Starting from ADF2009.01 the meta-hybrids M06, M06-2X, M06-HF, and TPSSH can be used during the SCF. Also starting from ADF2009.01 Hartree-Fock and the (meta-)hybrid potentials can be used in combination with geometry optimization, TS, IRC, LT, and numerical frequencies; hybrids can be used in calculating NMR chemical shift; PBE0 can be used in calculating NMR spin-spin coupling; Hartree-Fock and (meta-)hybrid can be used in calculating excitation energies, in which the kernel consists of the Hartree-Fock percentage times the Hartree-Fock kernel plus one minus the Hartree-Fock percentage times the ALDA kernel (thus no (meta-)GGA kernel). Hartree-Fock and the (meta-)hybrid potentials still can not or should not be used in combination with analytical frequencies, the (AO)RESPONSE key, CD spectra, EPR/ESR g-tensor, and frozen cores.
In ADF one can do unrestricted Hartree-Fock (or hybrid or meta-hybrid) calculations, as long as one has integer occupation numbers (ROHF is not implemented in ADF, only UHF).
Starting from ADF2009.01 it is possible to change the amount of HF exchange in the input for hybrids (not for meta-hybrids and Hartree-Fock). For many hybrid functionals the sum of the amount of Hartree-Fock exchange and the amount of LDA exchange (or GGA exchange) is one. If that is the case, then if one changes the amount of Hartree-Fock exchange in the input the amount of LDA exchange (or GGA exchange) will also be changed, such that the sum remains one. Example:
XC Hybrid B3LYP HF=0.25 END
In this case the amount of Hartree-Fock for the B3LYP functional will be changed to 25% (instead of 20%), and the amount of LDA exchange to 75% (instead of 80%). The LDA correlation and GGA exchange and correlation part will be left unaltered.
Numerical problems have been found with the present implementation of Hartree-Fock or (meta-)hybrids during the SCF, especially if the molecule has symmetry NOSYM and a basis set TZP or larger is used. Workaround is to use always the DEPENDENCY key with rather strict criteria for the basis set dependence, namely bas=4e-3. Starting from the ADF2006.01 the DEPENDENCY key is automatically switched on in the case of a Hartree-Fock or a (meta-)hybrid potential. The result of the DEPENDENCY key is that linear dependence of the basis set is reduced by removing linear combinations that correspond with eigenvalues in the virtual SFOs overlap matrix, which are smaller than, in this case, 4e-3. Note that this is a rather large value, such that it will have an effect on the bonding energy. For DZ and DZP basis sets this value will normally not result in reduction of the virtual space. However, for TZP, TZ2P, QZ4P and larger this will often result in reduction of the basis set, which will have an effect on the accuracy of the bonding energy. In these cases one could try a smaller value than 4e-3, but be aware that numerical problems may occur. If the molecule has symmetry the numerical problems are reduced.
The origin of this problem is that for an accurate description of Hartree-Fock exchange one needs more (diffuse) fit functions in the fit procedure which is used in ADF, which uses only fit fuctions on the two centers of the two STOs. One can get more diffuse fit functions if one adds in the Create run of an atom the key:
AddDiffuseFit
If the BASIS key is used one can also add this key in the molecular calculation (the scripts in ADF will then automatically add this in the Create runs of the atoms). If one adds this key preliminary results indicate that one can lower the value for the dependency key to bas=1e-4. Such a low value for the dependency key normally means that the basis set is not reduced for basis sets of TZP or TZ2P quality.
For benchmark calculations one could use a large basis set, like the QZ4P basis set. In such cases it is recommended to use at least an accuracy of 6 for the integration. Thus for accurate hybrid calculations of organic molecules one could use:
basis type QZ4P end AddDiffuseFit Dependency bas=1e-4 integration 6 6 6
For heavy elements (Z>36) one still should use rather strict criteria for the basis set dependence, such as bas=4e-3.
The amount of memory needed in the hybrid calculations, which may be needed in case of large basis sets, reduces if more nodes are used in a parallel calculation. The amount of memory used can also be influenced if one sets the number of atoms ATOMSPERPASS with the keyword HFATOMSPERPASS, which is the number of atoms ADF treats at the same time in the algorithm to calculate the Hartree-Fock exchange integrals. The ADF program tries to guess a reasonable value for ATOMSPERPASS, depending on the calculation, but this may sometimes lead to a too large value. Typically ADF will not use a value below 10, unless of course, the total of atoms is below 10. If ATOMSPERPASS=1, the lowest amount of memory will be used, but the calculation time may then take much longer.
HFAtomsPerPass AtomsPerPass
An accuracy issue is relevant for some of the meta-GGA functionals, in particular the M06 functionals. These need high integration accuracy (at least integration 7) for reasonable gradients. For TPSSH moderate integration accuracy for reasonable gradients is sufficient. For heavier elements (Z>36) and if one uses one of the M06 functionals it is also necessary to include the following keyword
FragMetaGGAToten
Using this key FRAGMETAGGATOTEN the difference in the metahybrid or metagga exchange-correlation energies between the molecule and its fragments will be calculated using the molecular integration grid, which is more accurate than the default, but is much more time consuming. Default is to calculate the meta-hybrid or meta-GGA exchange-correlation energies for the fragments in the numerical integration grid of the fragments.
