General remarks on the use of the TDDFT Response and Excitation functionality
Symmetry
As in calculations without TDDFT the symmetry is automatically
detected from the input atomic coordinates and need not be specified, except in
the following case: infinite symmetries cannot be handled in the current
release (ATOM, C(lin), D(lin)). For
such symmetries a subgroup with finite symmetry must be specified in the input.
The usual orientation requirements apply.
If higher multipole polarizabilities are required, it may also be necessary to
use a lower subgroup (the program will stop with an error message otherwise).
For verification of results one can always compare to a NOSYM calculation.
Closed-shell only
The current implementation supports only closed-shell molecules. If occupation numbers other than 0 or 2 are used the program will detect this, (but only at a later stage of the calculation) and abort. All 'RESPONSE' calculations must be spin-restricted.
Atomic coordinates in a RAMAN calculation
Atomic coordinate displacements in a RAMAN calculation must be Cartesian, not Z-matrix. Furthermore, the current implementation does not yet support constrained displacements, i.e. you must use all atomic coordinate displacements.
Use of diffuse functions
The properties described here may require diffuse functions to be added to the basis (and fit) sets. Poor results will be obtained if the user is unaware of this. As a general rule, diffuse functions are more important for smaller than for larger molecules, more important for hyperpolarizabilities than for normal polarizabilities, more important for high-lying excitation energies (Rydberg states) than for low-lying excitations, more important for higher multipole polarizabilities than for dipole polarizabilities. The user should know when diffuse functions are required and when they are not: the program will not check anything in this respect. For example, in a study on low-lying excitation energies of a large molecule, diffuse functions will usually have little effect, whereas a hyperpolarizability calculation on a small molecule is pointless unless diffuse functions are included. Diffuse even tempered basis sets are included in the ET/ directory of the database), for the elements H-Kr. Somewhat older basis sets can be found in the Special/Vdiff directory in the database. For some atoms diffuse basis sets may be available at the web site http:tc.chem.vu.nl/~vgisberg. For other atoms, the user will have to add diffuse basis and fit functions to the existing data base sets. It is not necessary to start from basis V as was done for the basis sets in Special/Vdiff. For example, for heavier elements it may be a good idea to start from the ZORA/QZ4P basis sets. It may be expected that even more extensive basis sets will come available in the future, when usage and experience increase.
Linear dependency in basis
If large diffuse basis sets are used, or if diffuse functions are used for atoms that are not far apart the calculation may suffer from numerical problems because of (near-) linear dependencies in the basis set. The user should be aware of this danger and use the Dependency key to check and solve this.
The TAILS input keyword
For reasons of numerical robustness and safety rather strict defaults apply for the neglect of tails of basis and fit functions (see the key tails) in a Response or Excitation calculation. This may result in longer CPU times than needed for non-TDDFT runs, in particular for larger molecules. Possibly this precaution is not necessary, but we have not yet tested this sufficiently to relax the tightened defaults.
Relativistic effects
The Response and Excitations options can be combined with scalar relativistic options (ZORA or Pauli). The one-electron relativistic orbitals and orbital energies are then used as input for the property calculation. Spin orbit effects have not yet been incorporated in this part of the code. In case of a ZORA calculation, the so-called 'scaled' orbital energies are used as default.
Choice of XC potential
For properties that depend strongly on the outer region of the molecule (high-lying excitation energies, (hyper) polarizabilities), it may be important to use a XC potential with correct asymptotic behavior (approaching -1/r as r tends to infinity). In ADF the LB94 potential has been implemented for this purpose [15].
With this particular XC functional, the XC potential is computed
from the exact charge density for reasons of stability and robustness (whereas
for other functions the (cheaper) fit density is used). This implies that
computation times may be longer. Another 'side effect' is that, since there is
no energy expression corresponding to the LB94 potential, the final (bonding) energy of a LB94 calculation
uses another GGA and hence the energy result is not (exactly) consistent with
the SCF procedure. Note, finally, that the LB94 potential is not suitable for
geometry optimizations because it is rather inaccurate in the bonding region,
see the discussion of the XC input key.
Applications with the LB94 potential to response calculations with ADF can be
found in [74] (polarizabilities),
[75-77] (hyperpolarizabilities),
[78] (high-lying excitation
energies), [79] (multipole polarizabilities
and dispersion coefficients)
Accuracy check list
As mentioned before, the TDDFT module is relatively new and not extensively tested for a wide range of applications. Therefore, we strongly recommend the user to build experience about aspects that may affect the accuracy of TDDFT results. In particular we advise to 'experiment' with
- Varying integration accuracy
- Varying the SCF convergence
- Varying the ORTHONORMALITY and TOLERANCE values in an Excitation calculation
- Varying the tails parameters
- Using diffuse functions
- Using the Dependency key
- Applying the ZORA relativistic corrections for molecules containing heavy nuclei
- Using an asymptotically correct XC potential such as LB94
