Appendix B: DL_POLY_4 Boundary Conditions

Introduction

DL_POLY_4 is designed to accommodate a number of different periodic boundary conditions, which are defined by the shape and size of the simulation cell. Briefly, these are as follows (which also indicates the IMCON flag defining the simulation cell type in the CONFIG file - see Section The CONFIG File):

  1. None e.g. isolated polymer in space (imcon \(=0\))

  2. Cubic periodic boundaries (imcon \(=1\))

  3. Orthorhombic periodic boundaries (imcon \(=2\))

  4. Parallelepiped periodic boundaries (imcon \(=3\))

  5. Slab (X,Y periodic; Z non-periodic) (imcon \(=6\))

We shall now look at each of these in more detail. Note that in all cases the cell vectors and the positions of the atoms in the cell are to be specified in Angstroms (Å).

No periodic boundary (\(\texttt{imcon}~=~0\))

Simulations requiring no periodic boundaries are best suited to in vacuuo simulations, such as the conformational study of an isolated polymer molecule. This boundary condition is not recommended for studies in a solvent, since evaporation is likely to be a problem.

Note this boundary condition have to be used with caution. DL_POLY_4 is not naturally suited to carry out efficient calculations on systems with great fluctuation of the local density in space, as is the case for clusters in vacuum. The parallelisation and domain decomposition is therefore limited to eight domains (maximum of two in each direction in space).

This boundary condition should not used with the SPM Ewald summation method.

Cubic periodic boundaries (\(\texttt{imcon}~=~1\))

The cubic MD cell

Fig. 16 The cubic MD cell

The cubic MD cell is perhaps the most commonly used in simulation and has the advantage of great simplicity. In DL_POLY_4 the cell is defined with the principle axes passing through the centres of the faces. Thus for a cube with sidelength D, the cell vectors appearing in the CONFIG file should be: (D,0,0); (0,D,0); (0,0,D). Note the origin of the atomic coordinates is the centre of the cell.

Orthorhombic periodic boundaries (\(\texttt{imcon}~=~2\))

The orthorhomic MD cell

Fig. 17 The orthorhomic MD cell

The orthorhombic cell is also a common periodic boundary, which closely resembles the cubic cell in use. In DL_POLY_4 the cell is defined with principle axes passing through the centres of the faces. For an orthorhombic cell with sidelengths D (in X-direction), E (in Y-direction) and F (in Z-direction), the cell vectors appearing in the CONFIG file should be: (D,0,0); (0,E,0); (0,0,F). Note the origin of the atomic coordinates is the centre of the cell.

Parallelepiped periodic boundaries (\(\texttt{imcon}~=~3\))

The parallelepiped MD cell

Fig. 18 The parallelepiped MD cell

The parallelepiped (e.g. monoclinic or triclinic) cell is generally used in simulations of crystalline materials, where its shape and dimension is commensurate with the unit cell of the crystal. Thus for a unit cell specified by three principal vectors \(\underline{a}\), \(\underline{b}\), \(\underline{c}\), the MD cell is defined in the DL_POLY_4 CONFIG file by the vectors (L\(a_{1}\),L\(a_{2}\),L\(a_{3}\)), (M\(b_{1}\),M\(b_{2}\),M\(b_{3}\)), (N\(c_{1}\),N\(c_{2}\),N\(c_{3}\)), in which L,M,N are integers, reflecting the multiplication of the unit cell in each principal direction. Note that the atomic coordinate origin is the centre of the MD cell.

Slab boundary conditions (\(\texttt{imcon}~=~6\))

Slab boundaries are periodic in the X- and Y-directions, but not in the Z-direction. They are particularly useful for simulating surfaces. The periodic cell in the XY plane can be any parallelogram. The origin of the X,Y atomic coordinates lies on an axis perpendicular to the centre of the parallelogram. The origin of the Z coordinate is where the user specifies it. However, it is recommended that it is in the middle of the slab. Domain decomposition division across Z axis is limited to \(2\).

If the XY parallelogram is defined by vectors \(\underline{A}\) and \(\underline{B}\), the vectors required in the CONFIG file are: (A\(_{1}\),A\(_{2}\),0), (B\(_{1}\),B\(_{2}\),0), (0,0,D), where D is any real number (including zero). If D is nonzero, it will be used by DL_POLY to help determine a ‘working volume’ for the system. This is needed to help calculate RDFs etc. (The working value of D is in fact taken as one of: 3\(\times\)cutoff; or 2\(\times\)max abs(Z coordinate)+cutoff; or the user specified D, whichever is the larger.)

The surface in a system with charges can also be modelled with if periodicity is allowed in the Z-direction. In this case slabs of ions well-separated by vacuum zones in the Z-direction can be handled with imcon = 1, 2 or 3.