# Polarization¶

Polarization can be treated by GROMACS by attaching shell (Drude) particles to atoms and/or virtual sites. The energy of the shell particle is then minimized at each time step in order to remain on the Born-Oppenheimer surface.

## Simple polarization¶

This is implemented as a harmonic potential with equilibrium distance 0. The input given in the topology file is the polarizability \(\alpha\) (in GROMACS units) as follows:

```
[ polarization ]
; Atom i j type alpha
1 2 1 0.001
```

in this case the polarizability volume is 0.001 nm\(^3\) (or 1 Å\(^3\)). In order to compute the harmonic force constant \(k_{cs}\) (where \(cs\) stands for core-shell), the following is used 45:

where \(q_s\) is the charge on the shell particle.

## Anharmonic polarization¶

For the development of the Drude force field by Roux and McKerell 93 it was found that some particles can overpolarize and this was fixed by introducing a higher order term in the polarization energy:

where \(\delta\) is a user-defined constant that is set to 0.02 nm for anions in the Drude force field 94. Since this original introduction it has also been used in other atom types 93.

```
[ polarization ]
;Atom i j type alpha (nm^3) delta khyp
1 2 2 0.001786 0.02 16.736e8
```

The above force constant \(k_{hyp}\) corresponds to 4\(\cdot\)10\(^8\) kcal/mol/nm\(^4\), hence the strange number.

## Water polarization¶

A special potential for water that allows anisotropic polarization of a single shell particle 45.

## Thole polarization¶

Based on early work by Thole 95, Roux and coworkers have implemented potentials for molecules like ethanol 96, 98. Within such molecules, there are intra-molecular interactions between shell particles, however these must be screened because full Coulomb would be too strong. The potential between two shell particles \(i\) and \(j\) is:

**Note** that there is a sign error in Equation 1 of Noskov
*et al.* 98:

where \(a\) is a magic (dimensionless) constant, usually chosen to be 2.6 98; \(\alpha_i\) and \(\alpha_j\) are the polarizabilities of the respective shell particles.