Excitation Input
You can perform a calculation of singlet-singlet and singlet-triplet excitation energies of a closed-shell molecule by supplying in the input file the block key EXCITATION. See the next sections for the calculation of excitation energies for open shell molecules.
EXCITATIONS
EXACT &
IRREP1 N1
IRREP2 N2
SUBEND
DAVIDSON &
IRREP3 N3
IRREP4 N4
SUBEND
ALLOWED
ONLYSING
ONLYTRIP
CDSPECTRUM
ANALYTIC
VELOCITY
LOWEST nlowest
VECTORS nvect
TOLERANCE tol
ORTHONORMALITY orth
ITERATIONS niter
{ Option }
{ Option }
...
End
Several options can be addressed with subkeys in the data block. This functionality is based on TDDFT and consequently has a different theoretical foundation than the SCF techniques described elsewhere in this User's Guide. Two possible ways are available to solve the eigenvalue equation from which the excitation energies and oscillator strengths are obtained, of which the iterative Davidson procedure is the default. In this case, the program needs to know how many excitation energies are needed per irrep, what accuracy is required, and what type of excitation energies are required (singlet-singlet or singlet-triplet). Suitable defaults have been defined for all of these. Each of these points is discussed below.
Exact diagonalization vs. iterative Davidson procedure
The most straightforward procedure is a direct diagonalization of the matrix from which the excitation energies and oscillator strengths are obtained. Since the matrix may become very large, this option is possible only for very small molecules. It can be activated by specifying the word EXACT as one of the subkeys in the Excitations data block. The default is the iterative Davidson method. A few of the lowest excitation energies and oscillator strengths are then found within an error tolerance. An advantage of the EXACT option is that additional information is produced, such as the Cauchy coefficients that determine the average dipole polarizability. The EXACT option not be used in unrestricted calculations.
Singlet versus triplet
By default, the singlet-singlet and singlet-triplet excitation energies are both calculated. The singlets are handled first, then the corresponding triplet excitation energies. One can skip one of these two parts of the calculation by specifying either ONLYSING or ONLYTRIP as a subkey in the data block.
In case of a calculation including spin-orbit coupling one can not separate the singlet-singlet and singlet-triplet excitations. The subkeys ONLYSING and ONLYTRIP are misused in this case to do a spin-restricted calculation, or a spin-polarized calculation, respectively. One should in fact only use the results of the spin-polarized calculation.
Dipole-allowed versus general excitations.
If you are interested in the optical absorption spectrum, you may not want to compute singlet-triplet excitation energies, nor singlet-singlet excitation energies which, by symmetry, have zero oscillator strengths. This subkey should not be used in case of spin-orbit coupling. The subkey ALLOWED tells ADF to treat only those irreducible representations for which the oscillator strengths will be nonzero. Of course, the oscillator strengths may still be negligibly small. The ALLOWED subkey automatically implies ONLYSING. The simplest, fastest, and recommended way to obtain information about the ten lowest dipole-allowed excitation energies would be:
EXCITATIONS
ALLOWED
LOWEST 10
END
If the subkey CDSPECTRUM is included the rotatory strengths for the calculated excitations are calculated, in order to simulate Circular Dichroism (CD) spectra [80,81]. Interesting for chiral molecules. This subkey should not be used in case of spin-orbit coupling. For accuracy reasons you should also use the subkey ANALYTIC in the block key EXCITATIONS, otherwise the results may be nonsense.
ANALYTIC
If the subkey ANALYTIC is included the required integrals for the CD spectrum are calculated analytically, instead of numerically. Only used in case of CD spectrum.
Velocity
If the subkey VELOCITY is included ADF calculates the dipole-velocity representation of the oscillator strength. If applicable (use of subkey CDSPECTRUM) the dipole-velocity representation of the rotatory strength is calculated. Default the dipole-length representation of the oscillator strength and rotatory strength is calculated.
Which excitation energies and how many?
The user can specify how many excitation energies per irrep should be calculated. If no pertaining input is available the program determines these numbers from the smallest differences between occupied and virtual Kohn-Sham orbital energies. By default it looks at the 10 lowest orbital energy differences. This number can be modified, by specifying inside the Excitation block key, for example:
LOWEST 30
One should be aware that this procedure does not guarantee that the lowest 10 (or 30) excitation energies will actually be found, since the orbital energy difference approximation to the excitation energy is rather crude. However, if the program decides on the basis of this procedure to calculate 4 excitation energies in a certain irreducible representation, these 4 excitation energies are certainly the lowest in that particular irrep.
The user has more control when the number of excitations per irrep is explicitly specified within the EXCITATION block key by the Davidson subkey:
DAVIDSON &
E'' 5
T1.u 2
SUBEND
The DAVIDSON sub key is a general (simple or block type) subkey. For usage as block type it must, be followed by the continuation code ( &). Its data block may contain any number of records and must end with a record SUBEND. In the subkey data block a list of irreps, followed by the number of requested excitation energies is specified. Note that the irrep name may not be identical to the usual ADF name. For example E'' is called EEE in ADF. The Excitation code will skip an irrep if the label is not recognized. For multidimensional irreps, only the first column is treated, because the other would produce identical output. This implies that the oscillator strengths for E-irreps have to be multiplied by 2 and the oscillator strengths for T-irreps by 3.
The EXACT subkey, mentioned already above, can also be used as a block type subkey to treat only a few irreps instead of all. The number of excitation energies does not have to be specified then.
Accuracy and other technical parameters
A summary of technical parameters with their defaults is:
EXCITATIONS
VECTORS 40
TOLERANCE 1e-6
ORTHONORMALITY 1e-8
ITERATIONS 200
END
VECTORS: the maximum number of trial vectors in the Davidson algorithm for which space is allocated. If this number is small less memory will be needed, but the trial vector space is smaller and has to be collapsed more often, at the expense of CPU time. The default if usually adequate.
TOLERANCE: specifies the error tolerance in the square of the excitation energies in hartree units. The default is probably acceptable but we recommend that you verify the results against a stricter default (e.g. 1e-8) for at least a few cases.
ORTHONORMALITY: the Davidson algorithm orthonormalizes its trial vectors. Increasing the default orthonormality criterion increases the CPU time somewhat, but is another useful check on the reliability of the results.
ITERATIONS: the maximum number of attempts within which the Davidson algorithm has to converge. The default appears to be adequate in most cases.
