Input description for the Response functionality
The calculation of frequency-dependent (hyper)polarizabilities and related properties is activated with the block key Response
RESPONSE
END
In this example only the zz component of the dipole polarizability tensor is calculated, at zero
frequency. The orientation of the molecule is therefore crucial. Be aware that
the program may modify the orientation of the molecule if the input coordinates
do not agree with the symmetry conventions in ADF!
(This calculation could equivalently be done through a finite field method).
The impact of various approximations on the quality of computed polarizabilities has been studied in, for instance, Refs. [74,82,89]. If you are new to this application field, we strongly recommend that you study a few general references first, in particular when you consider hyperpolarizability calculations. These have many pitfalls, technically (which basis sets to use, application of the DEPENDENCY key) and theoretically (how do theoretical tensor components relate to experimental quantities, different conventions used). Please, take a good look both at ADF-specific references [75-77,90] and at general references related to this subject: Refs. [91-93], the entire issues of Chem.Rev.94, the ACS Symposium Series #628, and further references in the ADF-specific references.
Let's have a look at the available subkeys in the Response data block. (Not all of them should be used at the same time!)
RESPONSE
ALLCOMPONENTS
HYPERPOL LaserFreq
DYNAHYP
Nfreq Nfreq
FrqBeg FirstFreq
FrqEnd LastFreq
[Optional Frequency/Energy Unit]
ALLTENSOR
DynaHyp
Quadrupole
Octupole
VANDERWAALS NvanDerWaals
RAMAN
OPTICALROTATION
END
Entire tensor or only one component
You specify the AllComponents subkey to get the entire polarizability tensor, instead of just the zz component.
Frequencies or wavelengths
Instead of performing the calculation at zero frequency (which results in the static polarizability), one can specify an even-spaced sequence of frequencies, using the subkeys Nfreq, FrqBeg, and FrqEnd with obvious meaning. The (first and last) frequency values are by default in eV. This can be changed into Hartree units (a.u.) or in wavelengths (angstroms) by typing HARTREE or ANGSTROM on a separate line within the RESPONSE block, instead of [Optional Frequency/Energy Unit].
Hyperpolarizabilities
The first hyperpolarizability tensor b is calculated (in atomic units in the 'theoreticians convention', i.e. convention T=AB in Ref. [92]) if the subkey hyperpol is present with a specification of the laser frequency (in hartree units). If also the subkey allcomponents is specified, all components of the hyperpolarizability tensor will be obtained.
As mentioned before, by default only the static dipole hyperpolarizability tensor is computed. If one is interested in the frequency-dependent hyperpolarizability, the input could look like:
RESPONSE
ALLCOMPONENTS
HYPERPOL 0.01
DYNAHYP
END
The subkey dynahyp has to be added and the main frequency ω has to be specified in Hartrees after the subkey hyperpol. In the output all nonzero components of the tensors governing the static first hyperpolarizability, second harmonic generation, electro-optic pockels effect, and optical rectification are printed.
Note: Second hyperpolarizabilities are currently not available
analytically. Some can however be obtained by calculating the first
hyperpolarizability in a finite field.
The effect of using different DFT functionals (LDA, LB94, BLYP) on
hyperpolarizabilities in small molecules has been investigated in [77].
Higher multipole polarizabilities
Instead of just calculating the dipole-dipole polarizability, one may address the dipole-quadrupole, quadrupole-quadrupole, dipole-octupole, quadrupole-octupole, and octupole-octupole polarizability tensors. These can all be calculated in a single run, using the subkey alltensor. If only quadrupole-quadrupole or octupole-octupole tensors are needed, the subkey quadrupole or octupole should be used.
Accuracy and convergence
RESPONSE
erralf 1e-6
erabsx 1e-6
errtmx 1e-6
END
The subkeys erralf, erabsx, errtmx determine the convergence criteria for a polarizability calculation. The strict defaults are shown. It is rarely necessary to change the defaults, as these are rather strict but do not lead to many iterations.
Dispersion coefficients
Simple dispersion coefficients (the dipole-dipole interaction
between two identical molecules, the C6 coefficient) are calculated
in a single ADF calculation. General dispersion coefficients are obtained with
the auxiliary program DISPER, which uses two output files (file named TENSOR)
of two separate ADF runs as input. See the Analysis and the Examples documents.
To get the dispersion coefficients one has to calculate polarizabilities at
imaginary frequencies between 0 and infinity. The ADF program chooses the
frequencies itself. The user has to specify the number of frequencies, which in
a sense defines the level of accuracy, as an argument to the subkey VanDerWaals.
RESPONSE
ALLCOMPONENTS
VANDERWAALS 10
END
Ten frequencies is reasonable. In the example only dipole-dipole interactions are considered. If alltensor is specified, higher dispersion coefficients are also calculated. This ADF calculation generates a file with name TENSOR, which contains the results of multipole polarizabilities at imaginary frequencies. This TENSOR file has to be saved. Similarly, the TENSOR file for the second monomer has to be saved. The files have to be renamed to files 'tensorA' and 'tensorB' (case sensitive) respectively. Then the program DISPER has to be called in the same directory where the 'tensorA' and 'tensorB' files are located. DISPER needs no further input. See the Analysis document.
Raman scattering
Raman scattering intensities and depolarization ratios for all molecular vibrations at a certain laser frequency can be calculated in a single run. The run type must be Frequencies, which is arranged with the geometry key.
GEOMETRY
FREQUENCIES
END
The Response key is used to specify that Raman intensities are computed.
RESPONSE
RAMAN
END
In this example the static Raman scattering is calculated (ω = 0). This type of calculation is very similar to an IR intensity calculation. In fact, all IR output is automatically generated as well. At all distorted geometries the dipole polarizability tensor is calculated. This is very time-consuming and is only feasible for small molecules.
There are a few caveats:
- Numerical integration accuracy must be high
- A calculation in which only a subset of the atoms is
displaced is not possible for Raman calculations.
- For good results, a well converged (with the same basis and functional)
equilibrium geometry must be used.
Because of this last point, it is wise to always start the RAMAN calculation with a TAPE13 restart file from a previous geometry optimization with the same basis, accuracy parameters, and density functional.
With the subkey OPTICALROTATION the (frequency dependent) optical rotation [80,94] will be calculated. For correct calculations one should calculate the entire tensor (see also the subkey ALLCOMPONENTS), which is done automatically.
