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Bond Potentials

 

The interatomic bond vector.

The bond potentials describe explicit bonds between specified atoms. They are functions of the interatomic distance only. The potential functions available are as follows.

1. Harmonic bond: (harm)
   

   $$U(r_{ij})=\frac{1}{2}k(r_{ij}-r_{o})^2;$$ (2.2)

   
   
2. Morse potential: (mors)
   

   $$U(r_{ij})=E_{o}[\{1-\exp(-k(r_{ij}-r_{o}))\}^{2}-1];$$ (2.3)

   
   
3. 12-6 potential bond: (12-6)
   

   $$U(r_{ij})=\left(\frac{A}{r_{ij}^{12}}\right)-\left(\frac{B}{r_{ij}^{6}}\right);$$ (2.4)

   
   
4. Restrained harmonic: (rhrm)
   

   $$U(r_{ij}) = \frac{1}{2}k(r_{ij}-r_{o})^2~~~~~~\vert r_{ij}-r_{o}\vert\le r_{c};$$ (2.5)

   $$U(r_{ij}) = \frac{1}{2}kr_{c}^2+kr_{c}(\vert r_{ij}-r_{o}\vert-r_{c})~~~~~~\vert r_{ij}-r_{o}\vert> r_{c};$$ (2.6)

   
   

5. Quartic potential: (quar)
   

   $$U(r_{ij})=\frac{k}{2}(r_{ij}-r_{o})^2+\frac{k'}{3}(r_{ij}-r_{o})^3+\frac{k''}{4}(r_{ij}-r_{o})^4.$$ (2.7)

   
   

In these formulae $r_{ij}$ is the distance between atoms labelled $i$ and $j$:

$$r_{ij}=\vert\mbox{$\underline{r}$}_{j}-\mbox{$\underline{r}$}_{i}\vert,$$ (2.8)

where $\mbox{$\underline{r}$}_{\ell}$ is the position vector of an atom labelled $\ell$. ^2.1

The force on the atom $j$ arising from a bond potential is obtained using the general formula:

$$\mbox{$\underline{f}$}_{j}=-\frac{1}{{r}_{ij}}\left[ \frac{\... ...}{\partial r_{ij}}U(r_{ij})\right]\mbox{$\underline{r}$}_{ij},$$ (2.9)

The force $\mbox{$\underline{f}$}_{i}$ acting on atom $i$ is the negative of this.

The contribution to be added to the atomic virial is given by

$${\cal W}=-\mbox{$\underline{r}$}_{ij}\cdot \mbox{$\underline{f}$}_{j},$$ (2.10)

with only one such contribution from each bond.

The contribution to be added to the atomic stress tensor is given by

$$\sigma^{\alpha \beta}=r_{ij}^{\alpha}f_{j}^{\beta},$$ (2.11)

where $\alpha$ and $\beta$ indicate the $x,y,z$ components. The atomic stress tensor derived in this way is symmetric.

In DL_POLY_2 bond forces are handled by the routine BNDFRC.

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