Three Body Potentials

The three-body potentials in DL_POLY_2 are mostly valence angle forms. (They are primarily included to permit simulation of amorphous materials e.g. silicate glasses.) However, these have been extended to include the Dreiding [8] hydrogen bond. The potential forms available are as follows.

1. Truncated harmonic: (thrm)
   

   $$U(\theta_{jik})= {k\over 2} (\theta_{jik} - \theta_0)^2 \exp[-(r_{ij}^8 + r_{ik}^8)/\rho^8];$$ (2.99)

   
   

2. Screened Harmonic: (shrm)
   

   $$U(\theta_{jik})= {k\over 2} (\theta_{jik} - \theta_0)^2 \exp[-(r_{ij}/\rho_1 + r_{ik}/\rho_2)] ;$$ (2.100)

   
   

3. Screened Vessal[24]: (bvs1)
   

   $$U(\theta_{jik}) = {k \over 8(\theta_{jik}-\pi)^2}\left\{ \left[ (\theta_0 -\pi)^2 -(\theta_{jik}-\pi)^2\right]^2 \right\}$$

   $$\exp[-(r_{ij}/\rho_1 + r_{ik}/\rho_2)];$$ (2.101)

   
   

4. Truncated Vessal[25]: (bvs2)
   

   $$U(\theta_{jik}) = k\big[ \theta_{jik}^a (\theta_{jik}-\theta_0)^2 (\theta_{jik}+\theta_0-2\pi)^2 - {a\over 2} \pi^{a-1}$$

   $$(\theta_{jik}-\theta_0)^2(\pi - \theta_0)^3\big] \exp[-(r_{ij}^8 + r_{ik}^8)/\rho^8].$$ (2.102)

   
   

5. Dreiding hydrogen bond [8]: (hbnd
   

   $$U(\theta_{jik})=D_{hb}cos^{4}(\theta_{jik})[5(R_{hb}/r_{jk})^{12}-6(R_{hb}/r_{jk})^{10}]$$ (2.103)

   
   

Note that for the hydrogen bond, the hydrogen atom must be the central atom. Several of these functions are identical to those appearing in the intra-molecular valenceangle descriptions above. There are significant differences in implementation however, arising from the fact that the three-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 three body terms. (The inclusion of pair potentials may in fact be essential to maintain the structure of the system.)

The three body potentials are very short ranged, typically of order 3 $\AA$. This property, plus the fact that three body potentials scale as $N^{3}$, 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 as described in the section valence angle potentials above.

DL_POLY_2 applies no long range corrections to the three body potentials. The three body forces are calculated by the routine THBFRC.