# Other built-in calculators¶

## TIP3P¶

class ase.calculators.tip3p.TIP3P(rc=5.0, width=1.0)[source]

TIP3P potential.

rc: float

width: float

Width for cutoff function for Coulomb part.

## TIP4P¶

class ase.calculators.tip4p.TIP4P(rc=7.0, width=1.0)[source]

TIP4P potential for water.

https://doi.org/10.1063/1.445869

Requires an atoms object of OHH,OHH, … sequence Correct TIP4P charges and LJ parameters set automatically.

Virtual interaction sites implemented in the following scheme: Original atoms object has no virtual sites. When energy/forces are requested:

• virtual sites added to temporary xatoms object

• energy / forces calculated

• forces redistributed from virtual sites to actual atoms object

This means you do not get into trouble when propagating your system with MD while having to skip / account for massless virtual sites.

This also means that if using for QM/MM MD with GPAW, the EmbedTIP4P class must be used.

## Lennard-Jones¶

class ase.calculators.lj.LennardJones(**kwargs)[source]

Lennard Jones potential calculator

The fundamental definition of this potential is a pairwise energy:

u_ij = 4 epsilon ( sigma^12/r_ij^12 - sigma^6/r_ij^6 )

For convenience, we’ll use d_ij to refer to “distance vector” and r_ij to refer to “scalar distance”. So, with position vectors $$r_i$$:

r_ij = | r_j - r_i | = | d_ij |

The derivative of u_ij is:

d u_ij / d r_ij
= (-24 epsilon / r_ij) ( sigma^12/r_ij^12 - sigma^6/r_ij^6 )


We can define a pairwise force

f_ij = d u_ij / d d_ij = d u_ij / d r_ij * d_ij / r_ij

The terms in front of d_ij are often combined into a “general derivative”

du_ij = (d u_ij / d d_ij) / r_ij

The force on an atom is:

f_i = sum_(j != i) f_ij

There is some freedom of choice in assigning atomic energies, i.e. choosing a way to partition the total energy into atomic contributions.

We choose a symmetric approach:

u_i = 1/2 sum_(j != i) u_ij

The total energy of a system of atoms is then:

u = sum_i u_i = 1/2 sum_(i, j != i) u_ij

The stress can be written as ( $$(x)$$ denoting outer product):

sigma = 1/2 sum_(i, j != i) f_ij (x) d_ij = sum_i sigma_i , with atomic contributions

sigma_i  = 1/2 sum_(j != i) f_ij (x) d_ij

Implementation note:

For computational efficiency, we minimise the number of pairwise evaluations, so we iterate once over all the atoms, and use NeighbourList with bothways=False. In terms of the equations, we therefore effectively restrict the sum over $$i != j$$ to $$j > i$$, and need to manually re-add the “missing” $$j < i$$ contributions.

Another consideration is the cutoff. We have to ensure that the potential goes to zero smoothly as an atom moves across the cutoff threshold, otherwise the potential is not continuous. In cases where the cutoff is so large that u_ij is very small at the cutoff this is automatically ensured, but in general, $$u_ij(rc) != 0$$.

In order to catch this case, this implementation shifts the total energy

u'_ij = u_ij - u_ij(rc)

which ensures that it is precisely zero at the cutoff. However, this means that the energy effectively depends on the cutoff, which might lead to unexpected results!

Parameters
• sigma (float) – The potential minimum is at 2**(1/6) * sigma, default 1.0

• epsilon (float) – The potential depth, default 1.0

• rc (float, None) – Cut-off for the NeighborList is set to 3 * sigma if None. The energy is upshifted to be continuous at rc. Default None

## Morse¶

class ase.calculators.morse.MorsePotential(**kwargs)[source]

Morse potential.

Default values chosen to be similar as Lennard-Jones.

Parameters
• epsilon (float) – Absolute minimum depth, default 1.0

• r0 (float) – Minimum distance, default 1.0

• rho0 (float) – Exponential prefactor. The force constant in the potential minimum is k = 2 * epsilon * (rho0 / r0)**2, default 6.0