- Actions

- Updating

- Minimization

- Dynamics
- thermostat = none
- andersen_coupling = 0.1
- nose_hoover_coupling = 1
- start_temperature = 0
- end_temperature = 0
- dt = 0.005
- electron_mass = 1
- adaptive_step_size = false
- adaptive_energy = 0.0001

- Electric field

- Electron size limit

- Output
- output_position = all
- output_velocity = all
- output_energy_forces = none
- output_restart = all
- output_restraints = all

- Random numbers

- Ewald parameters
- ewald_re_cutoff = 3.54
- ewald_autoset = true
- ewald_log_precision = -6
- ewald_max_re = 4.5
- ewald_r_cutoff = 7
- ewald_k_cutoff = 8
- ewald_nuc_r = 1e-10

- Periodic boundary conditions

- Pairwise cutoff

**Minimize** varies the nuclear and electron coordinates to minimize the total energy of the system, using gradient descent algorithms that find the nearest local minimum. See also **min**, which specifies the kind of descent algorithm to use, **min_freeze**, which permits the freezing of nuclei or electrons during minimization, and **num_steps** and **print_every**. Constraints and restraints are also applicable during minimization.

**Dynamics** propagates the nuclear and electron coordinates via semiclassical Ehrenfest dynamics using a velocity Verlet algorithm, making it possible to explore the quantum dynamics of excited systems. See also **dt** for specifying the time step; **thermostat**, **start_temperature**, and **end_temperature** for performing NVT dynamics; **electron_mass** for setting the dynamic electron mass; and **num_steps** and **print_every**. Constraints and restraints are also applicable during dynamics.

Dynamics

The Andersen thermostat uses a stochastic method to create the correct ensemble of velocities. At each time step, a particle has a chance, related to the parameter **andersen_coupling**, of having its velocity reset to a vector picked out of a Maxwell-Boltzmann distribution at the desired temperature. This simulates random collisions with an external heat bath.

The Nose-Hoover thermostat is a deterministic method where the particles are slowed down or sped up by a velocity dependent force. The force is proportional to the difference between the system's instantaneous temperature and the desired temperature, and also to the coupling parameter **nose_hoover_coupling**. This method is derived from an extended Lagrangian which contains an extra degree of freedom corresponding to the external heat reservoir.

If is too low, the thermostat is inefficient, but if is too high, random collisions dominate and the dynamics is destroyed.

Thus acts as a drag force on the particles, or equivalently a time-rescaling factor, while Q determines the response of to the difference between the actual and desired system temperature.

If Q is too large, the thermostat is inefficient, but if Q is too small, the temperature will oscillate too much, and the momentum fluctuations will not couple properly to the heat bath.

When the Andersen or Nosé-Hoover thermostats are selected, also sets the target temperature for the thermostat.

The minimum time step is determined by the fastest oscillations in the system, usually the vibrations of the core electrons surrounding the heaviest nuclei. Typically time steps of **0.01** to **0.02 fs** are reasonable, but for studying Auger processes, a very short time step of **0.001 fs** is needed. It is possible to freeze core electrons relative to nuclei by specifying a **tether** in the **@restraints** section, which makes longer time steps possible.

When the wave packet is in a harmonic potential, should be the true mass of the electron, 1/1822.89 amu = 0.000548579 amu.

In more complex potentials, however, the dynamic electron mass may be much higher. It can be estimated in semiconductors using band theory, or in metals using many-body theory. In eFF, is a fixed parameter that we set to reproduce some characteristic known time-scale of electron motion in the system we are studying. In general, the time step of the dynamics should be scaled to .

A large may be used to simulate adiabatic ground-state potentials, as in Car-Parinello dynamics. In some special cases, such as the motion of electrons near a core-hole, we have found it necessary to use a large to reproduce experimental core-hole lifetimes. Smaller on the order of the true electron mass is appropriate for studying the response of molecules to high electric fields, proton stopping in solids, and Auger ionization.

The dynamic electron mass is separate from the electron mass present in the kinetic energy term in Schrödinger's equation, and changing does not affect electron sizes or bonding in the ground state.

Output

Random numbers

Ewald parameters

The cutoffs are set by the program to minimize CPU time, assuming a certain ratio of computational expense between real space and reciprocal space sums. The formulas are

where (

If either **ewald_r_cutoff** or **ewald_k_cutoff** are set manually, the program assumes the user wishes to override the automatic settings, and the autoset feature is turned off.

Periodic boundary conditions

For case (1), **periodic = true** computes electrostatics using an Ewald sum, which uses a combined real and reciprocal space sum to efficiently sum periodic replicas. Pauli repulsion interactions are shorter range and are summed using a minimum image convention. When this option is used, the pairwise cutoff splines are turned off, and the parameter **taper_cutoff** has no effect.

For case (2), the periodic options starting with **minimage_** compute both electrostatic interactions and Pauli repulsion using a minimum image convention. For this method to be valid, the pairwise cutoff **taper_cutoff** must be smaller than
, where
is the minimum dimension of the rectangular unit cell. 1D and 2D and 3D periodic bounds can be treated in this way. For example, **periodic = minimage_xy** creates a system that is periodic in the and directions.

bound_x = -10000 10000

bound_y = -10000 10000

bound_z = -10000 10000

Pairwise cutoff

The function is the seventh-order spline

A
of 20 bohr is considered an aggressive cutoff with probable errors of 2 kcal/mol/atom, while 50 bohr is a mild cutoff with probable errors on the order of kcal/mol/atom.
If **taper_cutoff** is larger than half of the smallest box dimension, and minimum image periodic boundaries are applied, the program will terminate with an error.