Editing AMBER (section)

=== 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.)