# 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.

## Vibrationally resolved electronic spectra¶

## 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
```