Applies a uniform electric field gradient to the system. More...

#include <UniformGradient.hpp>

Inheritance diagram for OpenMD::UniformGradient:

Public Member Functions
	UniformGradient (SimInfo *info)

Additional Inherited Members
Protected Member Functions inherited from OpenMD::ForceModifier
	ForceModifier (SimInfo *info)

Protected Attributes inherited from OpenMD::ForceModifier
SimInfo *	info_ {nullptr}

Detailed Description

Applies a uniform electric field gradient to the system.

The gradient is applied as an external perturbation. The user specifies

uniformGradientStrength = c;

uniformGradientDirection1 = (a1, a2, a3)

uniformGradientDirection2 = (b1, b2, b3);

in the .omd file where the two direction vectors, $a$ and $b$ are unit vectors, and the value of $g$ is in units of $Undefined control sequence \AA$

The electrostatic potential corresponding to this uniform gradient is

$ϕ (r) = - \frac{g}{2} [(a_{1} b_{1} - \frac{\cos ψ}{3}) x^{2} + (a_{1} b_{2} + a_{2} b_{1}) x y + (a_{1} b_{3} + a_{3} b_{1}) x z + + (a_{2} b_{1} + a_{1} b_{2}) y x + (a_{2} b_{2} - \frac{\cos ψ}{3}) y^{2} + (a_{2} b_{3} + a_{3} b_{2}) y z + (a_{3} b_{1} + a_{1} b_{3}) z x + (a_{3} b_{2} + a_{2} b_{3}) z y + (a_{3} b_{3} - \frac{\cos ψ}{3}) z^{2}]$

where $\cos ψ = a \cdot b$ . Note that this potential grows unbounded and is not periodic. For these reasons, care should be taken in using a Uniform Gradient with point charges.

The corresponding field is:

$E = \frac{g}{2} (\begin{matrix} 2 (a_{1} b_{1} - \frac{\cos ψ}{3}) x + (a_{1} b_{2} + a_{2} b_{1}) y + (a_{1} b_{3} + a_{3} b_{1}) z \\ (a_{2} b_{1} + a_{1} b_{2}) x + 2 (a_{2} b_{2} - \frac{\cos ψ}{3}) y + (a_{2} b_{3} + a_{3} b_{2}) z \\ (a_{3} b_{1} + a_{1} b_{3}) x + (a_{3} b_{2} + a_{2} b_{3}) y + 2 (a_{3} b_{3} - \frac{\cos ψ}{3}) z \end{matrix})$

The field also grows unbounded and is not periodic. For these reasons, care should be taken in using a Uniform Gradient with point dipoles.

The corresponding field gradient is:

$\nabla E = \frac{g}{2} (\begin{array}{ccc} 2 (a_{1} b_{1} - \frac{\cos ψ}{3}) & (a_{1} b_{2} + a_{2} b_{1}) & (a_{1} b_{3} + a_{3} b_{1}) \\ (a_{2} b_{1} + a_{1} b_{2}) & 2 (a_{2} b_{2} - \frac{\cos ψ}{3}) & (a_{2} b_{3} + a_{3} b_{2}) \\ (a_{3} b_{1} + a_{1} b_{3}) & (a_{3} b_{2} + a_{2} b_{3}) & 2 (a_{3} b_{3} - \frac{\cos ψ}{3}) \end{array})$

which is uniform everywhere.

The uniform field gradient applies a force on charged atoms, $F = C E (r)$ . For dipolar atoms, the gradient applies both a potential, $U = - D \cdot E (r)$ , a force, $F = D \cdot \nabla E$ , and a torque, $τ = D \times E (r)$ .

For quadrupolar atoms, the uniform field gradient exerts a potential, $U = - Q : \nabla E$ , and a torque $F = 2 Q \times \nabla E$

Definition at line 122 of file UniformGradient.hpp.

Constructor & Destructor Documentation

◆ UniformGradient()

OpenMD::UniformGradient::UniformGradient ( SimInfo * info )

Definition at line 60 of file UniformGradient.cpp.

The documentation for this class was generated from the following files:

perturbations/UniformGradient.hpp
perturbations/UniformGradient.cpp

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ UniformGradient()