Time-Dependent

Name MaxwellFunctions
Section Time-Dependent
Type block

This block specifies the shape of a "spatial-dependent function", such as the envelope needed when using the MaxwellFunctions block. Each line in the block specifies one function. The first element of each line will be a string that defines the name of the function. The second element specifies which type of function we are using; in the following we provide an example for each of the possible types:

Options:

• mxf_const_wave:
  %MaxwellFunctions
     "function-name" | mxf_const_wave | kx | ky | kz | x0 | y0 | z0
  %

  The function is constant plane wave $ f(x,y,z) = a0 * \cos( kx*(x-x0) + ky*(y-y0) + kz*(z-z0) ) $

  
  
• mxf_const_phase:
  %MaxwellFunctions
     "function-name" | mxf_const_phase | kx | ky | kz | x0 | y0 | z0
  %

  The function is a constant phase of $ f(x,y,z) = a0 * (kx * x0 + ky * y0 + kz * z0) $

  
  
• mxf_gaussian_wave:
  %MaxwellFunctions
     "function-name" | mxf_gaussian_wave | kx | ky | kz | x0 | y0 | z0 | width
  %

  The function is a Gaussian, $ f(x,y,z) = a0 * \exp( -( kx*(x-x0) + ky*(y-y0) + kz*(z-z0) )^2 / (2 width^2) ) $

  
  
• mxf_cosinoidal_wave:
  %MaxwellFunctions
     "function-name" | mxf_cosinoidal_wave | kx | ky | kz | x0 | y0 | z0 | width
  %

  $ f(x,y,z) = \cos( \frac{\pi}{2} \frac{kx*(x-x0)+ky*(y-y0)+kz*(z-z0)-2 width}{width} + \pi ) $

  If $ | kxx + kyy + kz*z - x0 | > \xi_0 $, then $ f(x,y,z) = 0 $.

  
  
• mxf_logistic_wave:
  %MaxwellFunctions
     "function-name" | mxf_logistic_wave | kx | ky | kz | x0 | y0 | z0 | growth | width
  %

  The function is a logistic function, $ f(x,y,z) = a0 * 1/(1+\exp(growth*(kx*(x-x0)+ky*(y-y0)+kz*(kz*(z-z0))+width/2))) * 1/(1+\exp(-growth*(kx*(x-x0)+ky*(y-y0)+kz*(kz*(z-z0))-width/2))) $

  
  
• mxf_trapezoidal_wave:
  %MaxwellFunctions
     "function-name" | mxf_trapezoidal_wave | kx | ky | kz | x0 | y0 | z0 | growth | width
  %

  The function is a logistic function,
  $ f(x,y,z) = a0 * ( ( 1-growth*(k*(r-r0)-width/2)*\Theta(k*(r-r0)-width/2))*\Theta(-(k*(r-r0)+width/2+1/growth)) $
  $ \qquad \qquad \qquad + (-1+growth*(k*(r-r0)+width/2)*\Theta(k*(r-r0)+width/2))*\Theta(-(k*(r-r0)-width/2+1/growth)) ) $

  
  
• mxf_from_expr:
  %MaxwellFunctions
     "function-name" | mxf_from_expr | "expression"
  %

  The temporal shape of the field is given as an expression (e.g., cos(2.0x-3y+4*z). The letter x, y, z means spatial coordinates, obviously. The expression is used to construct the function f that defines the field.
  

Name MillerIndicesBasis
Section Time-Dependent
Type block

When this block is given, the polarisation of the TDExternalFields is understood to be defined in terms of Miller indices. This block define the corresponding basis, by defining the reduced coordinates of the X, Y, and Z high symmetry points, such that the code can do the corresponding transformation.

For example, in an FCC crystal with the conventional primitive cell, the following input allows to define the polarization in terms of Miller indices

%MillerIndicesBasis
0.0 | 0.5 | 0.5
0.5 | 0.0 | 0.5
0.5 | 0.5 | 0.0
%

Indeed, in this case, the reciprocal lattice vectors are (-1, 1, 1), (1, -1, 1), and (1, 1, -1) in units of 2*pi/a. This directly gives that the [100] direction correspond to the x direction, [111] gives the vector (1,1,1), etc.

Name TDExternalFields
Section Time-Dependent
Type block

The block TDExternalFields describes the type and shape of time-dependent external perturbations that are applied to the system, in the form $f(x,y,z) \cos(\omega t + \phi (t)) g(t)$, where $f(x,y,z)$ is defined by by a field type and polarization or a scalar potential, as below; $\omega$ is defined by omega; $g(t)$ is defined by envelope_function_name; and $\phi(t)$ is the (time-dependent) phase from phase.

These perturbations are only applied for time-dependent runs. If you want the value of the perturbation at time zero to be applied for time-independent runs, use TimeZero = yes.

Each line of the block describes an external field; this way you can actually have more than one laser (e.g. a "pump" and a "probe").

There are two ways to specify $f(x,y,z)$ but both use the same omega | envelope_function_name [| phase] for the time-dependence. The float omega will be the carrier frequency of the pulse (in energy units). The envelope of the field is a time-dependent function whose definition must be given in a TDFunctions block. envelope_function_name is a string (and therefore it must be surrounded by quotation marks) that must match one of the function names given in the first column of the TDFunctions block. phase is optional and is taken to be zero if not provided, and is also a string specifying a time-dependent function.

(A) type = electric field, magnetic field, vector_potential

For these cases, the syntax is:

%TDExternalFields
   type | nx | ny | nz | omega | envelope_function_name | phase
%

The vector_potential option (constant in space) permits us to describe an electric perturbation in the velocity gauge. The three (possibly complex) numbers (nx, ny, nz) mark the polarization direction of the field. By default, (nx, ny, nz) are defined in Cartesian space. However, it is possible for solids to define them using the Miller indices. This can be achieved by defining the block MillerIndicesBasis.

(B) type = scalar_potential

%TDExternalFields
   scalar_potential | "spatial_expression" | omega | envelope_function_name | phase
%

The scalar potential is any expression of the spatial coordinates given by the string "spatial_expression", allowing a field beyond the dipole approximation.

For DFTB runs, only fields of type type = electric field are allowed for the moment, and the type keyword is omitted.

A NOTE ON UNITS:

It is very common to describe the strength of a laser field by its intensity, rather than using the electric-field amplitude. In atomic units (or, more precisely, in any Gaussian system of units), the relationship between instantaneous electric field and intensity is: $ I(t) = \frac{c}{8\pi} E^2(t) $.

It is common to read intensities in W/cm$^2$. The dimensions of intensities are [W]/(L$^2$T), where [W] are the dimensions of energy. The relevant conversion factors are:

Hartree / ($a_0^2$ atomic_time) = $6.4364086 \times 10^{15} \mathrm{W/cm}^2$

eV / ( Å$^2 (\hbar$/eV) ) = $2.4341348 \times 10^{12} \mathrm{W/cm}^2$

If, in atomic units, we set the electric-field amplitude to $E_0$, then the intensity is:

$ I_0 = 3.51 \times 10^{16} \mathrm{W/cm}^2 (E_0^2) $

If, working with Units = ev_angstrom, we set $E_0$, then the intensity is:

$ I_0 = 1.327 \times 10^{13} (E_0^2) \mathrm{W/cm}^2 $

Options:

• electric_field:
  The external field is an electric field, the usual case when we want to describe a laser in the length gauge.
  
• magnetic_field:
  The external field is a (homogeneous) time-dependent magnetic field.
  
• vector_potential:
  The external field is a time-dependent homogeneous vector potential, which may describe a laser field in the velocity gauge.
  
• scalar_potential:
  The external field is an arbitrary scalar potential, which may describe an inhomogeneous electrical field.
  

Name TDFreezeDFTUOccupations
Section Time-Dependent
Type logical
Default no

The occupation matrices than enters in the LDA+U potential are not evolved during the time evolution.

Name TDFreezeHXC
Section Time-Dependent
Type logical
Default no

The electrons are evolved as independent particles feeling the Hartree and exchange-correlation potentials from the ground-state electronic configuration.

Name TDFreezeOrbitals
Section Time-Dependent
Type integer
Default 0

(Experimental) You have the possibility of "freezing" a number of orbitals during a time-propagation. The Hartree and exchange-correlation potential due to these orbitals (which will be the lowest-energy ones) will be added during the propagation, but the orbitals will not be propagated.

Options:

• sae:
  Single-active-electron approximation. This option is only valid for time-dependent calculations (CalculationMode = td). Also, the nuclei should not move. The idea is that all orbitals except the last one are frozen. The orbitals are to be read from a previous ground-state calculation. The active orbital is then treated as independent (whether it contains one electron or two) -- although it will feel the Hartree and exchange-correlation potentials from the ground-state electronic configuration.

  It is almost equivalent to setting TDFreezeOrbitals = N-1, where N is the number of orbitals, but not completely.
  

Name TDFreezeU
Section Time-Dependent
Type logical
Default no

The effective U of LDA+U is not evolved during the time evolution.

Name TDFunctions
Section Time-Dependent
Type block

This block specifies the shape of a "time-dependent function", such as the envelope needed when using the TDExternalFields block. Each line in the block specifies one function. The first element of each line will be a string that defines the name of the function. The second element specifies which type of function we are using; in the following we provide an example for each of the possible types:

Options:

• tdf_cw:
  %TDFunctions
     "function-name" | tdf_cw | amplitude
  %

  The function is just a constant of value amplitude: $ f(t) $ = amplitude

  
  
• tdf_gaussian:
  %TDFunctions
     "function-name" | tdf_gaussian | amplitude | tau0 | t0
  %

  The function is a Gaussian, $ f(t) = F_0 \exp( - (t-t_0)^2/(2\tau_0^2) ) $, where $F_0$ = amplitude.

  
  
• tdf_cosinoidal:
  %TDFunctions
     "function-name" | tdf_cosinoidal | amplitude | tau0 | t0
  %

  $ f(t) = F_0 \cos( \frac{\pi}{2} \frac{t-2\tau_0-t_0}{\tau0} ) $

  If $ | t - t_0 | > \tau_0 $, then $ f(t) = 0 $.

  
  
• tdf_trapezoidal:
  %TDFunctions
     "function-name" | tdf_trapezoidal | amplitude | tau0 | t0 | tau1
  %

  This function is a trapezoidal centered around t0. The shape is determined by tau0 and tau1. The function ramps linearly for tau1 time units, stays constant for tau0 time units, and then decays to zero linearly again for tau1 time units.

  
  
• tdf_from_file:
  %TDFunctions
     "function-name" | tdf_from_file | "filename"
  %

  The temporal shape of the function is contained in a file called filename. This file should contain three columns: first column is time, second and third column are the real part and the imaginary part of the temporal function f(t).

  
  
• tdf_from_expr:
  %TDFunctions
     "function-name" | tdf_from_expr | "expression"
  %

  The temporal shape of the field is given as an expression (e.g., cos(2.0*t). The letter t means time, obviously. The expression is used to construct the function f that defines the field.
  

Name TDGlobalForce
Section Time-Dependent
Type string

If this variable is set, a global time-dependent force will be applied to the ions in the x direction during a time-dependent run. This variable defines the base name of the force, that should be defined in the TDFunctions block. This force does not affect the electrons directly.

Name TDScissor
Section Time-Dependent
Type float
Default 0.0

(experimental) If set, a scissor operator will be applied in the Hamiltonian, shifting the excitation energies by the amount specified. By default, it is not applied.