Editing AMBER (section)

== Force field ==
The term ''AMBER [[Force field (chemistry)|force field]]'' generally refers to the functional form used by the family of AMBER force fields. This form includes several parameters; each member of the family of AMBER force fields provides values for these parameters and has its own name.

=== Functional form ===
The functional form of the AMBER force field is<ref name="Cornell1995">{{cite journal |vauthors=Cornell WD, Cieplak P, Bayly CI, Gould IR, ((Merz KM Jr)), Ferguson DM, Spellmeyer DC, Fox T, Caldwell JW, Kollman PA |title=A Second Generation Force Field for the Simulation of Proteins, Nucleic Acids, and Organic Molecules |journal=J. Am. Chem. Soc. |volume=117 |issue=19 |pages=5179–5197 |year=1995 |doi=10.1021/ja00124a002|citeseerx=10.1.1.323.4450 }}</ref>
:<math>
V(r^N)=\sum_{i \in \text{bonds}} {k_b}_i (l_i-l_i^0)^2 + \sum_{i \in \text{angles}} {k_a}_i (\theta_i - \theta_i^0)^2</math>
<blockquote>
<math>+ \sum_{i \in \text{torsions}} \sum_n \frac{1}{2} V_i^n [1+\cos(n \omega_i - \gamma_i)]</math> 
<math>+\sum_{j=1} ^{N-1} \sum_{i=j+1} ^N f_{ij}\biggl\{\epsilon_{ij}\biggl[\left(\frac{r^{0}_{ij}}{r_{ij}} \right)^{12} - 2\left(\frac{r^{0}_{ij}}{r_{ij}} \right)^{6} \biggr]+ \frac{q_iq_j}{4\pi \epsilon_0 r_{ij}}\biggr\}
</math>
</blockquote>
Despite the term ''force field'', this equation defines the potential energy of the system; the force is the derivative of this potential relative to position.

The meanings of right hand side [[term (logic)|term]]s are:
* First term ([[summation|summing]] over bonds): represents the energy between covalently bonded atoms. This harmonic (ideal spring) force is a good approximation near the equilibrium bond length, but becomes increasingly poor as atoms separate.
* Second term (summing over angles): represents the energy due to the geometry of electron orbitals involved in covalent bonding.
* Third term (summing over torsions): represents the energy for twisting a bond due to bond order (e.g., double bonds) and neighboring bonds or lone pairs of electrons. One bond may have more than one of these terms, such that the total torsional energy is expressed as a [[Fourier series]].
* Fourth term (double summation over <math>i</math> and <math>j</math>): represents the non-bonded energy between all atom pairs, which can be decomposed into [[van der Waals force|van der Waals]] (first term of summation) and [[electrostatics|electrostatic]] (second term of summation) energies.

The form of the van der Waals energy is calculated using the equilibrium distance (<math> r^{0}_{ij} </math>) and well depth (<math> \epsilon </math>). The factor of <math>2</math> ensures that the equilibrium distance is <math> r^{0}_{ij} </math>. The energy is sometimes reformulated in terms of <math>\sigma</math>, where <math> r^{0}_{ij} = 2^{1/6}(\sigma)</math>, as used e.g. in the implementation of the softcore potentials.

The form of the electrostatic energy used here assumes that the charges due to the protons and electrons in an atom can be represented by a single point charge (or in the case of parameter sets that employ lone pairs, a small number of point charges.)

=== Parameter sets ===
To use the AMBER force field, it is necessary to have values for the parameters of the force field (e.g. force constants, equilibrium bond lengths and angles, charges). A fairly large number of these parameter sets exist, and are described in detail in the AMBER software user manual. Each parameter set has a name, and provides parameters for certain types of molecules.
*[[Peptide]], [[protein]], and [[nucleic acid]] parameters are provided by parameter sets with names starting with "ff" and containing a two digit year number, for instance "ff99". As of 2018 the primary protein model used by the AMBER suit is the ff14SB<ref>{{Cite journal |doi = 10.1021/acs.jctc.5b00255|pmid = 26574453|pmc = 4821407|title = Ff14SB: Improving the Accuracy of Protein Side Chain and Backbone Parameters from ff99SB|journal = Journal of Chemical Theory and Computation|volume = 11|issue = 8|pages = 3696–3713|year = 2015|last1 = Maier|first1 = James A|last2 = Martinez|first2 = Carmenza|last3 = Kasavajhala|first3 = Koushik|last4 = Wickstrom|first4 = Lauren|last5 = Hauser|first5 = Kevin E|last6 = Simmerling|first6 = Carlos}}</ref><ref>{{Cite web|url=http://ambermd.org/AmberModels.php|title = The Amber Force Fields}}</ref> force field.
* ''General AMBER force field'' (GAFF) provides parameters for small organic molecules to facilitate simulations of drugs and small molecule ligands in conjunction with biomolecules.
*The GLYCAM force fields have been developed by Rob Woods for simulating carbohydrates.
*The primary force field used in the AMBER suit for lipids is lipid14.<ref>{{Cite journal |doi = 10.1021/ct4010307|pmid = 24803855|pmc = 3985482|title = Lipid14: The Amber Lipid Force Field|journal = Journal of Chemical Theory and Computation|volume = 10|issue = 2|pages = 865–879|year = 2014|last1 = Dickson|first1 = Callum J|last2 = Madej|first2 = Benjamin D|last3 = Skjevik|first3 = Åge A|last4 = Betz|first4 = Robin M|last5 = Teigen|first5 = Knut|last6 = Gould|first6 = Ian R|last7 = Walker|first7 = Ross C}}</ref>