Spectroscopy and properties¶

Electronic structure of periodic systems¶

Periodic
   EffectiveMass
      Enabled Yes/No
      KPointCoord float_list
      NumAbove integer
      NumBelow integer
      StepSize float
   End
   BandStructure
      Automatic Yes/No
      DeltaK float
      Enabled Yes/No
      FatBands Yes/No
      UseSymmetry Yes/No
   End
   BZPath
      Path # Non-standard block. See details.
         ...
      End
   End
   DOS
      EMax float
      EMin float
      Enabled Yes/No
      NSteps integer
   End
End

Periodic

Type: Block
Description: Block that sets various details of the calculation only relevant for periodic systems.

EffectiveMass

Type: Block
Description: In a semi-conductor, the mobility of electrons and holes is related to the curvature of the bands at the top of the valence band and the bottom of the conduction band. With the effective mass option, this curvature is obtained by numerical differentiation. The estimation is done with the specified step size, and twice the specified step size, and both results are printed to give a hint on the accuracy. By far the most convenient way to use this key is without specifying any options.

Enabled

Type: Bool
Default value: No
GUI name: Effective mass
Description: In a semi-conductor, the mobility of electrons and holes is related to the curvature of the bands at the top of the valence band and the bottom of the conduction band. With the effective mass option, this curvature is obtained by numerical differentiation. The estimation is done with the specified step size, and twice the specified step size, and both results are printed to give a hint on the accuracy. By far the most convenient way to use this key is without specifying any options.

KPointCoord

Type: Float List
Unit: 1/Bohr
Recurring: True
GUI name: At K-point
Description: Coordinate of the k-points for which you would like to compute the effective mass.

NumAbove

Type: Integer
Default value: 1
GUI name: Include N bands above
Description: Number of bands to take into account above the Fermi level.

NumBelow

Type: Integer
Default value: 1
GUI name: Include N bands below
Description: Number of bands to take into account below the Fermi level.

StepSize

Type: Float
Default value: 0.001
Description: Size of the step taken in reciprocal space to perform the numerical differentiation

BandStructure

Type: Block
Description: Options for band structure plotting. This has no effect on the calculated energy. [Warning: The band structure is only computed in case of k-space sampling, i.e. it is not computed for Gamma-only calculations (see: Periodic%KSpace).]

Automatic

Type: Bool
Default value: Yes
GUI name: Automatic generate path
Description: Generate and use the standard path through the Brillouin zone. If not, use the user defined path (set via Custom path in the GUI, or with the Periodic%BZPath keyword in the run script).

DeltaK

Type: Float
Default value: 0.1
Unit: 1/Bohr
GUI name: Interpolation delta-K
Description: Step size in reciprocal space for band structure interpolation. Using a smaller number will produce smoother band curves at an increased computational time.

Enabled

Type: Bool
Default value: Yes
GUI name: Calculate band structure
Description: Whether or not to calculate the band structure.

FatBands

Type: Bool
Default value: Yes
GUI name: Calculate fatbands
Description: Control the computation of the fat bands (only when the bandstructure is calculated). The fat bands are the periodic equivalent of the Mulliken population analysis. The definition of the fat bands can be found in the Band Documentation.

UseSymmetry

Type: Bool
Default value: Yes
Description: If set, only the irreducible wedge of the Wigner-Seitz cell is sampled. If not, the whole (inversion-unique) Wigner-Seitz cell is sampled.

BZPath

Type: Block
Description: If [BandStructure%Automatic] is disabled, DFTB will compute the band structure for the user-defined path in the [BZPath] block. You should define the vertices of your path in fractional coordinates (with respect to the reciprocal lattice vectors) in the [Path] sub-block. If you want to make a jump in your path, you need to specify a new [Path] sub-block.

Path

Type: Non-standard block
Recurring: True
Description: A section of a k space path.

DOS

Type: Block
Description: The subkeys of [DOS] allow to customize the calculation of the density of states.

EMax

Type: Float
Default value: 0.75
Unit: Hartree
Description: Upper end of the energy interval in which the density of states is calculated.

EMin

Type: Float
Default value: -0.75
Unit: Hartree
Description: Lower end of the energy interval in which the density of states is calculated.

Enabled

Type: Bool
Default value: Yes
GUI name: Calculate DOS
Description: Whether or not to calculate the DOS. Note that the DOS will always be calculated when also the band structure is calculated.

NSteps

Type: Integer
Default value: 300
Description: The number of energy intervals between [EMin] and [EMax] for which the density of states is calculated.

Excited states with time-dependent DFTB¶

DFTB allows for excited state calculations on molecular systems by means of single orbital transitions as well as time-dependent DFTB as published by Niehaus et al. in Phys. Rev. B 63, 085108 (2001). Singlet-singlet as well as singlet-triplet excitations can be calculated. DFTB also supports the calculation of excited state gradients, which allows geometry optimizations and vibrational frequency calculations for excited states.

The TD-DFTB implementation uses the PRIMME library (PReconditioned Iterative MultiMethod Eigensolver) by Andreas Stathopoulos and James R. McCombs, PRIMME: PReconditioned Iterative MultiMethod Eigensolver: Methods and software description ACM Transaction on Mathematical Software Vol. 37, No. 2, (2010), 21:1–21:30.

DFTB excited state calculations are controlled by the following keywords:

Properties
   Excitations
      SingleOrbTrans
         Enabled Yes/No
         Filter
            OSMin float
            dEMax float
            dEMin float
         End
         PrintLowest integer
      End
      TDDFTB
         Calc [None | Singlet | Triplet]
         DavidsonConfig
            ATCharges [Precalc | OnTheFly]
            SafetyMargin integer
            Tolerance float
         End
         Diagonalization [Auto | Davidson | Exact]
         Lowest integer
         Print string
         ScaleKernel float
         UpTo float
      End
      TDDFTBGradients
         Eigenfollow Yes/No
         Excitation integer_list
      End
   End
End

Properties

Type: Block
Description: DFTB can calculate various properties of the simulated system. This block configures which properties will be calculated.

Excitations

Type: Block
Description: Contains all options related to the calculation of excited states, either as simple single orbitals transitions or from a TD-DFTB calculation.

SingleOrbTrans

Type: Block
Description: The simplest approximation to the true excitations are the single orbital transitions (sometimes called Kohn-Sham transitions), that is transitions where a single electron is excited from an occupied Kohn-Sham orbital into a virtual orbital. The calculation of these transitions is configured in this section. Note that the SingleOrbTrans section is optional even though the single orbital transitions are also needed for TD-DFTB calculations. If the section is not present all single orbital transitions will still be calculated and used in a subsequent TD-DFTB calculation, but no output will be produced.

Enabled

Type: Bool
Default value: No
GUI name: Single orbital transisitions: Calculate
Description: Calculate the single orbital transitions.

Filter

Type: Block
Description: This section allows to remove single orbital transitions based on certain criteria. All filters are disabled by default.

OSMin

Type: Float
GUI name: Minimum oscillator strength
Description: Removes single orbital transitions with an oscillator strength smaller than this threshold. A typical value to start (if used at all) would be 1.0e-3.

dEMax

Type: Float
Unit: Hartree
Description: Removes single orbital transitions with an orbital energy difference larger than this threshold.

dEMin

Type: Float
Unit: Hartree
Description: Removes single orbital transitions with an orbital energy difference smaller than this threshold.

PrintLowest

Type: Integer
Default value: 10
Description: The number of single orbital transitions that are printed to the screen and written to disk. If not a TD-DFTB calculation, the default is to print the 10 lowest single orbital transitions. In case of a TD-DFTB calculation it is assumed that the single orbital transitions are only used as an input for TD-DFTB and nothing will be printed unless PrintLowest is specified explicitly.

TDDFTB

Type: Block
Description: Calculations with time-dependent DFTB can be configured in the TDDFTB section and should in general give better results than the raw single orbital transitions. TD-DFTB calculates the excitations in the basis of the single orbital transitions, whose calculation is configured in the SingleOrbTrans section. Using a filter in SingleOrbTrans can therefore be used to reduce the size of the basis for TD-DFTB. One possible application of this is to accelerate the calculation of electronic absorption spectra by removing single orbital transitions with small oscillator strengths from the basis. Note that the entire TDDFTB section is optional. If no TDDFTB section is found, the behavior depends on the existence of the SingleOrbTrans section: If no SingleOrbTrans section is found (the Excitations section is completely empty then) a TD-DFTB calculation with default parameters will be performed. If only the SingleOrbTrans section is present no TD-DFTB calculation will be done.

Calc

Type: Multiple Choice
Default value: None
Options: [None, Singlet, Triplet]
GUI name: Type of excitations
Description: Specifies the multiplicity of the excitations to be calculated.

DavidsonConfig

Type: Block
Description: This section contains a number of keywords that can be used to override various internals of the Davidson eigensolver. The default values should generally be fine.

ATCharges

Type: Multiple Choice
Default value: Precalc
Options: [Precalc, OnTheFly]
GUI name: Transition charges
Description: Select whether the atomic transition charges are precalculated in advance or reevaluated during the iterations of the Davidson solver. Precalculating the charges will improve the performance, but requires additional storage. The default is to precalculate the atomic transition charges, but the precalculation may be disabled if not not enough memory is available.

SafetyMargin

Type: Integer
Default value: 4
Description: The number of eigenvectors the Davidson method will calculate in addition to the ones requested by the user. With the Davidson eigensolver it is generally a good idea to calculate a few more eigenvectors than needed, as depending on the initial guess for the eigenvectors it can happen that the found ones are not exactly the lowest ones. This problem is especially prominent if one wants to calculate only a small number of excitations for a symmetric molecule, where the initial guesses for the eigenvectors might have the wrong symmetry. Note that the additionally calculated excitations will neither be written to the result file nor be visible in the output.

Tolerance

Type: Float
Default value: 1e-09
Description: Convergence criterion for the norm of the residual.

Diagonalization

Type: Multiple Choice
Default value: Auto
Options: [Auto, Davidson, Exact]
GUI name: Method
Description: Select the method used to solve the TD-DFTB eigenvalue equation. The most straightforward procedure is a direct diagonalization of the matrix from which the excitation energies and oscillator strengths are obtained. Since the matrix grows quickly with system size (number of used single orbital transitions squared), this option is possible only for small molecules. The alternative is the iterative Davidson method, which finds a few of the lowest excitations within an error tolerance without ever storing the full matrix. The default is to make this decision automatically based on the system size and the requested number of excitations.

Lowest

Type: Integer
Default value: 10
GUI name: Number of excitations
Description: Specifies the number of excitations that are calculated. Note that in case of the exact diagonalization all excitations are calculated, but only the lowest ones are printed to screen and written to the output file. Also note that if limited both by number and by energy, (lowest and upto), DFTB will always use whatever results in the smaller number of calculated excitations.

Print

Type: String
Description: Specifies whether to print details on the contribution of the individual single orbital transitions to the calculated excitations.

ScaleKernel

Type: Float
Default value: 1.0
Unit: None
Description: Set the scaling parameter of the response kernel. A scaling approach can be used to identify plasmons in molecules. While single-particle excitations are only slightly affected by scaling of the response kernel, plasmonic excitations are sensitive to variations in the scaling parameter. Default no scaling is used (scaling parameter = 1.0)

UpTo

Type: Float
Unit: Hartree
GUI name: Excitations up to
Description: Set the maximum excitation energy. Attempts to calculate all excitations up to a given energy by calculating a number of excitations equal to the number of single orbital transitions in this window. This is only approximately correct, so one should always add some safety margin. Note that if limited both by number and by energy, (lowest and upto), DFTB will always use whatever results in the smaller number of calculated excitations.

TDDFTBGradients

Type: Block
Description: This block configures the calculation of analytical gradients for the TD-DFTB excitation energies, which allows the optimization of excited state geometries and the calculation of vibrational frequencies in excited states (see J. Comput. Chem., 28: 2589-2601). If the gradients are calculated, they will automatically be used for geometry optimizations or vibrational frequency calculations, if the corresponding Task is selected and only 1 excitation is selected. Vibrationally resolved UV/Vis spectroscopy (Franck-Condon Factors) can be calculated in combination with the FCF program or using the Vibrational Analysis Tools in AMS. See the ADF documentation on Vibrationally resolved electronic spectra or the AMS documentation for the Vibrational Analysis Tools.

Eigenfollow

Type: Bool
Default value: No
GUI name: Follow initial excitation
Description: If this option is set, DFTB uses the transition density in atomic orbital basis to follow the initially selected excited state during a geometry optimization. This is useful if excited state potential energy surfaces cross each other and you want to follow the surface you started on.

Excitation

Type: Integer List
GUI name: Excitation number
Description: Select which excited states to calculate the gradients for. Gradients can only be calculated for an excited states that has been calculated using TD-DFTB. Make sure that enough excitations are calculated.

Excited state gradients¶

Excited state gradients can be calculated with TD-DFTB, see the section Excited states with time-dependent DFTB.

Frequencies, phonons, VCD¶

Frequencies, phonons, and VCD and can be computed via numerical differentiation by the AMS driver. Several thermodynamic properties, such as zero-point energy, internal energy, entropy, free energy and specific heat are computed by default when calculating phonons.

AMS manual: Vibrational Analysis

Vibrationally resolved electronic spectra¶

AMS manual: Vibrationally resolved electronic spectra.
- AMS manual: AH-FC Adiabatic Hessian Franck-Condon.
- AMS manual: VG-FC Vertical Gradient Franck-Condon.

Stress tensor, Elasticity¶

The stress tensor and elastic tensor (and related elastic properties such as bulk modulus, shear modulus and young modulus) can be computed via numerical differentiation by AMS.

Charges, Bond Orders, Dipole Moment, Polarizability¶

Charges, Mayer bond orders, Dipole Moment, and Polarizability can be requested to the DFTB engine in the AMS driver’s input:

Fragment orbital analysis¶

The fragment orbital analysis is not available for periodic systems calculated with multiple K-points.

A Mulliken population analysis based on the elementary atomic basis functions can be calculated with

Properties
   Fragments
   End
End

For an atomic Mulliken population one should not specify any subkey File in Properties%Fragments.

A Mulliken population analysis based on orbitals coming from larger fragments, that may consist of more than 1 atom, can be calculated if one includes the binary dftb.rkf result files of the calculated fragments in the input, for example, like:

Properties
   Fragments
      File frag1.results/dftb.rkf
      File frag2.results/dftb.rkf
   End
End

Note that the nuclear coordinates of the atoms in the fragments should be at the exact same position as in the whole system. In addition, each atom of the whole system should be present exactly once in one of the fragment dftb.rkf files.

Properties
   Fragments
      Analysis Yes/No
      EMax float
      Emin float
      File string
      TIDegeneracyThreshold float
      TransferIntegrals Yes/No
   End
End

Properties

Fragments

Type: Block
Description: Fragment files

Analysis

Type: Bool
Default value: Yes
GUI name: Fragment analysis
Description: Mulliken population analysis in terms of fragment orbitals.

EMax

Type: Float
Default value: 0.25
Unit: Hartree
Description: Upper end of the energy interval for which the orbitals are analyzed.

Emin

Type: Float
Default value: -0.75
Unit: Hartree
Description: Lower end of the energy interval for which the orbitals are analyzed.

File

Type: String
Recurring: True
Description: Path (either absolute or relative) of fragment file

TIDegeneracyThreshold

Type: Float
Default value: 0.1
Unit: eV
Description: If the orbital energy of the fragment MO is within this threshold with fragment HOMO or LUMO energy, then this fragment MO is included in the calculation of the transfer integrals. Relevant in case there is (near) degeneracy.

TransferIntegrals

Type: Bool
Default value: No
GUI name: Charge transfer integrals
Description: Calculate the charge transfer integrals, spatial overlap integrals and site energies. Charge transfer integrals can be used in models that calculate transport properties.

NBO analysis¶

An input for the GENNBO program of Prof. Weinholds Natural Bond Orbital (NBO) package, by E. Glendening et al. can be made, using the key Properties%NBOInput. Not available for periodic systems.

Properties
   NBOInput Yes/No
End

Properties

NBOInput

Type: Bool
Default value: No
Description: Whether or not an input file for the NBO program is written to disk as nboInput.FILE47. The input file follows the FILE47 format as described in the NBO6 manual available on nbo6.chem.wisc.edu. By default, only the calculation of the natural bond orbitals and the natural localized molecular orbitals is enabled, but the nboInput.FILE47 file can be edited by hand to enable other analysis models. Please refer to the NBO6 manual for details.

The GENNBO executable is included in the AMS distribution. The GENNBO program can be called with:

#!/bin/sh
$AMSBIN/gennbo6 ams.results/dftb-nboInput.FILE47

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Spectroscopy and properties¶

Electronic structure of periodic systems¶

Excited states with time-dependent DFTB¶

Excited state gradients¶

Frequencies, phonons, VCD¶

Vibrationally resolved electronic spectra¶

Stress tensor, Elasticity¶

Charges, Bond Orders, Dipole Moment, Polarizability¶

Fragment orbital analysis¶

NBO analysis¶