## SCF

SCFCalculateDipole
Section: SCF
Type: logical

This variable controls whether the dipole is calculated at the end of a self-consistent iteration. For finite systems the default is yes. For periodic systems the default is no, unless an electric field is being applied in a periodic direction. The single-point Berry`s phase approximation is used for periodic directions. Ref: E Yaschenko, L Fu, L Resca, and R Resta, Phys. Rev. B 58, 1222-1229 (1998).

SCFCalculateForces
Section: SCF
Type: logical

This variable controls whether the forces on the ions are calculated at the end of a self-consistent iteration. The default is yes, unless the system only has user-defined species.

SCFCalculatePartialCharges
Section: SCF
Type: logical
Default: no

(Experimental) This variable controls whether partial charges are calculated at the end of a self-consistent iteration.

SCFCalculateStress
Section: SCF
Type: logical

This variable controls whether the stress on the lattice is calculated at the end of a self-consistent iteration. The default is no.

SCFinLCAO
Section: SCF
Type: logical
Default: no

Performs the SCF cycle with the calculation restricted to the LCAO subspace. This may be useful for systems with convergence problems (first do a calculation within the LCAO subspace, then restart from that point for an unrestricted calculation).

## SCF::Convergence

ConvAbsDens
Section: SCF::Convergence
Type: float
Default: 0.0

Absolute convergence of the density:

$$\varepsilon = \int {\rm d}^3r \left| \rho^{out}(\bf r) -\rho^{inp}(\bf r) \right|$$.

A zero value (the default) means do not use this criterion.

If this criterion is used, the SCF loop will only stop once it is fulfilled for two consecutive iterations.

ConvAbsEv
Section: SCF::Convergence
Type: float
Default: 0.0

Absolute convergence of the sum of the eigenvalues:

$$\varepsilon = \left| \sum_{j=1}^{N_{occ}} \varepsilon_j^{out} - \sum_{j=1}^{N_{occ}} \varepsilon_j^{inp} \right|$$

A zero value (the default) means do not use this criterion.

If this criterion is used, the SCF loop will only stop once it is fulfilled for two consecutive iterations.

ConvEigenError
Section: SCF::Convergence
Type: logical
Default: false

If true, the calculation will not be considered converged unless all states have individual errors less than EigensolverTolerance.

If this criterion is used, the SCF loop will only stop once it is fulfilled for two consecutive iterations.

ConvEnergy
Section: SCF::Convergence
Type: float
Default: 0.0

Stop the SCF when the magnitude of change in energy during at one SCF iteration is smaller than this value.

ConvRelDens
Section: SCF::Convergence
Type: float
Default: 1e-6

Relative convergence of the density:

$$\varepsilon = \frac{1}{N} \mathrm{ConvAbsDens}$$.

N is the total number of electrons in the problem. A zero value means do not use this criterion.

If you reduce this value, you should also reduce EigensolverTolerance to a value of roughly 1/10 of ConvRelDens to avoid convergence problems.

If this criterion is used, the SCF loop will only stop once it is fulfilled for two consecutive iterations.

ConvRelEv
Section: SCF::Convergence
Type: float
Default: 0.0

Relative convergence of the sum of the eigenvalues:

$$\varepsilon = \frac{ \left| \sum_{j=1}^{N_{occ}} ( \varepsilon_j^{out} - \varepsilon_j^{inp} ) \right|} {\left| \sum_{j=1}^{N_{occ}} \varepsilon_j^{out} \right|}$$

MaximumIter
Section: SCF::Convergence
Type: integer
Default: 200

Maximum number of SCF iterations. The code will stop even if convergence has not been achieved. -1 means unlimited. 0 means just do LCAO (or read from restart), compute the eigenvalues and energy, and stop, without updating the wavefunctions or density.

If convergence criteria are set, the SCF loop will only stop once the criteria are fulfilled for two consecutive iterations.

Note that this variable is also used in the section Calculation Modes::Unoccupied States, where it denotes the maximum number of calls of the eigensolver. In this context, the default value is 50.

MaximumIterBerry
Section: SCF::Convergence
Type: integer
Default: 10

Maximum number of iterations for the Berry potential, within each SCF iteration. Only applies if a StaticElectricField is applied in a periodic direction. The code will move on to the next SCF iteration even if convergence has not been achieved. -1 means unlimited.

## SCF::Eigensolver

Section: SCF::Eigensolver
Type: logical
Default: no

Used by the cg solver only. Add additional terms during the line minimization, see PTA92, eq. 5.31ff. These terms can improve convergence for some systems, but they are quite costly. If you experience convergence problems, you might try out this option. This feature is still experimental.

CGDirection
Section: SCF::Eigensolver
Type: integer

Used by the cg solver only. The conjugate direction is updated using a certain coefficient to the previous direction. This coeffiction can be computed in different ways. The default is to use Fletcher-Reeves (FR), an alternative is Polak-Ribiere (PR).
Options:

• fletcher: The coefficient for Fletcher-Reeves consists of the current norm of the steepest descent vector divided by that of the previous iteration.
• polak: For the Polak-Ribiere scheme, a product of the current with the previous steepest descent vector is subtracted in the nominator.

CGEnergyChangeThreshold
Section: SCF::Eigensolver
Type: float
Default: 0.1

Used by the cg solver only. For each band, the CG iterations are stopped when the change in energy is smaller than the change in the first iteration multiplied by this factor. This limits the number of CG iterations for each band, while still showing good convergence for the SCF cycle. The criterion is discussed in Sec. V.B.6 of Payne et al. (1992), Rev. Mod. Phys. 64, 4. The default value is 0.1, which is usually a good choice for LDA and GGA potentials. If you are solving the OEP equation, you might want to set this value to 1e-3 or smaller. In general, smaller values might help if you experience convergence problems.

CGOrthogonalizeAll
Section: SCF::Eigensolver
Type: logical
Default: no

Used by the cg solver only. During the cg iterations, the current band can be orthogonalized against all other bands or only against the lower bands. Orthogonalizing against all other bands can improve convergence properties, whereas orthogonalizing against lower bands needs less operations.

Eigensolver
Section: SCF::Eigensolver
Type: integer

Which eigensolver to use to obtain the lowest eigenvalues and eigenfunctions of the Kohn-Sham Hamiltonian. The default is conjugate gradients (cg), except that when parallelization in states is enabled, the default is rmmdiis.
Options:

• rmmdiis: Residual minimization scheme, direct inversion in the iterative subspace eigensolver, based on the implementation of Kresse and Furthmüller [Phys. Rev. B 54, 11169 (1996)]. This eigensolver requires almost no orthogonalization so it can be considerably faster than the other options for large systems. To improve its performance a large number of ExtraStates are required (around 10-20% of the number of occupied states). Note: with unocc, you will need to stop the calculation by hand, since the highest states will probably never converge. Usage with more than one block of states per node is experimental, unfortunately.
• plan: Preconditioned Lanczos scheme. Ref: Y. Saad, A. Stathopoulos, J. Chelikowsky, K. Wu and S. Ogut, "Solution of Large Eigenvalue Problems in Electronic Structure Calculations", BIT 36, 1 (1996).
• cg_new: An alternative conjugate-gradients eigensolver, faster for larger systems but less mature. Ref: Jiang et al., Phys. Rev. B 68, 165337 (2003)
• evolution: (Experimental) Propagation in imaginary time.

EigensolverImaginaryTime
Section: SCF::Eigensolver
Type: float
Default: 0.1

The imaginary-time step that is used in the imaginary-time evolution method (Eigensolver = evolution) to obtain the lowest eigenvalues/eigenvectors. It must satisfy EigensolverImaginaryTime > 0. Increasing this value can make the propagation faster, but could lead to unstable propagations.

EigensolverMaxIter
Section: SCF::Eigensolver
Type: integer

Determines the maximum number of iterations that the eigensolver will perform if the desired tolerance is not achieved. The default is 25 iterations for all eigensolvers except for rmdiis, which performs only 5 iterations. Increasing this value for rmdiis increases the convergence speed, at the cost of an increased memory footprint. In the case of imaginary time propatation, this variable is not used.

EigensolverMinimizationIter
Section: SCF::Eigensolver
Type: integer
Default: 5

During the first iterations, the RMMDIIS eigensolver requires some steepest-descent minimizations to improve convergence. This variable determines the number of those minimizations.

EigensolverSkipKpoints
Section: SCF::Eigensolver
Type: logical

Only solve Hamiltonian for k-points with zero weight

EigensolverTolerance
Section: SCF::Eigensolver
Type: float

This is the tolerance for the eigenvectors. The default is 1e-7.

Preconditioner
Section: SCF::Eigensolver
Type: integer

Which preconditioner to use in order to solve the Kohn-Sham equations or the linear-response equations. The default is pre_filter, except for curvilinear coordinates, where no preconditioner is applied by default.
Options:

• no: Do not apply preconditioner.
• pre_filter: Filter preconditioner.
• pre_jacobi: Jacobi preconditioner. Only the local part of the pseudopotential is used. Not very helpful.
• pre_poisson: Uses the full Laplacian as preconditioner. The inverse is calculated through the solution of the Poisson equation. This is, of course, very slow.
• pre_multigrid: Multigrid preconditioner.

PreconditionerFilterFactor
Section: SCF::Eigensolver
Type: float

This variable controls how much filter preconditioner is applied. A value of 1.0 means no preconditioning, 0.5 is the standard.

The default is 0.5, except for periodic systems where the default is 0.6.

If you observe that the first eigenvectors are not converging properly, especially for periodic systems, you should increment this value.

The allowed range for this parameter is between 0.5 and 1.0. For other values, the SCF may converge to wrong results.

PreconditionerIterationsMiddle
Section: SCF::Eigensolver
Type: integer

This variable is the number of smoothing iterations on the coarsest grid for the multigrid preconditioner. The default is 1.

PreconditionerIterationsPost
Section: SCF::Eigensolver
Type: integer

This variable is the number of post-smoothing iterations for the multigrid preconditioner. The default is 2.

PreconditionerIterationsPre
Section: SCF::Eigensolver
Type: integer

This variable is the number of pre-smoothing iterations for the multigrid preconditioner. The default is 1.

StatesOrthogonalization
Section: SCF::Eigensolver
Type: integer

The full orthogonalization method used by some eigensolvers. The default is cholesky_serial, except with state parallelization, the default is cholesky_parallel.
Options:

• cholesky_serial: Cholesky decomposition implemented using BLAS/LAPACK. Can be used with domain parallelization but not state parallelization.
• cholesky_parallel: Cholesky decomposition implemented using ScaLAPACK. Compatible with states parallelization.
• cgs: Classical Gram-Schmidt (CGS) orthogonalization. Can be used with domain parallelization but not state parallelization. The algorithm is defined in Giraud et al., Computers and Mathematics with Applications 50, 1069 (2005).
• mgs: Modified Gram-Schmidt (MGS) orthogonalization. Can be used with domain parallelization but not state parallelization. The algorithm is defined in Giraud et al., Computers and Mathematics with Applications 50, 1069 (2005).
• drcgs: Classical Gram-Schmidt orthogonalization with double-step reorthogonalization. Can be used with domain parallelization but not state parallelization. The algorithm is taken from Giraud et al., Computers and Mathematics with Applications 50, 1069 (2005). According to this reference, this is much more precise than CGS or MGS algorithms. The MGS version seems not to improve much the stability and would require more communications over the domains.

SubspaceDiagonalization
Section: SCF::Eigensolver
Type: integer
Default: standard

Selects the method to perform subspace diagonalization. The default is standard, unless states parallelization is used, when the default is scalapack. Note that this variable is not parsed in the case of the evolution eigensolver.
Options:

• none: No subspace diagonalization. WARNING: this will generally give incorrect results.
• standard: The standard routine. Can be used with domain parallelization but not state parallelization.
• scalapack: State-parallelized version using ScaLAPACK. (Requires that Octopus was compiled with ScaLAPACK support.)

## SCF::LCAO

AtomsMagnetDirection
Section: SCF::LCAO
Type: block

This option is only used when GuessMagnetDensity is set to user_defined. It provides a direction for the magnetization vector of each atom when building the guess density. In order to do that, the user should specify the coordinates of a vector that has the desired direction and norm. Note that it is necessary to maintain the ordering in which the species were defined in the coordinates specifications.

For spin-polarized calculations, the vectors should have only one component; for non-collinear-spin calculations, they should have three components. If the norm of the vector is greater than the number of valence electrons in the atom, it will be rescaled to this number, which is the maximum possible magnetization.

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.

LCAOAlternative
Section: SCF::LCAO
Type: logical
Default: false

If this variable is set, the LCAO procedure will use an alternative (and experimental) implementation. It is faster for large systems and parallel in states. It is not working for spinors, however.

LCAOComplexYlms
Section: SCF::LCAO
Type: logical
Default: false

If set to true, and using complex states, complex spherical harmonics will be used, i.e. with $$e^{\pm i m \phi}$$. If false, real spherical harmonics with $$\sin(m \phi)$$ or $$\cos(m \phi)$$ are used. This variable will make it more likely to get states that are eigenvectors of the $$L_z$$ operator, with a definite angular momentum.

LCAODiagTol
Section: SCF::LCAO
Type: float
Default: 1e-10

Only applies if LCAOAlternative = true. The tolerance for the diagonalization of the LCAO Hamiltonian.

LCAODimension
Section: SCF::LCAO
Type: integer

(Only applies if LCAOAlternative = no.) Before starting the SCF cycle, an initial LCAO calculation can be performed in order to obtain reasonable initial guesses for spin-orbitals and densities. For this purpose, the code calculates a number of atomic orbitals. The number available for a species described by a pseudopotential is all the orbitals up the maximum angular momentum in the pseudopotential, minus any orbitals that are found to be unbound. For non-pseudopotential species, the number is equal to twice the valence charge. The default dimension for the LCAO basis set will be the sum of all these numbers, or twice the number of required orbitals for the full calculation, whichever is less.

This dimension however can be changed by making use of this variable. Note that LCAODimension cannot be smaller than the number of orbitals needed in the full calculation -- if LCAODimension is smaller, it will be silently increased to meet this requirement. In the same way, if LCAODimension is larger than the available number of atomic orbitals, it will be reduced. If you want to use the largest possible number, set LCAODimension to a negative number.

LCAOExtraOrbitals
Section: SCF::LCAO
Type: logical
Default: false

Only applies if LCAOAlternative = true, and all species are pseudopotentials. (experimental) If this variable is set to yes, the LCAO procedure will add an extra set of numerical orbitals (by using the derivative of the radial part of the original orbitals). Note that this corresponds roughly to adding orbitals with higher principal quantum numbers, but the same angular momentum. This option may cause problems for unoccupied states since you may miss some lower-lying states which correspond to higher angular momenta instead of higher principal quantum number.

LCAOKeepOrbitals
Section: SCF::LCAO
Type: logical
Default: yes

Only applies if LCAOAlternative = true. If set to yes (the default) Octopus keeps atomic orbitals in memory during the LCAO procedure. If set to no, the orbitals are generated each time that they are needed, increasing computational time but saving memory.

When set to yes, Octopus prints the amount of memory per node that is required to store the orbitals.

Section: SCF::LCAO
Type: float
Default: 20.0 a.u.

The LCAO procedure will ignore orbitals that have an extent greater that this value.

LCAOScaleFactor
Section: SCF::LCAO
Type: float
Default: 1.0

The coordinates of the atomic orbitals used by the LCAO procedure will be rescaled by the value of this variable. 1.0 means no rescaling.

LCAOStart
Section: SCF::LCAO
Type: integer

Before starting a SCF calculation, Octopus can perform a linear combination of atomic orbitals (LCAO) calculation. These can provide Octopus with a good set of initial wavefunctions and with a new guess for the density. (Up to the current version, only a minimal basis set is used.) The default is lcao_states if at least one species representing an atom is present. The default is lcao_none if all species are species_user_defined, species_charge_density, species_from_file, or species_jellium_slab.

The initial guess densities for LCAO are taken from the atomic orbitals for pseudopotential species; from the natural charge density for species_charge_density, species_point, species_jellium, and species_jellium_slab; or uniform for species_full_delta, species_full_gaussian, species_user_defined, or species_from_file. Pseudopotential species use the pseudo-wavefunctions as orbitals, full-potential atomic species (species_full_delta and species_full_gaussian) use hydrogenic wavefunctions, and others use harmonic-oscillator wavefunctions.

Note: Some pseudopotential files (CPI, FHI for example) do not contain full information about the orbitals. In this case, Octopus generates the starting density from the normalized square root of the local potential. If no orbitals are available at all from the pseudopotential files, Octopus will not be able to perform an LCAO and the initial states will be randomized.

Options:

• lcao_none: Do not perform a LCAO calculation before the SCF cycle. Instead use random wavefunctions.
• lcao_states: Do a LCAO calculation before the SCF cycle and use the resulting wavefunctions as initial wavefunctions without changing the guess density. This will speed up the convergence of the eigensolver during the first SCF iterations.
• lcao_full: Do a LCAO calculation before the SCF cycle and use the LCAO wavefunctions to build a new guess density and a new KS potential. Using the LCAO density as a new guess density may improve the convergence, but can also slow it down or yield wrong results (especially for spin-polarized calculations).

## SCF::Mixing

MixField
Section: SCF::Mixing
Type: integer

Selects what should be mixed during the SCF cycle. Note that currently the exact-exchange part of hybrid functionals is not mixed at all, which would require wavefunction-mixing, not yet implemented. This may lead to instabilities in the SCF cycle, so starting from a converged LDA/GGA calculation is recommended for hybrid functionals. The default depends on the TheoryLevel and the exchange-correlation potential used.
Options:

• none: No mixing is done. This is the default for independent particles.
• potential: The Kohn-Sham potential is mixed. This is the default for other cases.
• density: Mix the density.
• states: (Experimental) Mix the states. In this case, the mixing is always linear.

MixInterval
Section: SCF::Mixing
Type: integer
Default: 1

When this variable is set to a value different than 1 (the default) a combined mixing scheme will be used, with MixInterval - 1 steps of linear mixing followed by 1 step of the selected mixing. For the moment this variable only works with DIIS mixing.

MixNumberSteps
Section: SCF::Mixing
Type: integer
Default: 4

In the Broyden and Bowler_Gillan schemes, the new input density or potential is constructed from the values of the densities/potentials of a given number of previous iterations. This number is set by this variable. Must be greater than 1.

Mixing
Section: SCF::Mixing
Type: float
Default: 0.3

The linear, Broyden and DIIS scheme depend on a "mixing parameter", set by this variable. Must be 0 < Mixing <= 1.

MixingPreconditioner
Section: SCF::Mixing
Type: logical
Default: false

(Experimental) If set to yes, Octopus will use a preconditioner for the mixing operator. This preconditioner is disabled for systems with dimension other than 3.

MixingResidual
Section: SCF::Mixing
Type: float
Default: 0.05

In the DIIS mixing it is benefitial to include a bit of residual into the mixing. This parameter controls this amount.

MixingRestart
Section: SCF::Mixing
Type: integer
Default: 20

In the Broyden and Bowler_Gillan schemes, the mixing is restarted after the number of iterations given by this variable. Set this to zero to disable restarting the mixing.

MixingScheme
Section: SCF::Mixing
Type: integer
Default: broyden

The scheme used to produce, at each iteration in the self-consistent cycle that attempts to solve the Kohn-Sham equations, the input density from the value of the input and output densities of previous iterations.
Options:

• linear: Simple linear mixing.
• bowler_gillan: The Guaranteed-reduction modification of the Pulay scheme by Bowler and Gillan [D. R. Bowler and M. J. Gillan, Chem. Phys. Lett. 325, 473 (2000)].
• broyden: Broyden scheme [C. G Broyden, Math. Comp. 19, 577 (1965); D. D. Johnson, Phys. Rev. B 38, 12807 (1988)]. The scheme is slightly adapted, see the comments in the code. For complex functions (e.g. Sternheimer with EMEta > 0), we use the generalization with a complex dot product.
• diis: Direct inversion in the iterative subspace (diis) scheme [P. Pulay, Chem. Phys. Lett., 73, 393 (1980)] as described in [G. Kresse, and J. Hurthmueller, Phys. Rev. B 54, 11169 (1996)].

## SCF::RDMFT

RDMBasis
Section: SCF::RDMFT
Type: logical
Default: yes

If true, all the energy terms and corresponding derivatives involved in RDMFT will not be calculated on the grid but on the basis of the initial orbitals

RDMConvEner
Section: SCF::RDMFT
Type: float
Default: 1e-6 Ha

Convergence criterion for stopping the overall minimization of the energy with respect to occupation numbers and the orbitals. The minimization of the energy stops when the total energy difference between two subsequent minimizations of the energy with respect to the occupation numbers and the orbitals is smaller than this criterion. It is also used to exit the orbital minimization.

RDMHartreeFock
Section: SCF::RDMFT
Type: logical
Default: no

If true, the code simulates a HF calculation, by omitting the occ.num. optimization can be used for test reasons

RDMTolerance
Section: SCF::RDMFT
Type: float
Default: 1e-7 Ha

Convergence criterion for stopping the occupation numbers minimization. Minimization is stopped when all derivatives of the energy wrt. each occupation number are smaller than this criterion. The bisection for finding the correct mu that is needed for the occupation number minimization also stops according to this criterion.

RDMToleranceFO
Section: SCF::RDMFT
Type: float
Default: 1e-4 Ha

Convergence criterion for stopping the diagonalization of the Fock matrix in the Piris method. Orbital minimization is stopped when all off-diagonal ellements of the Fock matrix are smaller than this criterion.