A force field is used to minimize the bond stretching energy of this ethane molecule.

In the context of molecular mechanics, a force field (also called a forcefield) refers to the functional form and parameter sets used to describe the potential energy of a system of particles (typically but not necessarily atoms). Force field functions and parameter sets are derived from both experimental work and high-level quantum mechanical calculations. "All-atom" force fields provide parameters for every atom in a system, including hydrogen, while "united-atom" force fields treat the hydrogen and carbon atoms in methyl and methylene groups as a single interaction center. "Coarse-grained" force fields, which are frequently used in long-time simulations of proteins, provide even more abstracted representations for increased computational efficiency. Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... The term potential function can mean more than one thing. ... The factual accuracy of this article is disputed. ... Potential energy is the energy that is by virtue of the relative positions (configurations) of the objects within a physical system. ... “Atomic” redirects here. ... Fig. ... This article is about the chemistry of hydrogen. ... General Name, Symbol, Number carbon, C, 6 Chemical series nonmetals Group, Period, Block 14, 2, p Appearance black (graphite) colorless (diamond) Atomic mass 12. ... In chemistry a methyl-group is a hydrophobic Alkyl functional group which is derived from methane (CH4). ... In chemistry, methylene is a divalent functional group CH2 derived formally from methane. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ...

The usage of the term "force field" in chemistry and computational biology differs from the standard usage in physics. In chemistry usage a force field is defined as a potential function, while the term is used in physics to denote the negative gradient of a scalar potential. Physics (Greek: (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the fundamental laws of the universe and their precise formulation in a mathematical framework. ... Originally a term coined by Michael Faraday to provide an intuitive paradigm, but theoretical construct (in the Kuhnian sense), for the behavior of electromagnetic fields, the term force field refers to the lines of force one object (the source object) exerts on another object or a collection of other objects. ... Horizontal line (use sparingly)d grade for the grade or gradient of roads and other geographic features. ... It has been suggested that this article or section be merged with Potential. ...

Functional form

Further information: Molecular mechanics

The basic functional form of a force field encapsulates both bonded terms relating to atoms that are linked by covalent bonds, and nonbonded (also called "noncovalent") terms describing the long-range electrostatic and van der Waals forces. The specific decomposition of the terms depends on the force field, but a general form for the total energy can be written as The term molecular mechanics refers to the use of Newtonian mechanics to model molecular systems. ... A chemical bond is the physical process responsible for the attractive interactions between atoms and molecules, and that which confers stability to diatomic and polyatomic chemical compounds. ... Covalent bonding is a description of chemical bonding that is characterized by the sharing of pairs of electrons between atoms. ... Electrostatics is the branch of physics that deals with the force exerted by a static (i. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ...

The bond and angle terms are usually modeled as harmonic oscillators in force fields that do not allow bond breaking. The functional form is highly variable. It can include potentials for hydrogen bonds, an "improper torsion" term to account for the planarity of aromatic rings and other conjugated systems, and "cross-terms" that describe coupling of different internal variables, such as dihedral angles and bond lengths. The nonbonded terms are most computationally intensive because they include many more pairwise interactions per atom. The van der Waals term is usually computed with a Lennard-Jones potential and the electrostatic term with Coulomb's law, although both can be buffered or scaled by a constant factor to produce better agreement with experimental observation. In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ... Snapshot from a simulation of liquid water. ... In chemistry, an aromatic molecule is one in which electrons are free to cycle around circular arrangements of atoms, which are alternately singly and doubly bonded to one another. ... A chemically conjugated system, is a system of atoms covalently bonded with alternating single and double bonds (e. ... Neutral atoms and molecules are subject to two distinct forces in the limit of large distance, and short distance: an attractive van der Waals force, or dispersion force, at long ranges, and a repulsion force, the result of overlapping electron orbitals, referred to as Pauli repulsion (from Pauli exclusion principle). ... Coulombs torsion balance In physics, Coulombs law is an inverse-square law indicating the magnitude and direction of electrostatic force that one stationary, electrically charged object of small dimensions (ideally, a point source) exerts on another. ...

Parameterization

In addition to the functional form of the potentials, a force field defines a set of parameters for each type of atom. For example, a force field would include distinct parameters for an oxygen atom in a carbonyl functional group and in a hydroxyl group. The typical parameter set includes values for atomic mass, van der Waals radius, and partial charge for individual atoms, and equilibrium values of bond lengths, bond angles, and dihedral angles for pairs, triplets, and quandruplets of bonded atoms, and values corresponding to the effective spring constant for each potential. Most current force fields use a "fixed-charge" model by which each atom is assigned a single value for the atomic charge that is not affected by the local electrostatic environment; proposed developments in next-generation force fields incorporate models for polarizability, in which a particle's charge is influenced by electrostatic interactions with its neighbors. For example, polarizability can be approximated by the introduction of Drude particles, or massless, charge-carrying virtual sites attached by a springlike harmonic potential to each polarizable atom. The introduction of polarizability into force fields in common use has been inhibited by the high computational expense associated with calculating the local electrostatic field. General Name, Symbol, Number oxygen, O, 8 Chemical series Nonmetals, chalcogens Group, Period, Block 16, 2, p Appearance colorless (gas) very pale blue (liquid) Atomic mass 15. ... Carbonyl group In organic chemistry, a carbonyl group is a functional group composed of a carbon atom double-bonded to an oxygen atom. ... In organic chemistry, functional groups are specific groups of atoms within molecules, that are responsible for the characteristic chemical reactions of those molecules. ... // Hydroxyl group The term hydroxyl group is used to describe the functional group -OH when it is a substituent in an organic compound. ... The atomic mass of a chemical element is the mass of an atom at rest, most often expressed in unified atomic mass units. ... The van der Waals radius of an atom is the radius of an imaginary hard sphere which can be used to model the atom for many purposes. ... A partial charge is a charge with an absolute value of less than one elementary charge unit. ... In molecular geometry, bond length or bond distance is the distance between two bonded atoms in a molecule. ... In Aerospace engineering, the dihedral is the angle that the two wings make with each other. ... In physics, Hookes law of elasticity states that if a force (F) is applied to an elastic spring or prismatic rod (with length L and cross section A), its extension is linearly proportional to its tensile stress σ and modulus of elasticity (E): or It is named after the 17th... Electric charge is a fundamental conserved property of some subatomic particles, which determines their electromagnetic interactions. ... Electrostatics is the branch of physics that deals with the force exerted by a static (i. ... Polarizability is the relative tendency of the electron cloud of an atom to be distorted from its normal shape by the presence of a nearby ion or dipole--that is, by an external electric field. ... Drude particles are model oscillators used to simulate the effects of electronic polarizability in the context of a classical molecular mechanics force field. ... In classical mechanics, a Harmonic oscillator is a system which, when displaced from its equilibrium position, experiences a restoring force proportional to the displacement according to Hookes law: where is a positive constant. ...

Although many molecular simulations involve biological macromolecules such as proteins, DNA, and RNA, the parameters for given atom types are generally derived from observations on small organic molecules that are more tractable for experimental studies and quantum calculations. Different force fields can be derived from dissimilar types of experimental data, such as enthalpy of vaporization (OPLS), enthalpy of sublimation (CFF), dipole moments, or various spectroscopic parameters. A macromolecule is a large molecule with a large molecular mass bonded covalently, but generally the use of the term is restricted to polymers and molecules which structurally include polymers. ... A representation of the 3D structure of myoglobin, showing coloured alpha helices. ... The structure of part of a DNA double helix Deoxyribonucleic acid (DNA) is a nucleic acid that contains the genetic instructions for the development and function of living organisms. ... This article or section does not adequately cite its references or sources. ... Benzene is the simplest of the arenes, a family of organic compounds An organic compound is any member of a large class of chemical compounds whose molecules contain carbon and hydrogen; therefore, carbides, carbonates, carbon oxides and elementary carbon are not organic (see below for more on the definition controversy... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... Evaporation is the process whereby atoms or molecules in a liquid state (or solid state if the substance sublimes) gain sufficient energy to enter the gaseous state. ... The OPLS (Optimized Potential for Liquid Simulations) force field was developed by Prof. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... Sublimation has three separate meanings: Sublimation (physics), the change from solid to gas without passing the liquid state Sublimation (psychology), the transformation of emotions Dye sublimation, the transference of printed images to a synthetic substrate by the application of heat Category: ... CFF may refer to: Chemins de Fer Fédéraux, the French name of the SBB-CFF-FFS, the national railway company of Switzerland. ... This article is about the electromagnetic phenomenon. ...

Parameter sets and functional forms are defined by force field developers to be self-consistent. Because the functional forms of the potential terms vary extensively between even closely related force fields (or successive versions of the same force field), the parameters from one force field should never be used in conjunction with the potential from another.

Deficiencies

All force fields are based on numerous approximations and derived from different types of experimental data. Therefore they are called empirical. The existing force fields usually do not account for electronic polarization of the environment, an effect that can significantly reduce electrostatic interactions of partial atomic charges. This problem was addressed by developing “polarizable force fields” ^[1] or using macroscopic dielectric constant. However, application of a single value of dielectric constant is questionable in the highly heterogeneous environments of proteins or biological membranes ^[2]. In electrodynamics, polarization (also spelled polarisation) is the property of electromagnetic waves, such as light, that describes the direction of their transverse electric field. ... The dielectric constant εr (represented as or K in some cases) is defined as the ratio: where εs is the static permittivity of the material in question, and ε0 is the vacuum permittivity. ... The dielectric constant εr (represented as or K in some cases) is defined as the ratio: where εs is the static permittivity of the material in question, and ε0 is the vacuum permittivity. ...

All types of van der Waals forces are also strongly environment-dependent, because these forces originate from interactions of induced and “instantaneous” dipoles (see Intermolecular force). The original Fritz London theory of these forces can only be applied in vacuum. A more general theory of van der Waals forces in condensed media was developed by A. D. McLachlan in 1963 (this theory includes the original London’s approach as a special case) ^[3]. The McLachlan theory predicts that van der Waals attractions in media are weaker than in vacuum and follow the "like dissolves like" rule, which means that different types of atoms interact weaker than identical types of atoms. ^[4]. This is in contrast to “combinatorial rules” or Slater-Kirkwood equation applied for development of the classical force fields. The “combinatorial rules” state that 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 theory, the interactions of particles in a media can even be completely repulsive, as observed for liquid helium ^[3]. The conclusions of McLachlan theory are supported by direct measurements of attraction forces between different materials (Hamaker constant), as explained by Jacob Israelachvili in his book "Intermolecular and surface forces". It was concluded that "the interaction between hydrocarbons across water is about 10% of that across vacuum" ^[3]. Such effects are unaccounted in the standard molecular mechanics. In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ... This article or section is in need of attention from an expert on the subject. ... Fritz Wolfgang London (March 7, 1900–March 30, 1954) was a German-born American physicist for whom the London force is named. ... In chemistry, the term van der Waals force originally referred to all forms of intermolecular forces; however, in modern usage it tends to refer to intermolecular forces that deal with forces due to the polarization of molecules. ... For other uses of this term, see Helium (disambiguation). ... Dr. Jacob Israelachvili is a professor of chemical engineering and materials at the University of California, Santa Barbara (UCSB), and currently the associate director of the Materials Research Laboratory (MRL) at UCSB. Dr. Israelachvilis received his Ph. ...

Another round of criticism came from practical applications, such as protein structure refinement. It was noted that CASP participants did not try to refine their models to avoid "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". ^[5] Actually, the force fields have been successfully applied for protein structure refinement in different X-ray crystallography and NMR spectroscopy applications, especially using program XPLOR ^[6] However, such refinement is driven primarily by a set of experimental constraints, whereas the force fields serve merely to remove interatomic hindrances. The results of calculations are practically the same with rigid sphere potentials implemented in program DYANA ^[7] (calculations from NMR data), or with programs for crystallographic refinement that do not use any energy functions. The deficiencies of the force fields remain a major bottleneck in homology modeling of proteins ^[8] Such situation gave rise to development of alternative empirical scoring functions specifically for ligand docking ^[9], protein folding ^{[10] [11]}, computational protein design ^{[12] [13] [14]}, and modeling of proteins in membranes. ^[15] CASP, which stands for Critical Assessment of Techniques for Protein Structure Prediction, is a community-wide experiment (though it is commonly referred to as a competition) for protein structure prediction taking place every two years. ... X-ray crystallography or single-crystal X-ray diffraction is an analytical technique which uses the diffraction pattern produced by bombarding a single crystal with X-rays to solve the crystal structure. ... It has been suggested that NMR Data Processing be merged into this article or section. ... Homology modeling, also known as comparative modeling, is a class of techniques in protein structure prediction that seek to construct a model of a proteins tertiary structure based on its amino acid sequence. ... Computational molecular docking, sometimes called virtual screening or ligand docking, is a research technique for predicting whether a small molecule, called a ligand, will bind to a protein. ... Protein folding is the process by which a protein assumes its characteristic functional shape or tertiary structure, also known as the native state. ... Protein design is the design of new protein molecules from scratch. ...

There is also an opinion that molecular mechanics may operate with energy which is irrelevant to protein folding or ligand binding ^[16]. The parameters of typical force fields reproduce enthalpy of sublimation, i.e. energy of evaporation of molecular crystals. However, it was recognized that protein folding and ligand binding are thermodynamically very similar to crystallization, or liquid-solid transitions, because all these processes represent “freezing” of mobile molecules in condensed media ^{[17] [18] [19]}. Therefore, free energy changes during protein folding or ligand binding are expected to represent a combination of an energy similar to heat of fusion (energy absorbed during melting of molecular crystals), a conformational entropy contribution, and solvation free energy. The heat of fusion is significantly smaller than enthalpy of sublimation ^[3]. . Hence, the potentials describing protein folding or ligand binding must be weaker than potentials in molecular mechanics. Indeed, the energies of H-bonds in proteins are ~ -1.5 kcal/mol when estimated from protein engineering or alpha helix to coil transition data ^{[20] [21]}, but the same energies estimated from sublimation enthalpy of molecular crystals were -4 to -6 kcal/mol ^[22]. The depths of modified Lennard-Jones potentials derived from protein engineering data were also smaller than in typical force fields and followed the “like dissolves like” rule, as predicted by McLachlan theory^[16]. In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... Sublimation of an element or substance is a conversion between the solid and the gas phases with no intermediate liquid stage. ... Protein folding is the process by which a protein assumes its characteristic functional shape or tertiary structure, also known as the native state. ... Structural genomics or structural bioinformatics refers to the analysis of macromolecular structure particularly proteins, using computational tools and theoretical frameworks. ... Frost crystallization on a shrub. ... Heat of fusion is the amount of heat energy which must be absorbed or lost for 1 gram of a substance to change states from a solid to a liquid or vice versa. ... Conformational entropy is the entropy associated with the physical arrangement of a polymer chain that assumes a compact or globular state in solution. ... Solvation is the attraction and association of molecules of a solvent with molecules or ions of a solute. ... Heat of fusion is the amount of heat energy which must be absorbed or lost for 1 gram of a substance to change states from a solid to a liquid or vice versa. ... In chemistry, a hydrogen bond is a type of attractive intermolecular force that exists between two partial electric charges of opposite polarity. ... Protein engineering is the application of science, mathematics, and economics to the process of developing useful or valuable proteins. ... Side view of an α-helix of alanine residues in atomic detail. ... Illustration of a 3-dimensional polypeptide A random coil is a polymer conformation where the monomer subunits are oriented randomly while still being bonded to adjacent units. ... Sublimation of an element or substance is a conversion between the solid and the gas phases with no intermediate liquid stage. ... In thermodynamics and molecular chemistry, the enthalpy or heat content (denoted as H or ΔH, or rarely as χ) is a quotient or description of thermodynamic potential of a system, which can be used to calculate the useful work obtainable from a closed thermodynamic system under constant pressure. ... Quartz crystal Copper(II) sulfate and iodine crystal Synthetic bismuth crystal Insulin crystals Gallium, a metal that easily forms large single crystals A huge monocrystal of potassium dihydrogen phosphate grown from solution by Saint-Gobain for the megajoule laser of CEA. In chemistry and mineralogy, a crystal is a solid... Neutral atoms and molecules are subject to two distinct forces in the limit of large distance, and short distance: an attractive van der Waals force, or dispersion force, at long ranges, and a repulsion force, the result of overlapping electron orbitals, referred to as Pauli repulsion (from Pauli exclusion principle). ...

Popular force fields

Different force fields are designed for different purposes.

MM2 was developed primarily for conformational analysis of 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 MM4). MM2 is a force field developed by Allingers Molecular Mechanics Research Lab. ... MM3 is a force field developed by Norman Allinger. ...

ECEPP was developed specifically for modeling of peptides and proteins. It uses fixed geometries of amino acid residues to simplify the potential energy surface. Thus, the energy 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 Internal Coordinate Mechanics and FANTOM ^[23]. MM2 is a force field developed by Allingers Molecular Mechanics Research Lab. ... References Abagyan, R.A. and Totrov, M.M. Biased Probability Monte Carlo Conformational Searches and Electrostatic Calculations For Peptides and Proteins J. Mol. ...

AMBER, CHARMM and GROMOS have been developed primarily for molecular dynamics of macromolecules, although they are also commonly applied for energy minimization. Therefore, the coordinates of all atoms are considered as free variables. Amber pendants. ... CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ... GROMOS is a force field for molecular dynamics developed at the University of Groningen and the ETH Zurich. ... Molecular dynamics (MD) is a form of computer simulation where atoms and molecules are allowed to interact for a period of time under known laws of physics. ...

Classical force fields:

• AMBER (Assisted Model Building and Energy Refinement) - widely used for proteins and DNA
• CHARMM - originally developed at Harvard, widely used for both small molecules and macromolecules
• CHARMm - commercial version of CHARMM, available through Accelrys
• CVFF - also broadly used for small molecules and macromolecules
• GROMACS - The force field optimized for the package of the same name
• GROMOS - A force field that comes as part of the GROMOS (GROningen MOlecular Simulation package), 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. However, a gas phase version (B-version) for simulation of isolated molecules is also available
• OPLS-aa, OPLS-ua, OPLS-2001, OPLS-2005 - Members of the OPLS family of force fields developed by William L. Jorgensen at Yale Department of Chemistry.
• ECEPP/2 - First force field for polypeptide molecules - developed by F.A.Momany, H.A.Scheraga and colleagues.

Second-generation force fields: Amber pendants. ... CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ... CHARMM (Chemistry at HARvard Macromolecular Mechanics) is the name of a widely used set of force fields for molecular dynamics as well as the name for the molecular dynamics simulation and analysis package associated with them. ... Accelrys (NASDAQ: ACCL) is a San Diego, United States-based software company specializing in research software for bioinformatics, cheminformatics, molecular simulation, and quantum mechanics. ... GROMACS (Groningen Machine for Chemical Simulations) is a molecular dynamics simulation package developed in the University of Groningen. ... GROMOS is a force field for molecular dynamics developed at the University of Groningen and the ETH Zurich. ... The OPLS (Optimized Potential for Liquid Simulations) force field was developed by Prof. ...

• CFF - a family of forcefields adapted to a broad variety of organic compounds, includes forcefields for polymers, metals, etc.
• MMFF - developed at Merck, for a broad range of chemicals
• MM2, MM3, MM4 - developed by Norman L. Allinger, for a broad range of chemicals

Multipoles based Polarizable Force Fields: CFF may refer to: Chemins de Fer Fédéraux, the French name of the SBB-CFF-FFS, the national railway company of Switzerland. ... Merck Molecular Force Field (MMFF) is a family of force fields developed by Merck Research Laboratories. ... MM2 is a force field developed by Allingers Molecular Mechanics Research Lab. ... MM3 is a force field developed by Norman Allinger. ...

• - The SIBFA (Sum of Interactions Between Fragments Ab initio computed) force field for small molecules and proteins, developed by N. Gresh and J-P Piquemal. SIBFA is a molecular mechanics procedure formulated and calibrated on the basis of ab initio supermolecule computations. Its purpose is to enable the simultaneous and reliable computations of both intermolecular and conformational energies governing the binding specificities of biologically and pharmacologically relevant molecules. This procedure enables an accurate treatment of transition metals. The inclusion of a ligand field contribution allows computations on "open-shell" metalloproteins.
• - AMOEBA force field. developed by P. Ren and J. W. Ponder.
• - ORIENT procedure developed by A. J. Stone and coworkers.

Reactive force fields

• ReaxFF - reactive force field developed by William Goddard and coworkers. It is fast, transferable and is the computational method of choice for atomistic-scale dynamical simulations of chemical reactions.

ReaxFF (for “reactive force field”) is a force field developed by Adri van Duin, William A. Goddard, III and co- workers at the California Institute of Technology. ...

See also

• Comparisons and Evaluations of various forcefields
• Molecular dynamics
• Molecular modelling

Molecular dynamics (MD) is a form of computer simulation where atoms and molecules are allowed to interact for a period of time under known laws of physics. ... The backbone dihedral angles are included in the molecular model of a protein. ...

References

Further reading

1. Schlick T. (2000). Molecular Modeling and Simulation: An Interdisciplinary Guide Interdisciplinary Applied Mathematics: Mathematical Biology. Springer-Verlag New York, NY.
2. Israelachvili, J.N. (1992) Intermolecular and surface forces. Academic Press, San Diego.