# md.special_pair¶

Overview

 SpecialPair Base class special pair forces. LJ LJ special pair force. Coulomb Coulomb special pair force.

Details

Special pair forces.

Special pair force classes apply a force and virial on every particle in the simulation state commensurate with the potential energy:

$U_\mathrm{special~pairs} = \sum_{(j,k) \in \mathrm{special~pairs}} U_{jk}(r)$

Special pairs are used to implement interactions between designated pairs of particles. They act much like bonds, except that the interaction potential is typically a pair potential, such as LJ.

Each special pair is defined by an ordered pair of particle tags in the hoomd.State member pair_group. HOOMD-blue does not compute special pair groups, users must explicitly define special pairs in the initial condition.

In the special pair group (j,k), $$r$$ is the length of the vector between the particle positions $$r= |\mathrm{minimum\_image}(\vec{r}_k - \vec{r}_j)|$$.

Special pair force classes assign 1/2 of the potential energy to each of the particles in the bond group:

$U_i = \frac{1}{2} \sum_{(j,k) \in \mathrm{special~pairs}} U_{jk}(r) [i=j \lor i=k]$

and similarly for virials.

class hoomd.md.special_pair.Coulomb

Bases: SpecialPair

Coulomb special pair force.

Coulomb computes forces, virials, and energies on all special pairs in the simulation state with:

$\begin{split}U(r) = \begin{cases} \alpha \cdot \left[ \frac{q_{a}q_{b}}{r} \right] & r < r_{\mathrm{cut}} \\ 0 & r \ge r_{\mathrm{cut}} \\ \end{cases}\end{split}$

Note

Use Coulomb to implement special 1-4 interactions in atomistic force fields, such as the scaled 1-4 interactions in OPLS where both the 1-4 LJ and Coulomb interactions are scaled by 0.5.

params

The parameter of the Coulomb forces for each particle type. The dictionary has the following keys:

• alpha (float, required) - Coulomb scaling factor $$[\mathrm{energy}]$$

Type

TypeParameter[special pair type, dict]

r_cut

The cut-off distance for special pair potential $$[\mathrm{length}]$$

Type

TypeParameter[special pair type, float]

Examples:

coulomb = special_pair.Coulomb()
coulomb.params['cluster'] = dict(alpha=1.0)
coulomb.r_cut['cluster'] = 2

class hoomd.md.special_pair.LJ

Bases: SpecialPair

LJ special pair force.

LJ computes forces, virials, and energies on all special pairs in the simulation state with:

$\begin{split}U(r) = \begin{cases} 4 \varepsilon \left[ \left( \frac{\sigma}{r} \right)^{12} - \left( \frac{\sigma}{r} \right)^{6} \right] & r < r_{\mathrm{cut}} \\ 0 & r \ge r_{\mathrm{cut}} \\ \end{cases}\end{split}$

Note

Use LJ to implement special 1-4 interactions in atomistic force fields, such as the scaled 1-4 interactions in OPLS where both the 1-4 LJ and Coulomb interactions are scaled by 0.5.

params

The parameter of the lj forces for each particle type. The dictionary has the following keys:

Type

TypeParameter[special pair type, dict]

r_cut

The cut-off distance for special pair potential $$[\mathrm{length}]$$

Type

TypeParameter[special pair type, float]

Examples:

lj = special_pair.LJ()
lj.params['cluster'] = dict(epsilon=3, sigma=0.5)
lj.r_cut['cluster'] = 5

class hoomd.md.special_pair.SpecialPair

Bases: Force

Base class special pair forces.

SpecialPair is the base class for all special pair forces.

Warning

This class should not be instantiated by users. The class can be used for isinstance or issubclass checks.