Angle bending

Overview

Angles impose forces on specific triplets of particles to model chemical angles between two bonds. The angles are specified in MST format configuration file with the format:

angle
angle_type(str)  particle_i(int)  particle_j(int)  particle_k(int)
...

By themselves, angles do nothing. Only when an angle force object is instantiated(i.e. force.angle), are angle forces actually calculated.

Angle functions

force.angle
Principle of angle bending

Angle functions

Description:

Function of angle interactions could be either the one called from angle interaction function libary, or the one defined by user himself. Angle interaction function libary contains harmonic function named as ‘harmonic’ and harmonic cosine function named as ‘harmonic_cos’.

Harmonic function (harmonic)
\begin{eqnarray*} V_{\mathrm{angle}}(\theta) = \frac{1}{2}k\left( \theta -\theta_{0} \right)^{2} \end{eqnarray*}

Coefficients:

  • \(k\) - potential constant k (in units of energy/radians^2)

  • \(\theta_{0}\) - equilibrium angle theta0 (in radians)

Note

Angles for the functions in library should be given in script in the unit of degree, and the program will convert them into radian automatically.

Harmonic cosine function (harmonic_cos)
\begin{eqnarray*} V_{\mathrm{angle}}(\theta)=k\left[ 1-\cos \left( \theta - {\theta}_{0} \right) \right] \end{eqnarray*}

Coefficients:

  • \(k\) - potential constant k (in units of energy)

  • \(\theta_{0}\) - equilibrium angle theta0 (in radians)

Note

Angles for the functions in library should be given in script in the unit of degree, and the program will convert them into radian automatically.

class force.angle(info, func)

Constructor of an angle interaction object.

Parameters:

  • info – system information.

  • func – function that is either a string or a device function.

setParams(angle_type, param)

specifies the angle interaction parameters with angle type and a list of parameters.

Example:

fa = pygamd.force.angle(info=mst, func='harmonic')
fa.setParams(angle_type='a-a-a', param=[100.0, 90.0])
app.add(fa)

Self-defined bond functions

Description:

The device function for angle interactions could be written in script and conveyed to kernel funciton for calculation.

With the potential form of angle interactions \(p(\theta)\), the expression of parameters in script are:

  • p = \(p(\theta)\)

  • f = \(\partial p(\theta)/\partial \theta\)

Function code template:

@cuda.jit(device=True)
def func(cos_abc, sin_abc, param, fp):
        p0 = param[0]
        p1 = param[1]
        ...
        calculation codes
        ...
        fp[0]=f
        fp[1]=p

fa = pygamd.force.angle(info, func)
fa.setParams(bond_type, param=[p0, p1, ...])
app.add(fa)

Example:

from numba import cuda
import numba as nb

@cuda.jit(device=True)
def harmonic(cos_abc, sin_abc, param, fp):
        k = param[0]
        t0 = param[1]
        dth = math.acos(cos_abc) - math.pi*t0/180.0
        f = k * dth
        p = nb.float32(0.5) * f * dth
        fp[0]=f
        fp[1]=p

fa = pygamd.force.angle(info=mst, func=harmonic)
fa.setParams(angle_type='a-a-a', param=[400.0, 90.0])#param=[k, t0]
app.add(fa)