# Self Consistent Field (SCF)¶

The SCF procedure searches for a self-consistent density. The self-consistent error is the square root of the integral of the squared difference between the input and output density of the cycle operator. When the SCF error is below a certain criterion, controlled by subkey `Criterion`

of block key `Convergence`

, convergence is reached. In case of bad convergence the SCF looks at the subkeys `Mixing`

, and `Degenerate`

, and the subkeys of block key `DIIS`

.

See also

Troubleshooting: SCF does not converge

## SCF block¶

```
SCF
Eigenstates Yes/No
Iterations integer
Method [DIIS | MultiSecant]
Mixing float
PMatrix Yes/No
PrintAllOccupiedBands Yes/No
PrintAllVirtualBands Yes/No
PrintAlwaysBandRanges Yes/No
Rate float
VSplit float
End
```

`SCF`

Type: Block Description: Controls technical SCF parameters. `Eigenstates`

Type: Bool Description: The program knows two alternative ways to evaluate the charge density iteratively in the SCF procedure: from the P-matrix, and directly from the squared occupied eigenstates. By default the program actually uses both at least one time and tries to take the most efficient. If present, Eigenstates turns off this comparison and lets the program stick to one method (from the eigenstates). `Iterations`

Type: Integer Default value: 300 GUI name: Maximum number of cycles Description: The maximum number of SCF iterations to be performed. `Method`

Type: Multiple Choice Default value: DIIS Options: [DIIS, MultiSecant] Description: Choose the general scheme used to converge the density in the SCF. In case of scf problems one can try the MultiSecant alternative at no extra cost per SCF cycle. For more details see the DIIS and MultiSecantConfig block. `Mixing`

Type: Float Default value: 0.075 Description: Initial ‘damping’ parameter in the SCF procedure, for the iterative update of the potential: new potential = old potential + mix (computed potential-old potential). Note: the program automatically adapts Mixing during the SCF iterations, in an attempt to find the optimal mixing value. `PMatrix`

Type: Bool Description: If present, evaluate the charge density from the P-matrix. See also the key Eigenstates. `PrintAllOccupiedBands`

Type: Bool Default value: No Description: When printing the ranges of the bands, include all occupied ones. `PrintAllVirtualBands`

Type: Bool Default value: No Description: When printing the ranges of the bands, include all virtual ones. `PrintAlwaysBandRanges`

Type: Bool Default value: No Description: Normally the ranges of the bands are only printed at the last SCF cycle `Rate`

Type: Float Default value: 0.99 Description: Minimum rate of convergence for the SCF procedure. If progress is too slow the program will take measures (such as smearing out occupations around the Fermi level, see key Degenerate of block Convergence) or, if everything seems to fail, it will stop `VSplit`

Type: Float Default value: 0.05 Description: To disturb degeneracy of alpha and beta spin MOs the value of this key is added to the beta spin potential at the startup.

## Convergence¶

All options and parameters related to the convergence behavior of the SCF procedure are defined in the `Convergence`

block key. Also the finite temperature distribution is part of this

```
Convergence
Criterion float
CriterionFactor float
Degenerate string
ElectronicTemperature float
InitialDensity [rho | psi]
LessDegenerate Yes/No
ModestCriterion float
NoDegenerate Yes/No
NumBoltz integer
SpinFlip integer_list
SpinFlipEnabled Yes/No
SpinFlipRegion string
StartWithMaxSpin Yes/No
StartWithMaxSpinForSO Yes/No
End
```

`Convergence`

Type: Block Description: Options and parameters related to the convergence behavior of the SCF procedure. `Criterion`

Type: Float Description: Criterion for termination of the SCF procedure. The default depends on the NumericalQuality and on the number of atoms in the system. Can be used for EngineAutomations `CriterionFactor`

Type: Float Default value: 1.0 Description: Multiply Criterion (which depends on system and quality) with this factor. Can be used for EngineAutomations `Degenerate`

Type: String Default value: default Description: Smooths (slightly) occupation numbers around the Fermi level, so as to insure that nearly-degenerate states get (nearly-) identical occupations. Be aware: In case of problematic SCF convergence the program will turn this key on automatically, unless the key ‘Nodegenerate’ is set in input. The smoothing depends on the argument to this key, which can be considered a ‘degeneration width’. When the argument reads default, the program will use the value 1e-4 a.u. for the energy width. `ElectronicTemperature`

Type: Float Default value: 0.0 Unit: Hartree Description: (KT) Specify this key for a gradient independent electronic temperature `InitialDensity`

Type: Multiple Choice Default value: rho Options: [rho, psi] Description: The SCF is started with a guess of the density. There are the following choices RHO: the sum of atomic density. PSI: construct an initial eigensystem by occupying the atomic orbitals. The guessed eigensystem is orthonormalized, and from this the density is calculated/ `LessDegenerate`

Type: Bool Default value: No Description: If smoothing of occupations over nearly degenerate orbitals is applied (see Degenerate key), then, if this key is set in the input file, the program will limit the smoothing energy range to 1e-4 a.u. as soon as the SCF has converged ‘halfway’, i.e. when the SCF error has decreased to the square root of its convergence criterion. `ModestCriterion`

Type: Float Default value: -1.0 Description: If this is specified band will consider the SCF converged if the error is below this criterion (after using the maximum number of iterations). `NoDegenerate`

Type: Bool Default value: No Description: This key prevents any internal automatic setting of the key DEGENERATE. `NumBoltz`

Type: Integer Default value: 10 Description: The electronic temperature is done with a Riemann Stieltjes numerical integration, between zero and one occupation. This defines the number of points to be used. `SpinFlip`

Type: Integer List GUI name: Flip spin for atoms Description: List here the atoms for which you want the initial spin polarization to be flipped. This way you can distinguish between ferromagnetic and anti ferromagnetic states. Currently, it is not allowed to give symmetry equivalent atoms a different spin orientation. To achieve that you have to break the symmetry. `SpinFlipEnabled`

Type: Bool Default value: Yes Description: If set to False, the keys SpinFlip and SpinFlipRegion are ignored. Only useful/convenient when trying to compare in a script the effect of spin flip. `SpinFlipRegion`

Type: String Recurring: True GUI name: Flip spin for region Description: Specify here the region for which you want the initial spin polarization to be flipped. This way you can distinguish between ferromagnetic and anti ferromagnetic states. Currently, it is not allowed to give symmetry equivalent atoms a different spin orientation. To achieve that you have to break the symmetry. `StartWithMaxSpin`

Type: Bool Default value: Yes Description: To break the initial perfect symmetry of up and down densities there are two strategies. One is to occupy the numerical orbitals in a maximum spin configuration. The alternative is to add a constant to the potential. See also Vsplit key. `StartWithMaxSpinForSO`

Type: Bool Default value: No Description: Same as the StartWithMaxSpin option. In case of spin-orbit band always used to split the potential. Now will use maxspin in case of SpinFlip. With this option it will always do that.

## DIIS¶

The DIIS procedure to obtain the SCF solution depends on several parameters. Default values can be overruled with this block.

```
DIIS
Adaptable Yes/No
CHuge float
CLarge float
Condition float
DiMix float
DiMixMax float
DiMixMin float
NCycleDamp integer
NVctrx integer
Variant [DIIS | LISTi | LISTb | LISTd]
End
```

`DIIS`

Type: Block Description: Parameters for the DIIS procedure to obtain the SCF solution `Adaptable`

Type: Bool Default value: Yes Description: Change automatically the value of dimix during the SCF. `CHuge`

Type: Float Default value: 20.0 GUI name: No DIIS (but damping) when coefs > Description: When the largest coefficient in the DIIS expansion exceeds this value, damping is applied `CLarge`

Type: Float Default value: 20.0 GUI name: Reduce DIIS space when coefs > Description: When the largest DIIS coefficient exceeds this value, the oldest DIIS vector is removed and the procedure re-applied `Condition`

Type: Float Default value: 1000000.0 Description: The condition number of the DIIS matrix, the largest eigenvalue divided by the smallest, must not exceed this value. If this value is exceeded, this vector will be removed. `DiMix`

Type: Float Default value: 0.2 GUI name: Bias DIIS towards latest vector with Description: Mixing parameter for the DIIS procedure `DiMixMax`

Type: Float Default value: -1.0 Description: For adaptive diis: A negative value means automatic, see DiMixatnvctrx. If positive it is an absolute upper bound for (adaptive) dimix `DiMixMin`

Type: Float Default value: 0.01 Description: An absolute lower bound for adaptive dimix. `NCycleDamp`

Type: Integer Default value: 1 GUI name: Do not start DIIS before cycle Description: Number of initial iterations where damping is applied, before any DIIS is considered `NVctrx`

Type: Integer Default value: 20 GUI name: Size of DIIS space Description: Maximum number of DIIS expansion vectors `Variant`

Type: Multiple Choice Default value: DIIS Options: [DIIS, LISTi, LISTb, LISTd] Description: Which variant to use. In case of problematic SCF convergence, first try MultiSecant, and if that does not work the LISTi is the advised method. Note: LIST is computationally more expensive per SCF iteration than DIIS.

## Multisecant¶

For more detais on the multisecant method see ref [1].

```
MultiSecantConfig
CMax float
InitialSigmaN float
MaxSigmaN float
MaxVectors integer
MinSigmaN float
End
```

`MultiSecantConfig`

Type: Block Description: Parameters for the Multi-secant SCF convergence method. `CMax`

Type: Float Default value: 20.0 GUI name: Max coeff Description: Maximum coefficient allowed in expansion `InitialSigmaN`

Type: Float Default value: 0.1 GUI name: Initial Description: This is a lot like a mix factor: bigger means bolder `MaxSigmaN`

Type: Float Default value: 0.3 GUI name: Max Description: Upper bound for the SigmaN parameter `MaxVectors`

Type: Integer Default value: 20 GUI name: Number of cycles to use Description: Maximum number of previous cycles to be used `MinSigmaN`

Type: Float Default value: 0.01 GUI name: Min Description: Lower bound for the SigmaN parameter

## DIRIS¶

In the DIRIS block, which has the same options as the `DIIS`

block, you can specify the DIIS options to be used in the Dirac subprogram, for numerical single atom calculations, which constructs the radial tables for the NAOs.

[1] | L. D. Marks and D. R. Luke, Robust mixing for ab initio quantum mechanical calculations, Phys. Rev. B 78, 075114 (2008) |