Introduction to the DL_POLY_4 Force Field

The force field is the set of functions needed to define the interactions in a molecular system. These may have a wide variety of analytical forms, with some basis in chemical physics, which must be parameterised to give the correct energy and forces. A huge variety of forms is possible and for this reason the DL_POLY_4 force field is designed to be agnostic and adaptable. While it is not supplied with its own force field parameters, many of the functions familiar to GROMOS ¹¹⁹, Dreiding ⁶¹ and AMBER ¹²⁴ users have been coded in the package, as well as less familiar forms. In addition retains the possibility of the user defining additional potentials.

In DL_POLY_4 the total configuration energy of a molecular system may be written as:

(1)\[\begin{split}\begin{aligned} \label{eq:decomp-ene} U(\underline{r}_{1},\underline{r}_{2},\ldots,\underline{r}_{N})=& \sum_{i_{shel}=1}^{N_{shel}} U_{shel}(i_{shel},\underline{r}_{core},\underline{r}_{shell}) \nonumber \\ & + \sum_{i_{teth}=1}^{N_{teth}} U_{teth}(i_{teth},\underline{r}_{i}^{\mathbf{ t}=t},\underline{r}_{i}^{\mathbf{ t}=0}) \nonumber \\ & + \sum_{i_{bond}=1}^{N_{bond}} U_{bond}(i_{bond},\underline{r}_{a},\underline{r}_{b}) \nonumber \\ & + \sum_{i_{angl}=1}^{N_{angl}} U_{angl}(i_{angl},\underline{r}_{a},\underline{r}_{b},\underline{r}_{c}) \nonumber \\ & + \sum_{i_{dihd}=1}^{N_{dihd}} U_{dihd}(i_{dihd},\underline{r}_{a},\underline{r}_{b},\underline{r}_{c},\underline{r}_{d}) \nonumber \\ & + \sum_{i_{inv}=1}^{N_{inv}} U_{inv}(i_{inv},\underline{r}_{a},\underline{r}_{b},\underline{r}_{c},\underline{r}_{d}) \nonumber \\ & + \sum_{i=1}^{N-1}\sum_{j>i}^{N} U_{2\textrm{-}body}^{(metal,vdw,electostatics)}(i,j,|\underline{r}_{i}-\underline{r}_{j}|) \\ & + \sum_{i=1}^{N}\sum_{j{\ne}i}^{N}\sum_{k{\ne}j}^{N} U_{tersoff}(i,j,k,\underline{r}_{i},\underline{r}_{j},\underline{r}_{k}) \nonumber \\ & + \sum_{i=1}^{N-2}\sum_{j>i}^{N-1}\sum_{k>j}^{N} U_{3\textrm{-}body}(i,j,k,\underline{r}_{i},\underline{r}_{j},\underline{r}_{k}) \nonumber \\ & + \sum_{i=1}^{N-3}\sum_{j>i}^{N-2}\sum_{k>j}^{N-1}\sum_{n>k}^{N} U_{4\textrm{-}body}(i,j,k,n,\underline{r}_{i},\underline{r}_{j},\underline{r}_{k},\underline{r}_{n}) \nonumber \\ & + \sum_{i=1}^{N}U_{extn}(i,\underline{r}_{i},\underline{v}_{i})~~,\nonumber\end{aligned}\end{split}\]

where \(U_{shel},~U_{teth},~U_{bond},~U_{angl},~U_{dihd},~U_{inv},~U^{(metal)}_{2\textrm{-}body},~U_{tersoff},~U_{3\textrm{-}body}\) and \(U_{4\textrm{-}body}\) are empirical interaction functions representing ion core-shell polarisation, tethered particles, chemical bonds, valence angles, dihedral (and improper dihedral angles), inversion angles, two-body, Tersoff, three-body and four-body forces respectively. The first six are regarded by DL_POLY_4 as intra-molecular interactions and the next four as inter-molecular interactions. The final term \(U_{extn}\) represents an external field potential. The position vectors \(\underline{r}_{a},\underline{r}_{b},\underline{r}_{c}\) and \(\underline{r}_{d}\) refer to the positions of the atoms specifically involved in a given interaction. (Almost universally, it is the differences in position that determine the interaction.) The numbers \(N_{shel},~N_{teth},~N_{bond},~N_{angl}\), \(N_{dihd}\) and \(N_{inv}\) refer to the total numbers of these respective interactions present in the simulated system, and the indices \(i_{shel},~i_{teth},~i_{bond},~i_{angl},~i_{dihd}\) and \(i_{inv}\) uniquely specify an individual interaction of each type. It is important to note that there is no global specification of the intramolecular interactions in DL_POLY_4- all core-shell units, tethered particles, chemical bonds, valence angles, dihedral angles and inversion angles must be individually cited. The same applies for bond constraints and PMF constraints.

The indices \(i\), \(j\) (and \(k\), \(n\)) appearing in the intermolecular interactions’ (non-bonded) terms indicate the atoms involved in the interaction. There is normally a very large number of these and they are therefore specified globally according to the atom types involved rather than indices. In DL_POLY_4 it is assumed that the “pure” two-body terms arise from short-ranged interactions such as van der Waals interactions (or alternatively DPD soft interactions, coarse-grained interactions, hard-wall nuclear interactions) and electrostatic interactions (coulombic, also regarded as long-ranged). Long-ranged forces require special techniques to evaluate accurately (see Section Long Ranged Electrostatic (coulombic) Potentials). The metal terms are many-body interactions which are functionally presented in an expansion of many two-body contributions augmented by a function of the local density, which again is derived from the two-body spatial distribution (and these are, therefore, evaluated in the two-body routines). In DL_POLY_4 the three-body terms are restricted to valence angle and H-bond forms.

Throughout this chapter the description of the force field assumes the simulated system is described as an assembly of atoms. This is for convenience only, and readers should understand that DL_POLY_4 does recognize molecular entities, defined through constraint bonds and rigid bodies. In the case of rigid bodies, the atomic forces are resolved into molecular forces and torques. These matters are discussed in greater detail in Sections Bond Constraints and Rigid Bodies and Rotational Integration Algorithms.