View source for Force field (chemistry)

{{short description|Concept on molecular modeling}}
{{Other uses|Force field (disambiguation){{!}}Force field}}
{{Cleanup|date=January 2024|reason=Grammar issues}}
[[File: Bond stretching energy.png|thumb|right|Part of force field of ethane for the C-C stretching bond.]]

In the context of [[chemistry]], [[molecular physics]], [[physical chemistry]], and [[molecular modelling]], a '''force field''' is a [[computational chemistry|computational]] 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 [[interatomic potential]]s. More precisely, the force field refers to the [[Function (mathematics)|functional form]] and [[parameter]] sets used to calculate the [[potential energy]] of a system on the atomistic level. Force fields are usually used in [[molecular dynamics]] or [[Monte Carlo method|Monte Carlo]] simulations. The parameters for a chosen energy function may be derived from classical laboratory experiment data, calculations in [[quantum mechanics]], or both. Force fields utilize the same concept as [[Force field (physics)|force fields]] in [[classical physics]], 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 [[gradient]] of the potential energy with respect to the particle coordinates.<ref>{{cite book |last=Frenkel | first = Daan | name-list-style = vanc |title=Understanding molecular simulation : from algorithms to applications|date=2007|publisher=Academic Press|isbn=978-0-12-267351-1|oclc=254835355}}</ref>

A large number of different force field types exist today (e.g. for [[Organic compound|organic molecules]], [[ion]]s, [[polymer]]s, [[mineral]]s, and [[metal]]s). Depending on the material, different functional forms are usually chosen for the force fields since different types of atomistic interactions dominate the material behavior.

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 substance (e.g. water).<ref name=":1" /> For a transferable force field, all or some parameters are designed as building blocks and become transferable/ applicable for different substances (e.g. [[methyl group]]s in alkane transferable force fields).<ref name=":0">{{cite journal |vauthors=Siu SW, Pluhackova K, Böckmann RA |date=April 2012 |title=Optimization of the OPLS-AA Force Field for Long Hydrocarbons |journal=Journal of Chemical Theory and Computation |volume=8 |issue=4 |pages=1459–70 |doi=10.1021/ct200908r |pmid=26596756}}</ref> A different important differentiation addresses the physical structure of the models: A''ll-atom'' force fields provide parameters for every type of atom in a system, including [[hydrogen]], while ''united-atom'' interatomic potentials treat the hydrogen and [[carbon]] atoms in [[methyl group]]s and [[methylene bridge]]s as one interaction center.<ref name="Leach_2001" /><ref name="tandfonline.com">{{Cite journal |last1=Stephan |first1=Simon |last2=Horsch |first2=Martin T. |last3=Vrabec |first3=Jadran |last4=Hasse |first4=Hans |date=2019-07-03 |title=MolMod – an open access database of force fields for molecular simulations of fluids |url=https://www.tandfonline.com/doi/full/10.1080/08927022.2019.1601191 |journal=Molecular Simulation |language=en |volume=45 |issue=10 |pages=806–814 |doi=10.1080/08927022.2019.1601191 |s2cid=119199372 |issn=0892-7022|arxiv=1904.05206 }}</ref> ''Coarse-grained'' potentials, which are often used in long-time simulations of [[macromolecule]]s such as [[protein]]s, [[nucleic acid]]s, and multi-component complexes, sacrifice chemical details for higher computing efficiency.<ref name="Marrink_2007" />

==Force fields for molecular systems==
[[File:MM PEF.png|thumb|right|Molecular mechanics potential energy function with continuum solvent.]]
The basic functional form of [[potential energy]] for modeling molecular systems includes intramolecular interaction terms for interactions of atoms that are linked by [[covalent bond]]s, and intermolecular (i.e. nonbonded also termed ''noncovalent'') terms that describe the long-range [[electrostatic]] and [[van der Waals force]]s. 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
<math display="block">E_{\text{total}} = E_{\text{bonded}} + E_{\text{nonbonded}} </math>
where the components of the covalent and noncovalent contributions are given by the following summations:
<math display="block">E_{\text{bonded}} = E_{\text{bond}} + E_{\text{angle}} + E_{\text{dihedral}}</math>
<math display="block">E_{\text{nonbonded}} = E_{\text{electrostatic}} + E_{\text{van der Waals}} </math>

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 [[Morse potential]]. The functional form for dihedral energy is variable from one force field to another. Additionally, "improper torsional" terms may be added to enforce the planarity of [[aromatic]] rings and other [[conjugated system]]s, 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 [[hydrogen bond]]s.

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 [[Lennard-Jones potential]]<ref>{{Cite journal |last1=Lenhard |first1=Johannes |last2=Stephan |first2=Simon |last3=Hasse |first3=Hans |date=February 2024 |title=A child of prediction. On the History, Ontology, and Computation of the Lennard-Jonesium |url=http://dx.doi.org/10.1016/j.shpsa.2023.11.007 |journal=Studies in History and Philosophy of Science |volume=103 |pages=105–113 |doi=10.1016/j.shpsa.2023.11.007 |pmid=38128443 |s2cid=266440296 |issn=0039-3681}}</ref> or the [[Mie potential]]<ref>{{Cite journal |last1=Fischer |first1=Johann |last2=Wendland |first2=Martin |date=October 2023 |title=On the history of key empirical intermolecular potentials |journal=Fluid Phase Equilibria |volume=573 |pages=113876 |doi=10.1016/j.fluid.2023.113876 |issn=0378-3812|doi-access=free |bibcode=2023FlPEq.57313876F }}</ref> and the electrostatic term with [[Coulomb's law]]. However, both can be buffered or scaled by a constant factor to account for electronic [[polarizability]]. 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.

=== Bond stretching ===

As it is rare for bonds to deviate significantly from their equilibrium values, the most simplistic approaches utilize a [[Hooke's law]] formula:
<math display="block">E_{\text{bond}} = \frac{k_{ij}}{2} (l_{ij}-l_{0,ij})^2,</math>
where <math>k_{ij}</math> is the force constant, <math>l_{ij}</math> is the bond length, and <math>l_{0,ij}</math> is the value for the bond length between atoms <math>i </math> and <math>j </math> when all other terms in the force field are set to 0. The term <math>l_{0,ij}</math> is at times differently defined or taken at different thermodynamic conditions.

The bond stretching constant <math>k_{ij}</math> can be determined from the experimental [[Infrared spectroscopy|infrared]] spectrum, [[Raman spectroscopy|Raman]] spectrum, or high-level [[Quantum chemistry|quantum-mechanical]] calculations.<ref name="Leach_2001" /> The constant <math>k_{ij}</math> determines vibrational frequencies in [[molecular dynamics]] simulations. The stronger the bond is between atoms, the higher is the value of the force constant, and the higher the [[wavenumber]] (energy) in the IR/Raman spectrum.

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.<ref name="Leach_2001">{{Cite book| title=Molecular Modelling: Principles and Applications |last=Leach |first=Andrew | name-list-style = vanc |date=2001-01-30 |publisher=Prentice Hall|isbn=9780582382107 |edition=2nd |location=Harlow|language=en}}</ref><ref name="Sun_1994">{{cite journal |last1=Sun |first1=Huai |last2=Mumby |first2=Stephen J. |last3=Maple |first3=Jon R. |last4=Hagler |first4=Arnold T. |name-list-style=vanc |date=April 1994 |title=An ab Initio CFF93 All-Atom Force Field for Polycarbonates |journal=Journal of the American Chemical Society |volume=116 |issue=7 |pages=2978–2987 |doi=10.1021/ja00086a030 |bibcode=1994JAChS.116.2978S |issn=0002-7863}}</ref> However, for most practical applications these differences 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 [[Morse potential]] 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.

=== Electrostatic interactions ===

Electrostatic interactions are represented by a Coulomb energy, which utilizes [[Partial charge|atomic charges]] <math>q_i</math> to represent chemical bonding ranging from [[Covalent bond|covalent]] to [[Chemical polarity|polar covalent]] and [[ionic bonding]]. The typical formula is the [[Coulomb's law|Coulomb law]]:
<math display="block">E_{\text{Coulomb}} = \frac{1}{4\pi\varepsilon_0}\frac{q_i q_j}{r_{ij}},</math>
where <math>r_{ij}</math> is the distance between two atoms <math>i</math> and <math>j</math>. The total Coulomb energy is a sum over all pairwise combinations of atoms and usually excludes {{clarify span|1, 2 bonded atoms, 1, 3 bonded atoms, as well as 1, 4 bonded atoms|date=May 2024}}.<ref>{{cite journal | vauthors = Huang J, MacKerell AD | title = CHARMM36 all-atom additive protein force field: validation based on comparison to NMR data | journal = Journal of Computational Chemistry | volume = 34 | issue = 25 | pages = 2135–45 | date = September 2013 | pmid = 23832629 | pmc = 3800559 | doi = 10.1002/jcc.23354 }}</ref><ref>{{cite journal | vauthors = Wang J, Wolf RM, Caldwell JW, Kollman PA, Case DA | title = Development and testing of a general amber force field | journal = Journal of Computational Chemistry | volume = 25 | issue = 9 | pages = 1157–74 | date = July 2004 | pmid = 15116359 | doi = 10.1002/jcc.20035 | s2cid = 18734898 | doi-access = free }}</ref><ref name="Mishra_2014">{{cite journal | vauthors = Mishra RK, Fernández-Carrasco L, Flatt RJ, Heinz H | title = A force field for tricalcium aluminate to characterize surface properties, initial hydration, and organically modified interfaces in atomic resolution | journal = Dalton Transactions | volume = 43 | issue = 27 | pages = 10602–16 | date = July 2014 | pmid = 24828263 | doi = 10.1039/c4dt00438h | hdl = 2117/24209 | hdl-access = free }}</ref>

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 solutions.

== Force fields for crystal systems ==
Atomistic interactions in crystal systems significantly deviate from those in molecular systems,<ref>{{Cite journal |last1=Ashcroft |first1=N. W. |last2=Mermin |first2=N. D. |last3=Smoluchowski |first3=R. |date=1977-01-01 |title=''Solid State Physics'' |journal=Physics Today |volume=30 |issue=1 |pages=61–65 |doi=10.1063/1.3037370 |bibcode=1977PhT....30R..61A |issn=0031-9228|doi-access=free }}</ref> e.g. of organic molecules. For crystal systems, particularly multi-body interactions, these interactions are important and cannot be neglected if a high accuracy of the force field is the aim. For crystal systems with covalent bonding, [[bond order potential]]s are usually used, e.g. Tersoff potentials.<ref>{{Cite journal |last=Tersoff |first=J. |date=1988-04-15 |title=New empirical approach for the structure and energy of covalent systems |url=http://dx.doi.org/10.1103/physrevb.37.6991 |journal=Physical Review B |volume=37 |issue=12 |pages=6991–7000 |doi=10.1103/physrevb.37.6991 |pmid=9943969 |bibcode=1988PhRvB..37.6991T |issn=0163-1829}}</ref> For metal systems, usually [[Embedded atom model|embedded atom potentials]]<ref>{{Cite journal |last1=Daw |first1=Murray S. |last2=Baskes |first2=M. I. |date=1984-06-15 |title=Embedded-atom method: Derivation and application to impurities, surfaces, and other defects in metals |url=http://dx.doi.org/10.1103/physrevb.29.6443 |journal=Physical Review B |volume=29 |issue=12 |pages=6443–6453 |doi=10.1103/physrevb.29.6443 |bibcode=1984PhRvB..29.6443D |issn=0163-1829}}</ref><ref>{{Cite journal |last1=Daw |first1=Murray S. |last2=Foiles |first2=Stephen M. |last3=Baskes |first3=Michael I. |date=March 1993 |title=The embedded-atom method: a review of theory and applications |journal=Materials Science Reports |volume=9 |issue=7–8 |pages=251–310 |doi=10.1016/0920-2307(93)90001-u |issn=0920-2307|doi-access=free }}</ref> are used. Additionally, [[Drude model]] potentials have been developed,<ref>{{cite journal |vauthors=Lemkul JA, Huang J, Roux B, MacKerell AD |date=May 2016 |title=An Empirical Polarizable Force Field Based on the Classical Drude Oscillator Model: Development History and Recent Applications |journal=Chemical Reviews |volume=116 |issue=9 |pages=4983–5013 |doi=10.1021/acs.chemrev.5b00505 |pmc=4865892 |pmid=26815602}}</ref> which describe a form of attachment of electrons to nuclei.<ref>{{Cite journal |last=Lorentz |first=Hendrik A. |name-list-style=vanc |year=1905 |title=The Motion of Electrons in Metallic Bodies, I. |journal=Proc. K. Ned. Akad. Wet. |volume=7 |page=451 |bibcode=1904KNAB....7..438L}}</ref><ref name="Drude_1900">{{Cite journal |last=Drude |first=Paul |name-list-style=vanc |year=1900 |title=Zur Elekronentheorie der Metalle. I. Teil. |url=https://zenodo.org/record/1423977 |journal=Annalen der Physik |volume=306 |issue=3 |pages=566–613 |doi=10.1002/andp.19003060312 |doi-access=free}}</ref>

== Parameterization ==
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 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 [[enthalpy of vaporization]], [[enthalpy]] of [[Sublimation (chemistry)|sublimation]], [[Molecular dipole moment|dipole moments]], and various spectroscopic properties such as vibrational frequencies.<ref>{{Cite journal |last1=Jorgensen |first1=William L. |last2=Maxwell |first2=David S. |last3=Tirado-Rives |first3=Julian |name-list-style=vanc |date=January 1996 |title=Development and Testing of the OPLS All-Atom Force Field on Conformational Energetics and Properties of Organic Liquids |journal=Journal of the American Chemical Society |volume=118 |issue=45 |pages=11225–11236 |doi=10.1021/ja9621760 |bibcode=1996JAChS.11811225J |issn=0002-7863}}</ref><ref name="Sun_1994" /><ref name="Dauber-Osguthorpe_1988">{{cite journal |vauthors=Dauber-Osguthorpe P, Roberts VA, Osguthorpe DJ, Wolff J, Genest M, Hagler AT |year=1988 |title=Structure and energetics of ligand binding to proteins: Escherichia coli dihydrofolate reductase-trimethoprim, a drug-receptor system |journal=Proteins |volume=4 |issue=1 |pages=31–47 |doi=10.1002/prot.340040106 |pmid=3054871 |s2cid=2845395}}</ref> 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.<ref name=":0" /><ref>{{cite journal |vauthors=Aduri R, Psciuk BT, Saro P, Taniga H, Schlegel HB, SantaLucia J |date=July 2007 |title=AMBER Force Field Parameters for the Naturally Occurring Modified Nucleosides in RNA |journal=Journal of Chemical Theory and Computation |volume=3 |issue=4 |pages=1464–75 |doi=10.1021/ct600329w |pmid=26633217}}</ref><ref>{{cite journal |vauthors=Kirschner KN, Lins RD, Maass A, Soares TA |date=November 2012 |title=A Glycam-Based Force Field for Simulations of Lipopolysaccharide Membranes: Parametrization and Validation |journal=Journal of Chemical Theory and Computation |volume=8 |issue=11 |pages=4719–31 |doi=10.1021/ct300534j |pmid=26605626}}</ref>  The assignment of atomic charges often follows quantum mechanical protocols with some heuristics, which can lead to significant deviation in representing specific properties.<ref>{{Cite journal |last1=Gross |first1=Kevin C. |last2=Seybold |first2=Paul G. |last3=Hadad |first3=Christopher M. |name-list-style=vanc |year=2002 |title=Comparison of different atomic charge schemes for predicting pKa variations in substituted anilines and phenols |journal=International Journal of Quantum Chemistry |volume=90 |issue=1 |pages=445–458 |doi=10.1002/qua.10108 |issn=0020-7608}}</ref><ref>{{cite journal |vauthors=Wang B, Li SL, Truhlar DG |date=December 2014 |title=Modeling the Partial Atomic Charges in Inorganometallic Molecules and Solids and Charge Redistribution in Lithium-Ion Cathodes |journal=Journal of Chemical Theory and Computation |volume=10 |issue=12 |pages=5640–50 |doi=10.1021/ct500790p |pmid=26583247 |doi-access=free}}</ref><ref name="Heinz_2004">{{Cite journal |last1=Heinz |first1=Hendrik |last2=Suter |first2=Ulrich W. |name-list-style=vanc |date=November 2004 |title=Atomic Charges for Classical Simulations of Polar Systems |journal=The Journal of Physical Chemistry B |volume=108 |issue=47 |pages=18341–18352 |bibcode=2004APS..MAR.Y8006H |doi=10.1021/jp048142t |issn=1520-6106}}</ref>

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 for molecular simulations of biological [[macromolecule]]s such as [[protein]]s, [[DNA]], and [[RNA]] were often derived/transferred from observations for small [[organic compound|organic molecules]], which are more accessible for experimental studies and quantum calculations.

Atom types are defined for different elements as well as for the same elements in sufficiently different chemical environments. For example, [[oxygen]] atoms in [[water]] and an oxygen atoms in a [[carbonyl]] [[functional group]] are classified as different force field types.<ref name="Dauber-Osguthorpe_1988" /> Typical molecular force field parameter sets include values for [[atomic mass]], [[partial charge|atomic charge]], [[Lennard-Jones potential|Lennard-Jones parameters]] for every atom type, as well as equilibrium values of [[bond length]]s, [[Molecular geometry|bond angles]], and [[dihedral angle]]s.<ref>{{cite journal |last1=Dharmawardhana |first1=Chamila C. |last2=Kanhaiya |first2=Krishan |last3=Lin |first3=Tzu-Jen |last4=Garley |first4=Amanda |last5=Knecht |first5=Marc R. |last6=Zhou |first6=Jihan |last7=Miao |first7=Jianwei |last8=Heinz |first8=Hendrik | name-list-style = vanc |date=2017-06-19|title=Reliable computational design of biological-inorganic materials to the large nanometer scale using Interface-FF|journal=Molecular Simulation|volume=43|issue=13–16|pages=1394–1405|doi=10.1080/08927022.2017.1332414|s2cid=36710284 |issn=0892-7022}}</ref> The bonded terms refer to pairs, triplets, and quadruplets of bonded atoms, and include values for the effective [[spring constant]] for each potential.

Heuristic force field parametrization procedures have been very successful for many years, but recently criticized<ref>{{cite journal |vauthors=Wang LP, Martinez TJ, Pande VS |date=June 2014 |title=Building Force Fields: An Automatic, Systematic, and Reproducible Approach |journal=The Journal of Physical Chemistry Letters |volume=5 |issue=11 |pages=1885–91 |doi=10.1021/jz500737m |pmc=9649520 |pmid=26273869}}</ref><ref name="McDonagh J. L. 2019 4278–4288">{{cite journal |vauthors=McDonagh JL, Shkurti A, Bray DJ, Anderson RL, Pyzer-Knapp EO |date=October 2019 |title=Utilizing Machine Learning for Efficient Parameterization of Coarse Grained Molecular Force Fields |journal=Journal of Chemical Information and Modeling |volume=59 |issue=10 |pages=4278–4288 |doi=10.1021/acs.jcim.9b00646 |pmid=31549507 |s2cid=202745539}}</ref> 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 procedure.

Efforts to provide open source codes and methods include [http://openmm.org openMM] and [http://openmd.org openMD]. 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.

== Force field databases ==
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 example, the [https://openkim.org/browse/models/by-species openKim database] focuses on interatomic functions describing the individual interactions between specific elements.<ref>{{Cite journal |last1=Tadmor |first1=E. B. |last2=Elliott |first2=R. S. |last3=Sethna |first3=J. P. |last4=Miller |first4=R. E. |last5=Becker |first5=C. A. |date=July 2011 |title=The potential of atomistic simulations and the knowledgebase of interatomic models |journal=JOM |language=en |volume=63 |issue=7 |pages=17 |doi=10.1007/s11837-011-0102-6 |bibcode=2011JOM....63g..17T |issn=1047-4838|doi-access=free }}</ref> The [http://trappe.oit.umn.edu/ TraPPE database] focuses on transferable force fields of organic molecules (developed by the Siepmann group).<ref name=":2">{{Cite journal |last1=Eggimann |first1=Becky L. |last2=Sunnarborg |first2=Amara J. |last3=Stern |first3=Hudson D. |last4=Bliss |first4=Andrew P. |last5=Siepmann |first5=J. Ilja |date=2014-01-02 |title=An online parameter and property database for the TraPPE force field |url=https://www.tandfonline.com/doi/full/10.1080/08927022.2013.842994 |journal=Molecular Simulation |language=en |volume=40 |issue=1–3 |pages=101–105 |doi=10.1080/08927022.2013.842994 |issn=0892-7022 |s2cid=95716947}}</ref> The [https://molmod.boltzmann-zuse.de/ MolMod database] focuses on molecular and ionic force fields (both component-specific and transferable).<ref name="tandfonline.com"/><ref>{{Cite journal |last1=Schmitt |first1=Sebastian |last2=Kanagalingam |first2=Gajanan |last3=Fleckenstein |first3=Florian |last4=Froescher |first4=Daniel |last5=Hasse |first5=Hans |last6=Stephan |first6=Simon |date=2023-11-27 |title=Extension of the MolMod Database to Transferable Force Fields |url=https://pubs.acs.org/doi/10.1021/acs.jcim.3c01484 |journal=Journal of Chemical Information and Modeling |language=en |volume=63 |issue=22 |pages=7148–7158 |doi=10.1021/acs.jcim.3c01484 |pmid=37947503 |s2cid=265103133 |issn=1549-9596}}</ref>

== Transferability and mixing function types ==
Functional forms and parameter sets have been defined by the developers of interatomic potentials and feature variable degrees of [[self-consistent|self-consistency]] 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.<ref name="Heinz_2016">{{cite journal |vauthors=Heinz H, Ramezani-Dakhel H |date=January 2016 |title=Simulations of inorganic-bioorganic interfaces to discover new materials: insights, comparisons to experiment, challenges, and opportunities |journal=Chemical Society Reviews |volume=45 |issue=2 |pages=412–48 |doi=10.1039/c5cs00890e |pmid=26750724}}</ref> In some cases, modifications can be made with minor effort, for example, between 9-6 Lennard-Jones potentials to 12-6 Lennard-Jones potentials.<ref name="Mishra_2014" /> Transfers from Buckingham potentials to harmonic potentials, or from [[Embedded atom model|Embedded Atom Models]] to harmonic potentials, on the contrary, would require many additional assumptions and may not be possible.

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

== Limitations ==
All [[interatomic potential]]s are based on approximations and experimental data, therefore often termed ''empirical''. The performance varies from higher accuracy than [[density functional theory]] (DFT) calculations, with access to million times larger systems and time scales, to random guesses depending on the force field.<ref>{{Cite journal|last1=Emami|first1=Fateme S.|last2=Puddu|first2=Valeria|last3=Berry|first3=Rajiv J.|last4=Varshney|first4=Vikas|last5=Patwardhan|first5=Siddharth V.|last6=Perry|first6=Carole C.|last7=Heinz|first7=Hendrik | name-list-style = vanc |date=2014-04-22|title=Force Field and a Surface Model Database for Silica to Simulate Interfacial Properties in Atomic Resolution|journal=Chemistry of Materials|volume=26|issue=8|pages=2647–2658|doi=10.1021/cm500365c|issn=0897-4756|url=http://irep.ntu.ac.uk/id/eprint/4652/1/4652_Perry.pdf}}</ref> 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.<ref>{{Cite journal|last1=Ruiz|first1=Victor G.|last2=Liu|first2=Wei|last3=Tkatchenko|first3=Alexandre | name-list-style = vanc |date=2016-01-15|title=Density-functional theory with screened van der Waals interactions applied to atomic and molecular adsorbates on close-packed and non-close-packed surfaces|journal=Physical Review B|volume=93|issue=3|page=035118|doi=10.1103/physrevb.93.035118|bibcode=2016PhRvB..93c5118R|hdl=11858/00-001M-0000-0029-3035-8|issn=2469-9950|hdl-access=free}}</ref><ref>{{cite journal | vauthors = Ruiz VG, Liu W, Zojer E, Scheffler M, Tkatchenko A | title = Density-functional theory with screened van der Waals interactions for the modeling of hybrid inorganic-organic systems | journal = Physical Review Letters | volume = 108 | issue = 14 | pages = 146103 | date = April 2012 | pmid = 22540809 | doi = 10.1103/physrevlett.108.146103 | bibcode = 2012PhRvL.108n6103R | doi-access = free | hdl = 11858/00-001M-0000-000F-C6EA-3 | hdl-access = free }}</ref>

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 [[Anisotropy|anisotropic]] charge distributions.<ref>{{cite journal | vauthors = Kramer C, Spinn A, Liedl KR | title = Charge Anisotropy: Where Atomic Multipoles Matter Most | journal = Journal of Chemical Theory and Computation | volume = 10 | issue = 10 | pages = 4488–96 | date = October 2014 | pmid = 26588145 | doi = 10.1021/ct5005565 }}</ref> The remedy is that point charges have a clear interpretation<ref name="Heinz_2004" /> 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 π-conjugated systems, and lone pairs in water.<ref>{{Cite journal|last1=Mahoney|first1=Michael W.|last2=Jorgensen|first2=William L. | name-list-style = vanc |date=2000-05-22|title=A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions|journal=The Journal of Chemical Physics|volume=112|issue=20|pages=8910–8922|doi=10.1063/1.481505|bibcode=2000JChPh.112.8910M|issn=0021-9606}}</ref><ref name="Xu_2015">{{cite journal |display-authors=6 |vauthors=Xu R, Chen CC, Wu L, Scott MC, Theis W, Ophus C, Bartels M, Yang Y, Ramezani-Dakhel H, Sawaya MR, Heinz H, Marks LD, Ercius P, Miao J |date=November 2015 |title=Three-dimensional coordinates of individual atoms in materials revealed by electrontomography |journal=Nature Materials |volume=14 |issue=11 |pages=1099–103 |arxiv=1505.05938 |bibcode=2015NatMa..14.1099X |doi=10.1038/nmat4426 |pmid=26390325 |s2cid=5455024}}</ref><ref name="Pramanik_2017">{{cite journal | vauthors = Pramanik C, Gissinger JR, Kumar S, Heinz H | title = Carbon Nanotube Dispersion in Solvents and Polymer Solutions: Mechanisms, Assembly, and Preferences | journal = ACS Nano | volume = 11 | issue = 12 | pages = 12805–12816 | date = December 2017 | pmid = 29179536 | doi = 10.1021/acsnano.7b07684 }}</ref> Electronic [[Dielectric polarization|polarization]] of the environment may be better included by using ''polarizable force fields''<ref name="Lomize_2002">{{cite journal | vauthors = Lomize AL, Reibarkh MY, Pogozheva ID | title = Interatomic potentials and solvation parameters from protein engineering data for buried residues | journal = Protein Science | volume = 11 | issue = 8 | pages = 1984–2000 | date = August 2002 | pmid = 12142453 | pmc = 2373680 | doi = 10.1110/ps.0307002 }}</ref><ref name="warshel">{{cite journal | vauthors = Warshel A, Sharma PK, Kato M, Parson WW | title = Modeling electrostatic effects in proteins | journal = Biochimica et Biophysica Acta (BBA) - Proteins and Proteomics | volume = 1764 | issue = 11 | pages = 1647–76 | date = November 2006 | pmid = 17049320 | doi = 10.1016/j.bbapap.2006.08.007 }}</ref> or using a macroscopic [[dielectric constant]]. However, application of one value of dielectric constant is a coarse approximation in the highly heterogeneous environments of proteins, biological membranes, minerals, or electrolytes.<ref name="Shultz">{{cite journal | vauthors = Schutz CN, Warshel A | title = What are the dielectric "constants" of proteins and how to validate electrostatic models? | journal = Proteins | volume = 44 | issue = 4 | pages = 400–17 | date = September 2001 | pmid = 11484218 | doi = 10.1002/prot.1106 | s2cid = 9912122 }}</ref>

All types of [[van der Waals force]]s 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 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.<ref name="Israelachvili_2011" /> 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 more weakly than identical types of atoms.<ref name="Leckband">{{cite journal | vauthors = Leckband D, Israelachvili J | title = Intermolecular forces in biology | journal = Quarterly Reviews of Biophysics | volume = 34 | issue = 2 | pages = 105–267 | date = May 2001 | pmid = 11771120 | doi = 10.1017/S0033583501003687 | s2cid = 8401242 }}</ref> This is in contrast to ''combinatorial rules'' or Slater-Kirkwood equation applied for development of the classical force fields. The ''combinatorial rules'' 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 [[helium]],<ref name="Israelachvili_2011" /> 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 ([[Hamaker constant]]) have been explained by [[Jacob Israelachvili]].<ref name="Israelachvili_2011">{{Cite book |chapter=Intermolecular and Surface Forces |vauthors=Israelachvili JN |publisher=Elsevier |year=2011 |isbn=978-0-12-391927-4 |pages=iii |doi=10.1016/b978-0-12-391927-4.10024-6}}</ref> For example, "''the interaction between hydrocarbons across water is about 10% of that across vacuum''".<ref name="Israelachvili_2011" /> 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.

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.<ref>{{Cite journal| vauthors = Pramanik C, Jamil T, Gissinger JR, Guittet D, Arias-Monje PJ, Kumar S, Heinz H |date=2019-10-03|title=Polyacrylonitrile Interactions with Carbon Nanotubes in Solution: Conformations and Binding as a Function of Solvent, Temperature, and Concentration|journal=Advanced Functional Materials|volume=29|issue=50|pages=1905247|doi=10.1002/adfm.201905247|s2cid=208700020 |issn=1616-301X|doi-access=|bibcode=2019AdvFM..2905247P }}</ref> Participants in [[Critical Assessment of protein Structure Prediction]] (CASP) 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''".<ref name="Koehl">{{cite journal | vauthors = Koehl P, Levitt M | title = A brighter future for protein structure prediction | journal = Nature Structural Biology | volume = 6 | issue = 2 | pages = 108–11 | date = February 1999 | pmid = 10048917 | doi = 10.1038/5794 | s2cid = 3162636 }}</ref> Force fields have been applied successfully for protein structure refinement in different [[X-ray crystallography]] and [[NMR spectroscopy]] applications, especially using program XPLOR.<ref name="Brunger">{{cite journal | vauthors = Brunger AT, Adams PD | title = Molecular dynamics applied to X-ray structure refinement | journal = Accounts of Chemical Research | volume = 35 | issue = 6 | pages = 404–12 | date = June 2002 | pmid = 12069625 | doi = 10.1021/ar010034r }}</ref> 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 program DYANA<ref name="Guntert">{{cite journal | vauthors = Güntert P | title = Structure calculation of biological macromolecules from NMR data | journal = Quarterly Reviews of Biophysics | volume = 31 | issue = 2 | pages = 145–237 | date = May 1998 | pmid = 9794034 | doi = 10.1017/S0033583598003436 | s2cid = 43575627 }}</ref> (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.<ref>{{Cite journal|last1=Ostermeir|first1=Katja|last2=Zacharias|first2=Martin | name-list-style = vanc |s2cid=98441607|date=January 2013|title=163 Enhanced sampling of peptides and proteins with a new biasing replica exchange method|journal=Journal of Biomolecular Structure and Dynamics|volume=31|issue=sup1|pages=106|doi=10.1080/07391102.2013.786405|issn=0739-1102|doi-access=free}}</ref> Thereby also the development of parameters to tackle such large-scale problems requires new approaches. A specific problem area is [[homology modeling]] of proteins.<ref name="Tramontano">{{cite journal | vauthors = Tramontano A, Morea V | title = Assessment of homology-based predictions in CASP5 | journal = Proteins | volume = 53 | pages = 352–68 | year = 2003 | issue = Suppl 6 | pmid = 14579324 | doi = 10.1002/prot.10543 | s2cid = 33186021 | doi-access = free }}</ref> Meanwhile, alternative empirical scoring functions have been developed for [[ligand docking]],<ref name="Gohlke">{{cite journal | vauthors = Gohlke H, Klebe G | title = Approaches to the description and prediction of the binding affinity of small-molecule ligands to macromolecular receptors | journal = Angewandte Chemie | volume = 41 | issue = 15 | pages = 2644–76 | date = August 2002 | pmid = 12203463 | doi = 10.1002/1521-3773(20020802)41:15<2644::AID-ANIE2644>3.0.CO;2-O }}</ref> [[protein folding]],<ref name="Edgcomb">{{cite journal | vauthors = Edgcomb SP, Murphy KP | title = Structural energetics of protein folding and binding | journal = Current Opinion in Biotechnology | volume = 11 | issue = 1 | pages = 62–6 | date = February 2000 | pmid = 10679345 | doi = 10.1016/s0958-1669(99)00055-5 }}</ref><ref name="Lazaridis">{{cite journal | vauthors = Lazaridis T, Karplus M | title = Effective energy functions for protein structure prediction | journal = Current Opinion in Structural Biology | volume = 10 | issue = 2 | pages = 139–45 | date = April 2000 | pmid = 10753811 | doi = 10.1016/s0959-440x(00)00063-4 }}</ref><ref name="awml">{{Cite journal |doi = 10.1109/MCSE.2012.21|title = Computer Simulations of Protein Folding|journal = Computing in Science & Engineering|volume = 14|issue = 2|pages = 97–103|year = 2012|last1 = Javidpour|first1 = Leili | name-list-style = vanc |s2cid = 17613729|bibcode = 2012CSE....14b..97J}}</ref> homology model refinement,<ref name="krieger">{{cite journal | vauthors = Krieger E, Joo K, Lee J, Lee J, Raman S, Thompson J, Tyka M, Baker D, Karplus K | display-authors = 6 | title = Improving physical realism, stereochemistry, and side-chain accuracy in homology modeling: Four approaches that performed well in CASP8 | journal = Proteins | volume = 77 | pages = 114–22 | year = 2009 | issue = Suppl 9 | pmid = 19768677 | pmc = 2922016 | doi = 10.1002/prot.22570 }}</ref> computational [[protein design]],<ref name="Gordon">{{cite journal | vauthors = Gordon DB, Marshall SA, Mayo SL | title = Energy functions for protein design | journal = Current Opinion in Structural Biology | volume = 9 | issue = 4 | pages = 509–13 | date = August 1999 | pmid = 10449371 | doi = 10.1016/S0959-440X(99)80072-4 }}</ref><ref name="Mendes">{{cite journal | vauthors = Mendes J, Guerois R, Serrano L | title = Energy estimation in protein design | journal = Current Opinion in Structural Biology | volume = 12 | issue = 4 | pages = 441–6 | date = August 2002 | pmid = 12163065 | doi = 10.1016/s0959-440x(02)00345-7 }}</ref><ref name="Rohl">{{Cite book |doi = 10.1016/S0076-6879(04)83004-0|pmid = 15063647|chapter = Protein Structure Prediction Using Rosetta|title = Numerical Computer Methods, Part D|volume = 383|pages = 66–93|series = Methods in Enzymology|year = 2004|last1 = Rohl|first1 = Carol A.|last2 = Strauss|first2 = Charlie E.M.|last3 = Misura|first3 = Kira M.S.|last4 = Baker|first4 = David | name-list-style = vanc |isbn = 9780121827885}}</ref> and modeling of proteins in membranes.<ref name="Lomize1">{{cite journal | vauthors = Lomize AL, Pogozheva ID, Lomize MA, Mosberg HI | title = Positioning of proteins in membranes: a computational approach | journal = Protein Science | volume = 15 | issue = 6 | pages = 1318–33 | date = June 2006 | pmid = 16731967 | pmc = 2242528 | doi = 10.1110/ps.062126106 }}</ref>

It was also argued that some protein force fields operate with energies that are irrelevant to protein folding or ligand binding.<ref name="Lomize_2002" /> The parameters of proteins force fields reproduce the [[enthalpy]] of [[sublimation (physics)|sublimation]], i.e., energy of evaporation of molecular crystals. However, [[protein folding]] and [[ligand binding]] are thermodynamically closer to [[crystallization]], or liquid-solid transitions as these processes represent ''freezing'' of mobile molecules in condensed media.<ref name="Murphy">{{cite journal | vauthors = Murphy KP, Gill SJ | title = Solid model compounds and the thermodynamics of protein unfolding | journal = Journal of Molecular Biology | volume = 222 | issue = 3 | pages = 699–709 | date = December 1991 | pmid = 1660931 | doi = 10.1016/0022-2836(91)90506-2 }}</ref><ref name="Shakhnovich">{{cite journal | vauthors = Shakhnovich EI, Finkelstein AV | title = Theory of cooperative transitions in protein molecules. I. Why denaturation of globular protein is a first-order phase transition | journal = Biopolymers | volume = 28 | issue = 10 | pages = 1667–80 | date = October 1989 | pmid = 2597723 | doi = 10.1002/bip.360281003 | s2cid = 26981215 }}</ref><ref name="Graziano">{{cite journal | vauthors = Graziano G, Catanzano F, Del Vecchio P, Giancola C, Barone G | date = 1996 | title = Thermodynamic stability of globular proteins: a reliable model from small molecule studies | journal = Gazetta Chim. Italiana | volume = 126 | pages = 559–567 }}</ref> Thus, 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.<ref name="Israelachvili_2011" /> Hence, the potentials describing protein folding or ligand binding need more consistent parameterization protocols, e.g., as described for IFF. Indeed, the energies of [[H-bond]]s in proteins are ~ -1.5 kcal/mol when estimated from [[protein engineering]] or [[alpha helix]] to [[Random coil|coil]] transition data,<ref name="Myers">{{cite journal | vauthors = Myers JK, Pace CN | title = Hydrogen bonding stabilizes globular proteins | journal = Biophysical Journal | volume = 71 | issue = 4 | pages = 2033–9 | date = October 1996 | pmid = 8889177 | pmc = 1233669 | doi = 10.1016/S0006-3495(96)79401-8 | bibcode = 1996BpJ....71.2033M }}</ref><ref name="Scholtz">{{cite journal | vauthors = Scholtz JM, Marqusee S, Baldwin RL, York EJ, Stewart JM, Santoro M, Bolen DW | title = Calorimetric determination of the enthalpy change for the alpha-helix to coil transition of an alanine peptide in water | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 88 | issue = 7 | pages = 2854–8 | date = April 1991 | pmid = 2011594 | pmc = 51338 | doi = 10.1073/pnas.88.7.2854 | bibcode = 1991PNAS...88.2854S | doi-access = free }}</ref> but the same energies estimated from [[sublimation (physics)|sublimation]] [[enthalpy]] of molecular [[crystal]]s were -4 to -6 kcal/mol,<ref name="Gavezotti">{{cite journal | vauthors = Gavezzotti A, Filippini G | title = Geometry of the intermolecular XH. cntdot.. cntdot.. cntdot. Y (X, Y= N, O) hydrogen bond and the calibration of empirical hydrogen-bond potentials. | journal = The Journal of Physical Chemistry | date = May 1994 | volume = 98 | issue = 18 | pages = 4831–7 | doi = 10.1021/j100069a010 }}</ref> which is related to re-forming existing hydrogen bonds and not forming hydrogen bonds from scratch. The depths of modified [[Lennard-Jones potential]]s derived from protein engineering data were also smaller than in typical potential parameters and followed the ''like dissolves like'' rule, as predicted by McLachlan theory.<ref name="Lomize_2002" />

== Force fields available in literature==
{{Further|Comparison of force field implementations|Molecular design software|Comparison of software for molecular mechanics modeling}}
Different force fields are designed for different purposes:

=== Classical ===
* [[AMBER]] (Assisted Model Building and Energy Refinement) – widely used for proteins and DNA.
* 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 [[Arieh Warshel]], 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.
* [[CHARMM]] (Chemistry at HARvard Molecular Mechanics) – originally developed at Harvard, widely used for both small molecules and macromolecules
* 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 modelling package.<ref>{{cite journal | vauthors = Möllhoff M, Sternberg U | s2cid = 91705326 | title = Molecular mechanics with fluctuating atomic charges–a new force field with a semi-empirical charge calculation. | journal = Molecular Modeling Annual | date = May 2001 | volume = 7 | issue = 4 | pages = 90–102 | doi = 10.1007/s008940100008 }}</ref>
* CVFF – also used broadly for small molecules and macromolecules.<ref name="Dauber-Osguthorpe_1988" />
* ECEPP<ref>{{Cite web|url=https://biohpc.cornell.edu/software/eceppak/README.html|title=ECEPP|website=biohpc.cornell.edu}}</ref> – first force field for polypeptide molecules - developed by F.A. Momany, H.A. Scheraga and colleagues.<ref name="Momany">{{cite journal | vauthors = Momany FA, McGuire RF, Burgess AW, Scheraga HA | title = 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. | journal = The Journal of Physical Chemistry | date = October 1975 | volume = 79 | issue = 22 | pages = 2361–81 | doi = 10.1021/j100589a006 }}</ref><ref name="Arnautova">{{cite journal | vauthors = Arnautova YA, Jagielska A, Scheraga HA | title = A new force field (ECEPP-05) for peptides, proteins, and organic molecules | journal = The Journal of Physical Chemistry B | volume = 110 | issue = 10 | pages = 5025–44 | date = March 2006 | pmid = 16526746 | doi = 10.1021/jp054994x }}</ref> 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 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.<ref name="Schaumann">{{cite journal |vauthors=Schaumann T, Braun W, Wüthrich K |date=March 1990 |title=The program FANTOM for energy refinement of polypeptides and proteins using a Newton–Raphson minimizer in torsion angle space. |journal=Biopolymers |volume=29 |issue=4–5 |pages=679–94 |doi=10.1002/bip.360290403 |s2cid=94519023}}</ref>
* [[GROMOS]] (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.<ref>{{Cite web|url=https://www.igc.ethz.ch/gromos.html|title=GROMOS|website=www.igc.ethz.ch}}</ref> 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.
* IFF (Interface Force Field) – covers metals, minerals, 2D materials, and polymers. It uses 12-6 LJ and 9-6 LJ interactions.<ref name="Heinz_2013">{{cite journal |vauthors=Heinz H, Lin TJ, Mishra RK, Emami FS |date=February 2013 |title=Thermodynamically consistent force fields for the assembly of inorganic, organic, and biological nanostructures: the INTERFACE force field |journal=Langmuir |volume=29 |issue=6 |pages=1754–65 |doi=10.1021/la3038846 |pmid=23276161}}</ref><ref name="IFF">{{cite web |date=2 February 2016 |title=Interface Force Field (IFF) |url=https://bionanostructures.com/interface-md/ |work=Heinz Laboratory}}</ref> IFF was developed as for compounds across the periodic table. It assigs consistent charges, utilizes standard conditions as a reference state, reproduces structures, energies, and energy derivatives, and quantifies limitations for all included compounds.<ref name="Heinz_2013" /><ref name="Mishra_2017">{{cite journal |last1=Mishra |first1=Ratan K. |last2=Mohamed |first2=Aslam Kunhi |last3=Geissbühler |first3=David |last4=Manzano |first4=Hegoi |last5=Jamil |first5=Tariq |last6=Shahsavari |first6=Rouzbeh |last7=Kalinichev |first7=Andrey G. |last8=Galmarini |first8=Sandra |last9=Tao |first9=Lei |last10=Heinz |first10=Hendrik |last11=Pellenq |first11=Roland |name-list-style=vanc |date=December 2017 |title=A force field database for cementitious materials including validations, applications and opportunities |url=http://hal.in2p3.fr/in2p3-01633100/file/Mishra-CEMCON_2017-accepted.pdf |journal=Cement and Concrete Research |volume=102 |pages=68–89 |doi=10.1016/j.cemconres.2017.09.003}}</ref> The [https://bionanostructures.com/interface-md/ Interface force field] (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<ref name="Geada_2018">{{cite journal |vauthors=Geada IL, Ramezani-Dakhel H, Jamil T, Sulpizi M, Heinz H |date=February 2018 |title=Insight into induced charges at metal surfaces and biointerfaces using a polarizable Lennard-Jones potential |journal=Nature Communications |volume=9 |issue=1 |pages=716 |bibcode=2018NatCo...9..716G |doi=10.1038/s41467-018-03137-8 |pmc=5818522 |pmid=29459638}}</ref><ref name="Pramanik_2017" /><ref name="Xu_2015" />
* MMFF ([[Merck Molecular Force Field]]) – developed at Merck for a broad range of molecules.
* MM2 was developed by [[Norman Allinger]] mainly for conformational analysis of [[hydrocarbon]]s 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 MM4).<ref>{{cite journal |vauthors=Allinger NL |date=December 1977 |title=Conformational analysis. 130. MM2. A hydrocarbon force field utilizing V1 and V2 torsional terms. |journal=Journal of the American Chemical Society |volume=99 |issue=25 |pages=8127–34 |doi=10.1021/ja00467a001|bibcode=1977JAChS..99.8127A }}</ref><ref>{{cite web |title=MM2 and MM3 home page |url=http://europa.chem.uga.edu/allinger/mm2mm3.html |archive-url=https://web.archive.org/web/20090123023451/http://europa.chem.uga.edu/allinger/mm2mm3.html |archive-date=2009-01-23}}</ref><ref>{{cite journal |vauthors=Allinger NL, Yuh YH, Lii JH |date=November 1989 |title=Molecular mechanics. The MM3 force field for hydrocarbons. 1. |journal=Journal of the American Chemical Society |volume=111 |issue=23 |pages=8551–66 |doi=10.1021/ja00205a001|bibcode=1989JAChS.111.8551A }}</ref><ref>{{cite journal |vauthors=Lii JH, Allinger NL |date=November 1989 |title=Molecular mechanics. The MM3 force field for hydrocarbons. 2. Vibrational frequencies and thermodynamics. |journal=Journal of the American Chemical Society |volume=111 |issue=23 |pages=8566–75 |doi=10.1021/ja00205a002|bibcode=1989JAChS.111.8566L }}</ref><ref>{{cite journal |vauthors=Lii JH, Allinger NL |date=November 1989 |title=Molecular mechanics. The MM3 force field for hydrocarbons. 3. The van der Waals' potentials and crystal data for aliphatic and aromatic hydrocarbons. |journal=Journal of the American Chemical Society |volume=111 |issue=23 |pages=8576–82 |doi=10.1021/ja00205a003|bibcode=1989JAChS.111.8576L }}</ref>
* [[OPLS]] (Optimized Potential for Liquid Simulations) (variants include OPLS-AA, OPLS-UA, OPLS-2001, OPLS-2005, OPLS3e, OPLS4) – developed by [[William L. Jorgensen]] at the Yale University Department of Chemistry.
* QCFF/PI – A general force fields for conjugated molecules.<ref name="warshel2">{{cite journal | vauthors = Warshel A | title = Quantum mechanical consistent force field (QCFF/PI) method: Calculations of energies, conformations and vibronic interactions of ground and excited states of conjugated molecules. | journal = Israel Journal of Chemistry | date = 1973 | volume = 11 | issue = 5 | pages = 709–17 | doi = 10.1002/ijch.197300067 }}</ref><ref name="warshel-levitt">{{cite report | vauthors = Warshel A, Levitt M | date = 1974 | title = QCFF/PI: A Program for the Consistent Force Field Evaluation of Equilibrium Geometries and Vibrational Frequencies of Molecules | page = QCPE 247 | publisher = Quantum Chemistry Program Exchange | location = Indiana University }}</ref>
* 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.<ref name="Rappé_1992">{{Cite journal |vauthors=Rappé AK, Casewit CJ, Colwell KS, Goddard III WA, Skiff WM |date=December 1992 |title=UFF, a full periodic table force field for molecular mechanics and molecular dynamics simulations |journal=Journal of the American Chemical Society |volume=114 |issue=25 |pages=10024–10035 |doi=10.1021/ja00051a040 |bibcode=1992JAChS.11410024R |issn=0002-7863}}</ref> The reliability is known to be poor due to lack of validation and interpretation of the parameters for nearly all claimed compounds, especially metals and inorganic compounds.<ref name = "Heinz_2005">{{Cite journal| vauthors = Heinz H, Koerner H, Anderson KL, Vaia RA, Farmer BL |date=November 2005|title=Force Field for Mica-Type Silicates and Dynamics of Octadecylammonium Chains Grafted to Montmorillonite|journal=Chemistry of Materials|volume=17|issue=23|pages=5658–5669|doi=10.1021/cm0509328|issn=0897-4756}}</ref><ref name="Mishra_2017" />

=== Polarizable ===
Several force fields explicitly capture [[polarizability]], 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 [[harmonic oscillator]] potential.<ref>{{Cite journal |vauthors=Dick BG, Overhauser AW |date=1958-10-01 |title=Theory of the Dielectric Constants of Alkali Halide Crystals |journal=Physical Review |volume=112 |issue=1 |pages=90–103 |bibcode=1958PhRv..112...90D |doi=10.1103/physrev.112.90 |issn=0031-899X}}</ref><ref>{{Cite journal |vauthors=Mitchell PJ, Fincham D |date=1993-02-22 |title=Shell model simulations by adiabatic dynamics |journal=Journal of Physics: Condensed Matter |volume=5 |issue=8 |pages=1031–1038 |bibcode=1993JPCM....5.1031M |doi=10.1088/0953-8984/5/8/006 |issn=0953-8984 |s2cid=250752417}}</ref><ref>{{Cite journal |last1=Yu |first1=Haibo |last2=van Gunsteren |first2=Wilfred F. |name-list-style=vanc |date=November 2005 |title=Accounting for polarization in molecular simulation |journal=Computer Physics Communications |volume=172 |issue=2 |pages=69–85 |bibcode=2005CoPhC.172...69Y |doi=10.1016/j.cpc.2005.01.022 |issn=0010-4655}}</ref> Recent examples include polarizable models with virtual electrons that reproduce image charges in metals<ref name="Geada_2018" /> and polarizable biomolecular force fields.<ref name="CPFF0" /> 
* AMBER – polarizable force field developed by Jim Caldwell and coworkers.<ref>{{cite journal | vauthors = Yang L, Tan CH, Hsieh MJ, Wang J, Duan Y, Cieplak P, Caldwell J, Kollman PA, Luo R | title = New-generation amber united-atom force field | journal = The Journal of Physical Chemistry B | volume = 110 | issue = 26 | pages = 13166–76 | date = July 2006 | pmid = 16805629 | doi = 10.1021/jp060163v }}</ref>
* 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).<ref>{{Cite web|url=https://dasher.wustl.edu/tinker/|title=Tinker Molecular Modeling Package|website=dasher.wustl.edu}}</ref> AMOEBA force field is gradually moving to more physics-rich AMOEBA+.<ref>{{cite journal | vauthors = Liu C, Piquemal JP, Ren P | title = Implementation of Geometry-Dependent Charge Flux into the Polarizable AMOEBA+ Potential | journal = The Journal of Physical Chemistry Letters | volume = 11 | issue = 2 | pages = 419–426 | date = January 2020 | pmid = 31865706 | doi = 10.1021/acs.jpclett.9b03489 | pmc = 7384396 }}</ref><ref>{{cite journal | vauthors = Liu C, Piquemal JP, Ren P | title = AMOEBA+ Classical Potential for Modeling Molecular Interactions | journal = Journal of Chemical Theory and Computation | volume = 15 | issue = 7 | pages = 4122–4139 | date = July 2019 | pmid = 31136175 | doi = 10.1021/acs.jctc.9b00261 | pmc = 6615954 }}</ref>
* CHARMM – polarizable force field developed by S. Patel (University of Delaware) and C. L. Brooks III (University of Michigan).<ref name="CPFF0">{{cite journal | vauthors = Patel S, Brooks CL | title = CHARMM fluctuating charge force field for proteins: I parameterization and application to bulk organic liquid simulations | journal = Journal of Computational Chemistry | volume = 25 | issue = 1 | pages = 1–15 | date = January 2004 | pmid = 14634989 | doi = 10.1002/jcc.10355 | s2cid = 39320318 }}</ref><ref name="CPFF1">{{cite journal | vauthors = Patel S, Mackerell AD, Brooks CL | title = CHARMM fluctuating charge force field for proteins: II protein/solvent properties from molecular dynamics simulations using a nonadditive electrostatic model | journal = Journal of Computational Chemistry | volume = 25 | issue = 12 | pages = 1504–14 | date = September 2004 | pmid = 15224394 | doi = 10.1002/jcc.20077 | s2cid = 16741310 | doi-access = free }}</ref> Based on the classical Drude oscillator developed by [[Alexander D. MacKerell, Jr.|Alexander MacKerell]] (University of Maryland, Baltimore) and [[Benoît Roux|Benoit Roux]] (University of Chicago).<ref name="drude1">{{cite journal | vauthors = Anisimov VM, Lamoureux G, Vorobyov IV, Huang N, Roux B, MacKerell AD | title = Determination of Electrostatic Parameters for a Polarizable Force Field Based on the Classical Drude Oscillator | journal = Journal of Chemical Theory and Computation | volume = 1 | issue = 1 | pages = 153–68 | date = January 2005 | pmid = 26641126 | doi = 10.1021/ct049930p }}</ref><ref name="drude2">{{cite journal | vauthors = Yu H, Whitfield TW, Harder E, Lamoureux G, Vorobyov I, Anisimov VM, Mackerell AD, Roux B | title = Simulating Monovalent and Divalent Ions in Aqueous Solution Using a Drude Polarizable Force Field | journal = Journal of Chemical Theory and Computation | volume = 6 | issue = 3 | pages = 774–786 | date = 2010 | pmid = 20300554 | pmc = 2838399 | doi = 10.1021/ct900576a }}</ref>
* CFF/ind and ENZYMIX – The first polarizable force field<ref name="awml3">{{cite journal | vauthors = Warshel A, Levitt M | title = Theoretical studies of enzymic reactions: dielectric, electrostatic and steric stabilization of the carbonium ion in the reaction of lysozyme | journal = Journal of Molecular Biology | volume = 103 | issue = 2 | pages = 227–49 | date = May 1976 | pmid = 985660 | doi = 10.1016/0022-2836(76)90311-9 }}</ref> which has subsequently been used in many applications to biological systems.<ref name="warshel"/>
* 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.<ref>{{cite journal | vauthors = Sternberg U, Koch FT, Möllhoff M | title = New approach to the semiempirical calculation of atomic charges for polypeptides and large molecular systems. | journal = Journal of Computational Chemistry | date = May 1994 | volume = 15 | issue = 5 | pages = 524–31 | doi = 10.1002/jcc.540150505 | s2cid = 5227353 }}</ref> Atomic charge fluctuation is possible in each molecular dynamics step.
* DRF90 – developed by P. Th. van Duijnen and coworkers.<ref>{{cite journal | vauthors = Swart M, van Duijnen PT | title = DRF90: a polarizable force field. | journal = Molecular Simulation | date = May 2006 | volume = 32 | issue = 6 | pages = 471–84 | doi = 10.1080/08927020600631270 | s2cid = 96616243 }}</ref>
* NEMO (Non-Empirical Molecular Orbital) – procedure developed by Gunnar Karlström and coworkers at Lund University (Sweden)<ref name="NEMO">{{cite journal | vauthors = Engkvist O, Astrand PO, Karlström G | title = Accurate Intermolecular Potentials Obtained from Molecular Wave Functions: Bridging the Gap between Quantum Chemistry and Molecular Simulations | journal = Chemical Reviews | volume = 100 | issue = 11 | pages = 4087–108 | date = November 2000 | pmid = 11749341 | doi = 10.1021/cr9900477 }}</ref>
* 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 [http://jialigao.org Gao Research Group |] at the University of Minnesota.<ref name="pipf">{{cite journal | vauthors = Gao J, Habibollazadeh D, Shao L | title = A polarizable intermolecular potential function for simulation of liquid alcohols. | journal = The Journal of Physical Chemistry | date = November 1995 | volume = 99 | issue = 44 | pages = 16460–7 | doi = 10.1021/j100044a039 }}</ref><ref name="pipf2">{{cite journal | vauthors = Xie W, Pu J, Mackerell AD, Gao J | title = Development of a polarizable intermolecular potential function (PIPF) for liquid amides and alkanes | journal = Journal of Chemical Theory and Computation | volume = 3 | issue = 6 | pages = 1878–1889 | date = 2007 | pmid = 18958290 | pmc = 2572772 | doi = 10.1021/ct700146x }}</ref>
* Polarizable Force Field (PFF) – developed by Richard A. Friesner and coworkers.<ref name="pmid26641692">{{cite journal | vauthors = Maple JR, Cao Y, Damm W, Halgren TA, Kaminski GA, Zhang LY, Friesner RA | title = A Polarizable Force Field and Continuum Solvation Methodology for Modeling of Protein-Ligand Interactions | journal = Journal of Chemical Theory and Computation | volume = 1 | issue = 4 | pages = 694–715 | date = July 2005 | pmid = 26641692 | doi = 10.1021/ct049855i }}</ref>
* SP-basis Chemical Potential Equalization (CPE) – approach developed by R. Chelli and P. Procacci.<ref name="procacci">{{cite journal | vauthors = Chelli R, Procacci P | title = A transferable polarizable electrostatic force field for molecular mechanics based on the chemical potential equalization principle. | journal = The Journal of Chemical Physics | date = November 2002 | volume = 117 | issue = 20 | pages = 9175–89 | doi = 10.1063/1.1515773 | bibcode = 2002JChPh.117.9175C }}</ref>
* PHAST – polarizable potential developed by Chris Cioce and coworkers.<ref name=Cioce>{{cite journal | vauthors = Cioce CR, McLaughlin K, Belof JL, Space B | title = A Polarizable and Transferable PHAST N2 Potential for Use in Materials Simulation | journal = Journal of Chemical Theory and Computation | volume = 9 | issue = 12 | pages = 5550–7 | date = December 2013 | pmid = 26592288 | doi = 10.1021/ct400526a }}</ref>
* ORIENT – procedure developed by Anthony J. Stone (Cambridge University) and coworkers.<ref>{{Cite web|url=http://www-stone.ch.cam.ac.uk/programs.html|title=Anthony Stone: Computer programs|website=www-stone.ch.cam.ac.uk}}</ref>
* 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.<ref name="SIBGEM">{{cite journal | vauthors = Gresh N, Cisneros GA, Darden TA, Piquemal JP | title = Anisotropic, Polarizable Molecular Mechanics Studies of Inter- and Intramolecular Interactions and Ligand-Macromolecule Complexes. A Bottom-Up Strategy | journal = Journal of Chemical Theory and Computation | volume = 3 | issue = 6 | pages = 1960–1986 | date = November 2007 | pmid = 18978934 | pmc = 2367138 | doi = 10.1021/ct700134r }}</ref><ref name="GEM0">{{cite journal | vauthors = Piquemal JP, Cisneros GA, Reinhardt P, Gresh N, Darden TA | title = Towards a force field based on density fitting | journal = The Journal of Chemical Physics | volume = 124 | issue = 10 | pages = 104101 | date = March 2006 | pmid = 16542062 | pmc = 2080832 | doi = 10.1063/1.2173256 | bibcode = 2006JChPh.124j4101P }}</ref><ref name="GEM2">{{cite journal | vauthors = Cisneros GA, Piquemal JP, Darden TA | title = Generalization of the Gaussian electrostatic model: extension to arbitrary angular momentum, distributed multipoles, and speedup with reciprocal space methods | journal = The Journal of Chemical Physics | volume = 125 | issue = 18 | pages = 184101 | date = November 2006 | pmid = 17115732 | pmc = 2080839 | doi = 10.1063/1.2363374 | bibcode = 2006JChPh.125r4101C }}</ref>
* 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.<ref name="pmid19637900">{{cite journal | vauthors = Borodin O | title = Polarizable force field development and molecular dynamics simulations of ionic liquids | journal = The Journal of Physical Chemistry B | volume = 113 | issue = 33 | pages = 11463–78 | date = August 2009 | pmid = 19637900 | doi = 10.1021/jp905220k }}</ref>
* Polarizable procedure based on the Kim-Gordon approach developed by Jürg Hutter and coworkers (University of Zürich){{Citation needed|date=May 2010}}
* 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 University of Bonn.<ref name=gfnff>{{cite journal | vauthors = Spicher S, Grimme S | title = Robust Atomistic Modeling of Materials, Organometallic, and Biochemical Systems | journal = Angewandte Chemie International Edition | volume = 59 | issue = 36 | pages = 15665–15673 | date = September 2020 | doi = 10.1002/anie.202004239| pmid = 32343883 | pmc = 7267649 | doi-access = free }}</ref>
* 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 <ref name = WASABe>{{Cite journal | vauthors=Starovoytov ON | title = Development of Polarizable Force Field for Molecular Dynamics Simulation of Lithium-Ion Battery Electrolytes: Sulfonate Based Solvents and Lithium Salts | journal = The Journal of Physical Chemistry B | volume = 125 | issue = 40 | pages = 11242–11255 | date = September 2021 | doi = 10.1021/acs.jpcb.1c05744| pmid = 34586817 | s2cid = 238230196 }}</ref>
* 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 of using quantum mechanical methods. Primarily used by software packages supplied by Cresset Biomolecular Discovery.<ref>{{Cite journal |last=Vinter |first=J. G. |date=1994-12-01 |title=Extended electron distributions applied to the molecular mechanics of some intermolecular interactions |url=https://link.springer.com/article/10.1007/BF00124013 |journal=Journal of Computer-Aided Molecular Design |language=en |volume=8 |issue=6 |pages=653–668 |doi=10.1007/BF00124013 |pmid=7738602 |bibcode=1994JCAMD...8..653V |issn=1573-4951}}</ref><ref>{{Cite web |title=Cresset Science |url=https://www.cresset-group.com/science/overview/#xedforcefield}}</ref>

=== Reactive ===
* EVB ([[Empirical valence bond]]) – 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 [[enzyme]]s.
*[[ReaxFF]] – reactive force field (interatomic potential) developed by Adri van Duin, [[William Andrew Goddard III|William Goddard]] 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.<ref name="van_Duin_2001">{{cite journal |last1= van Duin |first1= Adri C. T. |last2= Dasgupta |first2= Siddharth |last3= Lorant |first3= Francois |last4= Goddard |first4= William A. |name-list-style= vanc |author-link4= William Andrew Goddard III |title= ReaxFF: A Reactive Force Field for Hydrocarbons |url= http://www.wag.caltech.edu/publications/sup/pdf/471.pdf |doi= 10.1021/jp004368u |journal= [[The Journal of Physical Chemistry A]] |volume= 105 |issue= 41 |pages= 9396–9409 |year= 2001 |bibcode= 2001JPCA..105.9396V |citeseerx= 10.1.1.507.6992 |access-date= 2015-08-29 |archive-date= 2018-03-21 |archive-url= https://web.archive.org/web/20180321193134/http://www.wag.caltech.edu/publications/sup/pdf/471.pdf |url-status= dead }}</ref> Parallelized ReaxFF allows reactive simulations on >>1,000,000 atoms on large supercomputers.

=== Coarse-grained ===
* DPD ([[Dissipative particle dynamics]]) – 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 [[Molecular dynamics]]. The potential was originally proposed by Hoogerbrugge and Koelman <ref name="HoogerbruggeKoelman1992">{{cite journal| vauthors = Hoogerbrugge PJ, Koelman JM |title=Simulating Microscopic Hydrodynamic Phenomena with Dissipative Particle Dynamics|journal=Europhysics Letters (EPL)|volume=19|issue=3|year=1992|pages=155–160|issn=0295-5075|doi=10.1209/0295-5075/19/3/001|bibcode=1992EL.....19..155H|s2cid=250796817 }}</ref><ref name="KoelmanHoogerbrugge1993">{{cite journal| vauthors = Koelman JM, Hoogerbrugge PJ |title=Dynamic Simulations of Hard-Sphere Suspensions Under Steady Shear|journal=Europhysics Letters (EPL)|volume=21|issue=3|year=1993|pages=363–368|issn=0295-5075|doi=10.1209/0295-5075/21/3/018|bibcode=1993EL.....21..363K|s2cid=250913111 }}</ref> with later modifications by Español and Warren <ref name="EspañolWarren1995">{{cite journal| vauthors = Español P, Warren P |s2cid=14385201|title=Statistical Mechanics of Dissipative Particle Dynamics|journal=Europhysics Letters (EPL)|volume=30|issue=4|year=1995|pages=191–196|issn=0295-5075|doi=10.1209/0295-5075/30/4/001|bibcode=1995EL.....30..191E}}</ref> The current state of the art was well documented in a [[CECAM]] workshop in 2008.<ref>[http://www.cecam.org/workshop-0-188.html Dissipative Particle Dynamics: Addressing deficiencies and establishing new frontiers] {{Webarchive|url=https://web.archive.org/web/20100715071125/http://www.cecam.org/workshop-0-188.html |date=2010-07-15 }}, CECAM workshop, July 16–18, 2008, Lausanne, Switzerland.</ref> 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 observables.<ref name="McDonagh J. L. 2019 4278–4288"/>
* [[MARTINI]] – a coarse-grained potential developed by Marrink and coworkers at the [[University of Groningen]], initially developed for molecular dynamics simulations of lipids,<ref name="Marrink_2007">{{cite journal | vauthors = Marrink SJ, Risselada HJ, Yefimov S, Tieleman DP, de Vries AH | title = The MARTINI force field: coarse grained model for biomolecular simulations | journal = The Journal of Physical Chemistry B | volume = 111 | issue = 27 | pages = 7812–24 | date = July 2007 | pmid = 17569554 | doi = 10.1021/jp071097f | s2cid = 13874240 | url = https://pure.rug.nl/ws/files/6707449/2007JPhysChemBMarrink.pdf }}</ref> 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.
*SAFT – A top-down coarse-grained model developed in the Molecular Systems Engineering group at [[Imperial College London]] fitted to liquid phase densities and vapor pressures of pure compounds by using the SAFT equation of state.<ref>{{Cite web|title=SAFT|url=http://molecularsystemsengineering.org/saft.html}}</ref> 
* 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 packages.
* 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 capture features dependent on secondary structure and on residue-specific contact information in proteins.<ref name="pmid19717427">{{cite journal | vauthors = Korkut A, Hendrickson WA | title = A force field for virtual atom molecular mechanics of proteins | journal = Proceedings of the National Academy of Sciences of the United States of America | volume = 106 | issue = 37 | pages = 15667–72 | date = September 2009 | pmid = 19717427 | pmc = 2734882 | doi = 10.1073/pnas.0907674106 | bibcode = 2009PNAS..10615667K | doi-access = free }}</ref>

=== Machine learning ===
* 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 system.<ref>{{cite journal | vauthors = Batatia I, Kovacs DP, Simm G, Ortner C, Csanyi G | title = MACE: Higher order equivariant message passing neural networks for fast and accurate force fields | journal = Advances in Neural Information Processing Systems | volume = 35 | pages = 11423–11436 | date = 2022 | arxiv = 2206.07697 | url = https://proceedings.neurips.cc/paper_files/paper/2022/hash/4a36c3c51af11ed9f34615b81edb5bbc-Abstract-Conference.html }}</ref> 
* 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.<ref>{{cite journal | vauthors = Smith JS, Isayev O, Roitberg AE | title = ANI-1: an extensible neural network potential with DFT accuracy at force field computational cost | journal = Chemical Science | volume = 8 | issue = 4 | pages = 3192–3203 | date = April 2017 | pmid = 28507695 | pmc = 5414547 | doi = 10.1039/C6SC05720A | url = }}</ref>
* FFLUX (originally QCTFF) <ref>{{cite journal | vauthors = Hughes ZE, Thacker JC, Wilson AL, Popelier PL | title = Description of Potential Energy Surfaces of Molecules Using FFLUX Machine Learning Models | journal = Journal of Chemical Theory and Computation | volume = 15 | issue = 1 | pages = 116–126 | date = January 2019 | pmid = 30507180 | doi = 10.1021/acs.jctc.8b00806 | hdl-access = free | hdl = 10454/16776 | s2cid = 54524604 }}</ref> A set of trained [[Kriging]] models which operate together to provide a molecular force field trained on [[Atoms in molecules]] or Quantum chemical topology energy terms including electrostatic, exchange and electron correlation.<ref>{{cite journal | vauthors = Fletcher TL, Popelier PL | title = Multipolar Electrostatic Energy Prediction for all 20 Natural Amino Acids Using Kriging Machine Learning | journal = Journal of Chemical Theory and Computation | volume = 12 | issue = 6 | pages = 2742–51 | date = June 2016 | pmid = 27224739 | doi = 10.1021/acs.jctc.6b00457 | doi-access = free }}</ref><ref name = "McDonagh_2018">{{cite journal | vauthors = McDonagh JL, Silva AF, Vincent MA, Popelier PL | title = Machine Learning of Dynamic Electron Correlation Energies from Topological Atoms | journal = Journal of Chemical Theory and Computation | volume = 14 | issue = 1 | pages = 216–224 | date = January 2018 | pmid = 29211469 | doi = 10.1021/acs.jctc.7b01157 | doi-access = free }}</ref>
* TensorMol, a mixed model, a [[neural network]] provides a short-range potential, whilst more traditional potentials add screened long-range terms.
* 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.<ref>{{cite journal | vauthors = Ramakrishnan R, Dral PO, Rupp M, von Lilienfeld OA | title = Big Data Meets Quantum Chemistry Approximations: The Δ-Machine Learning Approach | journal = Journal of Chemical Theory and Computation | volume = 11 | issue = 5 | pages = 2087–96 | date = May 2015 | pmid = 26574412 | doi = 10.1021/acs.jctc.5b00099 | arxiv = 1503.04987 | bibcode = 2015arXiv150304987R | s2cid = 28672393 }}</ref>
* SchNet a [[Neural network]] utilising continuous-filter convolutional layers, to predict chemical properties and potential energy surfaces.<ref>{{cite journal | vauthors = Schütt KT, Sauceda HE, Kindermans PJ, Tkatchenko A, [[Klaus-Robert Müller|Müller KR]] | title = SchNet - A deep learning architecture for molecules and materials | journal = The Journal of Chemical Physics | volume = 148 | issue = 24 | pages = 241722 | date = June 2018 | pmid = 29960322 | doi = 10.1063/1.5019779 | arxiv = 1712.06113 | s2cid = 4897444 | bibcode = 2018JChPh.148x1722S }}</ref>
* PhysNet is a Neural Network-based energy function to predict energies, forces and (fluctuating) partial charges.<ref>{{Cite journal|last=O. T. Unke and M. Meuwly|date=2019|title=PhysNet: A Neural Network for Predicting Energies, Forces, Dipole Moments, and Partial Charges|journal=J. Chem. Theo. Chem.|volume=15|issue=6|pages=3678–3693|doi=10.1021/acs.jctc.9b00181|pmid=31042390|arxiv=1902.08408|s2cid=85543050}}</ref>

=== Water ===
{{Main|Water model}}

The set of parameters used to model water or aqueous solutions (basically a force field for water) is called a [[water model]]. Many water models have been proposed;<ref name="tandfonline.com"/> some examples are TIP3P, TIP4P,<ref name=":1">{{cite journal | vauthors = Abascal JL, Vega C | title = A general purpose model for the condensed phases of water: TIP4P/2005 | journal = The Journal of Chemical Physics | volume = 123 | issue = 23 | pages = 234505 | date = December 2005 | pmid = 16392929 | doi = 10.1063/1.2121687 | s2cid = 9757894 | bibcode = 2005JChPh.123w4505A }}</ref> SPC, [[Water model#Flexible SPC water model|flexible simple point charge water model]] (flexible SPC), ST2, and mW.<ref>{{cite journal | vauthors = Molinero V, Moore EB | title = Water modeled as an intermediate element between carbon and silicon | journal = The Journal of Physical Chemistry B | volume = 113 | issue = 13 | pages = 4008–16 | date = April 2009 | pmid = 18956896 | doi = 10.1021/jp805227c | arxiv = 0809.2811 | s2cid = 20782587 }}</ref> Other solvents and methods of solvent representation are also applied within computational chemistry and physics; these are termed [[solvent model]]s.

=== Modified amino acids ===
*[https://web.archive.org/web/20131203043233/http://selene.princeton.edu/FFPTM/ Forcefield_PTM] – 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.<ref>{{cite journal | vauthors = Khoury GA, Thompson JP, Smadbeck J, Kieslich CA, Floudas CA | title = Ab Initio Charge and AMBER Forcefield Parameters for Frequently Occurring Post-Translational Modifications | journal = Journal of Chemical Theory and Computation | volume = 9 | issue = 12 | pages = 5653–5674 | date = December 2013 | pmid = 24489522 | pmc = 3904396 | doi = 10.1021/ct400556v }}</ref>
*[https://web.archive.org/web/20140106234603/http://selene.princeton.edu/FFNCAA/ Forcefield_NCAA] - An AMBER-based forcefield and webtool for modeling common non-natural amino acids in proteins in condensed-phase simulations using the ff03 charge model.<ref>{{cite journal | vauthors = Khoury GA, Smadbeck J, Tamamis P, Vandris AC, Kieslich CA, Floudas CA | title = 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 | journal = ACS Synthetic Biology | volume = 3 | issue = 12 | pages = 855–69 | date = December 2014 | pmid = 24932669 | pmc = 4277759 | doi = 10.1021/sb400168u }}</ref> The charges have been reported to be correlated with hydration free energies of corresponding side-chain analogs.<ref>{{Cite journal |doi= 10.1016/j.compchemeng.2014.07.017 |title= Hydration free energies calculated using the AMBER ff03 charge model for natural and unnatural amino acids and multiple water models |journal= Computers & Chemical Engineering |volume= 71 |pages= 745–752 |year= 2014 |vauthors = Khoury GA, Bhatia N, Floudas CA }}</ref>

===Other===
* LFMM (Ligand Field Molecular Mechanics)<ref>{{Cite journal |journal=Coordination Chemistry Reviews |volume=212 |doi=10.1016/S0010-8545(00)00354-4 |year=2001 |issue=212 |pages=11–34 |last=Deeth |first=Robert J. | name-list-style = vanc |title= The ligand field molecular mechanics model and the stereoelectronic effects of d and s electrons}}</ref> - 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 [[Tinker (software)|Tinker]]<ref>{{cite journal | vauthors = Foscato M, Deeth RJ, Jensen VR | title = Integration of Ligand Field Molecular Mechanics in Tinker | journal = Journal of Chemical Information and Modeling | volume = 55 | issue = 6 | pages = 1282–90 | date = June 2015 | pmid = 25970002 | doi = 10.1021/acs.jcim.5b00098 | hdl = 1956/10456 | hdl-access = free }}</ref>
* [[VALBOND]] - a function for angle bending that is based on [[valence bond theory]] and works for large angular distortions, [[hypervalent molecule]]s, and [[complex (chemistry)|transition metal complexes]]. It can be incorporated into other force fields such as CHARMM and UFF.

== See also ==
{{columns-list|colwidth=30em|
* [[Comparison of force field implementations]]
* [[Molecular dynamics]]
* [[Molecular mechanics]]
* [[Molecular design software]]
* [[Molecular modelling]]
* [[Comparison of software for molecular mechanics modeling]]
* [[Statistical potential]]
* [[Interatomic potential]]
* [[Bond order potential]]
* [[Embedded atom model]]
}}

== References ==
{{Reflist|30em}}

== Further reading ==
{{refbegin}}
* {{cite book | vauthors = Israelachvili JN |year=1992 |title=Intermolecular and surface forces |publisher=Academic Press |location=San Diego |isbn=978-0-12-375181-2 }}
* {{cite book | vauthors = Schlick T |year=2002 |title=Molecular Modeling and Simulation: An Interdisciplinary Guide |series=Interdisciplinary Applied Mathematics: Mathematical Biology |publisher=Springer-Verlag |location=New York |isbn=978-0-387-95404-2 }}
* {{cite book | vauthors = Warshel A |year=1991 |title=Computer Modeling of Chemical Reactions in Enzymes and Solutions |publisher=John Wiley & Sons |location=New York |isbn=978-0-471-53395-5 }}
{{refend}}

{{Statistical mechanics topics}}

[[Category:Force fields (chemistry)| ]]
[[Category:Intermolecular forces]]
[[Category:Molecular physics]]
[[Category:Molecular modelling]]