# Model Hamiltonians¶

As of the 2020 release, the DFTB engine supports two different classes of model Hamiltonians, Grimme’s extended tight-binding, and the classic Slater-Koster based DFTB. All of these model Hamiltonians are obtained by applying tight-binding approximations to the DFT total energy expression.

## Slater-Koster based DFTB¶

The efficiency of Slater-Koster based DFTB stems from its use of an optimized minimum valence orbital basis that reduces the linear algebra operations, and a two center-approximation for the Kohn-Sham potential that allows precalculation and storage of integrals using the Slater-Koster technique. This makes DFTB orders of magnitude faster than DFT, but requires parameter files (containing the integrals) for all pair-wise combinations of atoms in a molecule. Many elements can be handled with the parameter sets included in the distribution. Alternatively, sets of parameters in the SKF format can be downloaded and used from third party sources.

There are three flavors of Slater-Koster based DFTB available in our implementation:

The “plain” DFTB Hamiltonian as introduced by Porezag and Seifert without a self-consistency cycle.

The second order self-consistent charge extension SCC-DFTB (recently also called DFTB2), which accounts for density fluctuations and improves results on polar bonds. Note that the self-consistent calculations is about an order of magnitude slower than calculations with the “plain” DFTB Hamiltonian.

The third order extension known as DFTB3, which improve the description of hydrogen-bonded complexes and proton affinities. Note that DFTB3 calculations are only marginally slower than SCC-DFTB based calculations.

Note that since these methods have been respectively parametrized, it is important to specify a matching parameter set when applying one of these models.

## Extended tight-binding (xTB)¶

The extended tight-binding (xTB) model Hamiltonian as recently been introduced by Grimme and coworkers. It makes similar approximations as Slater-Koster based DFTB, but instead of using precalculated integrals, xTB employs a (small) basis of Slater-type orbitals and uses an extended Hückel-like approximation for the Hamiltonian.

The DFTB Engine supports the GFN1-xTB parameterization of xTB, which is optimized for geometries, frequencies and non-covalent interactions and covers all elements of the periodic table up to radon.

## Model Hamiltonian¶

The following keys allow you to select a model Hamiltonian and control different aspects of how the stationary Schroedinger equation is solved.

```
Model [DFTB | SCC-DFTB | DFTB3 | GFN1-xTB | NonSCC-GFN1-xTB]
```

`Model`

- Type
Multiple Choice

- Default value
GFN1-xTB

- Options
[DFTB, SCC-DFTB, DFTB3, GFN1-xTB, NonSCC-GFN1-xTB]

- Description
Selects the Hamiltonian used in the DFTB calculation: - DFTB/DFTB0/DFTB1 for classic DFTB without a self-consistent charge cycle - SCC-DFTB/DFTB2 with a self-consistency loop for the Mulliken charges - DFTB3 for additional third-order contributions. - GFN1-xTB for Grimme’s extended tight-binding model in the GFN1 version. - NonSCC-GFN1-xTB for a less accurate but faster version of GFN1-xTB without a self-consistency cycle The choice has to be supported by the selected parameter set.

Different parameters may be suitable for different model Hamiltonians. It is important to choose the appropriate parameter set for the type of calculation and molecular system under study, see parameter sets.

```
ResourcesDir string
```

`ResourcesDir`

- Type
String

- Description
The directory containing the parameter files. The path can be absolute or relative. Relative paths starting with ./ are considered relative to the directory in which the calculation is started, otherwise they are considered relative to $AMSRESOURCES/DFTB. This key is required for the Slater-Koster based DFTB models, but optional for xTB.

**Examples:**

`ResourcesDir Dresden`

Uses the resource directory $AMSRESOURCES/DFTB/Dresden.

`ResourcesDir /home/myusername/myparamsdir`

Uses the specified path /home/myusername/myparamsdir as the resource directory.

**NOTE:** Each resource directory must contain a file called *metainfo.yaml*, which specifies the capabilities of the parameter set. For details see metainfo.yaml.

## Dispersion correction¶

The selected model Hamiltonian can be extended with dispersion correction:

```
DispersionCorrection [None | Auto | UFF | ULG | D2 | D3-BJ | D4]
```

`DispersionCorrection`

- Type
Multiple Choice

- Default value
None

- Options
[None, Auto, UFF, ULG, D2, D3-BJ, D4]

- GUI name
Dispersion

- Description
This key is used to specify an empirical dispersion model. Please refer to the DFTB documentation for details on the different methods. By default no dispersion correction will be applied. Setting this to auto applies the dispersion correction recommended in the DFTB parameter set’s metainfo file. Note that the D3-BJ dispersion correction is enabled by default when using the GFN1-xTB model Hamiltonian, but can be disabled manually by setting this keyword to None.

The newest and most accurate dispersion correction is D4. We recommend both the D3-BJ and D4 dispersion corrections as good defaults, depending on their availability for the specific combination of the model Hamiltonian and parameterization. Note that the D4 dispersion corrections is computationally more expensive than D3-BJ for bulk periodic systems (it scales as O(N^{3}) with the number of atoms and is not parallelized), thus the user may first want to evaluate if the increased accuracy justifies the increased computational cost.

## Solvation (GBSA)¶

Solvation effects can be included via the implicit GBSA solvation model. We gratefully acknowledge the Grimme’s group in Bonn for their contribution of the GBSA solvation method code.

To enable the GBSA method, specify the desired solvent:

```
Solvation
Solvent [None | Acetone | Acetonitrile | CHCl3 | CS2 | DMSO | Ether | H2O | Methanol |
THF | Toluene]
End
```

`Solvation`

- Type
Block

- Description
Generalized Born solvation model with Solvent Accessible Surface Area (GBSA).

`Solvent`

- Type
Multiple Choice

- Default value
None

- Options
[None, Acetone, Acetonitrile, CHCl3, CS2, DMSO, Ether, H2O, Methanol, THF, Toluene]

- Description
Solvent used in the GBSA implicit solvation model.

More options can be specified in the `Solvation`

block:

```
Solvation
UseGSASA Yes/No
GSolvState [Gas1BarSolvent | Gas1MSolvent1M | Gas1BarSolvent1M]
Temperature float
SurfaceGrid [230 | 974 | 2030 | 5810]
End
```

`Solvation`

`UseGSASA`

- Type
Bool

- Default value
Yes

- GUI name
Solvation Free Energy

- Description
Include shift term and G(SASA) terms in the energy and gradient.

`GSolvState`

- Type
Multiple Choice

- Default value
Gas1MSolvent1M

- Options
[Gas1BarSolvent, Gas1MSolvent1M, Gas1BarSolvent1M]

- Description
Reference state for solvation free energy shift.

`Temperature`

- Type
Float

- Default value
298.15

- Unit
Kelvin

- Description
The temperature used when calculating the solvation free energy shift. Only used for ‘Gas1BarSolvent’ and ‘Gas1BarSolvent1M’ GSolvState options.

`SurfaceGrid`

- Type
Multiple Choice

- Default value
230

- Options
[230, 974, 2030, 5810]

- Description
Number of angular grid points for the construction of the solvent accessible surface area. Usually the default number of grid point suffices, but in case of suspicious behaviors you can increase the number of points.

## SCC details and spin-polarization¶

With SCC DFTB the parametrized Hamiltonian depends on partial atomic charges, that need to be determined self consistently. These charges are usually atomic charges, but they may be shell and/or spin resolved. The self consistency requirement

\(\vec{q}^\text{in}=\vec{q}^\text{in}\)

is numerically expressed as

\(\frac{1}{\sqrt{N_\text{atoms}}} | \vec{q}^\text{in}-\vec{q}^\text{in} | < \epsilon\)

The vector norm is by default the so-called L-infinity norm, being the maximum absolute value of the vector elements. The underlying algorithm, however, will minimize the L-2 norm. Based upon the history of past input and ouput charge vectors a next one is guessed

\(\vec{q}^\text{guess}=\sum_i c_{i-1}^N (\vec{q}^\text{in}_i + \sigma(\vec{q}^\text{out}_i-\vec{q}^\text{in}_i))\)

How many past vectors (N) are used and the value of the coefficients depends on the algorithm, as is the mix factor \(\sigma\). The default method is the MultiStepper, which is explained separately. The older DIIS method is more simple to tweak in case the SCC does not converge.

```
SCC
AlwaysClaimConvergence Yes/No
Converge
Charge float
Norm [L2 | L-Infinity]
End
HXDamping Yes/No
InheritMixFromPreviousResult Yes/No
Iterations integer
Method [DIIS | MultiStepper]
MinimumAdaptiveMixingFactor float
OrbitalDependent Yes/No
Unrestricted Yes/No
End
```

`SCC`

- Type
Block

- Description
This optional section configures various details of the self-consistent charge cycle. If the model Hamiltonian does not need a self-consistent solution (e.g. plain DFTB0), none of this information is used and the entire section will be ignored.

`AlwaysClaimConvergence`

- Type
Bool

- Default value
No

- Description
Even if the SCC does not converge, claim convergence.

`Converge`

- Type
Block

- Description
Controls the convergence criteria of the SCC cycle.

`Charge`

- Type
Float

- Default value
1e-08

- GUI name
Charge convergence

- Description
The maximum change in atomic charges between subsequent SCC iterations. If the charges change less, the SCC cycle is considered converged.

`Norm`

- Type
Multiple Choice

- Default value
L-Infinity

- Options
[L2, L-Infinity]

- Description
The LInfinity norm is the more stringent choice. The L2 norm is directly what is optimized by the DIIS procedure, it is scaled by the extra constant factor 2/sqrt(nAtoms).

`HXDamping`

- Type
Bool

- Description
This option activates the DFTB3 style damping for H-X bonds. Note that this is always enabled if the DFTB%Model key is set to DFTB3. Not used with xTB.

`InheritMixFromPreviousResult`

- Type
Bool

- Default value
No

- Description
For some run types, such as GeometryOptimization, a previous result is available. By using the charges from the previous geometry a better initial guess for the SCC procedure may be obtained. Also the last mix factor from the previous result can be loaded, possibly speeding up the SCC.

`Iterations`

- Type
Integer

- Default value
500

- Description
Allows to specify the maximum number of SCC iterations. The default should suffice for most standard calculations. Convergence issues may arise due to the use of the Aufbau occupations for systems with small HOMO-LUMO gaps. In this case the use of a Fermi broadening strategy may improve convergence. Choosing a smaller mixing parameter (see DFTB%SCC%Mixing) may also help with convergence issues: it often provides a more stable but slower way to converge the SCC cycle.

`Method`

- Type
Multiple Choice

- Default value
MultiStepper

- Options
[DIIS, MultiStepper]

- Description
The DIIS option is the old method. The MultiStepper is much more flexible and is controlled by the SCFMultiSolver block

`MinimumAdaptiveMixingFactor`

- Type
Float

- Default value
0.003

- Description
In case of AdaptiveMixing the lower bound for the MixingFactor.

`OrbitalDependent`

- Type
Bool

- Description
Activates or disables orbital resolved calculations. If this key is absent the recommended settings from the parameter file’s metainfo.

`Unrestricted`

- Type
Bool

- Default value
No

- Description
Enables spin unrestricted calculations. Only collinear spin polarization is supported, see Theor Chem Acc (2016) 135: 232, for details. Must be supported by the chosen parameter set. Not yet compatible with DFTB3, k-space sampling periodic calculations or the xTB models.

```
Occupation
KT float
NumBoltz integer
Strategy [Auto | Aufbau | Fermi]
Temperature float
End
```

`Occupation`

- Type
Block

- Description
Configures the details of how the molecular orbitals are occupied with electrons.

`KT`

- Type
Float

- Unit
Hartree

- Description
(KT) Boltmann constant times temperature, used for electronic temperature with strategy is auto. The default value is the default value for Temperature*3.166815423e-6. This key and Temperature are mutually exlusive.

`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.

`Strategy`

- Type
Multiple Choice

- Default value
Auto

- Options
[Auto, Aufbau, Fermi]

- GUI name
Occupation

- Description
This optional key allows to specify the fill strategy to use for the molecular orbitals. Can either be ‘Aufbau’ for simply filling the energetically lowest orbitals, or ‘Fermi’ for a smeared out Fermi-Dirac occupation. By default the occupation strategy is determined automatically, based on the other settings (such as the number of unpaired electrons).

`Temperature`

- Type
Float

- Default value
300.0

- Unit
Kelvin

- GUI name
Fermi temperature

- Description
The Fermi temperature used for the Fermi-Dirac distribution. Ignored in case of aufbau occupations.

```
UnpairedElectrons integer
```

`UnpairedElectrons`

- Type
Integer

- Default value
0

- GUI name
Spin polarization

- Description
This specifies the number of unpaired electrons (not the multiplicity!). This number will then be used in the orbital-filling strategy. Has to be compatible with the total number of electrons, meaning it must be an even number if the total number of electrons is even and odd if the total number is odd. Must be an integer value. Note that this does not activate spin polarization, it only affects the filling of the orbitals.

### MultiStepper¶

The MultiStepper introduces the concept of alternating between different steppers (methods). Methods are not switched at every SCF cycle, but rather after a sequence of them, called a stint. At the end of a stint it is considered whether it makes sense to try another stepper.

The key component is the Stepper. This wraps the type of the Stepper, say DIIS or SimpleMixing. Another important component is the MixAdapter. A step is controlled by a mix factor \(\sigma\), also often called greed. The next guess charge vector is a linear combination of previous input and output charges

\(\vec{q}^\text{guess}=\sum_i c_{i-1}^N (\vec{q}^\text{in}_i + \sigma(\vec{q}^\text{out}_i-\vec{q}^\text{in}_i))\)

The larger the mix factor the more aggressive the algorithm. Choosing it too small may simply stall the progress and choosing it too large can cause the error to grow. That is why using a MixAdapter is useful. It tries to predict a reasonable mix value, based on the progress of the error and also based on the number of previous iterations \(N\) that can be used without running into numerical problems.

A whole SCFMultiStepper block can be loaded from a file as a preset, and many reside in `$AMSHOME/data/presets/multi_stepper`

. Normal users are not recommended to try to improve the standard preset. Which preset to loaded is controlled by the `SCF%MultiStepperPresetPath`

key, and this may be an absolute path to your own preset.

The the log file (ams.log) shows the active stepper and mix factor.

```
<Nov22-2022> <15:24:28> cyc= 0 err=0.00E+00 cpu= 75s ela= 76s
<Nov22-2022> <15:25:26> cyc= 1 err=4.26E+00 meth=1 nvec= 1 mix=0.0750 cpu= 57s ela= 58s fit=7.06E-02
<Nov22-2022> <15:26:26> cyc= 2 err=8.33E+00 meth=1 nvec= 2 mix=0.1455 cpu= 59s ela= 60s fit=6.49E-02
<Nov22-2022> <15:27:23> cyc= 3 err=7.85E+00 meth=1 nvec= 3 mix=0.1499 cpu= 56s ela= 57s fit=6.42E-02
<Nov22-2022> <15:28:24> cyc= 4 err=7.09E+00 meth=1 nvec= 4 mix=0.1544 cpu= 60s ela= 61s fit=6.37E-02
<Nov22-2022> <15:29:21> cyc= 5 err=9.49E+00 meth=2 nvec= 1 mix=0.0060 cpu= 57s ela= 57s fit=7.91E-02
<Nov22-2022> <15:30:20> cyc= 6 err=2.63E+00 meth=2 nvec= 2 mix=0.0062 cpu= 59s ela= 59s fit=7.88E-02
<Nov22-2022> <15:31:18> cyc= 7 err=3.82E+00 meth=2 nvec= 3 mix=0.0060 cpu= 57s ela= 58s fit=7.84E-02
<Nov22-2022> <15:32:16> cyc= 8 err=3.53E+00 meth=2 nvec= 4 mix=0.0062 cpu= 58s ela= 58s fit=7.81E-02
```

From cycle 5 (cyc=5) on the second stepper is tried (meth=2), in this case because the error has grown too much since the start. Furthermore it restarts from the first density, not shown in the log file, using only one older density (nvec=1). Note that the second stepper starts with using a much more conservative mix factor (mix=0.006).

```
SCC
SCFMultiStepper
AlwaysChangeStepper Yes/No
ErrorGrowthAbortFactor float
FractionalStepFactor float
MinStintCyclesForAbort integer
Stepper header
AbortSlope float
DIISStepper
EDIISAlpha float
MaxCoefficient float
MaxVectors integer
MinVectors integer
Mix float
End
ErrorGrowthAbortFactor float
ExpectedSlope float
FractionalStepFactor float
MaxInitialError float
MaxIterationNumber integer
MaxStintNumber integer
MinInitialError float
MinIterationNumber integer
MinStintCyclesForAbort integer
MinStintNumber integer
MixAdapter
ErrorGrowthPanicFactor float
GrowthFactor float
MaxMix float
MinMix float
NTrialMixFactors integer
TrialMode [CurrentMixCentered | FullRange]
Type [Error | Energy | UnpredictedStep | Trial]
End
MixStepper
Mix float
End
MultiSecantStepper
MaxCoefficient float
MaxVectors integer
Mix float
Variant [MSB1 | MSB2 | MSR1 | MSR1s]
End
StintLength integer
End
StintLength integer
UsePreviousStintForErrorGrowthAbort Yes/No
End
MultiStepperPresetPath string
End
```

`SCC`

`SCFMultiStepper`

- Type
Block

- Description
To solve the self-consistent problem multiple steppers can be tried during stints using the ones that give the best progress.

`AlwaysChangeStepper`

- Type
Bool

- Default value
No

- Description
When the progress is fine there is no reason to change the stepper. In practice this is always set to true, because also the Stepper%ExpectedSlope can be used to achieve similar behavior.

`ErrorGrowthAbortFactor`

- Type
Float

- Default value
1000.0

- Description
Abort stint when the error grows too much, compared to the error at the start of the stint.

`FractionalStepFactor`

- Type
Float

- Default value
-1.0

- Description
Multiply the step by this factor. If smaller than zero this is not used.

`MinStintCyclesForAbort`

- Type
Integer

- Default value
0

- Description
Look at ErrorGrowthAbortFactor only when a number of steps has been completed since the start of the stint. A value of 0 means always.

`Stepper`

- Type
Block

- Recurring
True

- Description
??

`AbortSlope`

- Type
Float

- Default value
100.0

- Description
If the slope (at the end of a stint) is larger than this: abort the stepper

`DIISStepper`

- Type
Block

- Description
DIIS stepper

`EDIISAlpha`

- Type
Float

- Default value
0.01

- Description
The extra energy vector is weighed by this factor. .

`MaxCoefficient`

- Type
Float

- Default value
20.0

- Description
The largest allowed value of the expansion coefficients. If exceed the number of vectors is reduces until the criterion is met.

`MaxVectors`

- Type
Integer

- Default value
10

- Description
Maximum number of previous densities to be used (size of the history).

`MinVectors`

- Type
Integer

- Default value
-1

- Description
Try to prevent to make nVectors shrink below this value, by allowing for significantly larger coefficents.

`Mix`

- Type
Float

- Default value
0.2

- Description
Also known as greed. It determines the amount of output density to be used. May be changed by the MixAdapter.

`ErrorGrowthAbortFactor`

- Type
Float

- Default value
-1.0

- Description
Abort stint when the error grows too much, compared to the error at the start of the stint. Overides global ErrorGrowthAbortFactor when set to a value > 0

`ExpectedSlope`

- Type
Float

- Default value
-100.0

- Description
If the slope of the total SCF is better than this keep on going.

`FractionalStepFactor`

- Type
Float

- Default value
-1.0

- Description
Multiply the step by this factor. If smaller than zero this is not used.

`MaxInitialError`

- Type
Float

- Description
Only use the stepper when error is smaller than this.

`MaxIterationNumber`

- Type
Integer

- Default value
-1

- Description
Stepper will only be active for iterations smaller than this number. (Negative value means: Ignore this option)

`MaxStintNumber`

- Type
Integer

- Default value
-1

- Description
Stepper will only be active for stints smaller than this number. (Negative value means: Ignore this option)

`MinInitialError`

- Type
Float

- Description
Only use the stepper when error is larger than this.

`MinIterationNumber`

- Type
Integer

- Default value
-1

- Description
Stepper will only be active for iterations larger than this number.

`MinStintCyclesForAbort`

- Type
Integer

- Default value
0

- Description
Look at ErrorGrowthAbortFactor only when a number of steps has been completed since the start of the stint. A value of 0 means always. Overides global value.

`MinStintNumber`

- Type
Integer

- Default value
-1

- Description
Stepper will only be active for stints larger than this number.

`MixAdapter`

- Type
Block

- Description
Generic mix adapter

`ErrorGrowthPanicFactor`

- Type
Float

- Default value
10.0

- Description
When the error increases more than this factor, this mix is reduced a lot.

`GrowthFactor`

- Type
Float

- Default value
1.1

- Description
When the mix is considered too low it is multiplied by this factor. Otherwise it is divided by it.

`MaxMix`

- Type
Float

- Default value
0.3

- Description
Do not grow the mix above this value.

`MinMix`

- Type
Float

- Default value
0.1

- Description
Do not shrink the mix below this value.

`NTrialMixFactors`

- Type
Integer

- Default value
3

- Description
Only used with Type=Trial. Must be an odd number.

`TrialMode`

- Type
Multiple Choice

- Default value
CurrentMixCentered

- Options
[CurrentMixCentered, FullRange]

- Description
How are the NTrialMixFactors chosen?

`Type`

- Type
Multiple Choice

- Default value
Error

- Options
[Error, Energy, UnpredictedStep, Trial]

- Description
Adapt the mix factor based on the observed progress (slope).

`MixStepper`

- Type
Block

- Description
Simple mixing stepper, only using the previous (in/out) denstity.

`Mix`

- Type
Float

- Default value
0.1

- Description
???.

`MultiSecantStepper`

- Type
Block

- Description
Multi secant stepper.

`MaxCoefficient`

- Type
Float

- Default value
20.0

- Description
???.

`MaxVectors`

- Type
Integer

- Default value
10

- Description
???.

`Mix`

- Type
Float

- Default value
0.2

- Description
???.

`Variant`

- Type
Multiple Choice

- Default value
MSB2

- Options
[MSB1, MSB2, MSR1, MSR1s]

- Description
There are several version of the Multi secant method.

`StintLength`

- Type
Integer

- Description
Override global StintLength.

`StintLength`

- Type
Integer

- Default value
10

- Description
A stepper is active during a number of SCF cycles, called a stint.

`UsePreviousStintForErrorGrowthAbort`

- Type
Bool

- Default value
No

- Description
The error is normally checked against the first error of the stint. With this option that will be the one from the previous stint, if performed with the same stepper.

`MultiStepperPresetPath`

- Type
String

- Default value
DFTB/default2023.inc

- Description
Name of file containing a SCFMultiStepper key block. This will be used if no Explicit SCFMultiStepper block is in the input, and Method=MultiStepper. If the path is not absolute, it is relative to $AMSHOME/data/presets/multi_stepper’

### DIIS¶

When selecting the SCC method DIIS, these are the relevant options. Compared to the MultiStepper it is more straightforward to tweak.

```
SCC
AdaptiveMixing Yes/No
DIIS
Enabled Yes/No
MaxSamples integer
MaximumCoefficient float
MinSamples integer
MixingFactor float
End
End
```

`SCC`

`AdaptiveMixing`

- Type
Bool

- Default value
Yes

- Description
Change the mixing parameter based on the monitored energy. A significant increase of energy will strongly reduce the mixing. Then it will slowly grow back to the SCC%Mixing value.

`DIIS`

- Type
Block

- Description
Parameters influencing the DIIS self-consistency method

`Enabled`

- Type
Bool

- Default value
Yes

- Description
If not enabled simple mixing without DIIS acceleration will be used.

`MaxSamples`

- Type
Integer

- Default value
20

- Description
Specifies the maximum number of samples considered during the direct inversion of iteration of subspace (DIIS) extrapolation of the atomic charges during the SCC iterations. A smaller number of samples potentially leads to a more aggressive convergence acceleration, while a larger number often guarantees a more stable iteration. Due to often occurring linear dependencies within the set of sample vectors, the maximum number of samples is reached only in very rare cases.

`MaximumCoefficient`

- Type
Float

- Default value
10.0

- Description
When the diis expansion coefficients exceed this threshold, the solution is rejected. The vector space is too crowded. The oldest vector is discarded, and the expansion is re-evaluated.

`MinSamples`

- Type
Integer

- Default value
-1

- Description
When bigger than one, this affects the shrinking of the DIIS space on linear depence. It will not reduce to a smaller space than MinSamples unless there is extreme dependency.

`MixingFactor`

- Type
Float

- Default value
0.15

- Description
The parameter used to mix the DIIS linear combination of previously sampled atomic charge vectors with an analogous linear combination of charge vectors resulting from population analysis combination. It can assume real values between 0 and 1.

## k-space integration¶

As of the 2019 release, the k-space integration is unified between BAND and DFTB and uses the same keys as input, and the same defaults. See the page on k-space integration in the BAND manual for details and recommendations.

```
KSpace
Quality [GammaOnly | Basic | Normal | Good | VeryGood | Excellent]
Regular
NumberOfPoints integer_list
End
Symmetric
KInteg integer
End
Type [Regular | Symmetric]
End
```

`KSpace`

- Type
Block

- Description
Options for the k-space integration (i.e. the grid used to sample the Brillouin zone).

`Quality`

- Type
Multiple Choice

- Default value
Normal

- Options
[GammaOnly, Basic, Normal, Good, VeryGood, Excellent]

- GUI name
K-space

- Description
Select the quality of the K-space grid used to sample the Brillouin Zone. If ‘GammaOnly’, only one point (the gamma point) will be used. For the other options, the actual number of K points generated depends on the size of the unit cell. The larger the real space cell, the fewer K points will be generated. The CPU-time and accuracy strongly depend on this option.

`Regular`

- Type
Block

- Description
Options for the regular k-space integration grid.

`NumberOfPoints`

- Type
Integer List

- Description
Use a regular grid with the specified number of k-points along each reciprocal lattice vector. For 1D periodic systems you should specify only one number, for 2D systems two numbers, and for 3D systems three numbers.

`Symmetric`

- Type
Block

- Description
Options for the symmetric k-space integration grid.

`KInteg`

- Type
Integer

- GUI name
Accuracy

- Description
Specify the accuracy for the Symmetric method. 1: absolutely minimal (only the G-point is used) 2: linear tetrahedron method, coarsest spacing 3: quadratic tetrahedron method, coarsest spacing 4,6,… (even): linear tetrahedron method 5,7…. (odd): quadratic method The tetrahedron method is usually by far inferior.

`Type`

- Type
Multiple Choice

- Default value
Regular

- Options
[Regular, Symmetric]

- GUI name
K-space grid type

- Description
The type of k-space integration grid used to sample the Brillouin zone (BZ) used. ‘Regular’: simple regular grid. ‘Symmetric’: symmetric grid for the irreducible wedge of the first BZ (useful when high-symmetry points in the BZ are needed to capture the correct physics of the system, graphene being a notable example).

## xTB specific keywords¶

A few keywords only apply to the xTB model Hamiltonian.

```
XTBConfig
SlaterRadialThreshold float
useXBTerm Yes/No
End
```

`XTBConfig`

- Type
Block

- Description
This block allows for minor tweaking.

`SlaterRadialThreshold`

- Type
Float

- Default value
1e-05

- Description
Threshold determining the range of the basis functions. Using a larger threshold will speed up the calculation, but will also make the results less accurate.

`useXBTerm`

- Type
Bool

- Default value
No

- Description
Whether to use the Halogen bonding (XB) term. This is not advised as it has a non-continuous PES.

Note

The GFN1-xTB implementation in AMS currently does not implement the electronic entropy term from the article by Grimme et al. It therefore gives slightly different energies (but not gradients!) for systems with partially occupied molecular orbitals.

## Technical options¶

```
Technical
AnalyticalStressTensor Yes/No
EwaldSummation
CellRangeFactor float
Enabled Yes/No
Tolerance float
End
MatricesViaFullMaxSize integer
Parallel
nCoresPerGroup integer
nGroups integer
nNodesPerGroup integer
End
ReuseKSpaceConfig Yes/No
Screening
dMadel float
rMadel float
End
UseGeneralizedDiagonalization Yes/No
End
```

`Technical`

- Type
Block

- Description
This optional section is about technical aspects of the program that should not concern the normal user.

`AnalyticalStressTensor`

- Type
Bool

- Default value
Yes

- Description
Whether to compute the stress tensor analytically. Note: This can only be used together with Ewald summation as it will give (slightly) wrong results with Madelung screening.

`EwaldSummation`

- Type
Block

- Description
Configures the details of the Ewald summation of the Coulomb interaction.

`CellRangeFactor`

- Type
Float

- Default value
2.0

- Description
Smaller values will make the Ewald summation less accurate but faster.

`Enabled`

- Type
Bool

- Default value
Yes

- Description
Whether to use Ewald summation for the long-range part of the Coulomb interaction. Otherwise screening is used.

`Tolerance`

- Type
Float

- Default value
1e-10

- Description
Larger values will make the Ewald summation less accurate but faster.

`MatricesViaFullMaxSize`

- Type
Integer

- Default value
2047

- Description
Matrices smaller than this size are constructed via a full matrix. This is faster, but uses more memory in the construction.

`Parallel`

- Type
Block

- Description
Calculation of the orbitals in several k-points is trivially parallel.

`nCoresPerGroup`

- Type
Integer

- Description
Number of cores in each working group.

`nGroups`

- Type
Integer

- Description
Total number of processor groups. This is the number of tasks that will be executed in parallel.

`nNodesPerGroup`

- Type
Integer

- GUI name
Cores per task

- Description
Number of nodes in each group. This option should only be used on homogeneous compute clusters, where all used compute nodes have the same number of processor cores.

`ReuseKSpaceConfig`

- Type
Bool

- Default value
Yes

- Description
Keep the number of k-points constant during a lattice optimization. Otherwise the PES might display jumps, because the number of points depends on the lattice vector sizes. If this option is on it will always use the number of k-points that was used from a previous result.

`Screening`

- Type
Block

- Description
For SCC-DFTB in periodic systems the Coulomb interaction can (instead of using Ewald summation) be screened with a Fermi-Dirac like function defined as S(r)=1/(exp((r-r_madel)/d_madel)+1). This section allows to change some details of the screening procedure. Note that Coulomb screening is only used if the Ewald summation is disabled.

`dMadel`

- Type
Float

- Unit
Bohr

- Description
Sets the smoothness of the screening function. The default is 1/10 of [rMadel].

`rMadel`

- Type
Float

- Unit
Bohr

- Description
Sets the range of the screening function. The default is 2x the norm of the longest lattice vector.

`UseGeneralizedDiagonalization`

- Type
Bool

- Default value
Yes

- Description
Whether or not to use generalized diagonalization. Does not affect the results, but might be faster or slower.

```
StoreMatrices Yes/No
```

`StoreMatrices`

- Type
Bool

- Default value
No

- Description
Determines whether the Hamiltonian and overlap matrices are stored in the binary result file.