G

Name GaugeFieldDelay
Section Hamiltonian
Type float
Default 0.

The application of the gauge field acts as a probe of the system. For dynamical systems one can apply this probe with a delay relative to the start of the simulation.

Name GaugeFieldDynamics
Section Hamiltonian
Type integer
Default polarization

This variable select the dynamics of the gauge field used to apply a finite electric field to periodic systems in time-dependent runs.

Options:

• none:
  The gauge field does not have dynamics. The induced polarization field is zero.
  
• polarization:
  The gauge field follows the dynamic described in Bertsch et al, Phys. Rev. B 62 7998 (2000).
  

Name GaugeFieldPropagate
Section Hamiltonian
Type logical
Default no

Propagate the gauge field with initial condition set by GaugeVectorField or zero if not specified

Name GaugeVectorField
Section Hamiltonian
Type block

The gauge vector field is used to include a uniform (but time-dependent) external electric field in a time-dependent run for a periodic system. An optional second row specifies the initial value for the time derivative of the gauge field (which is set to zero by default). By default this field is not included. If KPointsUseSymmetries = yes, then SymmetryBreakDir must be set in the same direction. This is used with utility oct-dielectric_function according to GF Bertsch, J-I Iwata, A Rubio, and K Yabana, Phys. Rev. B 62, 7998-8002 (2000).

Name GOCenter
Section Calculation Modes::Geometry Optimization
Type logical
Default no

(Experimental) If set to yes, Octopus centers the geometry at every optimization step. It also reduces the degrees of freedom of the optimization by using the translational invariance.

Name GOConstrains
Section Calculation Modes::Geometry Optimization
Type block

If XYZGOConstrains, PDBConstrains, and XSFGOConstrains are not present, Octopus will try to fetch the geometry optimization contrains from this block. If this block is not present, Octopus will not set any constrains. The format of this block can be illustrated by this example:

%GOConstrains
  ‘C’ | 1 | 0 | 0
  ‘O’ |  1 | 0 | 0
%

Coordinates with a constrain value of 0 will be optimized, while coordinates with a constrain different from zero will be kept fixed. So, in this example the x coordinates of both atoms will remain fixed and the distance between the two atoms along the x axis will be constant.

Note: It is important for the constrains to maintain the ordering in which the atoms were defined in the coordinates specifications. Moreover, constrains impose fixed absolute coordinates, therefore constrains are not compatible with GOCenter = yes

Name GOFireIntegrator
Section Calculation Modes::Geometry Optimization
Type integer
Default verlet

The Fire algorithm (GOMethod = fire) uses a molecular dynamics integrator to compute new geometries and velocities. Currently, two integrator schemes can be selected

Options:

• verlet:
  The Velocity Verlet algorithm.
  
• euler:
  The Euler method.
  

Name GOFireMass
Section Calculation Modes::Geometry Optimization
Type float
Default 1.0 amu

The Fire algorithm (GOMethod = fire) assumes that all degrees of freedom are comparable. All the velocities should be on the same scale, which for heteronuclear systems can be roughly achieved by setting all the atom masses equal, to the value specified by this variable. By default the mass of a proton is selected (1 amu). However, a selection of GOFireMass = 0.01 can, in manys systems, speed up the geometry optimization procedure. If GOFireMass <= 0, the masses of each species will be used.

Name GOLineTol
Section Calculation Modes::Geometry Optimization
Type float
Default 0.1

Tolerance for line-minimization. Applies only to GSL methods that use the forces. WARNING: in some weird units.

Name GOMaxIter
Section Calculation Modes::Geometry Optimization
Type integer
Default 200

Even if the convergence criterion is not satisfied, the minimization will stop after this number of iterations.

Name GOMethod
Section Calculation Modes::Geometry Optimization
Type integer
Default fire

Method by which the minimization is performed. For more information see the GSL documentation.

Options:

• steep:
  Simple steepest descent.
  
• steep_native:
  (Experimental) Non-gsl implementation of steepest descent.
  
• cg_fr:
  Fletcher-Reeves conjugate-gradient algorithm. The conjugate-gradient algorithm proceeds as a succession of line minimizations. The sequence of search directions is used to build up an approximation to the curvature of the function in the neighborhood of the minimum.
  
• cg_pr:
  Polak-Ribiere conjugate-gradient algorithm.
  
• cg_bfgs:
  Vector Broyden-Fletcher-Goldfarb-Shanno (BFGS) conjugate-gradient algorithm. It is a quasi-Newton method which builds up an approximation to the second derivatives of the function f using the difference between successive gradient vectors. By combining the first and second derivatives, the algorithm is able to take Newton-type steps towards the function minimum, assuming quadratic behavior in that region.
  
• cg_bfgs2:
  The bfgs2 version of this minimizer is the most efficient version available, and is a faithful implementation of the line minimization scheme described in Fletcher, Practical Methods of Optimization, Algorithms 2.6.2 and 2.6.4.
  
• simplex:
  This is experimental, and in fact, not recommended unless you just want to fool around. It is the Nead-Melder simplex algorithm, as implemented in the GNU Scientific Library (GSL). It does not make use of the gradients (i.e., the forces) which makes it less efficient than other schemes. It is included here for completeness, since it is free.
  
• fire:
  The FIRE algorithm. See also GOFireMass and GOFireIntegrator. Ref: E. Bitzek, P. Koskinen, F. Gahler, M. Moseler, and P. Gumbsch, Phys. Rev. Lett. 97, 170201 (2006).
  

Name GOMinimumMove
Section Calculation Modes::Geometry Optimization
Type float

Convergence criterion, for stopping the minimization. In units of length; minimization is stopped when the coordinates of all species change less than GOMinimumMove, or the GOTolerance criterion is satisfied. If GOMinimumMove < 0, this criterion is ignored. Default is -1, except 0.001 b with GOMethod = simplex. Note that if you use GOMethod = simplex, then you must supply a non-zero GOMinimumMove.

Name GOObjective
Section Calculation Modes::Geometry Optimization
Type integer
Default minimize_energy

This rather esoteric option allows one to choose which objective function to minimize during a geometry minimization. The use of this variable may lead to inconsistencies, so please make sure you know what you are doing.

Options:

• minimize_energy:
  Use the total energy as objective function.
  
• minimize_forces:
  Use $\sqrt{\sum_i \left| f_i \right|^2}$ as objective function. Note that in this case one still uses the forces as the gradient of the objective function. This is, of course, inconsistent, and may lead to very strange behavior.
  

Name GOStep
Section Calculation Modes::Geometry Optimization
Type float

Initial step for the geometry optimizer. The default is 0.5. WARNING: in some weird units. For the FIRE minimizer, default value is 0.1 fs, and corresponds to the initial time-step for the MD.

Name GOTolerance
Section Calculation Modes::Geometry Optimization
Type float
Default 0.001 H/b (0.051 eV/A)

Convergence criterion, for stopping the minimization. In units of force; minimization is stopped when all forces on ions are smaller than this criterion, or the GOMinimumMove is satisfied. If GOTolerance < 0, this criterion is ignored.

Name GuessMagnetDensity
Section SCF::LCAO
Type integer
Default ferromagnetic

The guess density for the SCF cycle is just the sum of all the atomic densities. When performing spin-polarized or non-collinear-spin calculations this option sets the guess magnetization density.

For anti-ferromagnetic configurations, the user_defined option should be used.

Note that if the paramagnetic option is used, the final ground state will also be paramagnetic, but the same is not true for the other options.

Options:

• paramagnetic:
  Magnetization density is zero.
  
• ferromagnetic:
  Magnetization density is the sum of the atomic magnetization densities.
  
• random:
  Each atomic magnetization density is randomly rotated.
  
• user_defined:
  The atomic magnetization densities are rotated so that the magnetization vector has the same direction as a vector provided by the user. In this case, the AtomsMagnetDirection block has to be set.
  

Name GyromagneticRatio
Section Hamiltonian
Type float
Default 2.0023193043768

The gyromagnetic ratio of the electron. This is of course a physical constant, and the default value is the exact one that you should not touch, unless: (i) You want to disconnect the anomalous Zeeman term in the Hamiltonian (then set it to zero; this number only affects that term); (ii) You are using an effective Hamiltonian, as is the case when you calculate a 2D electron gas, in which case you have an effective gyromagnetic factor that depends on the material.