This is an old revision of the document!
Angular Pair Potentials
The way the angular pair potentials are implemented is similar as how it was done for the MEAM potential. The Pair+Angles component is precisely
$$ V=\frac{1}{2}\sum\phi_{ij}(r_{ij})+\frac{1}{2}\sum f_{ij}(r_{ij})f_{ik}(r_{ik})g_i(\cos(\theta_{ijk})) $$
Coulomb interactions are computed the same as in all the others electrostatic models.
With this approach we can consider immediately potentials such as the one used [here](http://www.sciencedirect.com/science/article/pii/S0022309396006047). It will be required only to introduce the special exponentials in eq. (2) in functions.c.
Or we can use it to consider non-bonded angular interactions as DL_POLY does for the three-body terms (see 'tbp' interaction, p. 174 in the [manual](http://goo.gl/3ns4i0) ). This can be achieved defining the f_ij = 1 between the pairs that will form 'triple-bonds' and with their cutoff controlling the central radius to account for angular bonded neighbours. Then, just choosing the _g_ function as an harmonic one.
In addition only for these interactions, I modified the way the threebody neighbours list are created in configs.c, by just adding the neighbours that fall inside the f_ij cutoff radius. This way a lot of memory (and time in _for_ loops) is saved for the systems with several species but angular interactions between only two types of them. And even in the case of having only two species, the angular interactions are usually considered among closest neighbours than the pair interactions, so we benefit of having a smaller angular-neighbours-list in this case also.
I added a couple of new functions also, an harmonic (despite parabola can contain this, I think is useful to have the classic formula), a Born-Mayer function, and an _acos®_ harmonic. The latter, by applying _acos_ to the argument, is useful for defining an angular _g_ function acting on the angle itself.
Number of potential functions
To describe a system of $N$ atom types you need $N(N+2)$ potentials.
| # atom types | $\phi_{ij}$ | $f_{ij}$ | $g_i$ | Total # potentials |
|---|---|---|---|---|
| $N$ | $N(N+1)/2$ | $N(N+1)/2$ | $N$ | $N(N+2)$ |
| 1 | 1 | 1 | 1 | 3 |
| 2 | 3 | 3 | 2 | 8 |
| 3 | 6 | 6 | 3 | 15 |
| 4 | 10 | 10 | 4 | 24 |
Order of potential functions
The potential table is assumed to be symmetric, i.e. the potential for the atom types 1-0 is the same as the potential 0-1.
The order of the potentials in the potential file for $N$ atom types is:
$\phi_{00}, \ldots, \phi_{0N}, \phi_{11}, \ldots, \phi_{1N}, \ldots, \phi_{NN}$
$f_{00}, \ldots, f_{0N}, f_{11}, \ldots, f_{1N}, \ldots, f_{NN}$
$g_0, \ldots, g_N$