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
in the .omd file where the two direction vectors, \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, and the value of \( g \) is in units of \( V / \AA^2 \)
The electrostatic potential corresponding to this uniform gradient is
\( \phi(\mathbf{r}) = - \frac{g}{2} \left[ \left(a_1 b_1 - \frac{\cos\psi}{3}\right) x^2 + (a_1 b_2 + a_2 b_1) x y + (a_1 b_3 + a_3 b_1) x z + + (a_2 b_1 + a_1 b_2) y x + \left(a_2 b_2 - \frac{\cos\psi}{3}\right) y^2 + (a_2 b_3 + a_3 b_2) y z + (a_3 b_1 + a_1 b_3) z x + (a_3 b_2 + a_2 b_3) z y + \left(a_3 b_3 - \frac{\cos\psi}{3}\right) z^2 \right] \)
where \( \cos \psi = \mathbf{a} \cdot \mathbf{b} \). 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:
\( \mathbf{E} = \frac{g}{2} \left( \begin{array}{c} 2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) x + (a_1 b_2 + a_2 b_1) y + (a_1 b_3 + a_3 b_1) z \\ (a_2 b_1 + a_1 b_2) x + 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) y + (a_2 b_3 + a_3 b_2) z \\ (a_3 b_1 + a_1 b_3) x + (a_3 b_2 + a_2 b_3) y + 2 \left(a_3 b_3 - \frac{\cos\psi}{3}\right) z \end{array} \right) \)
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:
\( \nabla \mathbf{E} = \frac{g}{2} \left( \begin{array}{ccc} 2\left(a_1 b_1 - \frac{\cos\psi}{3}\right) & (a_1 b_2 + a_2 b_1) & (a_1 b_3 + a_3 b_1) \\ (a_2 b_1 + a_1 b_2) & 2 \left(a_2 b_2 - \frac{\cos\psi}{3}\right) & (a_2 b_3 + a_3 b_2) \\ (a_3 b_1 + a_1 b_3) & (a_3 b_2 + a_2 b_3) & 2 \left(a_3 b_3 - \frac{\cos\psi}{3}\right) \end{array} \right) \)
which is uniform everywhere.
The uniform field gradient applies a force on charged atoms, \( \mathbf{F} = C \mathbf{E}(\mathbf{r}) \). For dipolar atoms, the gradient applies both a potential, \( U = -\mathbf{D} \cdot \mathbf{E}(\mathbf{r}) \), a force, \( \mathbf{F} = \mathbf{D} \cdot \nabla \mathbf{E} \), and a torque, \( \mathbf{\tau} = \mathbf{D} \times \mathbf{E}(\mathbf{r}) \).
For quadrupolar atoms, the uniform field gradient exerts a potential, \( U = - \mathsf{Q}:\nabla \mathbf{E} \), and a torque \( \mathbf{F} = 2 \mathsf{Q} \times \nabla \mathbf{E} \)
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
