# dynamics

### Syntax

dynamics dyn_style energy_min_freq damping_coefficient

• dyn_style = ld or qd or vv

ld is Langevin dynamics
qd is quenched dynamics
vv is Velocity Verlet

• energy_min_freq = positive integer

• damping_coefficient = positive real number

### Examples

dynamics ld 300 1.
dynamics qd 500 5.


### Description

This command sets the style of the dynamic run in CAC simulations.

When dyn_style = ld, the Langevin dynamics is performed, i.e.,

m \ddot{\mathbf{R}} = \mathbf{F} - \gamma m\dot{\mathbf{R}} + \Theta(t)

where $m$ is the normalized lumped mass or the atomic mass, $\mathbf{R}$ is the nodal/atomic position, $\mathbf{F}$ is the equivalent nodal/atomic force, $\gamma$ is the damping_coefficient in ps$^{-1}$, and $t$ is the time in ps. The Velocity Verlet form is employed to solve the equations of motion, as given in Eqs. 1-3 in Xu et al., 2016. The velocity $\dot{\mathbf{R}}$ is updated in langevin_vel.f90.

The ld style is used to keep a constant temperature in CAC simulations by adding to the force $\mathbf{F}$ a time-dependent Gaussian random variable $\Theta(t)$ with zero mean and variance of $\sqrt{2m\gamma k_\mathrm{B} T/\Delta t}$, where $m$ is the atomic mass, $k_\mathrm{B}$ is the Boltzmann constant ($8.6173324\times 10^{-5} \mathrm{eV/K}$), $T$ is the temperature in K, and $\Delta t$ is the time_step in ps. The random variable is calculated and added to the force in langevin_force.f90. Note that when $T = 0$, the equation above reduces to

m \ddot{\mathbf{R}} = \mathbf{F} - \gamma m\dot{\mathbf{R}}

which is the equation of motion in damped molecular dynamics.

When dyn_style = qd, the quenched dynamics is performed, in which

• if the force and velocity point in opposite directions, the velocity is zeroed, i.e.,
\mathrm{if}\ \dot{\mathbf{R}} \cdot \mathbf{F} < 0, \dot{\mathbf{R}} = 0
• otherwise, the velocity is projected along the direction of the force, such that only the component of velocity parallel to the force vector is used, i.e.,
\mathrm{if}\ \dot{\mathbf{R}} \cdot \mathbf{F} \geq 0, \dot{\mathbf{R}} = \frac{(\dot{\mathbf{R}} \cdot \mathbf{F})\mathbf{F}}{|\mathbf{F}|^2}

Note that with the qd style, which was first used in Xu et al., 2016, the temperature is considered 0 K or very nearly so.

When dyn_style = vv, a dynamic simulation following

m \ddot{\mathbf{R}} = \mathbf{F}

is performed using the Velocity Verlet scheme.

Note that the vv style cannot be used to keep a constant temperature and the qd style cannot be used to keep a finite temperature. When boolean = t, if the vv style is chosen and if, for a finite temperature, the qd style is chosen, the user will get a warning message.

The energy_min_freq is the frequency with which the energy minimization is performed during a dynamic run. This is relevant only if simulator_style = hybrid.

run and simulator.

dynamics_init.f90, dynamics.f90, langevin_dynamics.f90, quenched_dynamics.f90, hybrid.f90, among many

### Default

dynamics vv 500 1.