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 α (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 nm3 (or 1 Å3). In order to compute the harmonic force constant kcs (where cs stands for core-shell), the following is used 45:

(247)#kcs = qs2α

where qs 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:

(248)#Vpol =kcs2rcs2rcsδ=kcs2rcs2+khyp(rcsδ)4rcs>δ

where δ 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 khyp corresponds to 4108 kcal/mol/nm4, 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:

(249)#Vthole = qiqjrij[1(1+r¯ij2)expr¯ij]

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

(250)#r¯ij = arij(αiαj)1/6

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