# External Harmonic Potential Fix¶

## Overview¶

Applies an external potential to a group of atoms to mimic confinement in a harmonic well.

$U_{\text{ext}} = \frac{1}{2} \sum_{d=x,y,z} k_d(r_d - r_{d0})^2,$

where $$\mathbf{k}=(k_x,k_y,k_z), \mathbf{r}_0=(r_{x0},r_{y0},r_{z0})$$ are Vector parameters that must be set to define the harmonic well. As the parameters are vectors, one- and two-dimensional harmonic potentials may be created by setting some of the spring coefficients to zero.

The harmonic potentials are defined directly within the python input script as a Fix using its constructor.

## Constructor¶

FixExternalHarmonic(state,handle,groupHandle,k,r0)


Arguments

state
Simulation state to apply the fix.
handle
A name for the object. Named argument.
groupHandle
Group of atoms to which the fix is applied. Named argument. Defaults to all.
k
Vector of spring constant coefficient for $$k_x,k_y,k_z$$ for strength of confining potential in each dimension. These are specified as Vector(kx,ky,kz).
r0
Vector of minima $$r_{x0},r_{y0},r_{z0}$$ in each dimension for the harmonic potential. These are specified as Vector(rx,ry,rz).

## Examples¶

#Add Fix for external harmonic potential
UextHarm = FixExternalHarmonic(state,handle='Uharm',groupHandle='all',
k = Vector(1.0,0.0,0.5), r0 = Vector(0.0,0.0,1.0))
#Activate fix
state.activateFix(UextHarmt)