Hamiltonian

CalculateSelfInducedMagneticField
Section: Hamiltonian
Type: logical
Default: no

The existence of an electronic current implies the creation of a self-induced magnetic field, which may in turn back-react on the system. Of course, a fully consistent treatment of this kind of effect should be done in QED theory, but we will attempt a first approximation to the problem by considering the lowest-order relativistic terms plugged into the normal Hamiltonian equations (spin-other-orbit coupling terms, etc.). For the moment being, none of this is done, but a first step is taken by calculating the induced magnetic field of a system that has a current, by considering the magnetostatic approximation and Biot-Savart law:

\nabla^2 \vec{A} + 4\pi\alpha \vec{J} = 0

\vec{B} = \vec{\nabla} \times \vec{A}

If CalculateSelfInducedMagneticField is set to yes, this B field is calculated at the end of a gs calculation (nothing is done -- yet -- in the tdcase) and printed out, if the Output variable contains the potential keyword (the prefix of the output files is Bind).


ClassicalPotential
Section: Hamiltonian
Type: integer

Whether and how to add to the external potential the potential generated by the classical charges read from the PDB input (see PBDCoordinates).
Options:


ComplexScaling
Section: Hamiltonian
Type: logical
Default: false

(experimental) If set to yes, a complex scaled Hamiltonian will be used. When TheoryLevel=DFT Density functional resonance theory DFRT is employed. In order to reveal resonances ComplexScalingAngle bigger than zero should be set. D. L. Whitenack and A. Wasserman, Phys. Rev. Lett. 107, 163002 (2011).


ComplexScalingAngle
Section: Hamiltonian
Type: float
Default: 0.3

The complex scaling parameter theta in DFRT. It should be bound to 0 <= theta < pi/4.


FilterPotentials
Section: Hamiltonian
Type: integer
Default: filter_none

Octopus can filter the pseudopotentials so that they no longer contain Fourier components larger than the mesh itself. This is very useful to decrease the egg-box effect, and so should be used in all instances where atoms move (e.g. geometry optimization, molecular dynamics, and vibrational modes).
Options:


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. 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).


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.


IgnoreExternalIons
Section: Hamiltonian
Type: logical
Default: no

If this variable is set to "yes", then the ions that are outside the simulation box do not feel any external force (and therefore progress at constant velocity), and do not originate any force on other ions, or any potential on the electronic system.

This feature is only available for finite systems; if the system is periodic in any dimension, this variable cannot be set to "yes".


MassScaling
Section: Hamiltonian
Type: block

Scaling factor for anisotropic masses (different masses along each geometric direction).

%MassScaling
  1.0 | 1800.0 | 1800.0
%


would fix the mass of the particles to be 1800 along the y and z directions. This can be useful, e.g., to simulate 3 particles in 1D, in this case an electron and 2 protons.


ParticleMass
Section: Hamiltonian
Type: float
Default: 1.0

It is possible to make calculations for a particle with a mass different from one (atomic unit of mass, or mass of the electron). This is useful to describe non-electronic systems, or for esoteric purposes.


RelativisticCorrection
Section: Hamiltonian
Type: integer
Default: non_relativistic

The default value means that no relativistic correction is used. To include spin-orbit coupling turn RelativisticCorrection to spin_orbit (this will only work if SpinComponents has been set to non_collinear, which ensures the use of spinors).
Options:


SOStrength
Section: Hamiltonian
Type: float
Default: 1

Tuning of the spin-orbit coupling strength: setting this value to zero turns off spin-orbit terms in the Hamiltonian, and setting it to one corresponds to full spin-orbit.


StaticElectricField
Section: Hamiltonian
Type: block

A static constant electric field may be added to the usual Hamiltonian, by setting the block StaticElectricField. The three possible components of the block (which should only have one line) are the three components of the electric field vector. It can be applied in a periodic direction of a large supercell via the single-point Berry phase.


StaticMagneticField
Section: Hamiltonian
Type: block

A static constant magnetic field may be added to the usual Hamiltonian, by setting the block StaticMagneticField. The three possible components of the block (which should only have one line) are the three components of the magnetic field vector. Note that if you are running the code in 1D mode, this will not work, and if you are running the code in 2D mode the magnetic field will have to be in the z-direction, so that the first two columns should be zero.

The magnetic field should always be entered in atomic units, regardless of the Units variable. Note that we use the "Gaussian" system meaning 1 au[B] = 1.7152553 * 10^7 gauss, which corresponds to 1.7152553 * 10^3 Tesla.


StaticMagneticField2DGauge
Section: Hamiltonian
Type: integer

The gauge of the static vector potential A when a magnetic field B = (0,0,B_z) is applied onto a 2D-system.
Options:


TheoryLevel
Section: Hamiltonian
Type: integer
Default: dft

The calculations can be run with different "theory levels":
Options:


Hamiltonian::Poisson

AlphaFMM
Section: Hamiltonian::Poisson
Type: float
Default: 0.291262136

Dimensionless parameter for the correction of the self-interaction of the electrostatic Hartree potential.

Octopus represents charge density in real space grids, each point containing a value $\rho$ corresponding to the charge density in the cell centered in such point. Therefore, the integral for the Hartree potential at point $i$, this is $V_H(i)$, can be reduced to a summation:

$V_H(i) = (1/4\pi\epsilon_0) \Omega \sum_{i \neq j} \frac{\rho(\vec{r}(j))}{|\vec{r}(j) - \vec{r}(i)|} + V_{self.int.}(i)$ where $\Omega$ is the volume of the cell, and $\vec{r}(j)$ is the position of the point $j$. The $V_{self.int.}(i)$ corresponds to the integral over the cell centered on the point $i$ that is necessary to calculate the Hartree potential at point $i$:

$V_{self.int.}(i):=\int_{\Omega(i)}d\vec{r} \frac{\rho(\vec{r}(i))}{|\vec{r}-\vec{r}(i)|}$

In the FMM version implemented into Octopus, a correction method for $V_H(i)$ is used (see "A survey of the parallel performance and the accuracy of Poisson solvers for electronic structure calculations", by Pablo García-Risueño, Joseba Alberdi-Rodriguez, et al.) This method defines cells neighbouring cell $i$, which have volume $\Omega(i)/8$ (in 3D) and charge density obtained by interpolation. In the calculation of $V_H(i)$, in order to avoid double counting of charge, and to cancel part of the errors arising from considering the distances constant in the summation above, a term $-\alpha_{FMM}V_{self.int.}(i)$ is added to the summation (see the referred paper for the explicit formulae).


DeltaEFMM
Section: Hamiltonian::Poisson
Type: float
Default: 0.0001

Dimensionless parameter for relative convergence of FMM. Sets energy error bound. Strong inhomogeneous systems may violate the error bound. For inhomogeneous systems we have an error-controlled sequential version available (from Ivo Kabadshow).

Our implementation of FMM (based on H. Dachsel, J. Chem. Phys. 131, 244102 (2009)) can keep the error of the Hartree energy below an arbitrary bound. The quotient of the value chosen for the maximum error in the Hartree energy and the value of the Hartree energy is DeltaEFMM.


Poisson1DSoftCoulomParam
Section: Hamiltonian::Poisson
Type: float
Default: 1.0 bohr

When Dimensions = 1, to prevent divergence, the Coulomb interaction treated by the Poisson solver is not 1/r but 1/sqrt(a^2 + r^2), where this variable sets the value of "a".


PoissonCutoffRadius
Section: Hamiltonian::Poisson
Type: float

When PoissonSolver = fft and PoissonFFTKernel is neither multipole_corrections nor fft_nocut, this variable controls the distance after which the electron-electron interaction goes to zero. A warning will be written if the value is too large and will cause spurious interactions between images. The default is half of the FFT box max dimension in a finite direction.


PoissonFFTKernel
Section: Hamiltonian::Poisson
Type: integer

Defines which kernel is used to impose the correct boundary conditions when using FFTs to solve the Poisson equation. The default is selected depending on the dimensionality and periodicity of the system:
In 1D, spherical if finite, fft_nocut if periodic.
In 2D, spherical if finite, cylindrical if 1D-periodic, fft_nocut if 2D-periodic.
In 3D, spherical if finite, cylindrical if 1D-periodic, planar if 2D-periodic, fft_nocut if 3D-periodic. See C. A. Rozzi et al., Phys. Rev. B 73, 205119 (2006) for 3D implementation and A. Castro et al., Phys. Rev. B 80, 033102 (2009) for 2D implementation.
Options:


PoissonSolver
Section: Hamiltonian::Poisson
Type: integer

Defines which method to use to solve the Poisson equation. Some incompatibilities apply depending on dimensionality, periodicity, etc. For comparison of accuracy and performance of the methods in Octopus, see http://arxiv.org/abs/1211.2092. Defaults:
1D and 2D: fft.
3D: cg_corrected if curvilinear, isf if not periodic, fft if periodic.
Options:


PoissonSolverBoundaries
Section: Hamiltonian::Poisson
Type: integer
Default: multipole

For finite systems, some Poisson solvers (multigrid, cg_corrected, and fft with PoissonFFTKernel = multipole_correction) require the calculation of the boundary conditions with an auxiliary method. This variable selects that method.
Options:


PoissonSolverMaxIter
Section: Hamiltonian::Poisson
Type: integer
Default: 400

The maximum number of iterations for conjugate-gradient Poisson solvers.


PoissonSolverMaxMultipole
Section: Hamiltonian::Poisson
Type: integer

Order of the multipolar expansion for boundary corrections.

The Poisson solvers multigrid, cg, and cg_corrected (and fft with PoissonFFTKernel = multipole_correction) do a multipolar expansion of the given charge density, such that $\rho = \rho_{multip.expansion}+\Delta \rho$. The Hartree potential due to the \rho_{multip.expansion} is calculated analytically, while the Hartree potential due to $\Delta \rho$ is calculated with either a multigrid or cg solver. The order of the multipolar expansion is set by this variable.

Default is 4 for PoissonSolver = cg_corrected and multigrid, and 2 for fft with PoissonFFTKernel = multipole_correction.


PoissonSolverNodes
Section: Hamiltonian::Poisson
Type: integer

How many nodes to use to solve the Poisson equation. A value of 0, the default, implies that all available nodes are used.


PoissonSolverThreshold
Section: Hamiltonian::Poisson
Type: float
Default: 1e-5

The tolerance for the Poisson solution, used by the cg, cg_corrected, and multigrid solvers.


Hamiltonian::Poisson::Multigrid

PoissonSolverMGMaxCycles
Section: Hamiltonian::Poisson::Multigrid
Type: integer
Default: 60

Maximum number of multigrid cycles that are performed if convergence is not achieved.


PoissonSolverMGPostsmoothingSteps
Section: Hamiltonian::Poisson::Multigrid
Type: integer
Default: 4

Number of Gauss-Seidel smoothing steps after coarse-level correction in the multigrid Poisson solver.


PoissonSolverMGPresmoothingSteps
Section: Hamiltonian::Poisson::Multigrid
Type: integer
Default: 1

Number of Gauss-Seidel smoothing steps before coarse-level correction in the multigrid Poisson solver.


PoissonSolverMGRelaxationFactor
Section: Hamiltonian::Poisson::Multigrid
Type: float

Relaxation factor of the relaxation operator used for the multigrid method. This is mainly for debugging, since overrelaxation does not help in a multigrid scheme. The default is 1.0, except 0.6666 for the gauss_jacobi method.


PoissonSolverMGRelaxationMethod
Section: Hamiltonian::Poisson::Multigrid
Type: integer

Method used to solve the linear system approximately in each grid for the multigrid procedure that solves Poisson equation. Default is gauss_seidel, unless curvilinear coordinates are used, in which case the default is gauss_jacobi.
Options:


PoissonSolverMGRestrictionMethod
Section: Hamiltonian::Poisson::Multigrid
Type: integer
Default: fullweight

Method used from fine-to-coarse grid transfer.
Options:


Hamiltonian::XC

Interaction1D
Section: Hamiltonian::XC
Type: integer
Default: interaction_soft_coulomb

When running in 1D, one has to soften the Coulomb interaction. This softening is not unique, and several possibilities exist in the literature.
Options:


Interaction1DScreening
Section: Hamiltonian::XC
Type: float
Default: 1.0

Defines the screening parameter, alpha, of the softened Coulomb interaction when running in 1D. The default value is 1.0.


KSInversionLevel
Section: Hamiltonian::XC
Type: integer
Default: ks_inversion_adiabatic

At what level shall Octopus handle the KS inversion
Options:


MGGAimplementation
Section: Hamiltonian::XC
Type: integer
Default: mgga_gea

Decides how to implement the meta-GGAs (NOT WORKING).
Options:


OEPLevel
Section: Hamiltonian::XC
Type: integer
Default: oep_kli

At what level shall Octopus handle the optimized effective potential (OEP) equation.
Options:


OEPMixing
Section: Hamiltonian::XC
Type: float
Default: 1.0

The linear mixing factor used to solve the Sternheimer equation in the full OEP procedure. The default is 1.0.


SICCorrection
Section: Hamiltonian::XC
Type: integer
Default: sic_none

This variable controls which form of self-interaction correction to use. Note that this correction will be applied to the functional chosen by XCFunctional.
Options:


XCDensityCorrection
Section: Hamiltonian::XC
Type: integer
Default: none

This variable controls the long range correction of the XC potential using the XC density representation (http://arxiv.org/abs/1107.4339). By default, no correction is applied.
Options:


XCDensityCorrectionCutoff
Section: Hamiltonian::XC
Type: float
Default: 0.0

The value of the cutoff applied to the XC density. The default value is 0.


XCDensityCorrectionMinimum
Section: Hamiltonian::XC
Type: logical
Default: true

When enabled, the default, the cutoff optimization will return the first minimum of the q_xc function if it does not find a value of -1 (See http://arxiv.org/abs/1107.4339 for details). This is required for atoms or small molecules, but may cause numerical problems.


XCDensityCorrectionNormalize
Section: Hamiltonian::XC
Type: logical
Default: true

When enabled, the default, the correction will be normalized to reproduce the exact boundary conditions of the XC potential.


XCDensityCorrectionOptimize
Section: Hamiltonian::XC
Type: logical
Default: true

When enabled, the default, the density cutoff will be optimized to replicate the boundary conditions of the exact XC potential. If the variable is set to no, the value of the cutoff must be given by the XCDensityCorrectionCutoff variable.


XCFunctional
Section: Hamiltonian::XC
Type: integer

Defines the exchange and correlation functional to be used; they should be specified as a sum of a correlation term and an exchange term. Defaults:
1D: lda_x_1d + lda_c_1d_csc
2D: lda_x_2d + lda_c_2d_amgb
3D: lda_x + lda_c_pz_mod
Options:


XCKernel
Section: Hamiltonian::XC
Type: integer
Default: lda_x+lda_c_pz_mod

Defines the exchange-correlation kernel. Only LDA kernels are available currently.
Options:


XCTailCorrection
Section: Hamiltonian::XC
Type: logical
Default: no

(Experimental) This variable applies a correction to the value of the XC functional in near-zero-density regions. This zone might have numerical noise or it might even be set to zero by libxc. The correction is performed by forcing the "-1/r behaviour" of the XC potential in the zones where the density is lower then XCTailCorrectionTol.


XCTailCorrectionCMDistance
Section: Hamiltonian::XC
Type: integer

(Experimental) This variable allows the application of the tail correction to the XC potential only where the distance of the local point from the center of mass of the system is greater than XCTailCorrectionCMDistance.


XCTailCorrectionDelay
Section: Hamiltonian::XC
Type: integer

(Experimental) This variable skips the application of the tail correction during the first calls of the subroutine that build the exchange-correlation potential (XCTailCorrectionDelay = number of calls skipped): this can avoid problems caused by initial guess wavefunctions.


XCTailCorrectionLinkFactor
Section: Hamiltonian::XC
Type: float
Default: 1

(Experimental) This variable forces a smooth transition between the region where the values of the XC functional have been previously calculated and the region where the -1/r correction has been applied. The region of the transition starts where the electronic total density reaches the value of (XCTailCorrectionLinkFactor * XCTailCorrectionTol) and ends where the density reaches the value of XCTailCorrectionTol.


XCTailCorrectionTol
Section: Hamiltonian::XC
Type: float
Default: 5e-12