Available potentials

This section is a list of all the available potentials in Lumol, with the associated parameters. All potentials have to provide additional parameters in there definition, as a TOML table.

Using inline tables is the easiest way to do so:

# Additional parameters here are 'sigma' and 'epsilon'.
[pairs]
A-B = {type = "lj", sigma = "3 A", epsilon = "123 kJ/mol"}

Another option is to use a separated TOML table, for example when there are too many parameters to fit on a line

[pairs.A-B]
type = "lj"
sigma = "3 A"
epsilon = "123 kJ/mol"

The same potential can be used for either pairs (at distance \(r\)); or for angles (at angle \(\phi\)). In all the formulas, the \(x\) parameter represents either a distance or an angle.

Null potential

This potential is always 0, for all values of \(x\). It should be used to remove interactions between atoms in a pair/bond/angle/dihedral that are present in the system but should not be interacting.

This potential can be used by specifying the null key with an empty table {} as value.

[pairs]
O-O = {type = "null", }

Lennard-Jones potential

The Lennard-Jones potential is a classical potential for pair interactions expressed as:

\[ V(x) = 4 \epsilon \left[\left(\frac{\sigma}{x}\right)^{12} - \left(\frac{\sigma}{x}\right)^6\right].\]

The Lennard-Jones potential is defined using the lj key. The parameters are sigma (\(\sigma\)) and epsilon (\(\epsilon\)), which should be provided as strings.

[pairs]
O-O = {type = "lj", sigma = "3.16 A", epsilon = "0.155 kcal/mol"}

Buckingham potential

The Buckingham potential is a potential for pair interactions expressed as:

\[V(x) = A \exp(-r / \rho) - \frac{C}{r^6}.\]

The potential type keyword is buckingham, and the parameters A, rho (\(\rho\)) and C should be provided as strings.

[pairs]
C-C = {type = "buckingham", A = "40 kJ/mol", C = "120e-6 kJ/mol/A^6", rho = "3.0 A"}

Born-Mayer-Huggins potential

The Born-Mayer-Huggins potential is a potential for pair interactions, used in particular for halide alkali. Its expression is:

\[ V(x) = A \exp\left(\frac{\sigma -r}{\rho}\right) - \frac{C}{r^6} + \frac{D}{r^8}.\]

The potential type keyword is born, and the parameters A, C, D, sigma (\(\sigma\)) and rho (\(\rho\)) should be provided as strings.

[pairs.Li-Li]
type = "born"
A = "40 kJ/mol"
C = "120e-6 kJ/mol/A^6"
D = "23e-6 kJ/mol/A^8"
rho = "3.0 A"
sigma = "2.2 A"

Harmonic potential

The Harmonic potential is usually used for intramolecular interactions such as bonds, angles or dihedrals. It is expressed as:

\[V(x) = \frac 12 k \ (x - x_0)^2\]

The potential type keyword is harmonic, and the parameters are k and x0, provided as strings.

[bonds]
O-H = {type = "harmonic", k = "1054.2 kcal/mol/A^2", x0 = "1.0 A"}

[angles]
H-O-H = {type = "harmonic", k = "75.9 kcal/mol/rad^2", x0 = "109.5 deg"}

Cosine-Harmonic potential

This potential is usually used for angles and dihedral angles interactions, because it presents a \(2\pi\) periodicity. It is expressed as:

\[ V(x) = \frac 12 k \ (\cos x - \cos x_0)^2\]

The potential type keyword is cosine-harmonic, and the parameters k and x0 should be provided as strings.

[angles]
H-C-H = {type = "cosine-harmonic", k = "67 kJ/mol", x0 = "120 deg"}

Torsion potential

This potential is usually used for dihedral interactions. It is expressed as:

\[V(x) = k \ (1 + \cos(n x - \delta))\]

The potential type keyword is torsion, and the parameters k and delta (\(\delta\)) should be provided as strings, and n should be provided as an integer.

[dihedrals]
C-C-C-C = {type = "torsion", k = "40 kJ/mol", delta = "120 deg", n: 4}

Morse potential

This potential is usually used for intramolecular interaction such as bonds, angles or dihedrals. It is a better approximation for the vibrational structure of the molecule than the Harmonic potential. It is expressed as:

\[V(x) = \text{depth} \times (1 - \exp(- A (x - x_0))^2\]

The potential type keyword is morse, and the parameters A, x0 and depth should be provided as strings.

[pairs]
A-B = {type = "morse", depth = "40 kJ/mol", A = "2.0 A^-1", x0 = "1.3 A"}

For angles and dihedral angles, x0 and A should be provided in angle units:

[pairs]
A-B = {type = "morse", depth = "40 kJ/mol", A = "2.0 rad^-1", x0 = "109.7 deg"}

Gaussian potential

This potential is usually used to describe energy wells and is expressed as:

\[V(r) = -A \exp(-B r^2)\]

The potential type keyword is gaussian, and the parameters A (well depth) and B (well width) should be provided as strings. B has to be positive.

[pairs]
A-B = {type = "gaussian", A = "8.0 kJ/mol", B = "0.2 A^-2"}

Mie potential

The Mie potential is a classical potential for pair interactions expressed as:

\[V(r) = \frac{n}{n-m} \left(\frac{n}{m}\right)^{m/(n-m)}\epsilon \left[ \left( \frac{\sigma}{r}\right)^n - \left( \frac{\sigma}{r}\right)^m \right]\]

The potential type keyword is mie and the parameters are sigma (\(\sigma\)), the particle diameter, and epsilon (\(\epsilon\)), the energetic parameter, which should be provided as strings (with units). The repulsive exponent n and the attractive exponent m should be provided as numbers. The repulsive exponent n has to be larger than the attractive exponent m.

[pairs]
A-B = {type = "mie", sigma = "3 A", epsilon = "5.9 kJ/mol", n = 12.0, m = 6.0}