Force field (chemistry) - Knowledge (XXG)

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field. Different parametrization procedures have been developed for the parametrization of different substances, e.g. metals, ions, and molecules. For different material types, usually different parametrization strategies are used. In general, two main types can be distinguished for the parametrization, either using data/ information from the atomistic level, e.g. from quantum mechanical calculations or spectroscopic data, or using data from macroscopic properties, e.g. the hardness or compressibility of a given material. Often a combination of these routes is used. Hence, one way or the other, the force field parameters are always determined in an empirical way. Nevertheless, the term 'empirical' is often used in the context of force field parameters when macroscopic material property data was used for the fitting. Experimental data (microscopic and macroscopic) included for the fit, for example, the

1137:, and various spectroscopic properties such as vibrational frequencies. Often, for molecular systems, quantum mechanical calculations in the gas phase are used for parametrizing intramolecular interactions and parametrizing intermolecular dispersive interactions by using macroscopic properties such as liquid densities. The assignment of atomic charges often follows quantum mechanical protocols with some heuristics, which can lead to significant deviation in representing specific properties. 7631: 1369:

program DYANA (calculations from NMR data), or with programs for crystallographic refinement that use no energy functions at all. These shortcomings are related to interatomic potentials and to the inability to sample the conformation space of large molecules effectively. Thereby also the development of parameters to tackle such large-scale problems requires new approaches. A specific problem area is

1532:(GROningen MOlecular Simulation) – a force field that comes as part of the GROMOS software, a general-purpose molecular dynamics computer simulation package for the study of biomolecular systems. GROMOS force field A-version has been developed for application to aqueous or apolar solutions of proteins, nucleotides, and sugars. A B-version to simulate gas phase isolated molecules is also available. 1283:(DFT) calculations, with access to million times larger systems and time scales, to random guesses depending on the force field. The use of accurate representations of chemical bonding, combined with reproducible experimental data and validation, can lead to lasting interatomic potentials of high quality with much fewer parameters and assumptions in comparison to DFT-level quantum methods. 33: 250: 1505:, Lifson, and coworkers as a general method for unifying studies of energies, structures, and vibration of general molecules and molecular crystals. The CFF program, developed by Levitt and Warshel, is based on the Cartesian representation of all the atoms, and it served as the basis for many subsequent simulation programs. 1589:, where a particle's effective charge can be influenced by electrostatic interactions with its neighbors. Core-shell models are common, which consist of a positively charged core particle, representing the polarizable atom, and a negatively charged particle attached to the core atom through a spring-like 1827:– An AMBER-based forcefield and webtool for modeling common post-translational modifications of amino acids in proteins developed by Chris Floudas and coworkers. It uses the ff03 charge model and has several side-chain torsion corrections parameterized to match the quantum chemical rotational surface. 1665:

XED (eXtended Electron Distribution) - a polarizable force-field created as a modification of an atom-centered charge model, developed by Andy Vinter. Partially charged monopoles are placed surrounding atoms to simulate more geometrically accurate electrostatic potentials at a fraction of the expense

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Heuristic force field parametrization procedures have been very successfully for many year, but recently criticized. since they are usually not fully automated and therefore subject to some subjectivity of the developers, which also brings problems regarding the reproducibility of the parametrization

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Though the formula of Hooke's law provides a reasonable level of accuracy at bond lengths near the equilibrium distance, it is less accurate as one moves away. In order to model the Morse curve better one could employ cubic and higher powers. However, for most practical applications these differences

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state that the interaction energy of two dissimilar atoms (e.g., C...N) is an average of the interaction energies of corresponding identical atom pairs (i.e., C...C and N...N). According to McLachlan's theory, the interactions of particles in media can even be fully repulsive, as observed for liquid

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and transferability. When functional forms of the potential terms vary or are mixed, the parameters from one interatomic potential function can typically not be used together with another interatomic potential function. In some cases, modifications can be made with minor effort, for example, between

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COSMOS-NMR (Computer Simulation of Molecular Structure) – developed by Ulrich Sternberg and coworkers. Hybrid QM/MM force field enables explicit quantum-mechanical calculation of electrostatic properties using localized bond orbitals with fast BPT formalism. Atomic charge fluctuation is possible in

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IFF (Interface Force Field) – covers metals, minerals, 2D materials, and polymers. It uses 12-6 LJ and 9-6 LJ interactions. IFF was developed as for compounds across the periodic table. It assigs consistent charges, utilizes standard conditions as a reference state, reproduces structures, energies,

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applications, especially using program XPLOR. However, the refinement is driven mainly by a set of experimental constraints and the interatomic potentials serve mainly to remove interatomic hindrances. The results of calculations were practically the same with rigid sphere potentials implemented in

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In addition to the functional form of the potentials, a force fields consists of the parameters of these functions. Together, they specify the interactions on the atomistic level. The parametrization, i.e. determining of the parameter values, is crucial for the accuracy and reliability of the force

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WASABe v1.0 PFF (for Water, orgAnic Solvents, And Battery electrolytes) An isotropic atomic dipole polarizable force field for accurate description of battery electrolytes in terms of thermodynamic and dynamic properties for high lithium salt concentrations in sulfonate solvent by Oleg Starovoytov

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theory of these forces applies only in a vacuum. A more general theory of van der Waals forces in condensed media was developed by A. D. McLachlan in 1963 and included the original London's approach as a special case. The McLachlan theory predicts that van der Waals attractions in media are weaker

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A large number of workflows and parametrization procedures have been employed in the past decades using different data and optimization strategies for determining the force field parameters. They differ significantly, which is also due to different focuses of different developments. The parameters

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VAMM (Virtual atom molecular mechanics) – a coarse-grained force field developed by Korkut and Hendrickson for molecular mechanics calculations such as large scale conformational transitions based on the virtual interactions of C-alpha atoms. It is a knowledge based force field and formulated to

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and coworkers. It is slower than classical MD (50x), needs parameter sets with specific validation, and has no validation for surface and interfacial energies. Parameters are non-interpretable. It can be used atomistic-scale dynamical simulations of chemical reactions. Parallelized ReaxFF allows

1348:". Such effects are represented in molecular dynamics through pairwise interactions that are spatially more dense in the condensed phase relative to the gas phase and reproduced once the parameters for all phases are validated to reproduce chemical bonding, density, and cohesive/surface energy. 1230:

A large number of force fields has been published in the past decades - mostly in scientific publications. In recent years, some databases have attempted to collect, categorize and make force fields digitally available. Therein, different databases, focus on different types of force fields. For

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Atomistic interactions in crystal systems significantly deviate from those in molecular systems, e.g. of organic molecules. For crystal systems, in particular multi-body interactions are important and cannot be neglected if a high accuracy of the force field is the aim. For crystal systems with

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COSMOS-NMR – hybrid QM/MM force field adapted to various inorganic compounds, organic compounds, and biological macromolecules, including semi-empirical calculation of atomic charges NMR properties. COSMOS-NMR is optimized for NMR-based structure elucidation and implemented in COSMOS molecular

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Atomic charges can make dominant contributions to the potential energy, especially for polar molecules and ionic compounds, and are critical to simulate the geometry, interaction energy, and the reactivity. The assignment of charges usually uses some heuristic approach, with different possible

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GFN-FF (Geometry, Frequency, and Noncovalent Interaction Force-Field) – a completely automated partially polarizable generic force-field for the accurate description of structures and dynamics of large molecules across the periodic table developed by Stefan Grimme and Sebastian Spicher at the

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UFF (Universal Force Field) – A general force field with parameters for the full periodic table up to and including the actinoids, developed at Colorado State University. The reliability is known to be poor due to lack of validation and interpretation of the parameters for nearly all claimed

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ECEPP – first force field for polypeptide molecules - developed by F.A. Momany, H.A. Scheraga and colleagues. ECEPP was developed specifically for the modeling of peptides and proteins. It uses fixed geometries of amino acid residues to simplify the potential energy surface. Thus, the energy

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There are various criteria that can be used for categorizing force field parametrization strategies. An important differentiation is 'component-specific' and 'transferable'. For a component-specific parametrization, the considered force field is developed solely for describing a single given

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charge distributions. The remedy is that point charges have a clear interpretation and virtual electrons can be added to capture essential features of the electronic structure, such additional polarizability in metallic systems to describe the image potential, internal multipole moments in

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Momany FA, McGuire RF, Burgess AW, Scheraga HA (October 1975). "Energy parameters in polypeptides. VII. Geometric parameters, partial atomic charges, nonbonded interactions, hydrogen bond interactions, and intrinsic torsional potentials for the naturally occurring amino acids".

1222:. The use of semi-automation or full automation, without input from chemical knowledge, is likely to increase inconsistencies at the level of atomic charges, for the assignment of remaining parameters, and likely to dilute the interpretability and performance of parameters. 1558:

and other small organic molecules. It is designed to reproduce the equilibrium covalent geometry of molecules as precisely as possible. It implements a large set of parameters that is continuously refined and updated for many different classes of organic compounds (MM3 and

1778:Δ-ML not a force field method but a model that adds learnt correctional energy terms to approximate and relatively computationally cheap quantum chemical methods in order to provide an accuracy level of a higher order, more computationally expensive quantum chemical model. 1833:- An AMBER-based forcefield and webtool for modeling common non-natural amino acids in proteins in condensed-phase simulations using the ff03 charge model. The charges have been reported to be correlated with hydration free energies of corresponding side-chain analogs. 99: 1728:, initially developed for molecular dynamics simulations of lipids, later extended to various other molecules. The force field applies a mapping of four heavy atoms to one CG interaction site and is parameterized with the aim of reproducing thermodynamic properties. 1351:

Limitations have been strongly felt in protein structure refinement. The major underlying challenge is the huge conformation space of polymeric molecules, which grows beyond current computational feasibility when containing more than ~20 monomers. Participants in

486:. A large number of force fields based on this or similar energy expressions have been proposed in the past decades for modeling different types of materials such as molecular substances, metals, glasses etc. - see below for a comprehensive list of force fields. 1738:

SIRAH – a coarse-grained force field developed by Pantano and coworkers of the Biomolecular Simulations Group, Institut Pasteur of Montevideo, Uruguay; developed for molecular dynamics of water, DNA, and proteins. Free available for AMBER and GROMACS

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AMOEBA (Atomic Multipole Optimized Energetics for Biomolecular Applications) – force field developed by Pengyu Ren (University of Texas at Austin) and Jay W. Ponder (Washington University). AMOEBA force field is gradually moving to more physics-rich

1540:(IFF) assumes one single energy expression for all compounds across the periodic (with 9-6 and 12-6 LJ options). The IFF is in most parts non-polarizable, but also comprises polarizable parts, e.g. for some metals (Au, W) and pi-conjugated molecules 1709:) – This is a method commonly applied in chemical engineering. It is typically used for studying the hydrodynamics of various simple and complex fluids which require consideration of time and length scales larger than those accessible to classical 3978:

Pramanik C, Jamil T, Gissinger JR, Guittet D, Arias-Monje PJ, Kumar S, Heinz H (2019-10-03). "Polyacrylonitrile Interactions with Carbon Nanotubes in Solution: Conformations and Binding as a Function of Solvent, Temperature, and Concentration".

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PIPF – The polarizable intermolecular potential for fluids is an induced point-dipole force field for organic liquids and biopolymers. The molecular polarization is based on Thole's interacting dipole (TID) model and was developed by Jiali Gao

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minimization is conducted in the space of protein torsion angles. Both MM2 and ECEPP include potentials for H-bonds and torsion potentials for describing rotations around single bonds. ECEPP/3 was implemented (with some modifications) in

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Warshel A, Levitt M (1974). QCFF/PI: A Program for the Consistent Force Field Evaluation of Equilibrium Geometries and Vibrational Frequencies of Molecules (Report). Indiana University: Quantum Chemistry Program Exchange. p. QCPE

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workshop in 2008. Recently, work has been undertaken to capture some of the chemical subtitles relevant to solutions. This has led to work considering automated parameterisation of the DPD interaction potentials against experimental

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MACE (Multi Atomic Cluster Expansion) is a highly accurate machine learning force field architecture that combines the rigorous many-body expansion of the total potential energy with rotationally equivariant representations of the

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LFMM (Ligand Field Molecular Mechanics) - functions for the coordination sphere around transition metals based on the angular overlap model (AOM). Implemented in the Molecular Operating Environment (MOE) as DommiMOE and in

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is significantly smaller than enthalpy of sublimation. Hence, the potentials describing protein folding or ligand binding need more consistent parameterization protocols, e.g., as described for IFF. Indeed, the energies of

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Dauber-Osguthorpe P, Roberts VA, Osguthorpe DJ, Wolff J, Genest M, Hagler AT (1988). "Structure and energetics of ligand binding to proteins: Escherichia coli dihydrofolate reductase-trimethoprim, a drug-receptor system".

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Mishra RK, Fernández-Carrasco L, Flatt RJ, Heinz H (July 2014). "A force field for tricalcium aluminate to characterize surface properties, initial hydration, and organically modified interfaces in atomic resolution".

7363:"Forcefield_NCAA: ab initio charge parameters to aid in the discovery and design of therapeutic proteins and peptides with unnatural amino acids and their application to complement inhibitors of the compstatin family" 597: 328: 3081:

Dharmawardhana CC, Kanhaiya K, Lin TJ, Garley A, Knecht MR, Zhou J, Miao J, Heinz H (2017-06-19). "Reliable computational design of biological-inorganic materials to the large nanometer scale using Interface-FF".

1680:) – reactive force field introduced by Warshel and coworkers for use in modeling chemical reactions in different environments. The EVB facilitates calculating activation free energies in condensed phases and in 450:

The bond and angle terms are usually modeled by quadratic energy functions that do not allow bond breaking. A more realistic description of a covalent bond at higher stretching is provided by the more expensive

166:, with the main difference being that the force field parameters in chemistry describe the energy landscape on the atomistic level. From a force field, the acting forces on every particle are derived as a 3448:

Ruiz VG, Liu W, Tkatchenko A (2016-01-15). "Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces".

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Engkvist O, Astrand PO, Karlström G (November 2000). "Accurate Intermolecular Potentials Obtained from Molecular Wave Functions: Bridging the Gap between Quantum Chemistry and Molecular Simulations".

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Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD (January 2005). "Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator".

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Warshel A (1973). "Quantum mechanical consistent force field (QCFF/PI) method: Calculations of energies, conformations and vibronic interactions of ground and excited states of conjugated molecules".

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can be employed instead to enable bond breaking and higher accuracy, even though it is less efficient to compute. For reactive force fields, bond breaking and bond orders are additionally considered.

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Gaussian Electrostatic Model (GEM) – a polarizable force field based on Density Fitting developed by Thomas A. Darden and G. Andrés Cisneros at NIEHS; and Jean-Philip Piquemal at Paris VI University.

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Atomistic Polarizable Potential for Liquids, Electrolytes, and Polymers(APPLE&P), developed by Oleg Borogin, Dmitry Bedrov and coworkers, which is distributed by Wasatch Molecular Incorporated.

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Possible limitations include atomic charges, also called point charges. Most force fields rely on point charges to reproduce the electrostatic potential around molecules, which works less well for

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Heinz H, Lin TJ, Mishra RK, Emami FS (February 2013). "Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the INTERFACE force field".

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Maple JR, Cao Y, Damm W, Halgren TA, Kaminski GA, Zhang LY, Friesner RA (July 2005). "A Polarizable Force Field and Continuum Solvation Methodology for Modeling of Protein-Ligand Interactions".

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Starovoytov ON (September 2021). "Development of Polarizable Force Field for Molecular Dynamics Simulation of Lithium-Ion Battery Electrolytes: Sulfonate Based Solvents and Lithium Salts".

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Lii JH, Allinger NL (November 1989). "Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals' potentials and crystal data for aliphatic and aromatic hydrocarbons".

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Gavezzotti A, Filippini G (May 1994). "Geometry of the intermolecular XH. cntdot.. cntdot.. cntdot. Y (X, Y= N, O) hydrogen bond and the calibration of empirical hydrogen-bond potentials".

1303:. However, application of one value of dielectric constant is a coarse approximation in the highly heterogeneous environments of proteins, biological membranes, minerals, or electrolytes. 3371:

Heinz H, Ramezani-Dakhel H (January 2016). "Simulations of inorganic-bioorganic interfaces to discover new materials: insights, comparisons to experiment, challenges, and opportunities".

1336:, however, the lack of vaporization and presence of a freezing point contradicts a theory of purely repulsive interactions. Measurements of attractive forces between different materials ( 1388:

It was also argued that some protein force fields operate with energies that are irrelevant to protein folding or ligand binding. The parameters of proteins force fields reproduce the

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are negligible, and inaccuracies in predictions of bond lengths are on the order of the thousandth of an angstrom, which is also the limit of reliability for common force fields. A

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Shakhnovich EI, Finkelstein AV (October 1989). "Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first-order phase transition".

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Jorgensen WL, Maxwell DS, Tirado-Rives J (January 1996). "Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids".

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CHARMM – polarizable force field developed by S. Patel (University of Delaware) and C. L. Brooks III (University of Michigan). Based on the classical Drude oscillator developed by

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McDonagh JL, Shkurti A, Bray DJ, Anderson RL, Pyzer-Knapp EO (October 2019). "Utilizing Machine Learning for Efficient Parameterization of Coarse Grained Molecular Force Fields".

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substance (e.g. water). For a transferable force field, all or some parameters are designed as building blocks and become transferable/ applicable for different substances (e.g.

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Warshel A, Levitt M (May 1976). "Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme".

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Rappé AK, Casewit CJ, Colwell KS, Goddard III WA, Skiff WM (December 1992). "UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations".

193:). Depending on the material, different functional forms are usually chosen for the force fields since different types of atomistic interactions dominate the material behavior. 7410:

Khoury GA, Bhatia N, Floudas CA (2014). "Hydration free energies calculated using the AMBER ff03 charge model for natural and unnatural amino acids and multiple water models".

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Heinz H, Koerner H, Anderson KL, Vaia RA, Farmer BL (November 2005). "Force Field for Mica-Type Silicates and Dynamics of Octadecylammonium Chains Grafted to Montmorillonite".

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Schaumann T, Braun W, Wüthrich K (March 1990). "The program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space".

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Xu R, Chen CC, Wu L, Scott MC, Theis W, Ophus C, et al. (November 2015). "Three-dimensional coordinates of individual atoms in materials revealed by electrontomography".

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CFF (Consistent Force Field) – a family of force fields adapted to a broad variety of organic compounds, includes force fields for polymers, metals, etc. CFF was developed by

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ANI (Artificial Narrow Intelligence) is a transferable neural network potential, built from atomic environment vectors, and able to provide DFT accuracy in terms of energies.

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model that is used to describe the forces between atoms (or collections of atoms) within molecules or between molecules as well as in crystals. Force fields are a variety of

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Chelli R, Procacci P (November 2002). "A transferable polarizable electrostatic force field for molecular mechanics based on the chemical potential equalization principle".

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a central embarrassment of molecular mechanics, namely that energy minimization or molecular dynamics generally leads to a model that is less like the experimental structure

398: 333: 1713:. The potential was originally proposed by Hoogerbrugge and Koelman with later modifications by Español and Warren The current state of the art was well documented in a 1412:

of mobile molecules in condensed media. Thus, free energy changes during protein folding or ligand binding are expected to represent a combination of an energy similar to

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The nonbonded terms are computationally most intensive. A popular choice is to limit interactions to pairwise energies. The van der Waals term is usually computed with a

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Kirschner KN, Lins RD, Maass A, Soares TA (November 2012). "A Glycam-Based Force Field for Simulations of Lipopolysaccharide Membranes: Parametrization and Validation".

769: 693: 455:. The functional form for dihedral energy is variable from one force field to another. Additional, "improper torsional" terms may be added to enforce the planarity of 3596:

Mahoney MW, Jorgensen WL (2000-05-22). "A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions".

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Aduri R, Psciuk BT, Saro P, Taniga H, Schlegel HB, SantaLucia J (July 2007). "AMBER Force Field Parameters for the Naturally Occurring Modified Nucleosides in RNA".

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Graziano G, Catanzano F, Del Vecchio P, Giancola C, Barone G (1996). "Thermodynamic stability of globular proteins: a reliable model from small molecule studies".

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Pramanik C, Gissinger JR, Kumar S, Heinz H (December 2017). "Carbon Nanotube Dispersion in Solvents and Polymer Solutions: Mechanisms, Assembly, and Preferences".

463:, and "cross-terms" that describe the coupling of different internal variables, such as angles and bond lengths. Some force fields also include explicit terms for 6309:"Generalization of the Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods" 5535:

Patel S, Brooks CL (January 2004). "CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations".

1811:(flexible SPC), ST2, and mW. Other solvents and methods of solvent representation are also applied within computational chemistry and physics; these are termed 1593:

potential. Recent examples include polarizable models with virtual electrons that reproduce image charges in metals and polarizable biomolecular force fields.

1081: 1061: 733: 713: 5731:"CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model" 4241:

Gohlke H, Klebe G (August 2002). "Approaches to the description and prediction of the binding affinity of small-molecule ligands to macromolecular receptors".

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Sternberg U, Koch FT, Möllhoff M (May 1994). "New approach to the semiempirical calculation of atomic charges for polypeptides and large molecular systems".

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Hughes ZE, Thacker JC, Wilson AL, Popelier PL (January 2019). "Description of Potential Energy Surfaces of Molecules Using FFLUX Machine Learning Models".

277:. The specific decomposition of the terms depends on the force field, but a general form for the total energy in an additive force field can be written as 2959:

Gross KC, Seybold PG, Hadad CM (2002). "Comparison of different atomic charge schemes for predicting pKa variations in substituted anilines and phenols".

7652: 7585: 6203:"Anisotropic, Polarizable Molecular Mechanics Studies of Inter- and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-Up Strategy" 6864: 4838:

Möllhoff M, Sternberg U (May 2001). "Molecular mechanics with fluctuating atomic charges–a new force field with a semi-empirical charge calculation".

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Ramakrishnan R, Dral PO, Rupp M, von Lilienfeld OA (May 2015). "Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach".

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were -4 to -6 kcal/mol, which is related to re-forming existing hydrogen bonds and not forming hydrogen bonds from scratch. The depths of modified

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Lii JH, Allinger NL (November 1989). "Molecular mechanics. The MM3 force field for hydrocarbons. 2. Vibrational frequencies and thermodynamics".

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Cioce CR, McLaughlin K, Belof JL, Space B (December 2013). "A Polarizable and Transferable PHAST N2 Potential for Use in Materials Simulation".

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Yang L, Tan CH, Hsieh MJ, Wang J, Duan Y, Cieplak P, Caldwell J, Kollman PA, Luo R (July 2006). "New-generation amber united-atom force field".

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Mishra RK, Mohamed AK, Geissbühler D, Manzano H, Jamil T, Shahsavari R, Kalinichev AG, Galmarini S, Tao L, Heinz H, Pellenq R (December 2017).

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Atom types are defined for different elements as well as for the same elements in sufficiently different chemical environments. For example,

4391:"Improving physical realism, stereochemistry, and side-chain accuracy in homology modeling: Four approaches that performed well in CASP8" 6559: 6002:

Gao J, Habibollazadeh D, Shao L (November 1995). "A polarizable intermolecular potential function for simulation of liquid alcohols".

6551: 1565:(Optimized Potential for Liquid Simulations) (variants include OPLS-AA, OPLS-UA, OPLS-2001, OPLS-2005, OPLS3e, OPLS4) – developed by 1511:(Chemistry at HARvard Molecular Mechanics) – originally developed at Harvard, widely used for both small molecules and macromolecules 1310:

are also strongly environment-dependent because these forces originate from interactions of induced and "instantaneous" dipoles (see

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Schutz CN, Warshel A (September 2001). "What are the dielectric "constants" of proteins and how to validate electrostatic models?".

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CFF/ind and ENZYMIX – The first polarizable force field which has subsequently been used in many applications to biological systems.

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In many cases, force fields can be straight forwardly combined. Yet, often, additional specifications and assumptions are required.

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9-6 Lennard-Jones potentials to 12-6 Lennard-Jones potentials. Transfers from Buckingham potentials to harmonic potentials, or from

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O. T. Unke and M. Meuwly (2019). "PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges".

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Arnautova YA, Jagielska A, Scheraga HA (March 2006). "A new force field (ECEPP-05) for peptides, proteins, and organic molecules".

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simulations. The parameters for a chosen energy function may be derived from classical laboratory experiment data, calculations in

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Functional forms and parameter sets have been defined by the developers of interatomic potentials and feature variable degrees of

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Allinger NL (December 1977). "Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms".

2698:"An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications" 2996:"Modeling the Partial Atomic Charges in Inorganometallic Molecules and Solids and Charge Redistribution in Lithium-Ion Cathodes" 3316:

Schmitt, Sebastian; Kanagalingam, Gajanan; Fleckenstein, Florian; Froescher, Daniel; Hasse, Hans; Stephan, Simon (2023-11-27).

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in alkane transferable force fields). A different important differentiation addresses the physical structure of the models: A

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rule, which means that different types of atoms interact more weakly than identical types of atoms. This is in contrast to

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NEMO (Non-Empirical Molecular Orbital) – procedure developed by Gunnar Karlström and coworkers at Lund University (Sweden)

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As it is rare for bonds to deviate significantly from their equilibrium values, the most simplistic approaches utilize a

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Hoogerbrugge PJ, Koelman JM (1992). "Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics".

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simulations. The stronger the bond is between atoms, the higher is the value of the force constant, and the higher the

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for modeling molecular systems includes intramolecular interaction terms for interactions of atoms that are linked by

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Deeth RJ (2001). "The ligand field molecular mechanics model and the stereoelectronic effects of d and s electrons".

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Borodin O (August 2009). "Polarizable force field development and molecular dynamics simulations of ionic liquids".

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of using quantum mechanical methods. Primarily used by software packages supplied by Cresset Biomolecular Discovery.

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Polarizable procedure based on the Kim-Gordon approach developed by Jürg Hutter and coworkers (University of Zürich)

7952: 7723: 7639: 6547: 1691: 1203:. The bonded terms refer to pairs, triplets, and quadruplets of bonded atoms, and include values for the effective 2318:

Sun H, Mumby SJ, Maple JR, Hagler AT (April 1994). "An ab Initio CFF93 All-Atom Force Field for Polycarbonates".

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Siu SW, Pluhackova K, Böckmann RA (April 2012). "Optimization of the OPLS-AA Force Field for Long Hydrocarbons".

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PhysNet is a Neural Network-based energy function to predict energies, forces and (fluctuating) partial charges.

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The set of parameters used to model water or aqueous solutions (basically a force field for water) is called a

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utilising continuous-filter convolutional layers, to predict chemical properties and potential energy surfaces.

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are classified as different force field types. Typical molecular force field parameter sets include values for

1122: 5105:"Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard-Jones potential" 3269:

Eggimann, Becky L.; Sunnarborg, Amara J.; Stern, Hudson D.; Bliss, Andrew P.; Siepmann, J. Ilja (2014-01-02).

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derived from protein engineering data were also smaller than in typical potential parameters and followed the

5205:

Allinger NL, Yuh YH, Lii JH (November 1989). "Molecular mechanics. The MM3 force field for hydrocarbons. 1".

3408:"Force Field and a Surface Model Database for Silica to Simulate Interfacial Properties in Atomic Resolution" 1977:

Abascal JL, Vega C (December 2005). "A general purpose model for the condensed phases of water: TIP4P/2005".

7746: 7662: 7314:"Ab Initio Charge and AMBER Forcefield Parameters for Frequently Occurring Post-Translational Modifications" 1732: 1725: 1457: 1292: 1260:

to harmonic potentials, on the contrary, would require many additional assumptions and may not be possible.

1188: 1134: 1130: 471: 127: 1735:

fitted to liquid phase densities and vapor pressures of pure compounds by using the SAFT equation of state.

7793: 7259:

Molinero V, Moore EB (April 2009). "Water modeled as an intermediate element between carbon and silicon".

7142: 7000:"Multipolar Electrostatic Energy Prediction for all 20 Natural Amino Acids Using Kriging Machine Learning" 6576: 5067: 1743:

capture features dependent on secondary structure and on residue-specific contact information in proteins.

1677: 1417: 330:

where the components of the covalent and noncovalent contributions are given by the following summations:

135: 7464:

Foscato M, Deeth RJ, Jensen VR (June 2015). "Integration of Ligand Field Molecular Mechanics in Tinker".

6669:

Koelman JM, Hoogerbrugge PJ (1993). "Dynamic Simulations of Hard-Sphere Suspensions Under Steady Shear".

5068:"A force field database for cementitious materials including validations, applications and opportunities" 4598:

Murphy KP, Gill SJ (December 1991). "Solid model compounds and the thermodynamics of protein unfolding".

7678: 7601: 6495:"Extended electron distributions applied to the molecular mechanics of some intermolecular interactions" 1911: 1906: 1446: 1393: 1361: 1272: 805: 159: 131: 3798:

Warshel A, Sharma PK, Kato M, Parson WW (November 2006). "Modeling electrostatic effects in proteins".

2610:"Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals" 1235:

focuses on interatomic functions describing the individual interactions between specific elements. The

3561:

Kramer C, Spinn A, Liedl KR (October 2014). "Charge Anisotropy: Where Atomic Multipoles Matter Most".

7821: 7164: 7099: 6817: 6729: 6678: 6627: 6568: 6320: 6263: 6122: 6031:"Development of a polarizable intermolecular potential function (PIPF) for liquid amides and alkanes" 5498: 5447: 5404: 5395:

Dick BG, Overhauser AW (1958-10-01). "Theory of the Dielectric Constants of Alkali Halide Crystals".

5116: 4765: 4708: 4355: 3661: 3605: 3515: 3458: 3233: 3047: 2754: 2621: 2566: 2517: 2279: 2102: 1986: 1916: 1858: 1768:

or Quantum chemical topology energy terms including electrostatic, exchange and electron correlation.

1566: 1311: 1101: 6581: 4311:

Lazaridis T, Karplus M (April 2000). "Effective energy functions for protein structure prediction".

3270: 43: 7887: 7866: 6898:"ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost" 6865:"MACE: Higher order equivariant message passing neural networks for fast and accurate force fields" 5815:"Simulating Monovalent and Divalent Ions in Aqueous Solution Using a Drude Polarizable Force Field" 3748:"Interatomic potentials and solvation parameters from protein engineering data for buried residues" 1921: 1896: 1886: 1862: 1854: 1775:

provides a short-range potential, whilst more traditional potentials add screened long-range terms.

1590: 1434: 1341: 1307: 1300: 1257: 1105: 274: 119: 1006:{\displaystyle E_{\text{Coulomb}}={\frac {1}{4\pi \varepsilon _{0}}}{\frac {q_{i}q_{j}}{r_{ij}}},} 7914: 7826: 7803: 7784: 7764: 7728: 7294: 7268: 7241: 7215: 7188: 7154: 7123: 7089: 6980: 6876: 6753: 6702: 6651: 6475: 5949: 5914: 5813:

Yu H, Whitfield TW, Harder E, Lamoureux G, Vorobyov I, Anisimov VM, Mackerell AD, Roux B (2010).

5760: 5560: 5471: 4971: 4855: 4658: 4371: 4223: 4174: 4125: 4047: 4004: 3960: 3908: 3858: 3685: 3651: 3353: 3298: 3202: 3107: 2871: 2433: 2248: 2193: 2162: 2140: 2114: 2010: 1881: 1765: 1710: 1639:

SP-basis Chemical Potential Equalization (CPE) – approach developed by R. Chelli and P. Procacci.

1239:

focuses on transferable force fields of organic molecules (developed by the Siepmann group). The

1196: 1083:. The total Coulomb energy is a sum over all pairwise combinations of atoms and usually excludes 847: 809: 151: 147: 115: 6532: 3038:

Heinz H, Suter UW (November 2004). "Atomic Charges for Classical Simulations of Polar Systems".

5489:

Yu H, van Gunsteren WF (November 2005). "Accounting for polarization in molecular simulation".

4276:

Edgcomb SP, Murphy KP (February 2000). "Structural energetics of protein folding and binding".

1731:

SAFT – A top-down coarse-grained model developed in the Molecular Systems Engineering group at

7919: 7816: 7789: 7700: 7690: 7683: 7657: 7556: 7537: 7518: 7491: 7392: 7343: 7286: 7233: 7180: 7115: 7062: 7021: 6972: 6927: 6845: 6745: 6694: 6643: 6514: 6467: 6432: 6381: 6346: 6289: 6232: 6165: 6095: 6060: 5984: 5879: 5844: 5795: 5752: 5711: 5662: 5595: 5552: 5514: 5463: 5420: 5377: 5342: 5142: 5027: 4936: 4793: 4734: 4650: 4615: 4580: 4531: 4521: 4508:

Rohl CA, Strauss CE, Misura KM, Baker D (2004). "Protein Structure Prediction Using Rosetta".

4490: 4455: 4420: 4328: 4293: 4258: 4215: 4166: 4117: 4082: 4065:

Brunger AT, Adams PD (June 2002). "Molecular dynamics applied to X-ray structure refinement".

4039: 3996: 3952: 3894: 3850: 3815: 3777: 3723: 3677: 3621: 3578: 3543: 3484: 3430: 3388: 3345: 3337: 3290: 3251: 3194: 3156: 3099: 3063: 3017: 2976: 2941: 2906: 2863: 2822: 2727: 2678: 2637: 2590: 2582: 2535: 2482: 2425: 2384: 2335: 2297: 2240: 2232: 2185: 2132: 2076: 2048: 2002: 1956: 1946: 1845: 1370: 905: 813: 738: 662: 460: 163: 155: 111: 1360:". Force fields have been applied successfully for protein structure refinement in different 241:, and multi-component complexes, sacrifice chemical details for higher computing efficiency. 7861: 7811: 7481: 7473: 7446: 7419: 7382: 7374: 7333: 7325: 7278: 7225: 7172: 7107: 7052: 7011: 6962: 6954: 6917: 6909: 6835: 6825: 6737: 6686: 6635: 6586: 6506: 6459: 6422: 6412: 6373: 6336: 6328: 6279: 6271: 6222: 6214: 6157: 6130: 6087: 6050: 6042: 6011: 5976: 5941: 5906: 5871: 5834: 5826: 5787: 5742: 5701: 5693: 5652: 5644: 5587: 5544: 5506: 5455: 5412: 5369: 5334: 5295: 5268: 5241: 5214: 5169: 5132: 5124: 5082: 5019: 4963: 4928: 4901: 4847: 4820: 4783: 4773: 4724: 4716: 4642: 4607: 4570: 4562: 4513: 4482: 4447: 4410: 4402: 4363: 4320: 4285: 4250: 4205: 4156: 4109: 4074: 4031: 3988: 3944: 3886: 3842: 3807: 3767: 3759: 3715: 3669: 3613: 3570: 3533: 3523: 3474: 3466: 3422: 3380: 3329: 3282: 3241: 3186: 3146: 3138: 3091: 3055: 3007: 2968: 2933: 2898: 2855: 2814: 2785: 2717: 2709: 2668: 2629: 2574: 2525: 2472: 2464: 2415: 2374: 2366: 2355:"CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data" 2327: 2287: 2224: 2177: 2124: 2040: 1994: 1365: 1337: 1176: 1158: 1112:

potentials have been developed, which describe a form of attachment of electrons to nuclei.

1016: 913: 819: 777: 632: 602: 479: 258: 222: 174: 143: 4752:

Scholtz JM, Marqusee S, Baldwin RL, York EJ, Stewart JM, Santoro M, Bolen DW (April 1991).

4145:"163 Enhanced sampling of peptides and proteins with a new biasing replica exchange method" 876: 7856: 7851: 7779: 7774: 7741: 7668: 7536:. Interdisciplinary Applied Mathematics: Mathematical Biology. New York: Springer-Verlag. 6777: 6594: 4873: 4100:

Güntert P (May 1998). "Structure calculation of biological macromolecules from NMR data".

3921: 3538: 3479: 2213:"A child of prediction. On the History, Ontology, and Computation of the Lennard-Jonesium" 1551: 1405: 1397: 1378: 1252: 1204: 859: 452: 5633:"Implementation of Geometry-Dependent Charge Flux into the Polarizable AMOEBA+ Potential" 4022:

Koehl P, Levitt M (February 1999). "A brighter future for protein structure prediction".

482:. However, both can be buffered or scaled by a constant factor to account for electronic 7168: 7103: 6821: 6733: 6682: 6631: 6572: 6324: 6267: 6126: 5502: 5451: 5408: 5120: 4769: 4712: 4359: 3665: 3609: 3519: 3462: 3407: 3406:

Emami FS, Puddu V, Berry RJ, Varshney V, Patwardhan SV, Perry CC, Heinz H (2014-04-22).

3237: 3220:

Tadmor, E. B.; Elliott, R. S.; Sethna, J. P.; Miller, R. E.; Becker, C. A. (July 2011).

3051: 2758: 2625: 2570: 2521: 2283: 1990: 1373:

of proteins. Meanwhile, alternative empirical scoring functions have been developed for

1243:

focuses on molecular and ionic force fields (both component-specific and transferable).

7904: 7620: 7387: 7362: 7361:

Khoury GA, Smadbeck J, Tamamis P, Vandris AC, Kieslich CA, Floudas CA (December 2014).

7338: 7313: 6922: 6897: 6840: 6805: 6494: 6427: 6400: 6341: 6308: 6284: 6251: 6227: 6202: 6055: 6030: 5839: 5814: 5706: 5681: 5657: 5632: 5137: 5104: 4729: 4696: 4575: 4550: 4415: 4390: 3890: 3772: 3747: 3151: 3126: 2722: 2697: 2379: 2354: 1782: 1772: 1609: 1586: 1425: 1413: 1401: 1382: 1374: 1327:

or Slater-Kirkwood equation applied for development of the classical force fields. The

1200: 1184: 1066: 1046: 871: 718: 698: 495: 483: 98: 7450: 7423: 6720:

Español P, Warren P (1995). "Statistical Mechanics of Dissipative Particle Dynamics".

5438:

Mitchell PJ, Fincham D (1993-02-22). "Shell model simulations by adiabatic dynamics".

4720: 4517: 4486: 4451: 4438:

Gordon DB, Marshall SA, Mayo SL (August 1999). "Energy functions for protein design".

4324: 4289: 3885:

Israelachvili JN (2011). "Intermolecular and Surface Forces". Elsevier. pp. iii.

2103:"MolMod – an open access database of force fields for molecular simulations of fluids" 1645:

ORIENT – procedure developed by Anthony J. Stone (Cambridge University) and coworkers.

441:{\displaystyle E_{\text{nonbonded}}=E_{\text{electrostatic}}+E_{\text{van der Waals}}} 389:{\displaystyle E_{\text{bonded}}=E_{\text{bond}}+E_{\text{angle}}+E_{\text{dihedral}}} 7936: 7892: 6771:

Dissipative Particle Dynamics: Addressing deficiencies and establishing new frontiers

6741: 6706: 6690: 6655: 6639: 6479: 5875: 5475: 4788: 4753: 4611: 4473:

Mendes J, Guerois R, Serrano L (August 2002). "Energy estimation in protein design".

4008: 3357: 3206: 2673: 2656: 2252: 2144: 1812: 1502: 1142: 909: 901: 475: 464: 270: 262: 230: 17: 7298: 7245: 7127: 6984: 6757: 5953: 5764: 5564: 5459: 5086: 4975: 4859: 4662: 4375: 4227: 4178: 4129: 3317: 3302: 3222:"The potential of atomistic simulations and the knowledgebase of interatomic models" 3111: 2437: 2197: 1346:

the interaction between hydrocarbons across water is about 10% of that across vacuum

7909: 7192: 6790: 5918: 4051: 3964: 3862: 3689: 3528: 3503: 2875: 2014: 1536:

and energy derivatives, and quantifies limitations for all included compounds. The

1498:(Assisted Model Building and Energy Refinement) – widely used for proteins and DNA. 1315: 238: 218: 198: 7145:(June 2018). "SchNet - A deep learning architecture for molecules and materials". 7041:"Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms" 5191: 3095: 2128: 6401:"Robust Atomistic Modeling of Materials, Organometallic, and Biochemical Systems" 4161: 4144: 3811: 3286: 2212: 7718: 7713: 5648: 2713: 2292: 2267: 2228: 1808: 1804: 1798: 1555: 1442: 1438: 1192: 1180: 1109: 771:

is at times differently defined or taken at different thermodynamic conditions.

6810:

Proceedings of the National Academy of Sciences of the United States of America

5128: 4758:

Proceedings of the National Academy of Sciences of the United States of America

3470: 1636:

Polarizable Force Field (PFF) – developed by Richard A. Friesner and coworkers.

1232: 1161:, which are more accessible for experimental studies and quantum calculations. 870:

Electrostatic interactions are represented by a Coulomb energy, which utilizes

7708: 6183: 5945: 5510: 5045: 4113: 3948: 3246: 3221: 2609: 2554: 1537: 1287: 851: 205:

force fields provide parameters for every type of atom in a system, including

7477: 7312:

Khoury GA, Thompson JP, Smadbeck J, Kieslich CA, Floudas CA (December 2013).

7229: 7111: 7057: 7040: 7016: 6999: 6958: 6749: 6698: 6647: 6518: 6463: 5697: 5518: 5467: 5424: 5381: 5346: 4170: 4000: 3625: 3488: 3434: 3341: 3333: 3294: 3255: 3190: 3103: 3067: 2980: 2826: 2790: 2682: 2641: 2633: 2586: 2578: 2539: 2339: 2301: 2236: 2136: 2101:

Stephan, Simon; Horsch, Martin T.; Vrabec, Jadran; Hasse, Hans (2019-07-03).

1960: 1807:. Many water models have been proposed; some examples are TIP3P, TIP4P, SPC, 7769: 6830: 3935:

Leckband D, Israelachvili J (May 2001). "Intermolecular forces in biology".

3719: 3127:"Building Force Fields: An Automatic, Systematic, and Reproducible Approach" 2163:"The MARTINI force field: coarse grained model for biomolecular simulations" 1764:

models which operate together to provide a molecular force field trained on

1421: 139: 107: 7495: 7396: 7347: 7290: 7237: 7184: 7119: 7066: 7025: 6976: 6931: 6849: 6770: 6471: 6436: 6417: 6385: 6350: 6293: 6236: 6169: 6099: 6064: 5988: 5848: 5799: 5756: 5715: 5666: 5599: 5556: 5416: 5299: 5146: 5031: 4940: 4778: 4584: 4535: 4494: 4459: 4424: 4332: 4297: 4262: 4219: 4086: 4043: 3992: 3956: 3854: 3819: 3781: 3727: 3681: 3582: 3547: 3392: 3349: 3198: 3160: 3021: 2945: 2910: 2859: 2731: 2486: 2429: 2388: 2244: 2189: 2161:

Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH (July 2007).

2052: 2006: 1690:– reactive force field (interatomic potential) developed by Adri van Duin, 5910: 5103:

Geada IL, Ramezani-Dakhel H, Jamil T, Sulpizi M, Heinz H (February 2018).

4967: 4851: 4797: 4738: 4654: 4646: 4619: 4255:

10.1002/1521-3773(20020802)41:15<2644::AID-ANIE2644>3.0.CO;2-O

4121: 2867: 2594: 1275:

are based on approximations and experimental data, therefore often termed

7673: 5883: 4566: 4389:

Krieger E, Joo K, Lee J, Lee J, Raman S, Thompson J, et al. (2009).

4367: 2555:"New empirical approach for the structure and energy of covalent systems" 1943:

Understanding molecular simulation : from algorithms to applications

1449: 1389: 1173: 1126: 592:{\displaystyle E_{\text{bond}}={\frac {k_{ij}}{2}}(l_{ij}-l_{0,ij})^{2},} 456: 206: 167: 7570: 6250:

Piquemal JP, Cisneros GA, Reinhardt P, Gresh N, Darden TA (March 2006).

6015: 5932:

Swart M, van Duijnen PT (May 2006). "DRF90: a polarizable force field".

5338: 5272: 5245: 5218: 5173: 4905: 4824: 2331: 1865:. It can be incorporated into other force fields such as CHARMM and UFF. 1695:

reactive simulations on >>1,000,000 atoms on large supercomputers.

1597:

AMBER – polarizable force field developed by Jim Caldwell and coworkers.

7838: 6967: 6913: 6510: 4406: 4210: 4193: 3763: 3384: 2468: 1850: 1761: 1724:– a coarse-grained potential developed by Marrink and coworkers at the 1721: 1453: 1146: 323:{\displaystyle E_{\text{total}}=E_{\text{bonded}}+E_{\text{nonbonded}}} 234: 186: 182: 7486: 7378: 7329: 7282: 7176: 6590: 6377: 6332: 6275: 6218: 6161: 6134: 6091: 6046: 5980: 5830: 5791: 5747: 5730: 5591: 5548: 5373: 5023: 4989: 4932: 4078: 3846: 3574: 3426: 3271:"An online parameter and property database for the TraPPE force field" 3142: 3059: 3012: 2995: 2972: 2937: 2902: 2818: 2530: 2501: 2477: 2420: 2403: 2370: 2181: 2044: 1998: 1104:

are usually used, e.g. Tersoff potentials. For metal systems, usually

3673: 3617: 2745:

Lorentz HA (1905). "The Motion of Electrons in Metallic Bodies, I.".

2655:

Daw, Murray S.; Foiles, Stephen M.; Baskes, Michael I. (March 1993).

1687: 1681: 1642:

PHAST – polarizable potential developed by Chris Cioce and coworkers.

1529: 1508: 1430: 1333: 1165: 253:

Molecular mechanics potential energy function with continuum solvent.

214: 146:

of a system on the atomistic level. Force fields are usually used in

2773: 1240: 173:

A large number of different force field types exist today (e.g. for

7220: 7159: 7094: 6881: 5613: 3656: 2119: 7273: 1714: 1495: 1169: 1085:

1, 2 bonded atoms, 1, 3 bonded atoms, as well as 1, 4 bonded atoms

249: 248: 190: 170:

of the potential energy with respect to the particle coordinates.

97: 5682:"AMOEBA+ Classical Potential for Modeling Molecular Interactions" 4035: 3502:

Ruiz VG, Liu W, Zojer E, Scheffler M, Tkatchenko A (April 2012).

7553:

Computer Modeling of Chemical Reactions in Enzymes and Solutions

6806:"A force field for virtual atom molecular mechanics of proteins" 4551:"Positioning of proteins in membranes: a computational approach" 3172: 3170: 2211:

Lenhard, Johannes; Stephan, Simon; Hasse, Hans (February 2024).

1562: 1518:

CVFF – also used broadly for small molecules and macromolecules.

7574: 7039:

McDonagh JL, Silva AF, Vincent MA, Popelier PL (January 2018).

4346:

Javidpour L (2012). "Computer Simulations of Protein Folding".

3318:"Extension of the MolMod Database to Transferable Force Fields" 2657:"The embedded-atom method: a review of theory and applications" 2500:

Ashcroft, N. W.; Mermin, N. D.; Smoluchowski, R. (1977-01-01).

2402:

Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA (July 2004).

735:

when all other terms in the force field are set to 0. The term

6201:

Gresh N, Cisneros GA, Darden TA, Piquemal JP (November 2007).

1396:, i.e., energy of evaporation of molecular crystals. However, 1154: 1150: 178: 26: 7534:

Molecular Modeling and Simulation: An Interdisciplinary Guide

3800:

Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics

1236: 229:

potentials, which are often used in long-time simulations of

4549:

Lomize AL, Pogozheva ID, Lomize MA, Mosberg HI (June 2006).

1486:

Different force fields are designed for different purposes:

1157:

were often derived/ transferred from observations for small

2268:"On the history of key empirical intermolecular potentials" 1408:, or liquid-solid transitions as these processes represent 6780:, CECAM workshop, July 16–18, 2008, Lausanne, Switzerland. 1572:

QCFF/PI – A general force fields for conjugated molecules.

1416:(energy absorbed during melting of molecular crystals), a 1291:π-conjugated systems, and lone pairs in water. Electronic 102:

Part of force field of ethane for the C-C stretching bond.

6863:

Batatia I, Kovacs DP, Simm G, Ortner C, Csanyi G (2022).

2840: 2838: 2836: 1214:

Efforts to provide open source codes and methods include

4512:. Methods in Enzymology. Vol. 383. pp. 66–93. 2404:"Development and testing of a general amber force field" 1902:

Comparison of software for molecular mechanics modeling

1482:

Comparison of software for molecular mechanics modeling

1630: 1622:

DRF90 – developed by P. Th. van Duijnen and coworkers.

1547:) – developed at Merck for a broad range of molecules. 1445:

transition data, but the same energies estimated from

1191:

for every atom type, as well as equilibrium values of

6307:

Cisneros GA, Piquemal JP, Darden TA (November 2006).

3880: 3878: 3876: 3874: 3872: 2696:

Lemkul JA, Huang J, Roux B, MacKerell AD (May 2016).

1576:

compounds, especially metals and inorganic compounds.

1069: 1049: 1019: 922: 879: 822: 780: 741: 721: 701: 665: 635: 605: 504: 401: 336: 283: 7141:

Schütt KT, Sauceda HE, Kindermans PJ, Tkatchenko A,

3746:

Lomize AL, Reibarkh MY, Pogozheva ID (August 2002).

1433:

in proteins are ~ -1.5 kcal/mol when estimated from

1356:(CASP) did not try to refine their models to avoid " 1219: 1215: 158:, or both. Force fields utilize the same concept as 7875: 7837: 7802: 7757: 7699: 7638: 7608: 5729:Patel S, Mackerell AD, Brooks CL (September 2004). 4194:"Assessment of homology-based predictions in CASP5" 1354:

Critical Assessment of protein Structure Prediction

1295:of the environment may be better included by using 1279:. The performance varies from higher accuracy than 2266:Fischer, Johann; Wendland, Martin (October 2023). 1075: 1055: 1035: 1005: 892: 838: 796: 763: 727: 707: 687: 651: 621: 591: 440: 388: 322: 6869:Advances in Neural Information Processing Systems 6552:"ReaxFF: A Reactive Force Field for Hydrocarbons" 2096: 2094: 2092: 6252:"Towards a force field based on density fitting" 3701: 3699: 2073:Molecular Modelling: Principles and Applications 1853:- a function for angle bending that is based on 134:. More precisely, the force field refers to the 4697:"Hydrogen bonding stabilizes globular proteins" 1569:at the Yale University Department of Chemistry. 695:is the value for the bond length between atoms 265:and intermolecular (i.e. nonbonded also termed 6896:Smith JS, Isayev O, Roitberg AE (April 2017). 5061: 5059: 4149:Journal of Biomolecular Structure and Dynamics 3741: 3739: 3737: 2449: 2447: 2156: 2154: 213:interatomic potentials treat the hydrogen and 7586: 5098: 5096: 5005: 5003: 3033: 3031: 8: 7466:Journal of Chemical Information and Modeling 3322:Journal of Chemical Information and Modeling 3179:Journal of Chemical Information and Modeling 3125:Wang LP, Martinez TJ, Pande VS (June 2014). 2608:Daw, Murray S.; Baskes, M. I. (1984-06-15). 2217:Studies in History and Philosophy of Science 2066: 2064: 2062: 6804:Korkut A, Hendrickson WA (September 2009). 2994:Wang B, Li SL, Truhlar DG (December 2014). 2774:"Zur Elekronentheorie der Metalle. I. Teil" 1760:FFLUX (originally QCTFF) A set of trained 1381:, homology model refinement, computational 900:to represent chemical bonding ranging from 7593: 7579: 7571: 7318:Journal of Chemical Theory and Computation 7082:Journal of Chemical Theory and Computation 7045:Journal of Chemical Theory and Computation 7004:Journal of Chemical Theory and Computation 6947:Journal of Chemical Theory and Computation 6499:Journal of Computer-Aided Molecular Design 6207:Journal of Chemical Theory and Computation 6150:Journal of Chemical Theory and Computation 6080:Journal of Chemical Theory and Computation 6035:Journal of Chemical Theory and Computation 5819:Journal of Chemical Theory and Computation 5780:Journal of Chemical Theory and Computation 5686:Journal of Chemical Theory and Computation 5631:Liu C, Piquemal JP, Ren P (January 2020). 3793: 3791: 3637: 3635: 3563:Journal of Chemical Theory and Computation 3000:Journal of Chemical Theory and Computation 2961:International Journal of Quantum Chemistry 2926:Journal of Chemical Theory and Computation 2891:Journal of Chemical Theory and Computation 2313: 2311: 2033:Journal of Chemical Theory and Computation 7485: 7386: 7337: 7272: 7219: 7158: 7093: 7056: 7015: 6966: 6921: 6880: 6839: 6829: 6580: 6426: 6416: 6340: 6283: 6226: 6054: 6029:Xie W, Pu J, Mackerell AD, Gao J (2007). 5838: 5746: 5705: 5656: 5637:The Journal of Physical Chemistry Letters 5136: 4787: 4777: 4728: 4574: 4414: 4209: 4160: 4143:Ostermeir K, Zacharias M (January 2013). 3771: 3655: 3537: 3527: 3478: 3245: 3150: 3131:The Journal of Physical Chemistry Letters 3011: 2789: 2721: 2672: 2529: 2476: 2419: 2378: 2291: 2118: 1877:Comparison of force field implementations 1857:and works for large angular distortions, 1474:Comparison of force field implementations 1385:, and modeling of proteins in membranes. 1247:Transferability and mixing function types 1068: 1048: 1024: 1018: 989: 978: 968: 961: 952: 936: 927: 921: 884: 878: 827: 821: 785: 779: 746: 740: 720: 700: 670: 664: 640: 634: 610: 604: 580: 561: 545: 524: 518: 509: 503: 432: 419: 406: 400: 380: 367: 354: 341: 335: 314: 301: 288: 282: 76:Learn how and when to remove this message 5530: 5528: 5327:Journal of the American Chemical Society 5261:Journal of the American Chemical Society 5234:Journal of the American Chemical Society 5207:Journal of the American Chemical Society 5162:Journal of the American Chemical Society 2807:Journal of the American Chemical Society 2353:Huang J, MacKerell AD (September 2013). 2320:Journal of the American Chemical Society 1809:flexible simple point charge water model 1608:(University of Maryland, Baltimore) and 1585:Several force fields explicitly capture 1464:rule, as predicted by McLachlan theory. 1141:for molecular simulations of biological 804:can be determined from the experimental 6405:Angewandte Chemie International Edition 5680:Liu C, Piquemal JP, Ren P (July 2019). 2075:(2nd ed.). Harlow: Prentice Hall. 1933: 6998:Fletcher TL, Popelier PL (June 2016). 6399:Spicher S, Grimme S (September 2020). 4348:Computing in Science & Engineering 3917: 3906: 1554:mainly for conformational analysis of 846:determines vibrational frequencies in 4475:Current Opinion in Structural Biology 4440:Current Opinion in Structural Biology 4313:Current Opinion in Structural Biology 1108:are used. For metals, also so-called 269:) terms that describe the long-range 7: 7412:Computers & Chemical Engineering 5440:Journal of Physics: Condensed Matter 2026: 2024: 1972: 1970: 1468:Force fields available in literature 7555:. New York: John Wiley & Sons. 7261:The Journal of Physical Chemistry B 6560:The Journal of Physical Chemistry A 6546:van Duin AC, Dasgupta S, Lorant F, 6452:The Journal of Physical Chemistry B 6366:The Journal of Physical Chemistry B 5614:"Tinker Molecular Modeling Package" 5580:The Journal of Physical Chemistry B 4921:The Journal of Physical Chemistry B 3040:The Journal of Physical Chemistry B 2170:The Journal of Physical Chemistry B 854:(energy) in the IR/Raman spectrum. 6184:"Anthony Stone: Computer programs" 5899:Journal of Computational Chemistry 5735:Journal of Computational Chemistry 5537:Journal of Computational Chemistry 4695:Myers JK, Pace CN (October 1996). 4510:Numerical Computer Methods, Part D 3891:10.1016/b978-0-12-391927-4.10024-6 2408:Journal of Computational Chemistry 2359:Journal of Computational Chemistry 1043:is the distance between two atoms 245:Force fields for molecular systems 25: 7515:Intermolecular and surface forces 7424:10.1016/j.compchemeng.2014.07.017 6004:The Journal of Physical Chemistry 4894:The Journal of Physical Chemistry 4813:The Journal of Physical Chemistry 7629: 4278:Current Opinion in Biotechnology 1404:are thermodynamically closer to 1095:Force fields for crystal systems 478:and the electrostatic term with 31: 7147:The Journal of Chemical Physics 6313:The Journal of Chemical Physics 6256:The Journal of Chemical Physics 6115:The Journal of Chemical Physics 5491:Computer Physics Communications 5087:10.1016/j.cemconres.2017.09.003 4102:Quarterly Reviews of Biophysics 3937:Quarterly Reviews of Biophysics 3598:The Journal of Chemical Physics 1979:The Journal of Chemical Physics 1633:at the University of Minnesota. 7439:Coordination Chemistry Reviews 4192:Tramontano A, Morea V (2003). 3539:11858/00-001M-0000-000F-C6EA-3 3529:10.1103/physrevlett.108.146103 3480:11858/00-001M-0000-0029-3035-8 1319:than in vacuum and follow the 577: 538: 1: 7517:. San Diego: Academic Press. 7451:10.1016/S0010-8545(00)00354-4 5046:"Interface Force Field (IFF)" 4721:10.1016/S0006-3495(96)79401-8 4518:10.1016/S0076-6879(04)83004-0 4487:10.1016/s0959-440x(02)00345-7 4452:10.1016/S0959-440X(99)80072-4 4325:10.1016/s0959-440x(00)00063-4 4290:10.1016/s0958-1669(99)00055-5 4067:Accounts of Chemical Research 3981:Advanced Functional Materials 3096:10.1080/08927022.2017.1332414 2129:10.1080/08927022.2019.1601191 1707:Dissipative particle dynamics 1619:each molecular dynamics step. 1524:Internal Coordinate Mechanics 912:. The typical formula is the 774:The bond stretching constant 257:The basic functional form of 88:Concept on molecular modeling 7616:Principle of maximum entropy 6493:Vinter, J. G. (1994-12-01). 5876:10.1016/0022-2836(76)90311-9 5864:Journal of Molecular Biology 5075:Cement and Concrete Research 4612:10.1016/0022-2836(91)90506-2 4600:Journal of Molecular Biology 4162:10.1080/07391102.2013.786405 3812:10.1016/j.bbapap.2006.08.007 3287:10.1080/08927022.2013.842994 2674:10.1016/0920-2307(93)90001-u 1771:TensorMol, a mixed model, a 5649:10.1021/acs.jpclett.9b03489 5288:Israel Journal of Chemistry 2714:10.1021/acs.chemrev.5b00505 2293:10.1016/j.fluid.2023.113876 2229:10.1016/j.shpsa.2023.11.007 1545:Merck Molecular Force Field 816:calculations. The constant 225:as one interaction center. 142:sets used to calculate the 51:. The specific problem is: 7974: 7640:Statistical thermodynamics 6742:10.1209/0295-5075/30/4/001 6691:10.1209/0295-5075/21/3/018 6640:10.1209/0295-5075/19/3/001 5129:10.1038/s41467-018-03137-8 3471:10.1103/physrevb.93.035118 2553:Tersoff, J. (1988-04-15). 1863:transition metal complexes 1796: 1471: 866:Electrostatic interactions 90: 47:to meet Knowledge (XXG)'s 7627: 7513:Israelachvili JN (1992). 6722:Europhysics Letters (EPL) 6671:Europhysics Letters (EPL) 6620:Europhysics Letters (EPL) 5946:10.1080/08927020600631270 5511:10.1016/j.cpc.2005.01.022 5460:10.1088/0953-8984/5/8/006 4840:Molecular Modeling Annual 4114:10.1017/S0033583598003436 4024:Nature Structural Biology 3949:10.1017/S0033583501003687 3247:10.1007/s11837-011-0102-6 2661:Materials Science Reports 1892:Molecular design software 1478:Molecular design software 1340:) have been explained by 1281:density functional theory 1172:and an oxygen atoms in a 7943:Force fields (chemistry) 7900:Condensed matter physics 7883:Statistical field theory 7478:10.1021/acs.jcim.5b00098 7230:10.1021/acs.jctc.9b00181 7112:10.1021/acs.jctc.5b00099 7058:10.1021/acs.jctc.7b01157 7017:10.1021/acs.jctc.6b00457 6959:10.1021/acs.jctc.8b00806 6464:10.1021/acs.jpcb.1c05744 5698:10.1021/acs.jctc.9b00261 3373:Chemical Society Reviews 3334:10.1021/acs.jcim.3c01484 3191:10.1021/acs.jcim.9b00646 2791:10.1002/andp.19003060312 2634:10.1103/physrevb.29.6443 2579:10.1103/physrevb.37.6991 1612:(University of Chicago). 1458:Lennard-Jones potentials 1297:polarizable force fields 1189:Lennard-Jones parameters 1123:enthalpy of vaporization 1106:embedded atom potentials 812:spectrum, or high-level 764:{\displaystyle l_{0,ij}} 688:{\displaystyle l_{0,ij}} 659:is the bond length, and 7758:Mathematical approaches 7747:Lennard-Jones potential 7663:thermodynamic potential 6831:10.1073/pnas.0907674106 5188:"MM2 and MM3 home page" 3720:10.1021/acsnano.7b07684 3508:Physical Review Letters 2747:Proc. K. Ned. Akad. Wet 1733:Imperial College London 1726:University of Groningen 1299:or using a macroscopic 629:is the force constant, 472:Lennard-Jones potential 7794:conformal field theory 6418:10.1002/anie.202004239 6188:www-stone.ch.cam.ac.uk 5417:10.1103/physrev.112.90 5362:Chemistry of Materials 5300:10.1002/ijch.197300067 4779:10.1073/pnas.88.7.2854 4678:Gazetta Chim. Italiana 3993:10.1002/adfm.201905247 3415:Chemistry of Materials 2860:10.1002/prot.340040106 2272:Fluid Phase Equilibria 2071:Leach A (2001-01-30). 1678:Empirical valence bond 1418:conformational entropy 1273:interatomic potentials 1077: 1057: 1037: 1036:{\displaystyle r_{ij}} 1007: 894: 840: 839:{\displaystyle k_{ij}} 798: 797:{\displaystyle k_{ij}} 765: 729: 709: 689: 653: 652:{\displaystyle l_{ij}} 623: 622:{\displaystyle k_{ij}} 593: 442: 390: 324: 254: 132:interatomic potentials 103: 7948:Intermolecular forces 7709:Ferromagnetism models 7602:Statistical mechanics 7367:ACS Synthetic Biology 5911:10.1002/jcc.540150505 5109:Nature Communications 4968:10.1002/bip.360290403 4852:10.1007/s008940100008 4647:10.1002/bip.360281003 1912:Interatomic potential 1907:Statistical potential 1859:hypervalent molecules 1550:MM2 was developed by 1538:Interface force field 1472:Further information: 1362:X-ray crystallography 1226:Force field databases 1102:bond order potentials 1078: 1058: 1038: 1008: 895: 893:{\displaystyle q_{i}} 841: 799: 766: 730: 710: 690: 654: 624: 594: 443: 391: 325: 252: 101: 18:Universal force field 5934:Molecular Simulation 4567:10.1110/ps.062126106 4368:10.1109/MCSE.2012.21 3275:Molecular Simulation 3090:(13–16): 1394–1405. 3084:Molecular Simulation 2107:Molecular Simulation 1917:Bond order potential 1819:Modified amino acids 1631:Gao Research Group | 1567:William L. Jorgensen 1312:Intermolecular force 1308:van der Waals forces 1258:Embedded Atom Models 1207:for each potential. 1067: 1047: 1017: 920: 877: 820: 778: 739: 719: 699: 663: 633: 603: 502: 399: 334: 281: 275:van der Waals forces 91:For other uses, see 58:improve this article 7958:Molecular modelling 7888:elementary particle 7653:partition functions 7208:J. Chem. Theo. Chem 7169:2018JChPh.148x1722S 7104:2015arXiv150304987R 6822:2009PNAS..10615667K 6734:1995EL.....30..191E 6683:1993EL.....21..363K 6632:1992EL.....19..155H 6573:2001JPCA..105.9396V 6458:(40): 11242–11255. 6411:(36): 15665–15673. 6325:2006JChPh.125r4101C 6268:2006JChPh.124j4101P 6127:2002JChPh.117.9175C 6016:10.1021/j100044a039 5503:2005CoPhC.172...69Y 5452:1993JPCM....5.1031M 5409:1958PhRv..112...90D 5339:10.1021/ja00051a040 5333:(25): 10024–10035. 5273:10.1021/ja00205a003 5246:10.1021/ja00205a002 5219:10.1021/ja00205a001 5174:10.1021/ja00467a001 5121:2018NatCo...9..716G 4906:10.1021/j100589a006 4825:10.1021/j100069a010 4770:1991PNAS...88.2854S 4713:1996BpJ....71.2033M 4701:Biophysical Journal 4401:(Suppl 9): 114–22. 4360:2012CSE....14b..97J 4204:(Suppl 6): 352–68. 3714:(12): 12805–12816. 3666:2015NatMa..14.1099X 3610:2000JChPh.112.8910M 3520:2012PhRvL.108n6103R 3463:2016PhRvB..93c5118R 3238:2011JOM....63g..17T 3052:2004APS..MAR.Y8006H 3046:(47): 18341–18352. 2813:(45): 11225–11236. 2759:1904KNAB....7..438L 2626:1984PhRvB..29.6443D 2571:1988PhRvB..37.6991T 2522:1977PhT....30R..61A 2504:Solid State Physics 2457:Dalton Transactions 2332:10.1021/ja00086a030 2284:2023FlPEq.57313876F 1991:2005JChPh.123w4505A 1922:Embedded atom model 1897:Molecular modelling 1887:Molecular mechanics 1855:valence bond theory 1658:University of Bonn. 1606:Alexander MacKerell 1591:harmonic oscillator 1462:like dissolves like 1435:protein engineering 1342:Jacob Israelachvili 1329:combinatorial rules 1325:combinatorial rules 1321:like dissolves like 1301:dielectric constant 120:molecular modelling 7915:information theory 7822:correlation length 7817:Critical exponents 7804:Critical phenomena 7785:stochastic process 7765:Boltzmann equation 7658:equations of state 7551:Warshel A (1991). 7532:Schlick T (2002). 6914:10.1039/C6SC05720A 6776:2010-07-15 at the 6511:10.1007/BF00124013 5052:. 2 February 2016. 4878:biohpc.cornell.edu 4407:10.1002/prot.22570 4211:10.1002/prot.10543 3764:10.1110/ps.0307002 3385:10.1039/c5cs00890e 2778:Annalen der Physik 2469:10.1039/c4dt00438h 1945:. Academic Press. 1941:Frenkel D (2007). 1882:Molecular dynamics 1766:Atoms in molecules 1711:Molecular dynamics 1515:modelling package. 1420:contribution, and 1100:covalent bonding, 1073: 1053: 1033: 1003: 890: 848:molecular dynamics 836: 814:quantum-mechanical 794: 761: 725: 705: 685: 649: 619: 589: 461:conjugated systems 438: 386: 320: 255: 148:molecular dynamics 116:physical chemistry 106:In the context of 104: 7953:Molecular physics 7930: 7929: 7920:Boltzmann machine 7790:mean-field theory 7691:Maxwell relations 7562:978-0-471-53395-5 7543:978-0-387-95404-2 7524:978-0-12-375181-2 7379:10.1021/sb400168u 7330:10.1021/ct400556v 7324:(12): 5653–5674. 7283:10.1021/jp805227c 7177:10.1063/1.5019779 6591:10.1021/jp004368u 6567:(41): 9396–9409. 6533:"Cresset Science" 6378:10.1021/jp905220k 6333:10.1063/1.2363374 6276:10.1063/1.2173256 6219:10.1021/ct700134r 6162:10.1021/ct400526a 6135:10.1063/1.1515773 6092:10.1021/ct049855i 6047:10.1021/ct700146x 5981:10.1021/cr9900477 5831:10.1021/ct900576a 5792:10.1021/ct049930p 5748:10.1002/jcc.20077 5592:10.1021/jp060163v 5549:10.1002/jcc.10355 5374:10.1021/cm0509328 5368:(23): 5658–5669. 5024:10.1021/la3038846 4933:10.1021/jp054994x 4243:Angewandte Chemie 4079:10.1021/ar010034r 3916:Missing or empty 3900:978-0-12-391927-4 3847:10.1002/prot.1106 3604:(20): 8910–8922. 3575:10.1021/ct5005565 3451:Physical Review B 3427:10.1021/cm500365c 3328:(22): 7148–7158. 3185:(10): 4278–4288. 3143:10.1021/jz500737m 3060:10.1021/jp048142t 3013:10.1021/ct500790p 2973:10.1002/qua.10108 2938:10.1021/ct300534j 2903:10.1021/ct600329w 2819:10.1021/ja9621760 2620:(12): 6443–6453. 2614:Physical Review B 2565:(12): 6991–7000. 2559:Physical Review B 2531:10.1063/1.3037370 2421:10.1002/jcc.20035 2371:10.1002/jcc.23354 2182:10.1021/jp071097f 2045:10.1021/ct200908r 1999:10.1063/1.2121687 1952:978-0-12-267351-1 1424:free energy. The 1371:homology modeling 1159:organic molecules 1076:{\displaystyle j} 1056:{\displaystyle i} 998: 959: 930: 728:{\displaystyle j} 708:{\displaystyle i} 536: 512: 435: 422: 409: 383: 370: 357: 344: 317: 304: 291: 223:methylene bridges 175:organic molecules 164:classical physics 156:quantum mechanics 112:molecular physics 86: 85: 78: 49:quality standards 40:This article may 16:(Redirected from 7965: 7812:Phase transition 7633: 7632: 7595: 7588: 7581: 7572: 7566: 7547: 7528: 7500: 7499: 7489: 7461: 7455: 7454: 7434: 7428: 7427: 7407: 7401: 7400: 7390: 7358: 7352: 7351: 7341: 7309: 7303: 7302: 7276: 7256: 7250: 7249: 7223: 7214:(6): 3678–3693. 7203: 7197: 7196: 7162: 7138: 7132: 7131: 7097: 7077: 7071: 7070: 7060: 7036: 7030: 7029: 7019: 6995: 6989: 6988: 6970: 6942: 6936: 6935: 6925: 6908:(4): 3192–3203. 6902:Chemical Science 6893: 6887: 6886: 6884: 6860: 6854: 6853: 6843: 6833: 6816:(37): 15667–72. 6801: 6795: 6794: 6787: 6781: 6768: 6762: 6761: 6717: 6711: 6710: 6666: 6660: 6659: 6615: 6609: 6608: 6606: 6605: 6599: 6593:. Archived from 6584: 6556: 6543: 6537: 6536: 6529: 6523: 6522: 6490: 6484: 6483: 6447: 6441: 6440: 6430: 6420: 6396: 6390: 6389: 6372:(33): 11463–78. 6361: 6355: 6354: 6344: 6304: 6298: 6297: 6287: 6247: 6241: 6240: 6230: 6213:(6): 1960–1986. 6198: 6192: 6191: 6180: 6174: 6173: 6145: 6139: 6138: 6110: 6104: 6103: 6075: 6069: 6068: 6058: 6041:(6): 1878–1889. 6026: 6020: 6019: 5999: 5993: 5992: 5975:(11): 4087–108. 5969:Chemical Reviews 5964: 5958: 5957: 5929: 5923: 5922: 5894: 5888: 5887: 5859: 5853: 5852: 5842: 5810: 5804: 5803: 5775: 5769: 5768: 5750: 5726: 5720: 5719: 5709: 5692:(7): 4122–4139. 5677: 5671: 5670: 5660: 5628: 5622: 5621: 5618:dasher.wustl.edu 5610: 5604: 5603: 5586:(26): 13166–76. 5575: 5569: 5568: 5532: 5523: 5522: 5486: 5480: 5479: 5446:(8): 1031–1038. 5435: 5429: 5428: 5392: 5386: 5385: 5357: 5351: 5350: 5322: 5316: 5315: 5310: 5304: 5303: 5283: 5277: 5276: 5256: 5250: 5249: 5229: 5223: 5222: 5202: 5196: 5195: 5190:. Archived from 5184: 5178: 5177: 5157: 5151: 5150: 5140: 5100: 5091: 5090: 5072: 5063: 5054: 5053: 5050:Heinz Laboratory 5042: 5036: 5035: 5007: 4998: 4997: 4986: 4980: 4979: 4951: 4945: 4944: 4916: 4910: 4909: 4888: 4882: 4881: 4870: 4864: 4863: 4835: 4829: 4828: 4808: 4802: 4801: 4791: 4781: 4749: 4743: 4742: 4732: 4692: 4686: 4685: 4673: 4667: 4666: 4630: 4624: 4623: 4595: 4589: 4588: 4578: 4546: 4540: 4539: 4505: 4499: 4498: 4470: 4464: 4463: 4435: 4429: 4428: 4418: 4386: 4380: 4379: 4343: 4337: 4336: 4308: 4302: 4301: 4273: 4267: 4266: 4238: 4232: 4231: 4213: 4189: 4183: 4182: 4164: 4140: 4134: 4133: 4097: 4091: 4090: 4062: 4056: 4055: 4019: 4013: 4012: 3975: 3969: 3968: 3932: 3926: 3925: 3919: 3914: 3912: 3904: 3882: 3867: 3866: 3830: 3824: 3823: 3795: 3786: 3785: 3775: 3758:(8): 1984–2000. 3743: 3732: 3731: 3703: 3694: 3693: 3674:10.1038/nmat4426 3659: 3650:(11): 1099–103. 3644:Nature Materials 3639: 3630: 3629: 3618:10.1063/1.481505 3593: 3587: 3586: 3558: 3552: 3551: 3541: 3531: 3499: 3493: 3492: 3482: 3445: 3439: 3438: 3421:(8): 2647–2658. 3412: 3403: 3397: 3396: 3368: 3362: 3361: 3313: 3307: 3306: 3281:(1–3): 101–105. 3266: 3260: 3259: 3249: 3217: 3211: 3210: 3174: 3165: 3164: 3154: 3122: 3116: 3115: 3078: 3072: 3071: 3035: 3026: 3025: 3015: 2991: 2985: 2984: 2956: 2950: 2949: 2921: 2915: 2914: 2886: 2880: 2879: 2842: 2831: 2830: 2802: 2796: 2795: 2793: 2772:Drude P (1900). 2769: 2763: 2762: 2742: 2736: 2735: 2725: 2708:(9): 4983–5013. 2702:Chemical Reviews 2693: 2687: 2686: 2676: 2667:(7–8): 251–310. 2652: 2646: 2645: 2605: 2599: 2598: 2550: 2544: 2543: 2533: 2497: 2491: 2490: 2480: 2463:(27): 10602–16. 2451: 2442: 2441: 2423: 2399: 2393: 2392: 2382: 2350: 2344: 2343: 2326:(7): 2978–2987. 2315: 2306: 2305: 2295: 2263: 2257: 2256: 2208: 2202: 2201: 2167: 2158: 2149: 2148: 2122: 2098: 2087: 2086: 2068: 2057: 2056: 2028: 2019: 2018: 1974: 1965: 1964: 1938: 1748:Machine learning 1366:NMR spectroscopy 1344:. For example, " 1338:Hamaker constant 1314:). The original 1253:self-consistency 1233:openKim database 1177:functional group 1116:Parameterization 1086: 1082: 1080: 1079: 1074: 1062: 1060: 1059: 1054: 1042: 1040: 1039: 1034: 1032: 1031: 1012: 1010: 1009: 1004: 999: 997: 996: 984: 983: 982: 973: 972: 962: 960: 958: 957: 956: 937: 932: 931: 928: 899: 897: 896: 891: 889: 888: 845: 843: 842: 837: 835: 834: 803: 801: 800: 795: 793: 792: 770: 768: 767: 762: 760: 759: 734: 732: 731: 726: 714: 712: 711: 706: 694: 692: 691: 686: 684: 683: 658: 656: 655: 650: 648: 647: 628: 626: 625: 620: 618: 617: 598: 596: 595: 590: 585: 584: 575: 574: 553: 552: 537: 532: 531: 519: 514: 513: 510: 459:rings and other 447: 445: 444: 439: 437: 436: 433: 424: 423: 420: 411: 410: 407: 395: 393: 392: 387: 385: 384: 381: 372: 371: 368: 359: 358: 355: 346: 345: 342: 329: 327: 326: 321: 319: 318: 315: 306: 305: 302: 293: 292: 289: 259:potential energy 144:potential energy 81: 74: 70: 67: 61: 35: 34: 27: 21: 7973: 7972: 7968: 7967: 7966: 7964: 7963: 7962: 7933: 7932: 7931: 7926: 7871: 7833: 7798: 7780:BBGKY hierarchy 7775:Vlasov equation 7753: 7742:depletion force 7735:Particles with 7695: 7634: 7630: 7625: 7604: 7599: 7569: 7563: 7550: 7544: 7531: 7525: 7512: 7508: 7506:Further reading 7503: 7463: 7462: 7458: 7436: 7435: 7431: 7409: 7408: 7404: 7360: 7359: 7355: 7311: 7310: 7306: 7267:(13): 4008–16. 7258: 7257: 7253: 7205: 7204: 7200: 7140: 7139: 7135: 7079: 7078: 7074: 7038: 7037: 7033: 6997: 6996: 6992: 6944: 6943: 6939: 6895: 6894: 6890: 6875:: 11423–11436. 6862: 6861: 6857: 6803: 6802: 6798: 6789: 6788: 6784: 6778:Wayback Machine 6769: 6765: 6719: 6718: 6714: 6668: 6667: 6663: 6617: 6616: 6612: 6603: 6601: 6597: 6582:10.1.1.507.6992 6554: 6545: 6544: 6540: 6531: 6530: 6526: 6492: 6491: 6487: 6449: 6448: 6444: 6398: 6397: 6393: 6363: 6362: 6358: 6306: 6305: 6301: 6249: 6248: 6244: 6200: 6199: 6195: 6182: 6181: 6177: 6147: 6146: 6142: 6121:(20): 9175–89. 6112: 6111: 6107: 6077: 6076: 6072: 6028: 6027: 6023: 6010:(44): 16460–7. 6001: 6000: 5996: 5966: 5965: 5961: 5931: 5930: 5926: 5896: 5895: 5891: 5861: 5860: 5856: 5812: 5811: 5807: 5777: 5776: 5772: 5741:(12): 1504–14. 5728: 5727: 5723: 5679: 5678: 5674: 5630: 5629: 5625: 5612: 5611: 5607: 5577: 5576: 5572: 5534: 5533: 5526: 5488: 5487: 5483: 5437: 5436: 5432: 5397:Physical Review 5394: 5393: 5389: 5359: 5358: 5354: 5324: 5323: 5319: 5312: 5311: 5307: 5285: 5284: 5280: 5267:(23): 8576–82. 5258: 5257: 5253: 5240:(23): 8566–75. 5231: 5230: 5226: 5213:(23): 8551–66. 5204: 5203: 5199: 5186: 5185: 5181: 5168:(25): 8127–34. 5159: 5158: 5154: 5102: 5101: 5094: 5070: 5065: 5064: 5057: 5044: 5043: 5039: 5009: 5008: 5001: 4994:www.igc.ethz.ch 4988: 4987: 4983: 4962:(4–5): 679–94. 4953: 4952: 4948: 4927:(10): 5025–44. 4918: 4917: 4913: 4900:(22): 2361–81. 4890: 4889: 4885: 4872: 4871: 4867: 4837: 4836: 4832: 4810: 4809: 4805: 4751: 4750: 4746: 4694: 4693: 4689: 4675: 4674: 4670: 4641:(10): 1667–80. 4632: 4631: 4627: 4597: 4596: 4592: 4555:Protein Science 4548: 4547: 4543: 4528: 4507: 4506: 4502: 4472: 4471: 4467: 4437: 4436: 4432: 4388: 4387: 4383: 4345: 4344: 4340: 4310: 4309: 4305: 4275: 4274: 4270: 4249:(15): 2644–76. 4240: 4239: 4235: 4191: 4190: 4186: 4142: 4141: 4137: 4099: 4098: 4094: 4064: 4063: 4059: 4021: 4020: 4016: 3987:(50): 1905247. 3977: 3976: 3972: 3934: 3933: 3929: 3915: 3905: 3901: 3884: 3883: 3870: 3832: 3831: 3827: 3806:(11): 1647–76. 3797: 3796: 3789: 3752:Protein Science 3745: 3744: 3735: 3705: 3704: 3697: 3641: 3640: 3633: 3595: 3594: 3590: 3569:(10): 4488–96. 3560: 3559: 3555: 3501: 3500: 3496: 3447: 3446: 3442: 3410: 3405: 3404: 3400: 3370: 3369: 3365: 3315: 3314: 3310: 3268: 3267: 3263: 3219: 3218: 3214: 3176: 3175: 3168: 3137:(11): 1885–91. 3124: 3123: 3119: 3080: 3079: 3075: 3037: 3036: 3029: 3006:(12): 5640–50. 2993: 2992: 2988: 2958: 2957: 2953: 2932:(11): 4719–31. 2923: 2922: 2918: 2888: 2887: 2883: 2844: 2843: 2834: 2804: 2803: 2799: 2771: 2770: 2766: 2744: 2743: 2739: 2695: 2694: 2690: 2654: 2653: 2649: 2607: 2606: 2602: 2552: 2551: 2547: 2499: 2498: 2494: 2453: 2452: 2445: 2401: 2400: 2396: 2365:(25): 2135–45. 2352: 2351: 2347: 2317: 2316: 2309: 2265: 2264: 2260: 2210: 2209: 2205: 2176:(27): 7812–24. 2165: 2160: 2159: 2152: 2113:(10): 806–814. 2100: 2099: 2090: 2083: 2070: 2069: 2060: 2030: 2029: 2022: 1976: 1975: 1968: 1953: 1940: 1939: 1935: 1931: 1926: 1872: 1840: 1831:Forcefield_NCAA 1821: 1801: 1795: 1750: 1702: 1692:William Goddard 1673: 1583: 1552:Norman Allinger 1492: 1484: 1470: 1406:crystallization 1398:protein folding 1379:protein folding 1269: 1249: 1241:MolMod database 1237:TraPPE database 1228: 1205:spring constant 1201:dihedral angles 1118: 1097: 1084: 1065: 1064: 1045: 1044: 1020: 1015: 1014: 985: 974: 964: 963: 948: 941: 923: 918: 917: 880: 875: 874: 868: 860:Morse potential 823: 818: 817: 781: 776: 775: 742: 737: 736: 717: 716: 697: 696: 666: 661: 660: 636: 631: 630: 606: 601: 600: 576: 557: 541: 520: 505: 500: 499: 492: 490:Bond stretching 453:Morse potential 428: 415: 402: 397: 396: 376: 363: 350: 337: 332: 331: 310: 297: 284: 279: 278: 247: 136:functional form 96: 89: 82: 71: 65: 62: 55: 53:Grammar issues. 36: 32: 23: 22: 15: 12: 11: 5: 7971: 7969: 7961: 7960: 7955: 7950: 7945: 7935: 7934: 7928: 7927: 7925: 7924: 7923: 7922: 7917: 7912: 7905:Complex system 7902: 7897: 7896: 7895: 7890: 7879: 7877: 7873: 7872: 7870: 7869: 7864: 7859: 7854: 7849: 7843: 7841: 7835: 7834: 7832: 7831: 7830: 7829: 7824: 7814: 7808: 7806: 7800: 7799: 7797: 7796: 7787: 7782: 7777: 7772: 7767: 7761: 7759: 7755: 7754: 7752: 7751: 7750: 7749: 7744: 7733: 7732: 7731: 7726: 7721: 7716: 7705: 7703: 7697: 7696: 7694: 7693: 7688: 7687: 7686: 7681: 7676: 7671: 7660: 7655: 7650: 7644: 7642: 7636: 7635: 7628: 7626: 7624: 7623: 7621:ergodic theory 7618: 7612: 7610: 7606: 7605: 7600: 7598: 7597: 7590: 7583: 7575: 7568: 7567: 7561: 7548: 7542: 7529: 7523: 7509: 7507: 7504: 7502: 7501: 7472:(6): 1282–90. 7456: 7445:(212): 11–34. 7429: 7402: 7373:(12): 855–69. 7353: 7304: 7251: 7198: 7153:(24): 241722. 7133: 7088:(5): 2087–96. 7072: 7051:(1): 216–224. 7031: 7010:(6): 2742–51. 6990: 6953:(1): 116–126. 6937: 6888: 6855: 6796: 6782: 6763: 6728:(4): 191–196. 6712: 6677:(3): 363–368. 6661: 6626:(3): 155–160. 6610: 6538: 6524: 6505:(6): 653–668. 6485: 6442: 6391: 6356: 6319:(18): 184101. 6299: 6262:(10): 104101. 6242: 6193: 6175: 6156:(12): 5550–7. 6140: 6105: 6086:(4): 694–715. 6070: 6021: 5994: 5959: 5924: 5889: 5854: 5825:(3): 774–786. 5805: 5770: 5721: 5672: 5643:(2): 419–426. 5623: 5605: 5570: 5524: 5481: 5430: 5387: 5352: 5317: 5305: 5278: 5251: 5224: 5197: 5194:on 2009-01-23. 5179: 5152: 5092: 5055: 5037: 5018:(6): 1754–65. 4999: 4981: 4946: 4911: 4883: 4865: 4830: 4819:(18): 4831–7. 4803: 4744: 4687: 4668: 4625: 4606:(3): 699–709. 4590: 4561:(6): 1318–33. 4541: 4526: 4500: 4465: 4430: 4381: 4338: 4303: 4268: 4233: 4184: 4135: 4108:(2): 145–237. 4092: 4057: 4014: 3970: 3943:(2): 105–267. 3927: 3899: 3868: 3825: 3787: 3733: 3695: 3631: 3588: 3553: 3514:(14): 146103. 3494: 3440: 3398: 3363: 3308: 3261: 3212: 3166: 3117: 3073: 3027: 2986: 2967:(1): 445–458. 2951: 2916: 2897:(4): 1464–75. 2881: 2832: 2797: 2784:(3): 566–613. 2764: 2737: 2688: 2647: 2600: 2545: 2492: 2443: 2414:(9): 1157–74. 2394: 2345: 2307: 2258: 2203: 2150: 2088: 2081: 2058: 2039:(4): 1459–70. 2020: 1985:(23): 234505. 1966: 1951: 1932: 1930: 1927: 1925: 1924: 1919: 1914: 1909: 1904: 1899: 1894: 1889: 1884: 1879: 1873: 1871: 1868: 1867: 1866: 1848: 1839: 1836: 1835: 1834: 1828: 1825:Forcefield_PTM 1820: 1817: 1813:solvent models 1797:Main article: 1794: 1791: 1790: 1789: 1786: 1783:Neural network 1779: 1776: 1773:neural network 1769: 1758: 1755: 1749: 1746: 1745: 1744: 1740: 1736: 1729: 1719: 1701: 1700:Coarse-grained 1698: 1697: 1696: 1685: 1672: 1669: 1668: 1667: 1663: 1659: 1655: 1652: 1649: 1646: 1643: 1640: 1637: 1634: 1626: 1623: 1620: 1616: 1613: 1602: 1598: 1587:polarizability 1582: 1579: 1578: 1577: 1573: 1570: 1560: 1548: 1541: 1533: 1527: 1519: 1516: 1512: 1506: 1499: 1491: 1488: 1469: 1466: 1426:heat of fusion 1414:heat of fusion 1402:ligand binding 1383:protein design 1375:ligand docking 1268: 1265: 1248: 1245: 1227: 1224: 1143:macromolecules 1135:dipole moments 1117: 1114: 1096: 1093: 1072: 1052: 1030: 1027: 1023: 1002: 995: 992: 988: 981: 977: 971: 967: 955: 951: 947: 944: 940: 935: 926: 906:polar covalent 887: 883: 872:atomic charges 867: 864: 833: 830: 826: 791: 788: 784: 758: 755: 752: 749: 745: 724: 704: 682: 679: 676: 673: 669: 646: 643: 639: 616: 613: 609: 588: 583: 579: 573: 570: 567: 564: 560: 556: 551: 548: 544: 540: 535: 530: 527: 523: 517: 508: 491: 488: 484:polarizability 465:hydrogen bonds 431: 427: 418: 414: 405: 379: 375: 366: 362: 353: 349: 340: 313: 309: 300: 296: 287: 263:covalent bonds 246: 243: 231:macromolecules 227:Coarse-grained 87: 84: 83: 39: 37: 30: 24: 14: 13: 10: 9: 6: 4: 3: 2: 7970: 7959: 7956: 7954: 7951: 7949: 7946: 7944: 7941: 7940: 7938: 7921: 7918: 7916: 7913: 7911: 7908: 7907: 7906: 7903: 7901: 7898: 7894: 7893:superfluidity 7891: 7889: 7886: 7885: 7884: 7881: 7880: 7878: 7874: 7868: 7865: 7863: 7860: 7858: 7855: 7853: 7850: 7848: 7845: 7844: 7842: 7840: 7836: 7828: 7825: 7823: 7820: 7819: 7818: 7815: 7813: 7810: 7809: 7807: 7805: 7801: 7795: 7791: 7788: 7786: 7783: 7781: 7778: 7776: 7773: 7771: 7768: 7766: 7763: 7762: 7760: 7756: 7748: 7745: 7743: 7740: 7739: 7738: 7734: 7730: 7727: 7725: 7722: 7720: 7717: 7715: 7712: 7711: 7710: 7707: 7706: 7704: 7702: 7698: 7692: 7689: 7685: 7682: 7680: 7677: 7675: 7672: 7670: 7667: 7666: 7664: 7661: 7659: 7656: 7654: 7651: 7649: 7646: 7645: 7643: 7641: 7637: 7622: 7619: 7617: 7614: 7613: 7611: 7607: 7603: 7596: 7591: 7589: 7584: 7582: 7577: 7576: 7573: 7564: 7558: 7554: 7549: 7545: 7539: 7535: 7530: 7526: 7520: 7516: 7511: 7510: 7505: 7497: 7493: 7488: 7483: 7479: 7475: 7471: 7467: 7460: 7457: 7452: 7448: 7444: 7440: 7433: 7430: 7425: 7421: 7417: 7413: 7406: 7403: 7398: 7394: 7389: 7384: 7380: 7376: 7372: 7368: 7364: 7357: 7354: 7349: 7345: 7340: 7335: 7331: 7327: 7323: 7319: 7315: 7308: 7305: 7300: 7296: 7292: 7288: 7284: 7280: 7275: 7270: 7266: 7262: 7255: 7252: 7247: 7243: 7239: 7235: 7231: 7227: 7222: 7217: 7213: 7209: 7202: 7199: 7194: 7190: 7186: 7182: 7178: 7174: 7170: 7166: 7161: 7156: 7152: 7148: 7144: 7137: 7134: 7129: 7125: 7121: 7117: 7113: 7109: 7105: 7101: 7096: 7091: 7087: 7083: 7076: 7073: 7068: 7064: 7059: 7054: 7050: 7046: 7042: 7035: 7032: 7027: 7023: 7018: 7013: 7009: 7005: 7001: 6994: 6991: 6986: 6982: 6978: 6974: 6969: 6964: 6960: 6956: 6952: 6948: 6941: 6938: 6933: 6929: 6924: 6919: 6915: 6911: 6907: 6903: 6899: 6892: 6889: 6883: 6878: 6874: 6870: 6866: 6859: 6856: 6851: 6847: 6842: 6837: 6832: 6827: 6823: 6819: 6815: 6811: 6807: 6800: 6797: 6792: 6786: 6783: 6779: 6775: 6772: 6767: 6764: 6759: 6755: 6751: 6747: 6743: 6739: 6735: 6731: 6727: 6723: 6716: 6713: 6708: 6704: 6700: 6696: 6692: 6688: 6684: 6680: 6676: 6672: 6665: 6662: 6657: 6653: 6649: 6645: 6641: 6637: 6633: 6629: 6625: 6621: 6614: 6611: 6600:on 2018-03-21 6596: 6592: 6588: 6583: 6578: 6574: 6570: 6566: 6562: 6561: 6553: 6549: 6542: 6539: 6534: 6528: 6525: 6520: 6516: 6512: 6508: 6504: 6500: 6496: 6489: 6486: 6481: 6477: 6473: 6469: 6465: 6461: 6457: 6453: 6446: 6443: 6438: 6434: 6429: 6424: 6419: 6414: 6410: 6406: 6402: 6395: 6392: 6387: 6383: 6379: 6375: 6371: 6367: 6360: 6357: 6352: 6348: 6343: 6338: 6334: 6330: 6326: 6322: 6318: 6314: 6310: 6303: 6300: 6295: 6291: 6286: 6281: 6277: 6273: 6269: 6265: 6261: 6257: 6253: 6246: 6243: 6238: 6234: 6229: 6224: 6220: 6216: 6212: 6208: 6204: 6197: 6194: 6189: 6185: 6179: 6176: 6171: 6167: 6163: 6159: 6155: 6151: 6144: 6141: 6136: 6132: 6128: 6124: 6120: 6116: 6109: 6106: 6101: 6097: 6093: 6089: 6085: 6081: 6074: 6071: 6066: 6062: 6057: 6052: 6048: 6044: 6040: 6036: 6032: 6025: 6022: 6017: 6013: 6009: 6005: 5998: 5995: 5990: 5986: 5982: 5978: 5974: 5970: 5963: 5960: 5955: 5951: 5947: 5943: 5940:(6): 471–84. 5939: 5935: 5928: 5925: 5920: 5916: 5912: 5908: 5905:(5): 524–31. 5904: 5900: 5893: 5890: 5885: 5881: 5877: 5873: 5870:(2): 227–49. 5869: 5865: 5858: 5855: 5850: 5846: 5841: 5836: 5832: 5828: 5824: 5820: 5816: 5809: 5806: 5801: 5797: 5793: 5789: 5786:(1): 153–68. 5785: 5781: 5774: 5771: 5766: 5762: 5758: 5754: 5749: 5744: 5740: 5736: 5732: 5725: 5722: 5717: 5713: 5708: 5703: 5699: 5695: 5691: 5687: 5683: 5676: 5673: 5668: 5664: 5659: 5654: 5650: 5646: 5642: 5638: 5634: 5627: 5624: 5619: 5615: 5609: 5606: 5601: 5597: 5593: 5589: 5585: 5581: 5574: 5571: 5566: 5562: 5558: 5554: 5550: 5546: 5542: 5538: 5531: 5529: 5525: 5520: 5516: 5512: 5508: 5504: 5500: 5496: 5492: 5485: 5482: 5477: 5473: 5469: 5465: 5461: 5457: 5453: 5449: 5445: 5441: 5434: 5431: 5426: 5422: 5418: 5414: 5410: 5406: 5403:(1): 90–103. 5402: 5398: 5391: 5388: 5383: 5379: 5375: 5371: 5367: 5363: 5356: 5353: 5348: 5344: 5340: 5336: 5332: 5328: 5321: 5318: 5309: 5306: 5301: 5297: 5294:(5): 709–17. 5293: 5289: 5282: 5279: 5274: 5270: 5266: 5262: 5255: 5252: 5247: 5243: 5239: 5235: 5228: 5225: 5220: 5216: 5212: 5208: 5201: 5198: 5193: 5189: 5183: 5180: 5175: 5171: 5167: 5163: 5156: 5153: 5148: 5144: 5139: 5134: 5130: 5126: 5122: 5118: 5114: 5110: 5106: 5099: 5097: 5093: 5088: 5084: 5080: 5076: 5069: 5062: 5060: 5056: 5051: 5047: 5041: 5038: 5033: 5029: 5025: 5021: 5017: 5013: 5006: 5004: 5000: 4995: 4991: 4985: 4982: 4977: 4973: 4969: 4965: 4961: 4957: 4950: 4947: 4942: 4938: 4934: 4930: 4926: 4922: 4915: 4912: 4907: 4903: 4899: 4895: 4887: 4884: 4879: 4875: 4869: 4866: 4861: 4857: 4853: 4849: 4846:(4): 90–102. 4845: 4841: 4834: 4831: 4826: 4822: 4818: 4814: 4807: 4804: 4799: 4795: 4790: 4785: 4780: 4775: 4771: 4767: 4764:(7): 2854–8. 4763: 4759: 4755: 4748: 4745: 4740: 4736: 4731: 4726: 4722: 4718: 4714: 4710: 4707:(4): 2033–9. 4706: 4702: 4698: 4691: 4688: 4683: 4679: 4672: 4669: 4664: 4660: 4656: 4652: 4648: 4644: 4640: 4636: 4629: 4626: 4621: 4617: 4613: 4609: 4605: 4601: 4594: 4591: 4586: 4582: 4577: 4572: 4568: 4564: 4560: 4556: 4552: 4545: 4542: 4537: 4533: 4529: 4527:9780121827885 4523: 4519: 4515: 4511: 4504: 4501: 4496: 4492: 4488: 4484: 4480: 4476: 4469: 4466: 4461: 4457: 4453: 4449: 4446:(4): 509–13. 4445: 4441: 4434: 4431: 4426: 4422: 4417: 4412: 4408: 4404: 4400: 4396: 4392: 4385: 4382: 4377: 4373: 4369: 4365: 4361: 4357: 4354:(2): 97–103. 4353: 4349: 4342: 4339: 4334: 4330: 4326: 4322: 4319:(2): 139–45. 4318: 4314: 4307: 4304: 4299: 4295: 4291: 4287: 4283: 4279: 4272: 4269: 4264: 4260: 4256: 4252: 4248: 4244: 4237: 4234: 4229: 4225: 4221: 4217: 4212: 4207: 4203: 4199: 4195: 4188: 4185: 4180: 4176: 4172: 4168: 4163: 4158: 4155:(sup1): 106. 4154: 4150: 4146: 4139: 4136: 4131: 4127: 4123: 4119: 4115: 4111: 4107: 4103: 4096: 4093: 4088: 4084: 4080: 4076: 4073:(6): 404–12. 4072: 4068: 4061: 4058: 4053: 4049: 4045: 4041: 4037: 4033: 4030:(2): 108–11. 4029: 4025: 4018: 4015: 4010: 4006: 4002: 3998: 3994: 3990: 3986: 3982: 3974: 3971: 3966: 3962: 3958: 3954: 3950: 3946: 3942: 3938: 3931: 3928: 3923: 3910: 3902: 3896: 3892: 3888: 3881: 3879: 3877: 3875: 3873: 3869: 3864: 3860: 3856: 3852: 3848: 3844: 3841:(4): 400–17. 3840: 3836: 3829: 3826: 3821: 3817: 3813: 3809: 3805: 3801: 3794: 3792: 3788: 3783: 3779: 3774: 3769: 3765: 3761: 3757: 3753: 3749: 3742: 3740: 3738: 3734: 3729: 3725: 3721: 3717: 3713: 3709: 3702: 3700: 3696: 3691: 3687: 3683: 3679: 3675: 3671: 3667: 3663: 3658: 3653: 3649: 3645: 3638: 3636: 3632: 3627: 3623: 3619: 3615: 3611: 3607: 3603: 3599: 3592: 3589: 3584: 3580: 3576: 3572: 3568: 3564: 3557: 3554: 3549: 3545: 3540: 3535: 3530: 3525: 3521: 3517: 3513: 3509: 3505: 3498: 3495: 3490: 3486: 3481: 3476: 3472: 3468: 3464: 3460: 3457:(3): 035118. 3456: 3452: 3444: 3441: 3436: 3432: 3428: 3424: 3420: 3416: 3409: 3402: 3399: 3394: 3390: 3386: 3382: 3379:(2): 412–48. 3378: 3374: 3367: 3364: 3359: 3355: 3351: 3347: 3343: 3339: 3335: 3331: 3327: 3323: 3319: 3312: 3309: 3304: 3300: 3296: 3292: 3288: 3284: 3280: 3276: 3272: 3265: 3262: 3257: 3253: 3248: 3243: 3239: 3235: 3231: 3227: 3223: 3216: 3213: 3208: 3204: 3200: 3196: 3192: 3188: 3184: 3180: 3173: 3171: 3167: 3162: 3158: 3153: 3148: 3144: 3140: 3136: 3132: 3128: 3121: 3118: 3113: 3109: 3105: 3101: 3097: 3093: 3089: 3085: 3077: 3074: 3069: 3065: 3061: 3057: 3053: 3049: 3045: 3041: 3034: 3032: 3028: 3023: 3019: 3014: 3009: 3005: 3001: 2997: 2990: 2987: 2982: 2978: 2974: 2970: 2966: 2962: 2955: 2952: 2947: 2943: 2939: 2935: 2931: 2927: 2920: 2917: 2912: 2908: 2904: 2900: 2896: 2892: 2885: 2882: 2877: 2873: 2869: 2865: 2861: 2857: 2853: 2849: 2841: 2839: 2837: 2833: 2828: 2824: 2820: 2816: 2812: 2808: 2801: 2798: 2792: 2787: 2783: 2779: 2775: 2768: 2765: 2760: 2756: 2752: 2748: 2741: 2738: 2733: 2729: 2724: 2719: 2715: 2711: 2707: 2703: 2699: 2692: 2689: 2684: 2680: 2675: 2670: 2666: 2662: 2658: 2651: 2648: 2643: 2639: 2635: 2631: 2627: 2623: 2619: 2615: 2611: 2604: 2601: 2596: 2592: 2588: 2584: 2580: 2576: 2572: 2568: 2564: 2560: 2556: 2549: 2546: 2541: 2537: 2532: 2527: 2523: 2519: 2515: 2511: 2510:Physics Today 2507: 2505: 2496: 2493: 2488: 2484: 2479: 2474: 2470: 2466: 2462: 2458: 2450: 2448: 2444: 2439: 2435: 2431: 2427: 2422: 2417: 2413: 2409: 2405: 2398: 2395: 2390: 2386: 2381: 2376: 2372: 2368: 2364: 2360: 2356: 2349: 2346: 2341: 2337: 2333: 2329: 2325: 2321: 2314: 2312: 2308: 2303: 2299: 2294: 2289: 2285: 2281: 2277: 2273: 2269: 2262: 2259: 2254: 2250: 2246: 2242: 2238: 2234: 2230: 2226: 2222: 2218: 2214: 2207: 2204: 2199: 2195: 2191: 2187: 2183: 2179: 2175: 2171: 2164: 2157: 2155: 2151: 2146: 2142: 2138: 2134: 2130: 2126: 2121: 2116: 2112: 2108: 2104: 2097: 2095: 2093: 2089: 2084: 2082:9780582382107 2078: 2074: 2067: 2065: 2063: 2059: 2054: 2050: 2046: 2042: 2038: 2034: 2027: 2025: 2021: 2016: 2012: 2008: 2004: 2000: 1996: 1992: 1988: 1984: 1980: 1973: 1971: 1967: 1962: 1958: 1954: 1948: 1944: 1937: 1934: 1928: 1923: 1920: 1918: 1915: 1913: 1910: 1908: 1905: 1903: 1900: 1898: 1895: 1893: 1890: 1888: 1885: 1883: 1880: 1878: 1875: 1874: 1869: 1864: 1860: 1856: 1852: 1849: 1847: 1842: 1841: 1837: 1832: 1829: 1826: 1823: 1822: 1818: 1816: 1814: 1810: 1806: 1800: 1792: 1787: 1784: 1780: 1777: 1774: 1770: 1767: 1763: 1759: 1756: 1752: 1751: 1747: 1741: 1737: 1734: 1730: 1727: 1723: 1720: 1716: 1712: 1708: 1704: 1703: 1699: 1693: 1689: 1686: 1683: 1679: 1675: 1674: 1670: 1664: 1660: 1656: 1653: 1650: 1647: 1644: 1641: 1638: 1635: 1632: 1627: 1624: 1621: 1617: 1614: 1611: 1607: 1603: 1599: 1596: 1595: 1594: 1592: 1588: 1580: 1574: 1571: 1568: 1564: 1561: 1557: 1553: 1549: 1546: 1542: 1539: 1534: 1531: 1528: 1525: 1520: 1517: 1513: 1510: 1507: 1504: 1503:Arieh Warshel 1500: 1497: 1494: 1493: 1489: 1487: 1483: 1479: 1475: 1467: 1465: 1463: 1459: 1455: 1452:of molecular 1451: 1448: 1444: 1440: 1436: 1432: 1427: 1423: 1419: 1415: 1411: 1407: 1403: 1399: 1395: 1391: 1386: 1384: 1380: 1376: 1372: 1367: 1363: 1359: 1355: 1349: 1347: 1343: 1339: 1335: 1330: 1326: 1322: 1317: 1313: 1309: 1306:All types of 1304: 1302: 1298: 1294: 1289: 1284: 1282: 1278: 1274: 1266: 1264: 1261: 1259: 1254: 1246: 1244: 1242: 1238: 1234: 1231:example, the 1225: 1223: 1221: 1217: 1212: 1208: 1206: 1202: 1198: 1194: 1190: 1186: 1185:atomic charge 1182: 1178: 1175: 1171: 1167: 1162: 1160: 1156: 1152: 1148: 1144: 1138: 1136: 1132: 1128: 1124: 1115: 1113: 1111: 1107: 1103: 1094: 1092: 1088: 1070: 1050: 1028: 1025: 1021: 1000: 993: 990: 986: 979: 975: 969: 965: 953: 949: 945: 942: 938: 933: 924: 915: 911: 910:ionic bonding 907: 903: 885: 881: 873: 865: 863: 861: 855: 853: 849: 831: 828: 824: 815: 811: 807: 789: 786: 782: 772: 756: 753: 750: 747: 743: 722: 702: 680: 677: 674: 671: 667: 644: 641: 637: 614: 611: 607: 586: 581: 571: 568: 565: 562: 558: 554: 549: 546: 542: 533: 528: 525: 521: 515: 506: 497: 489: 487: 485: 481: 480:Coulomb's law 477: 476:Mie potential 473: 468: 466: 462: 458: 454: 448: 434:van der Waals 429: 425: 421:electrostatic 416: 412: 403: 377: 373: 364: 360: 351: 347: 338: 311: 307: 298: 294: 285: 276: 272: 271:electrostatic 268: 264: 260: 251: 244: 242: 240: 239:nucleic acids 236: 232: 228: 224: 220: 219:methyl groups 216: 212: 208: 204: 200: 199:methyl groups 194: 192: 188: 184: 180: 176: 171: 169: 165: 161: 157: 153: 149: 145: 141: 137: 133: 129: 128:computational 125: 121: 117: 113: 109: 100: 94: 80: 77: 69: 59: 54: 50: 46: 45: 38: 29: 28: 19: 7876:Applications 7827:size scaling 7736: 7552: 7533: 7514: 7469: 7465: 7459: 7442: 7438: 7432: 7415: 7411: 7405: 7370: 7366: 7356: 7321: 7317: 7307: 7264: 7260: 7254: 7211: 7207: 7201: 7150: 7146: 7136: 7085: 7081: 7075: 7048: 7044: 7034: 7007: 7003: 6993: 6950: 6946: 6940: 6905: 6901: 6891: 6872: 6868: 6858: 6813: 6809: 6799: 6785: 6766: 6725: 6721: 6715: 6674: 6670: 6664: 6623: 6619: 6613: 6602:. Retrieved 6595:the original 6564: 6558: 6541: 6527: 6502: 6498: 6488: 6455: 6451: 6445: 6408: 6404: 6394: 6369: 6365: 6359: 6316: 6312: 6302: 6259: 6255: 6245: 6210: 6206: 6196: 6187: 6178: 6153: 6149: 6143: 6118: 6114: 6108: 6083: 6079: 6073: 6038: 6034: 6024: 6007: 6003: 5997: 5972: 5968: 5962: 5937: 5933: 5927: 5902: 5898: 5892: 5867: 5863: 5857: 5822: 5818: 5808: 5783: 5779: 5773: 5738: 5734: 5724: 5689: 5685: 5675: 5640: 5636: 5626: 5617: 5608: 5583: 5579: 5573: 5540: 5536: 5497:(2): 69–85. 5494: 5490: 5484: 5443: 5439: 5433: 5400: 5396: 5390: 5365: 5361: 5355: 5330: 5326: 5320: 5308: 5291: 5287: 5281: 5264: 5260: 5254: 5237: 5233: 5227: 5210: 5206: 5200: 5192:the original 5182: 5165: 5161: 5155: 5112: 5108: 5078: 5074: 5049: 5040: 5015: 5011: 4993: 4984: 4959: 4955: 4949: 4924: 4920: 4914: 4897: 4893: 4886: 4877: 4868: 4843: 4839: 4833: 4816: 4812: 4806: 4761: 4757: 4747: 4704: 4700: 4690: 4681: 4677: 4671: 4638: 4634: 4628: 4603: 4599: 4593: 4558: 4554: 4544: 4509: 4503: 4481:(4): 441–6. 4478: 4474: 4468: 4443: 4439: 4433: 4398: 4394: 4384: 4351: 4347: 4341: 4316: 4312: 4306: 4281: 4277: 4271: 4246: 4242: 4236: 4201: 4197: 4187: 4152: 4148: 4138: 4105: 4101: 4095: 4070: 4066: 4060: 4036:10.1038/5794 4027: 4023: 4017: 3984: 3980: 3973: 3940: 3936: 3930: 3918:|title= 3838: 3834: 3828: 3803: 3799: 3755: 3751: 3711: 3707: 3647: 3643: 3601: 3597: 3591: 3566: 3562: 3556: 3511: 3507: 3497: 3454: 3450: 3443: 3418: 3414: 3401: 3376: 3372: 3366: 3325: 3321: 3311: 3278: 3274: 3264: 3229: 3225: 3215: 3182: 3178: 3134: 3130: 3120: 3087: 3083: 3076: 3043: 3039: 3003: 2999: 2989: 2964: 2960: 2954: 2929: 2925: 2919: 2894: 2890: 2884: 2854:(1): 31–47. 2851: 2847: 2810: 2806: 2800: 2781: 2777: 2767: 2750: 2746: 2740: 2705: 2701: 2691: 2664: 2660: 2650: 2617: 2613: 2603: 2562: 2558: 2548: 2516:(1): 61–65. 2513: 2509: 2503: 2495: 2460: 2456: 2411: 2407: 2397: 2362: 2358: 2348: 2323: 2319: 2275: 2271: 2261: 2220: 2216: 2206: 2173: 2169: 2110: 2106: 2072: 2036: 2032: 1982: 1978: 1942: 1936: 1802: 1718:observables. 1584: 1556:hydrocarbons 1485: 1461: 1409: 1387: 1357: 1350: 1345: 1328: 1324: 1320: 1316:Fritz London 1305: 1296: 1293:polarization 1285: 1276: 1270: 1262: 1250: 1229: 1213: 1209: 1193:bond lengths 1163: 1139: 1119: 1098: 1089: 869: 856: 773: 493: 469: 449: 266: 256: 226: 210: 202: 195: 172: 160:force fields 123: 105: 72: 66:January 2024 63: 56:Please help 52: 41: 7867:von Neumann 7737:force field 7729:percolation 7418:: 745–752. 6968:10454/16776 5543:(1): 1–15. 4956:Biopolymers 4635:Biopolymers 4284:(1): 62–6. 2223:: 105–113. 1805:water model 1799:Water model 1610:Benoit Roux 1581:Polarizable 1526:and FANTOM. 1447:sublimation 1439:alpha helix 1394:sublimation 1288:anisotropic 1267:Limitations 1211:procedure. 1197:bond angles 1181:atomic mass 1131:sublimation 1110:Drude model 1091:solutions. 914:Coulomb law 496:Hooke's law 267:noncovalent 211:united-atom 152:Monte Carlo 124:force field 93:Force field 60:if you can. 7937:Categories 7724:Heisenberg 7487:1956/10456 7221:1902.08408 7160:1712.06113 7095:1503.04987 6882:2206.07697 6604:2015-08-29 6548:Goddard WA 5115:(1): 716. 4684:: 559–567. 3657:1505.05938 2478:2117/24209 2278:: 113876. 2120:1904.05206 1929:References 852:wavenumber 808:spectrum, 7847:Boltzmann 7770:H-theorem 7648:Ensembles 7274:0809.2811 7143:Müller KR 6750:0295-5075 6707:250913111 6699:0295-5075 6656:250796817 6648:0295-5075 6577:CiteSeerX 6519:1573-4951 6480:238230196 5519:0010-4655 5476:250752417 5468:0953-8984 5425:0031-899X 5382:0897-4756 5347:0002-7863 5081:: 68–89. 4171:0739-1102 4009:208700020 4001:1616-301X 3909:cite book 3626:0021-9606 3489:2469-9950 3435:0897-4756 3358:265103133 3342:1549-9596 3295:0892-7022 3256:1047-4838 3232:(7): 17. 3207:202745539 3104:0892-7022 3068:1520-6106 2981:0020-7608 2827:0002-7863 2683:0920-2307 2642:0163-1829 2587:0163-1829 2540:0031-9228 2340:0002-7863 2302:0378-3812 2253:266440296 2237:0039-3681 2145:119199372 2137:0892-7022 1961:254835355 1781:SchNet a 1739:packages. 1490:Classical 1422:solvation 1277:empirical 1168:atoms in 950:ε 946:π 555:− 498:formula: 408:nonbonded 316:nonbonded 217:atoms in 140:parameter 108:chemistry 7857:Tsallis 7496:25970002 7397:24932669 7348:24489522 7299:20782587 7291:18956896 7246:85543050 7238:31042390 7185:29960322 7128:28672393 7120:26574412 7067:29211469 7026:27224739 6985:54524604 6977:30507180 6932:28507695 6850:19717427 6774:Archived 6758:14385201 6550:(2001). 6472:34586817 6437:32343883 6386:19637900 6351:17115732 6294:16542062 6237:18978934 6170:26592288 6100:26641692 6065:18958290 5989:11749341 5954:96616243 5849:20300554 5800:26641126 5765:16741310 5757:15224394 5716:31136175 5667:31865706 5600:16805629 5565:39320318 5557:14634989 5147:29459638 5032:23276161 5012:Langmuir 4990:"GROMOS" 4976:94519023 4941:16526746 4860:91705326 4663:26981215 4585:16731967 4536:15063647 4495:12163065 4460:10449371 4425:19768677 4395:Proteins 4376:17613729 4333:10753811 4298:10679345 4263:12203463 4228:33186021 4220:14579324 4198:Proteins 4179:98441607 4130:43575627 4087:12069625 4044:10048917 3957:11771120 3855:11484218 3835:Proteins 3820:17049320 3782:12142453 3728:29179536 3708:ACS Nano 3682:26390325 3583:26588145 3548:22540809 3393:26750724 3350:37947503 3303:95716947 3199:31549507 3161:26273869 3112:36710284 3022:26583247 2946:26605626 2911:26633217 2848:Proteins 2732:26815602 2487:24828263 2438:18734898 2430:15116359 2389:23832629 2245:38128443 2198:13874240 2190:17569554 2053:26596756 2007:16392929 1870:See also 1671:Reactive 1601:AMOEBA+. 1454:crystals 1450:enthalpy 1410:freezing 1390:enthalpy 1174:carbonyl 1147:proteins 1145:such as 1127:enthalpy 902:covalent 806:infrared 457:aromatic 382:dihedral 235:proteins 233:such as 209:, while 207:hydrogen 187:minerals 183:polymers 168:gradient 42:require 7852:Shannon 7839:Entropy 7388:4277759 7339:3904396 7193:4897444 7165:Bibcode 7100:Bibcode 6923:5414547 6841:2734882 6818:Bibcode 6730:Bibcode 6679:Bibcode 6628:Bibcode 6569:Bibcode 6428:7267649 6342:2080839 6321:Bibcode 6285:2080832 6264:Bibcode 6228:2367138 6123:Bibcode 6056:2572772 5919:5227353 5840:2838399 5707:6615954 5658:7384396 5499:Bibcode 5448:Bibcode 5405:Bibcode 5138:5818522 5117:Bibcode 4874:"ECEPP" 4798:2011594 4766:Bibcode 4739:8889177 4730:1233669 4709:Bibcode 4655:2597723 4620:1660931 4576:2242528 4416:2922016 4356:Bibcode 4122:9794034 4052:3162636 3965:8401242 3863:9912122 3773:2373680 3690:5455024 3662:Bibcode 3606:Bibcode 3516:Bibcode 3459:Bibcode 3234:Bibcode 3152:9649520 3048:Bibcode 2876:2845395 2868:3054871 2755:Bibcode 2753:: 451. 2723:4865892 2622:Bibcode 2595:9943969 2567:Bibcode 2518:Bibcode 2380:3800559 2280:Bibcode 2015:9757894 1987:Bibcode 1851:VALBOND 1762:Kriging 1754:system. 1722:MARTINI 1682:enzymes 1431:H-bonds 929:Coulomb 474:or the 203:ll-atom 44:cleanup 7701:Models 7609:Theory 7559: 7540: 7521: 7494: 7395: 7385: 7346: 7336: 7297: 7289: 7244: 7236: 7191: 7183: 7126: 7118: 7065: 7024: 6983: 6975: 6930: 6920: 6848: 6838: 6791:"SAFT" 6756: 6748: 6705: 6697: 6654: 6646: 6579: 6517: 6478: 6470: 6435: 6425: 6384: 6349: 6339: 6292: 6282: 6235: 6225: 6168: 6098: 6063: 6053: 5987: 5952: 5917: 5884:985660 5882: 5847: 5837: 5798: 5763: 5755: 5714: 5704: 5665: 5655: 5598: 5563: 5555: 5517: 5474: 5466: 5423: 5380: 5345: 5145: 5135: 5030: 4974: 4939: 4858: 4796: 4786: 4737: 4727: 4661: 4653: 4618: 4583: 4573: 4534: 4524: 4493: 4458: 4423: 4413: 4374: 4331: 4296: 4261: 4226: 4218: 4177: 4169: 4128: 4120: 4085: 4050: 4042: 4007: 3999: 3963: 3955: 3897: 3861: 3853: 3818: 3780: 3770: 3726: 3688: 3680: 3624: 3581: 3546: 3487: 3433: 3391: 3356: 3348: 3340: 3301: 3293: 3254: 3205: 3197: 3159: 3149: 3110: 3102: 3066: 3020: 2979: 2944: 2909: 2874: 2866: 2825: 2730: 2720: 2681: 2640: 2593: 2585: 2538: 2485: 2436: 2428: 2387: 2377: 2338: 2300: 2251: 2243: 2235: 2196: 2188: 2143: 2135: 2079: 2051: 2013: 2005: 1959: 1949: 1861:, and 1846:Tinker 1688:ReaxFF 1543:MMFF ( 1530:GROMOS 1509:CHARMM 1480:, and 1334:helium 1220:openMD 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