Four Body Potentials

The four-body potentials in DL_POLY_2 are entirely inversion angle forms, primarily included to permit simulation of amorphous materials (particularly borate glasses). The potential forms available in DL_POLY_2 are as follows.

1. Harmonic: (harm)
   

   $$U(\phi_{ijkn})= {1\over 2} k (\phi_{ijkn} - \phi_0)^2$$ (2.104)

   
   

2. Harmonic cosine: (hcos)
   

   $$U(\phi_{ijkn})={k\over 2}(cos(\phi_{ijkn}) -cos(\phi_{0}))^{2}$$ (2.105)

   
   

3. Planar potential: (plan)
   

   $$U(\phi_{ijkn})= A [ 1 - \cos (\phi_{ijkn})]$$ (2.106)

   
   

These functions are identical to those appearing in the intra-molecular inversion angle descriptions above. There are significant differences in implementation however, arising from the fact that the four-body potentials are regarded as inter-molecular. Firstly, the atoms involved are defined by atom types, not specific indices. Secondly, there are no excluded atoms arising from the four-body terms. (The inclusion of other potentials, for example pair potentials, may in fact be essential to maintain the structure of the system.)

The four body potentials are very short ranged, typically of order 3 $\AA$. This property, plus the fact that four body potentials scale as $N^{4}$, where $N$ is the number of particles, makes it essential that these terms are calculated by the link-cell method [29].

The calculation of the forces, virial and stress tensor described in the section on inversion angle potentials above.

DL_POLY_2 applies no long range corrections to the four body potentials. The four-body forces are calculated by the routine FBPFRC.