Force field (chemistry)

In the context of molecular modelling, a force field (a special case of energy functions or interatomic potentials; not to be confused with force field in classical physics) refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics and molecular dynamics simulations. The parameters of the energy functions may be derived from experiments in physics or chemistry, calculations in quantum mechanics, or both. In the context of molecular modelling, a force field (a special case of energy functions or interatomic potentials; not to be confused with force field in classical physics) refers to the functional form and parameter sets used to calculate the potential energy of a system of atoms or coarse-grained particles in molecular mechanics and molecular dynamics simulations. The parameters of the energy functions may be derived from experiments in physics or chemistry, calculations in quantum mechanics, or both. All-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 each methyl group (terminal methyl) and each methylene bridge as one interaction center. Coarse-grained potentials, which are often used in long-time simulations of macromolecules such as proteins, nucleic acids, and multi-component complexes, provide even cruder representations for higher computing efficiency. The basic functional form of potential energy in molecular mechanics includes bonded terms for interactions of atoms that are linked by covalent bonds, and nonbonded (also termed noncovalent) terms that describe the long-range electrostatic and van der Waals forces. The specific decomposition of the terms depends on the force field, but a general form for the total energy in an additive force field can be written as   E total = E bonded + E nonbonded {displaystyle E_{ ext{total}}=E_{ ext{bonded}}+E_{ ext{nonbonded}}} where the components of the covalent and noncovalent contributions are given by the following summations:   E bonded = E bond + E angle + E dihedral {displaystyle E_{ ext{bonded}}=E_{ ext{bond}}+E_{ ext{angle}}+E_{ ext{dihedral}}}   E nonbonded = E electrostatic + E van der Waals {displaystyle E_{ ext{nonbonded}}=E_{ ext{electrostatic}}+E_{ ext{van der Waals}}} 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 highly variable. Additional, 'improper torsional' terms may be added to enforce the planarity of aromatic rings and other conjugated systems, and 'cross-terms' that describe coupling of different internal variables, such as angles and bond lengths. Some force fields also include explicit terms for hydrogen bonds. The nonbonded terms are most computationally intensive. A popular choice is to limit interactions to pairwise energies. The van der Waals term is usually computed with a Lennard-Jones potential and the electrostatic term with Coulomb's law, although both can be buffered or scaled by a constant factor to account for electronic polarizability. As it is rare for bonds to deviate significantly from their reference values the Morse potential is seldom employed for molecular mechanics due to it not being efficient to compute. The most simplistic approaches utilize a Hooke's law formula: v ( l ) = k 2 ( l − l 0 ) 2 {displaystyle v(l)={frac {k}{2}}(l-l_{0})^{2}}