Model Hamiltonians¶

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(N³) 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.

QM/FQ Embedding¶

Environmental effects can be included in the calculation by means of the Fluctuating Charge (FQ) model. The theory behind the model is presented in the corresponding ADF manual page . The method can be used for both ground-state and TD-DFTB calculations.

To enable the FQ model one must include the QMFQ block keyword containing the method options, parameters, and coordinates of the environment atoms. More details on the input structure can also be found in the ADF manual page .

QMFQ
   AtomType
      Alpha float
      Charge float
      Chi float
      Eta float
      Symbol string
   End
   Coords # Non-standard block. See details.
      ...
   End
   Forcefield [FQ | FQFMU | NOPOL]
   Frozen Yes/No
   Kernel [OHNO | COUL | GAUS]
   MolCharge float
End

QMFQ

Type:

Block

Description:

Block input key for QM/FQ(FMu).

AtomType

Type:

Block

Recurring:

True

Description:

Definition of atomic types in MM environment

Alpha

Type:

Float

Description:

Polarizability of FQFMU atom

Charge

Type:

Float

Description:

MM fixed charge (non-polarizable only)

Chi

Type:

Float

Description:

Electronegativity of FQ atom

Eta

Type:

Float

Description:

Chemical Hardness of FQ atom

Symbol

Type:

String

Description:

Symbol associated with atom type

Coords

Type:

Non-standard block

Description:

Coordinates and fragment information (FQ only)

Forcefield

Type:

Multiple Choice

Default value:

FQ

Options:

[FQ, FQFMU, NOPOL]

Description:

Version of the FQ family of polarizable forcefields

Frozen

Type:

Bool

Default value:

No

Description:

Expert option. Do not introduce polarization effect in response calculations.

Kernel

Type:

Multiple Choice

Default value:

OHNO

Options:

[OHNO, COUL, GAUS]

Description:

Expert option. KERNEL can be used to choose the functional form of the charge-charge interaction kernel between MM atoms. Recommended is to use the default OHNO. The COUL screening is the standard Coulomb interaction 1/r. The OHNO choice introduce the Ohno functional (see [K. Ohno, Theoret. Chim. Acta 2, 219 (1964)]), which depends on a parameter n that is set equal to 2. Finally, the GAUS screening models each FQ charge by means of a spherical Gaussian-type distribution, and the interaction kernel is obtained accordingly. For QM/FQFMU only GAUS SCREEN is implemented.

MolCharge

Type:

Float

Default value:

0.0

Description:

Total charge of each fragment (FQ only)

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
   SpinOrbit 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.

SpinOrbit

Type:

Bool

Default value:

No

Description:

test

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) Boltzmann 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 exclusive.

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.

<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

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

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 [Auto | 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:

Auto

Options:

[Auto, 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 ‘Auto’, the quality defined in the ‘NumericalQuality’ will be used. If ‘GammaOnly’, only one point (the gamma point) will be used. The actual number of K points generated depends on this option and 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.

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.