simulations of biomolecule in aqueous. In this paper, a scheme is proposed based on the polarizable dipole-dipole interaction model and used to rapidly estimate the intermolecular many-body polarization effect in water clusters. We use a bond-dipole-based polarization function to evaluate the polarization energy. We regard two OH bonds of a water molecule as two bond-dipoles and set the permanent OH bond-dipole moment of a water molecule to be 1.51 Debye. We estimate the induced OH bond-dipole moment via a simple formula in which only one correction factor is needed. This scheme is then applied to tens of water clusters to calculate the three- and four-body interaction energies. The three-body interaction energies of 93 water clusters produced by our scheme are compared with those produced by the counterpoise-corrected CCSD(T)/aug-cc-pVDZ, MP2/aug-cc-pVDZ, M06-2X/jul-cc-pVTZ methods, by the AMOEBApro13, iAMOEBA, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The four-body interaction energies of 47 water clusters yielded by our scheme are compared with those yielded by the counterpoise-corrected MP2/aug-cc-pVDZ and M06-2X/ jul-cc-pVTZ methods, by the AMOEBApro13, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The comparison results show that the scheme proposed in this paper can reproduce the counterpoise-corrected CCSD(T)/aug-cc-pVDZ three-body interaction energies and reproduce the counterpoise-corrected MP2/aug-cc-pVDZ four-body interaction energies both accurately and efficiently. We anticipate the scheme proposed here can be useful for computer simulations of liquid water and aqueous solutions.
Collapse
Affiliation(s)
- Xiao-Lei Li
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Chao-Ming Li
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Jia-Yi Zhu
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Zhan Zhou
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Qiang Hao
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Chang-Sheng Wang
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| |
Collapse
|
21
|
Brown M, Skelton JM, Popelier PLA. Construction of a Gaussian Process Regression Model of Formamide for Use in Molecular Simulations. J Phys Chem A 2023; 127:1702-1714. [PMID: 36756842 PMCID: PMC9969515 DOI: 10.1021/acs.jpca.2c06566] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/10/2023]
Abstract
FFLUX, a novel force field based on quantum chemical topology, can perform molecular dynamics simulations with flexible multipole moments that change with geometry. This is enabled by Gaussian process regression machine learning models, which accurately predict atomic energies and multipole moments up to the hexadecapole. We have constructed a model of the formamide monomer at the B3LYP/aug-cc-pVTZ level of theory capable of sub-kJ mol-1 accuracy, with the maximum prediction error for the molecule being 0.8 kJ mol-1. This model was used in FFLUX simulations along with Lennard-Jones parameters to successfully optimize the geometry of formamide dimers with errors smaller than 0.1 Å compared to those obtained with D3-corrected B3LYP/aug-cc-pVTZ. Comparisons were also made to a force field constructed with static multipole moments and Lennard-Jones parameters. FFLUX recovers the expected energy ranking of dimers compared to the literature, and changes in C═O and C-N bond lengths associated with hydrogen bonding were found to be consistent with density functional theory.
Collapse
|
22
|
Ignatov SK, Masunov AE. Unexpected polarization properties of sub-nanosized magnesium clusters. RSC Adv 2023; 13:4065-4076. [PMID: 36756583 PMCID: PMC9890678 DOI: 10.1039/d2ra08086a] [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: 12/18/2022] [Accepted: 01/20/2023] [Indexed: 01/29/2023] Open
Abstract
The isotropic electrostatic polarizability (IEP) of sub-nanosized magnesium clusters Mg2-Mg32 was studied in an extensive set comprising 1237 structurally unique isomers. These isomers were found in the course of the global search for the potential energy surface minima of the magnesium clusters at the BP86/6-31G(d) level. The calculation of the polarizability at the same DFT level reveals an unexpected property of the IEP: the linear correlation between the polarizability of the most favorable isomers (and only them) and the cluster nuclearity n. Moreover, for each n, the most stable cluster isomer demonstrates nearly minimal IEP value among all found isomers of a given nuclearity. Surprisingly, these observed features are independent of the cluster structures which are quite different. We hypothesize that the energetic favorability of a cluster structure is related to their low polarizability. Apparently, the atoms forming the cluster tend to arrange themselves in such a way as to provide the most compact distribution of the cluster electron density. A possible explanation of the observed trends, their significance for cluster structure prediction, and the practical applications are discussed.
Collapse
Affiliation(s)
| | - Artëm E. Masunov
- NanoScience Technology Center, University of Central FloridaOrlandoFlorida 32826USA,School of Modeling, Simulations and Training, University of Central FloridaOrlandoFlorida 32826USA,South Ural State University (National Research University)ChelyabinskRussia
| |
Collapse
|
23
|
Wang X, Tse YLS. Flexible Polarizable Water Model Parameterized via Gaussian Process Regression. J Chem Theory Comput 2022; 18:7155-7165. [PMID: 36374554 DOI: 10.1021/acs.jctc.2c00529] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022]
Abstract
Water is one of the most common components in molecular dynamics (MD) simulations. Using Gaussian process regression for predicting the properties of a water model without the need of running a simulation whenever the parameters are changed, we obtained a flexible polarizable water model, named SWM4/Fw, that is able to reproduce many reference water properties. The added flexibility is critical for modeling chemical reactions in which chemical bonds can be stretched or even broken and for directly calculating vibrational spectra. In addition to being one of the few water models that are both flexible and polarizable, SWM4/Fw is also efficient thanks to the extended Lagrangian scheme with Drude oscillators. The overall accuracy is on par with or better than the related SWM4-NDP model.
Collapse
Affiliation(s)
- Xinyan Wang
- Department of Chemistry, The Chinese University of Hong Kong, Sha Tin, Hong Kong000000, China
| | - Ying-Lung Steve Tse
- Department of Chemistry, The Chinese University of Hong Kong, Sha Tin, Hong Kong000000, China
| |
Collapse
|
24
|
Boittier ED, Devereux M, Meuwly M. Molecular Dynamics with Conformationally Dependent, Distributed Charges. J Chem Theory Comput 2022; 18:7544-7554. [PMID: 36346403 DOI: 10.1021/acs.jctc.2c00693] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
Accounting for geometry-induced changes in the electronic distribution in molecular simulation is important for capturing effects such as charge flow, charge anisotropy, and polarization. Multipolar force fields have demonstrated their ability to correctly represent chemically significant features such as anisotropy and sigma holes. It has also been shown that off-center point charges offer a compact alternative with similar accuracy. Here, it is demonstrated that allowing relocation of charges within a minimally distributed charge model (MDCM) with respect to their reference atoms is a viable route to capture changes in the molecular charge distribution depending on geometry, i.e., intramolecular polarization. The approach, referred to as "flexible MDCM" (fMDCM), is validated on a number of small molecules and provides accuracies in the electrostatic potential (ESP) of 0.5 kcal/mol on average compared with reference data from electronic structure calculations, whereas MDCM and point charges have root mean squared errors of a factor of 2 to 5 higher. In addition, MD simulations in the NVE ensemble using fMDCM for a box of flexible water molecules with periodic boundary conditions show a width of 0.1 kcal/mol for the fluctuation around the mean at 300 K on the 10 ns time scale. For water, the equilibrium valence angle in the gas phase is found to increase by 2° for simulations in the condensed phase which is consistent with experiment. The accuracy in capturing the geometry dependence of the ESP together with the long-time stability in energy conserving simulations makes fMDCM a promising tool to introduce advanced electrostatics into atomistic simulations.
Collapse
Affiliation(s)
- Eric D Boittier
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Mike Devereux
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| |
Collapse
|
25
|
Mauger N, Plé T, Lagardère L, Huppert S, Piquemal JP. Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field. J Phys Chem B 2022; 126:8813-8826. [PMID: 36270033 DOI: 10.1021/acs.jpcb.2c04454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.
Collapse
Affiliation(s)
- Nastasia Mauger
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Thomas Plé
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Louis Lagardère
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Simon Huppert
- Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| |
Collapse
|
26
|
Walker B, Liu C, Wait E, Ren P. Automation of AMOEBA polarizable force field for small molecules: Poltype 2. J Comput Chem 2022; 43:1530-1542. [PMID: 35778723 PMCID: PMC9329217 DOI: 10.1002/jcc.26954] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2022] [Revised: 05/02/2022] [Accepted: 06/09/2022] [Indexed: 11/10/2022]
Abstract
A next-generation protocol (Poltype 2) has been developed which automatically generates AMOEBA polarizable force field parameters for small molecules. Both features and computational efficiency have been drastically improved. Notable advances include improved database transferability using SMILES, robust torsion fitting, non-aromatic ring torsion parameterization, coupled torsion-torsion parameterization, Van der Waals parameter refinement using ab initio dimer data and an intelligent fragmentation scheme that produces parameters with dramatically reduced ab initio computational cost. Additional improvements include better local frame assignment for atomic multipoles, automated formal charge assignment, Zwitterion detection, smart memory resource defaults, parallelized fragment job submission, incorporation of Psi4 quantum package, ab initio error handling, ionization state enumeration, hydration free energy prediction and binding free energy prediction. For validation, we have applied Poltype 2 to ~1000 FDA approved drug molecules from DrugBank. The ab initio molecular dipole moments and electrostatic potential values were compared with Poltype 2 derived AMOEBA counterparts. Parameters were further substantiated by calculating hydration free energy (HFE) on 40 small organic molecules and were compared with experimental data, resulting in an RMSE error of 0.59 kcal/mol. The torsion database has expanded to include 3543 fragments derived from FDA approved drugs. Poltype 2 provides a convenient utility for applications including binding free energy prediction for computational drug discovery. Further improvement will focus on automated parameter refinement by experimental liquid properties, expansion of the Van der Waals parameter database and automated parametrization of modified bio-fragments such as amino and nucleic acids.
Collapse
Affiliation(s)
- Brandon Walker
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Chengwen Liu
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Elizabeth Wait
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
27
|
Symons BCB, Popelier PLA. Application of Quantum Chemical Topology Force Field FFLUX to Condensed Matter Simulations: Liquid Water. J Chem Theory Comput 2022; 18:5577-5588. [PMID: 35939826 PMCID: PMC9476653 DOI: 10.1021/acs.jctc.2c00311] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
![]()
We present here the first application of the quantum
chemical topology
force field FFLUX to condensed matter simulations. FFLUX offers many-body
potential energy surfaces learnt exclusively from ab initio data using Gaussian process regression. FFLUX also includes high-rank,
polarizable multipole moments (up to quadrupole moments in this work)
that are learnt from the same ab initio calculations
as the potential energy surfaces. Many-body effects (where a body
is an atom) and polarization are captured by the machine learning
models. The choice to use machine learning in this way allows the
force field’s representation of reality to be improved (e.g., by including higher order many-body effects) with
little detriment to the computational scaling of the code. In this
manner, FFLUX is inherently future-proof. The “plug and play”
nature of the machine learning models also ensures that FFLUX can
be applied to any system of interest, not just liquid water. In this
work we study liquid water across a range of temperatures and compare
the predicted bulk properties to experiment as well as other state-of-the-art
force fields AMOEBA(+CF), HIPPO, MB-Pol and SIBFA21. We find that
FFLUX finds a place amongst these.
Collapse
Affiliation(s)
- Benjamin C B Symons
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| | - Paul L A Popelier
- Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| |
Collapse
|
28
|
Symons BCB, Popelier PLA. Flexible multipole moments in smooth particle mesh Ewald. J Chem Phys 2022; 156:244107. [DOI: 10.1063/5.0095581] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The smooth particle mesh Ewald sum is extended with additional force terms that arise from the so-called flexible multipole moments. These are multipole moments (of any rank) that depend explicitly on atomic positions in some local environment that can be made arbitrarily large. By introducing explicit dependence on atomic positions, flexible multipole moments are polarized by their local environment, allowing both intramolecular and intermolecular polarizations to be captured. Multipolar torques are discussed in detail, and it is shown that they arise naturally in the presented framework. Furthermore, we give details of how we validated our implementation of the flexible smooth particle mesh Ewald sum by considering two mathematical limits of the smooth particle mesh Ewald summation.
Collapse
Affiliation(s)
- Benjamin C. B. Symons
- Department of Chemistry, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Paul L. A. Popelier
- Department of Chemistry, The University of Manchester, Manchester M13 9PL, United Kingdom
| |
Collapse
|
29
|
Naseem-Khan S, Lagardère L, Narth C, Cisneros GA, Ren P, Gresh N, Piquemal JP. Development of the Quantum-Inspired SIBFA Many-Body Polarizable Force Field: Enabling Condensed-Phase Molecular Dynamics Simulations. J Chem Theory Comput 2022; 18:3607-3621. [PMID: 35575306 PMCID: PMC10851344 DOI: 10.1021/acs.jctc.2c00029] [Citation(s) in RCA: 10] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
We present the extension of the Sum of Interactions Between Fragments Ab initio Computed (SIBFA) many-body polarizable force field to condensed-phase molecular dynamics (MD) simulations. The quantum-inspired SIBFA procedure is grounded on simplified integrals obtained from localized molecular orbital theory and achieves full separability of its intermolecular potential. It embodies long-range multipolar electrostatics (up to quadrupole) coupled to a short-range penetration correction (up to charge-quadrupole), exchange repulsion, many-body polarization, many-body charge transfer/delocalization, exchange dispersion, and dispersion (up to C10). This enables the reproduction of all energy contributions of ab initio symmetry-adapted perturbation theory (SAPT(DFT)) gas-phase reference computations. The SIBFA approach has been integrated within the Tinker-HP massively parallel MD package. To do so, all SIBFA energy gradients have been derived and the approach has been extended to enable periodic boundary conditions simulations using smooth particle mesh Ewald. This novel implementation also notably includes a computationally tractable simplification of the many-body charge transfer/delocalization contribution. As a proof of concept, we perform a first computational experiment defining a water model fitted on a limited set of SAPT(DFT) data. SIBFA is shown to enable a satisfactory reproduction of both gas-phase energetic contributions and condensed-phase properties highlighting the importance of its physically motivated functional form.
Collapse
Affiliation(s)
- Sehr Naseem-Khan
- LCT, UMR 7616 CNRS, Sorbonne Université, 75005 Paris, France
- Department of Chemistry, University of North Texas, Denton, Texas 76201, United States
| | - Louis Lagardère
- LCT, UMR 7616 CNRS, Sorbonne Université, 75005 Paris, France
- IP2CT, FR 2622, CNRS, Sorbonne Université, 75005 Paris, France
| | | | - G Andrés Cisneros
- Department of Chemistry, University of North Texas, Denton, Texas 76201, United States
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Nohad Gresh
- LCT, UMR 7616 CNRS, Sorbonne Université, 75005 Paris, France
| | - Jean-Philip Piquemal
- LCT, UMR 7616 CNRS, Sorbonne Université, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
- Institut Universitaire de France, 75005 Paris, France
| |
Collapse
|
30
|
Steinmann SN, Michel C. How to Gain Atomistic Insights on Reactions at the Water/Solid Interface? ACS Catal 2022. [DOI: 10.1021/acscatal.2c00594] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Affiliation(s)
- Stephan N. Steinmann
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Chimie
UMR 5182, 46 allée d’Italie, F-69364 Lyon, France
| | - Carine Michel
- Ecole Normale Supérieure de Lyon, CNRS, Laboratoire de Chimie
UMR 5182, 46 allée d’Italie, F-69364 Lyon, France
| |
Collapse
|
31
|
Bodo E. Perspectives in the Computational Modeling of New Generation, Biocompatible Ionic Liquids. J Phys Chem B 2022; 126:3-13. [PMID: 34978449 PMCID: PMC8762658 DOI: 10.1021/acs.jpcb.1c09476] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/02/2021] [Revised: 12/15/2021] [Indexed: 12/11/2022]
Abstract
In this Perspective, I review the current state of computational simulations on ionic liquids with an emphasis on the recent biocompatible variants. These materials are used here as an example of relatively complex systems that highlights the limits of some of the approaches commonly used to study their structure and dynamics. The source of these limits consists of the coexistence of nontrivial electrostatic, many-body quantum effects, strong hydrogen bonds, and chemical processes affecting the mutual protonation state of the constituent molecular ions. I also provide examples on how it is possible to overcome these problems using suitable simulation paradigms and recently improved techniques that, I expect, will be gradually introduced in the state-of-the-art of computational simulations of ionic liquids.
Collapse
Affiliation(s)
- Enrico Bodo
- Chemistry Department, University of Rome “La Sapienza”, P. A. Moro 5, 00185 Rome, Italy
| |
Collapse
|
32
|
Abstract
Thole-style mutual induction models for molecular polarization have been adopted by several popular polarizable force fields (FFs) for their simplicity and transferability. The atomic polarizability parameters of these models are typically derived by fitting to ab initio or/and experimental molecular polarizabilities. In this work, we improve upon Thole polarizability parameters by employing both high-level quantum mechanics molecular polarizabilities and electrostatic potential (ESP) responses on three-dimensional grids. Our results indicate that the two approaches to derive atomic polarizability parameters are both effective, while the ESP approaches can also capture the polarization for the atoms with lone pair electrons. The resulting polarizability parameters have been validated on a set of over 7200 molecules covering the most common elements found in organic molecules (C, H, O, N, P, S, F, Cl, Br, and I). These parameters have also been tested on the experimentally measured molecular polarizabilities of 422 molecules. The final set of parameters derived in this work show notable improvement over the current AMOEBA set. The result is a highly transferable, expanded set of atomic polarizabilities defined by the local chemical environment in the form of SMARTS patterns. These parameters can be used directly in molecular mechanics polarizable potential energy functions such as AMOEBA, AMOEBA+, and other Thole-style models.
Collapse
Affiliation(s)
| | | | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
33
|
Rackers JA, Silva RR, Wang Z, Ponder JW. Polarizable Water Potential Derived from a Model Electron Density. J Chem Theory Comput 2021; 17:7056-7084. [PMID: 34699197 DOI: 10.1021/acs.jctc.1c00628] [Citation(s) in RCA: 20] [Impact Index Per Article: 6.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
A new empirical potential for efficient, large scale molecular dynamics simulation of water is presented. The HIPPO (Hydrogen-like Intermolecular Polarizable POtential) force field is based upon the model electron density of a hydrogen-like atom. This framework is used to derive and parametrize individual terms describing charge penetration damped permanent electrostatics, damped polarization, charge transfer, anisotropic Pauli repulsion, and damped dispersion interactions. Initial parameter values were fit to Symmetry Adapted Perturbation Theory (SAPT) energy components for ten water dimer configurations, as well as the radial and angular dependence of the canonical dimer. The SAPT-based parameters were then systematically refined to extend the treatment to water bulk phases. The final HIPPO water model provides a balanced representation of a wide variety of properties of gas phase clusters, liquid water, and ice polymorphs, across a range of temperatures and pressures. This water potential yields a rationalization of water structure, dynamics, and thermodynamics explicitly correlated with an ab initio energy decomposition, while providing a level of accuracy comparable or superior to previous polarizable atomic multipole force fields. The HIPPO water model serves as a cornerstone around which similarly detailed physics-based models can be developed for additional molecular species.
Collapse
Affiliation(s)
- Joshua A Rackers
- Program in Computational & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States.,Center for Computing Research, Sandia National Laboratories, Albuquerque, New Mexico 87123, United States
| | - Roseane R Silva
- Program in Computational & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States
| | - Zhi Wang
- Department of Chemistry, Washington University in Saint Louis, Saint Louis, Missouri 63130, United States
| | - Jay W Ponder
- Department of Chemistry, Washington University in Saint Louis, Saint Louis, Missouri 63130, United States.,Department of Biochemistry & Molecular Biophysics, Washington University School of Medicine, Saint Louis, Missouri 63110, United States
| |
Collapse
|
34
|
Symons BCB, Bane MK, Popelier PLA. DL_FFLUX: A Parallel, Quantum Chemical Topology Force Field. J Chem Theory Comput 2021; 17:7043-7055. [PMID: 34617748 PMCID: PMC8582247 DOI: 10.1021/acs.jctc.1c00595] [Citation(s) in RCA: 12] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
![]()
DL_FFLUX is a force
field based on quantum chemical topology that
can perform molecular dynamics for flexible molecules endowed with
polarizable atomic multipole moments (up to hexadecapole). Using the
machine learning method kriging (aka Gaussian process regression),
DL_FFLUX has access to atomic properties (energy, charge, dipole moment,
etc.) with quantum mechanical accuracy. Newly optimized and parallelized
using domain decomposition Message Passing Interface (MPI), DL_FFLUX
is now able to deliver this rigorous methodology at scale while still
in reasonable time frames. DL_FFLUX is delivered as an add-on to the
widely distributed molecular dynamics code DL_POLY 4.08. For the systems
studied here (103–105 atoms), DL_FFLUX
is shown to add minimal computational cost to the standard DL_POLY
package. In fact, the optimization of the electrostatics in DL_FFLUX
means that, when high-rank multipole moments are enabled, DL_FFLUX
is up to 1.25× faster than standard DL_POLY. The parallel DL_FFLUX
preserves the quality of the scaling of MPI implementation in standard
DL_POLY. For the first time, it is feasible to use the full capability
of DL_FFLUX to study systems that are large enough to be of real-world
interest. For example, a fully flexible, high-rank polarized (up to
and including quadrupole moments) 1 ns simulation of a system of 10 125
atoms (3375 water molecules) takes 30 h (wall time) on 18 cores.
Collapse
Affiliation(s)
- Benjamin C B Symons
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain.,Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| | - Michael K Bane
- High End Compute LTD, 23 Welby Street, Manchester M13 0EL, Great Britainhttps://highendcompute.co.uk.,Department of Computing and Mathematics, Manchester Metropolitan University, Manchester M15 6BH, Great Britain
| | - Paul L A Popelier
- Manchester Institute of Biotechnology (MIB), 131 Princess Street, Manchester M1 7DN, Great Britain.,Department of Chemistry, University of Manchester, Oxford Road, Manchester M13 9PL, Great Britain
| |
Collapse
|
35
|
Mauger N, Plé T, Lagardère L, Bonella S, Mangaud É, Piquemal JP, Huppert S. Nuclear Quantum Effects in Liquid Water at Near Classical Computational Cost Using the Adaptive Quantum Thermal Bath. J Phys Chem Lett 2021; 12:8285-8291. [PMID: 34427440 DOI: 10.1021/acs.jpclett.1c01722] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQEs) in molecular simulations: the adaptive quantum thermal bath (adQTB). In this method, zero-point energy is introduced through a generalized Langevin thermostat designed to precisely enforce the quantum fluctuation-dissipation theorem. We propose a refined adQTB algorithm with improved accuracy and report adQTB simulations of liquid water. Through extensive comparison with reference path integral calculations, we demonstrate that it provides excellent accuracy for a broad range of structural and thermodynamic observables as well as infrared vibrational spectra. The adQTB has a computational cost comparable to that of classical molecular dynamics, enabling simulations of up to millions of degrees of freedom.
Collapse
Affiliation(s)
- Nastasia Mauger
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Thomas Plé
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
| | - Louis Lagardère
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Sara Bonella
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - Étienne Mangaud
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
- Institut Universitaire de France, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Simon Huppert
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
| |
Collapse
|
36
|
Jing Z, Liu C, Ren P. Advanced Electrostatic Model for Monovalent Ions Based on Ab Initio Energy Decomposition. J Chem Inf Model 2021; 61:2806-2817. [PMID: 34096706 PMCID: PMC8323402 DOI: 10.1021/acs.jcim.1c00426] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2022]
Abstract
Ions play important roles in the structures and functions of biomolecules. In biomolecular simulations, ions either directly interact with biomolecules or provide an ionic environment that influences electrostatic interactions of solutes. The AMOEBA+ water model has demonstrated significant advancement of the classical force field for describing molecular interactions due to its improvements on the functional forms to account for essential physics. This work expands the applicability of the AMOEBA+ model toward alkali metal (Li, Na, K, Rb, and Cs) and halogen (F, Cl, Br, and I) ions. Various quantum chemical data on ion-ion and ion-water interactions, experimental ion hydration free energies, and lattice energies of salt crystals are used in the parametrization. The final parameters are verified with other properties outside of the parametrization data, including lattice energies of additional salt crystals and ionic activity coefficients in solution. The new model captures a wide range of ion properties from the gas phase to solution phase and crystals. More importantly, AMOEBA+ provides energy components that are consistent with ab initio energy decomposition. Thus, we expect AMOEBA+ to be more general, transferable, and valuable for the interpretation of intermolecular forces in efficient classical simulations.
Collapse
Affiliation(s)
- Zhifeng Jing
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Chengwen Liu
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, TX 78712
| |
Collapse
|
37
|
Kozuch J, Schneider SH, Zheng C, Ji Z, Bradshaw RT, Boxer SG. Testing the Limitations of MD-Based Local Electric Fields Using the Vibrational Stark Effect in Solution: Penicillin G as a Test Case. J Phys Chem B 2021; 125:4415-4427. [PMID: 33900769 PMCID: PMC8522303 DOI: 10.1021/acs.jpcb.1c00578] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Noncovalent interactions underlie nearly all molecular processes in the condensed phase from solvation to catalysis. Their quantification within a physically consistent framework remains challenging. Experimental vibrational Stark effect (VSE)-based solvatochromism can be combined with molecular dynamics (MD) simulations to quantify the electrostatic forces in solute-solvent interactions for small rigid molecules and, by extension, when these solutes bind in enzyme active sites. While generalizing this approach toward more complex (bio)molecules, such as the conformationally flexible and charged penicillin G (PenG), we were surprised to observe inconsistencies in MD-based electric fields. Combining synthesis, VSE spectroscopy, and computational methods, we provide an intimate view on the origins of these discrepancies. We observe that the electric fields are correlated to conformation-dependent effects of the flexible PenG side chain, including both the local solvation structure and solute conformational sampling in MD. Additionally, we identified that MD-based electric fields are consistently overestimated in three-point water models in the vicinity of charged groups; this cannot be entirely ameliorated using polarizable force fields (AMOEBA) or advanced water models. This work demonstrates the value of the VSE as a direct method for experiment-guided refinements of MD force fields and establishes a general reductionist approach to calibrating vibrational probes for complex (bio)molecules.
Collapse
Affiliation(s)
- Jacek Kozuch
- Department of Chemistry, Stanford University, Stanford, California 94305-5012, United States
| | - Samuel H Schneider
- Department of Chemistry, Stanford University, Stanford, California 94305-5012, United States
| | - Chu Zheng
- Department of Chemistry, Stanford University, Stanford, California 94305-5012, United States
| | - Zhe Ji
- Department of Chemistry, Stanford University, Stanford, California 94305-5012, United States
| | - Richard T Bradshaw
- Department of Chemistry, King's College London, Britannia House, 7 Trinity Street, London SE1 1DB, U.K
| | - Steven G Boxer
- Department of Chemistry, Stanford University, Stanford, California 94305-5012, United States
| |
Collapse
|
38
|
Naseem-Khan S, Gresh N, Misquitta AJ, Piquemal JP. Assessment of SAPT and Supermolecular EDA Approaches for the Development of Separable and Polarizable Force Fields. J Chem Theory Comput 2021; 17:2759-2774. [DOI: 10.1021/acs.jctc.0c01337] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Sehr Naseem-Khan
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
| | - Nohad Gresh
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
| | - Alston J. Misquitta
- School of Physics and Astronomy and the Thomas Young Centre for Theory and Simulation of Materials at Queen Mary University of London, London E1 4NS, U.K
| | - Jean-Philip Piquemal
- Laboratoire de Chimie Théorique, Sorbonne Université, UMR 7616 CNRS, 75005 Paris, France
- Institut Universitaire de France, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
39
|
Corrigan RA, Qi G, Thiel AC, Lynn JR, Walker BD, Casavant TL, Lagardere L, Piquemal JP, Ponder JW, Ren P, Schnieders MJ. Implicit Solvents for the Polarizable Atomic Multipole AMOEBA Force Field. J Chem Theory Comput 2021; 17:2323-2341. [PMID: 33769814 DOI: 10.1021/acs.jctc.0c01286] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
Computational protein design, ab initio protein/RNA folding, and protein-ligand screening can be too computationally demanding for explicit treatment of solvent. For these applications, implicit solvent offers a compelling alternative, which we describe here for the polarizable atomic multipole AMOEBA force field based on three treatments of continuum electrostatics: numerical solutions to the nonlinear and linearized versions of the Poisson-Boltzmann equation (PBE), the domain-decomposition conductor-like screening model (ddCOSMO) approximation to the PBE, and the analytic generalized Kirkwood (GK) approximation. The continuum electrostatics models are combined with a nonpolar estimator based on novel cavitation and dispersion terms. Electrostatic model parameters are numerically optimized using a least-squares style target function based on a library of 103 small-molecule solvation free energy differences. Mean signed errors for the adaptive Poisson-Boltzmann solver (APBS), ddCOSMO, and GK models are 0.05, 0.00, and 0.00 kcal/mol, respectively, while the mean unsigned errors are 0.70, 0.63, and 0.58 kcal/mol, respectively. Validation of the electrostatic response of the resulting implicit solvents, which are available in the Tinker (or Tinker-HP), OpenMM, and Force Field X software packages, is based on comparisons to explicit solvent simulations for a series of proteins and nucleic acids. Overall, the emergence of performative implicit solvent models for polarizable force fields opens the door to their use for folding and design applications.
Collapse
Affiliation(s)
- Rae A Corrigan
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Guowei Qi
- Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242, United States
| | - Andrew C Thiel
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Jack R Lynn
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Brandon D Walker
- Department of Biomedical Engineering, University of Texas in Austin, Austin, Texas 78712, United States
| | - Thomas L Casavant
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States
| | - Louis Lagardere
- Department of Chemistry, Sorbonne Université, F-75005 Paris, France
| | | | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis, St. Louis, Missouri 63130, United States
| | - Pengyu Ren
- Department of Biomedical Engineering, University of Texas in Austin, Austin, Texas 78712, United States
| | - Michael J Schnieders
- Roy J Carver Department of Biomedical Engineering, University of Iowa, Iowa City, Iowa 52242, United States.,Department of Biochemistry, University of Iowa, Iowa City, Iowa 52242, United States
| |
Collapse
|
40
|
Adjoua O, Lagardère L, Jolly LH, Durocher A, Very T, Dupays I, Wang Z, Inizan TJ, Célerse F, Ren P, Ponder JW, Piquemal JP. Tinker-HP: Accelerating Molecular Dynamics Simulations of Large Complex Systems with Advanced Point Dipole Polarizable Force Fields Using GPUs and Multi-GPU Systems. J Chem Theory Comput 2021; 17:2034-2053. [PMID: 33755446 PMCID: PMC8047816 DOI: 10.1021/acs.jctc.0c01164] [Citation(s) in RCA: 31] [Impact Index Per Article: 10.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2020] [Indexed: 11/29/2022]
Abstract
We present the extension of the Tinker-HP package (Lagardère, Chem. Sci. 2018, 9, 956-972) to the use of Graphics Processing Unit (GPU) cards to accelerate molecular dynamics simulations using polarizable many-body force fields. The new high-performance module allows for an efficient use of single- and multiple-GPU architectures ranging from research laboratories to modern supercomputer centers. After detailing an analysis of our general scalable strategy that relies on OpenACC and CUDA, we discuss the various capabilities of the package. Among them, the multiprecision possibilities of the code are discussed. If an efficient double precision implementation is provided to preserve the possibility of fast reference computations, we show that a lower precision arithmetic is preferred providing a similar accuracy for molecular dynamics while exhibiting superior performances. As Tinker-HP is mainly dedicated to accelerate simulations using new generation point dipole polarizable force field, we focus our study on the implementation of the AMOEBA model. Testing various NVIDIA platforms including 2080Ti, 3090, V100, and A100 cards, we provide illustrative benchmarks of the code for single- and multicards simulations on large biosystems encompassing up to millions of atoms. The new code strongly reduces time to solution and offers the best performances to date obtained using the AMOEBA polarizable force field. Perspectives toward the strong-scaling performance of our multinode massive parallelization strategy, unsupervised adaptive sampling and large scale applicability of the Tinker-HP code in biophysics are discussed. The present software has been released in phase advance on GitHub in link with the High Performance Computing community COVID-19 research efforts and is free for Academics (see https://github.com/TinkerTools/tinker-hp).
Collapse
Affiliation(s)
- Olivier Adjoua
- Sorbonne
Université, LCT, UMR 7616
CNRS, F-75005 Paris, France
| | - Louis Lagardère
- Sorbonne
Université, LCT, UMR 7616
CNRS, F-75005 Paris, France
- Sorbonne
Université, IP2CT, FR2622 CNRS, F-75005 Paris, France
| | - Luc-Henri Jolly
- Sorbonne
Université, IP2CT, FR2622 CNRS, F-75005 Paris, France
| | | | | | | | - Zhi Wang
- Department
of Chemistry, Washington University in Saint
Louis, Saint Louis, Missouri 63110, United
States
| | | | - Frédéric Célerse
- Sorbonne
Université, LCT, UMR 7616
CNRS, F-75005 Paris, France
- Sorbonne
Université, CNRS, IPCM, F-75005 Paris, France
| | - Pengyu Ren
- Department
of Biomedical Engineering, The University
of Texas at Austin, Austin, Texas 78712, United States
| | - Jay W. Ponder
- Department
of Chemistry, Washington University in Saint
Louis, Saint Louis, Missouri 63110, United
States
| | - Jean-Philip Piquemal
- Sorbonne
Université, LCT, UMR 7616
CNRS, F-75005 Paris, France
- Department
of Biomedical Engineering, The University
of Texas at Austin, Austin, Texas 78712, United States
| |
Collapse
|
41
|
Shi Y, Laury ML, Wang Z, Ponder JW. AMOEBA binding free energies for the SAMPL7 TrimerTrip host-guest challenge. J Comput Aided Mol Des 2021; 35:79-93. [PMID: 33140208 PMCID: PMC7867568 DOI: 10.1007/s10822-020-00358-2] [Citation(s) in RCA: 14] [Impact Index Per Article: 4.7] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2020] [Accepted: 10/28/2020] [Indexed: 12/22/2022]
Abstract
As part of the SAMPL7 host-guest binding challenge, the AMOEBA force field was applied to calculate the absolute binding free energy for 16 charged organic ammonium guests to the TrimerTrip host, a recently reported acyclic cucurbituril-derived clip host structure with triptycene moieties at its termini. Here we report binding free energy calculations for this system using the AMOEBA polarizable atomic multipole force field and double annihilation free energy methodology. Conformational analysis of the host suggests three families of conformations that do not interconvert in solution on a time scale available to nanosecond molecular dynamics (MD) simulations. Two of these host conformers, referred to as the "indent" and "overlap" structures, are capable of binding guest molecules. As a result, the free energies of all 16 guests binding to both conformations were computed separately, and combined to produce values for comparison with experiment. Initial ranked results submitted as part of the SAMPL7 exercise had a mean unsigned error (MUE) from experimental binding data of 2.14 kcal/mol. Subsequently, a rigorous umbrella sampling reference calculation was used to better determine the free energy difference between unligated "indent" and "overlap" host conformations. Revised binding values for the 16 guests pegged to this umbrella sampling reference reduced the MUE to 1.41 kcal/mol, with a correlation coefficient (Pearson R) between calculated and experimental binding values of 0.832 and a rank correlation (Kendall τ) of 0.65. Overall, the AMOEBA results demonstrate no significant systematic error, suggesting the force field provides an accurate energetic description of the TrimerTrip host, and an appropriate balance of solvation and desolvation effects associated with guest binding.
Collapse
Affiliation(s)
- Yuanjun Shi
- Department of Chemistry, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| | - Marie L Laury
- Department of Chemistry, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| | - Zhi Wang
- Department of Chemistry, Washington University in St. Louis, Saint Louis, MO, 63130, USA
| | - Jay W Ponder
- Department of Chemistry, Washington University in St. Louis, Saint Louis, MO, 63130, USA.
- Department of Biochemistry & Molecular Biophysics, Washington University School of Medicine, Saint Louis, MO, 63110, USA.
| |
Collapse
|
42
|
Konovalov A, Symons BCB, Popelier PLA. On the many-body nature of intramolecular forces in FFLUX and its implications. J Comput Chem 2020; 42:107-116. [PMID: 33107993 DOI: 10.1002/jcc.26438] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2020] [Revised: 09/28/2020] [Accepted: 09/28/2020] [Indexed: 12/24/2022]
Abstract
FFLUX is a biomolecular force field under construction, based on Quantum Chemical Topology (QCT) and machine learning (kriging), with a minimalistic and physically motivated design. A detailed analysis of the forces within the kriging models as treated in FFLUX is presented, taking as a test example a liquid water model. The energies of topological atoms are modeled as 3Natoms -6 dimensional potential energy surfaces, using atomic local frames to represent the internal degrees of freedom. As a result, the forces within the kriging models in FFLUX are inherently N-body in nature where N refers to Natoms . This provides a fuller picture that is closer to a true quantum mechanical representation of interactions between atoms. The presented computational example quantitatively showcases the non-negligible (as much as 9%) three-body nature of bonded forces and angular forces in a water molecule. We discuss the practical impact on the pressure calculation with N-body forces and periodic boundary conditions (PBC) in molecular dynamics, as opposed to classical force fields with two-body forces. The equivalence between the PBC-related correction terms in the general virial equation is shown mathematically.
Collapse
Affiliation(s)
- Anton Konovalov
- Manchester Institute of Biotechnology (MIB), Manchester, United Kingdom.,Department of Chemistry, University of Manchester, Manchester, United Kingdom
| | - Benjamin C B Symons
- Manchester Institute of Biotechnology (MIB), Manchester, United Kingdom.,Department of Chemistry, University of Manchester, Manchester, United Kingdom
| | - Paul L A Popelier
- Manchester Institute of Biotechnology (MIB), Manchester, United Kingdom.,Department of Chemistry, University of Manchester, Manchester, United Kingdom
| |
Collapse
|
43
|
Calio PB, Li C, Voth GA. Molecular Origins of the Barriers to Proton Transport in Acidic Aqueous Solutions. J Phys Chem B 2020; 124:8868-8876. [PMID: 32924490 DOI: 10.1021/acs.jpcb.0c06223] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
The self-consistent iterative multistate empirical valence bond (SCI-MS-EVB) method is used to analyze the structure, thermodynamics, and dynamics of hydrochloric acid solutions. The reorientation time scales of irreversible proton transport are elucidated by simulating 0.43, 0.85, 1.68, and 3.26 M HCl solutions at 270, 285, 300, 315, and 330 K. The results indicate increased counterion pairing with increasing concentration, which manifests itself via a reduced hydronium oxygen-chloride (O*-Cl) structuring in the radial distribution functions. Increasing ionic concentration also reduces the diffusion of the hydrated excess protons, principally by reducing the contribution of the Grotthuss proton hopping (shuttling) mechanism to the overall diffusion process. In agreement with prior experimental findings, a decrease in the activation energy of reorientation time scales was also observed, which is explicitly explained by using activated rate theory and an energy-entropy decomposition of the state-averaged radial distribution functions. These results provide atomistic verification of suggestions from recent two-dimensional infrared spectroscopy experiments that chloride anions (as opposed to hydrated excess protons) create entropic barriers to proton transport.
Collapse
Affiliation(s)
- Paul B Calio
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
| | - Chenghan Li
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
| | - Gregory A Voth
- Department of Chemistry, Chicago Center for Theoretical Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 South Ellis Avenue, Chicago, Illinois 60637, United States
| |
Collapse
|
44
|
Lambros E, Paesani F. How good are polarizable and flexible models for water: Insights from a many-body perspective. J Chem Phys 2020; 153:060901. [DOI: 10.1063/5.0017590] [Citation(s) in RCA: 19] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, USA
| |
Collapse
|
45
|
Yang X, Liu C, Walker BD, Ren P. Accurate description of molecular dipole surface with charge flux implemented for molecular mechanics. J Chem Phys 2020; 153:064103. [DOI: 10.1063/5.0016376] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Xudong Yang
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712 Texas, USA
| | - Chengwen Liu
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712 Texas, USA
| | - Brandon D. Walker
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712 Texas, USA
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, 78712 Texas, USA
| |
Collapse
|
46
|
Qiu Y, Smith DGA, Stern CD, Feng M, Jang H, Wang LP. Driving torsion scans with wavefront propagation. J Chem Phys 2020; 152:244116. [PMID: 32610969 DOI: 10.1063/5.0009232] [Citation(s) in RCA: 18] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/06/2023] Open
Abstract
The parameterization of torsional/dihedral angle potential energy terms is a crucial part of developing molecular mechanics force fields. Quantum mechanical (QM) methods are often used to provide samples of the potential energy surface (PES) for fitting the empirical parameters in these force field terms. To ensure that the sampled molecular configurations are thermodynamically feasible, constrained QM geometry optimizations are typically carried out, which relax the orthogonal degrees of freedom while fixing the target torsion angle(s) on a grid of values. However, the quality of results and computational cost are affected by various factors on a non-trivial PES, such as dependence on the chosen scan direction and the lack of efficient approaches to integrate results started from multiple initial guesses. In this paper, we propose a systematic and versatile workflow called TorsionDrive to generate energy-minimized structures on a grid of torsion constraints by means of a recursive wavefront propagation algorithm, which resolves the deficiencies of conventional scanning approaches and generates higher quality QM data for force field development. The capabilities of our method are presented for multi-dimensional scans and multiple initial guess structures, and an integration with the MolSSI QCArchive distributed computing ecosystem is described. The method is implemented in an open-source software package that is compatible with many QM software packages and energy minimization codes.
Collapse
Affiliation(s)
- Yudong Qiu
- Department of Chemistry, UC Davis, Davis, California 95616, USA
| | - Daniel G A Smith
- The Molecular Sciences Software Institute, Blacksburg, Virginia 24060, USA
| | - Chaya D Stern
- Computational and Systems Biology Program, Sloan-Kettering Institute, New York, New York 10065, USA
| | - Mudong Feng
- Department of Chemistry and Biochemistry, UC San Diego, La Jolla, California 92093, USA
| | - Hyesu Jang
- Department of Chemistry, UC Davis, Davis, California 95616, USA
| | - Lee-Ping Wang
- Department of Chemistry, UC Davis, Davis, California 95616, USA
| |
Collapse
|