For calculating geometries, all of our work suggests that B3LYP is fairly robust. There is a series of papers by Michael Buhl (see for example J. Chem. Theory Comput.2008, 4, 1449-1459) in which they evaluate a whole lot of functionals. Apart from B3LYP, other functionals which give good (perhaps slightly better) geometries are BP86, TPSS, B3P86 or M06. BP86 and TPSS have the advantage of being computationally faster (non-hybrid DFT). So the choices are:
2. Energies (single-point calculations)
2.1 Basis set
I think there is good consensus now that although DFT is less susceptible to basis set extension than, say, HF, MP2 or CCSD(T), nevertheless you need a decent basis set to make sure that you remove any small problems due to not representing the density well enough. Broadly speaking, one should use TZVP, with an ecp on the metal. There are some recent papers on these sorts of basis sets coupled with ecps:
J. Chem. Theory Comput.2008, 4, 1029-1031 new LANL2TZ(f)
J. Chem. Phys.2007, 126, 124101 new SDD
The LANL2TZ(f) basis set uses the f polarisation functions developed by Frenking’s group: Chem. Phys. Lett.1993, 208, 111-114.
The following paper by Jan Martin defines some augmented basis sets for SDD:
He determined diffuse spdf and polarisation f functions for the SDD basis set for all the transition metals (see Table S2 in the supporting information for the above paper). Interestingly, the spd functions are almost the same as what you would get if you used even tempered extrapolation, and the f polarisation function is almost identical to Frenking's (this is true for Pd at least). The extra f diffuse function looks funny to me, but it is consistent with the protocol used by Dunning for his aug-cc basis sets. These augmented basis sets for SDD are recommended to be used with Dunning's cc-pVDZ and aug-cc-pVDZ basis sets on main group elements.
Thus the choices are:
b) SDD(f):6-311+G(2d,p) Includes Frenking f polarisation
c) SDD def2-QZVP:6-311+G(2d,p) Different basis set to default SDD in Gaussian,
download from the EMSL library (bse.pnl.gov).
d) New SDD aug-cc-pVnZ-PP:6-311+G(2d,p) n = D, T, Q, 5
These are very extensive, very flexible basis sets, good for CBS calculations. But:
- requires new SDD ecp
- optimised for HF and CCSD(T) (not DFT)
- only for second row TM at the moment (1st row is all electron)
I have tested these options:
a) and b) are doable and give reasonable results.
c) is a reasonable option and it sticks to a defined (and well-matched) ecp and basis set.
d) and e) may be useful for very high level calculations.
2.2 Density functional
This is where it gets interesting! People get passionate about their own particular preference. I think the truth is that no one functional works in every case. Maybe in 10 years time we will have something that works well for all transition metal complexes in different spin states, etc.
J. Chem. Phys.2006, 125, 124302
J. Chem. Theory Comput.2008, 4, 2057-2066
These papers discuss energies of simple metal hydrides. From these papers and some additional calculations that I have done there are several functionals that perform reasonably for these hydrides: B3LYP, OPBE, TPSS, PBE0, BP86. BMK and M06-2X are also reported to work well. In our experience different functionals work best for different cases. We have found in one case for example that OPBE gives very inconsistent results, while in another BMK gives odd results. I think it is actually quite difficult to distinguish between all these different functionals.
J. Phys. Chem. A2006, 110, 709-716
This is an interesting benchmark by Martin of a lot of DFT methods for some organometallic reactions. He concludes that BMK is not suited for organometallic chemistry.
J. Phys. Chem. A2007, 111, 10439-10452
Comprehensive Organometallic Chemistry III2007, Vol. 1, p 639-669
These two articles suggest that we should routinely do our single point calculations with, say, three different functionals and see if they give consistent results. We have done this using B3LYP, TPSS and BP86 and it worked out quite well. It is fairly easy to set up the three calculations as different steps within the same job in Gaussian. So one recommended approach is to do the single-point calculations with several functionals and see if the resulting potential energy surfaces are consistent. This ‘consensus’ approach certainly helps to satisfy the wishes of referees!
There are errors introduced into the DFT calculations for very bulky systems due to dispersion energy issues. There are some new functionals that take account of dispersion energy in a better way; see Grimme (BP86-D, B3LYP-D), Head-Gordon (wB97XD) and Truhlar (M06).
PCCP, 2009, 11, 10757-10816
This is a very useful paper by Cramer and Truhlar which gives a good overview of DFT for transition metal chemistry.
Thus some recommended functionals to try for organometallic chemistry are:
a) BP86 (or BP86-D)
When undertaking lanthanide calculations using Gaussian, the following tips may be helpful:
Select the appropriate level of theory:
DFT provides good results at reasonable computational expense. The B3LYP functional is used frequently and provides good results. For spin unrestricted calculations, use the unrestricted version, uB3LYP.
Basis set choice is important:
Incorporation of the lanthanide f electrons into an effective core potential (ECP) has a great benefit on computational time, and for conformational studies/reaction pathways provides an appropriate level of agreement with experiment. For higher level electronic/energetic studies, the f electrons should be treated explicitly. The SDD basis sets are well proven for lanthanides – the MWB## keyword specifies the SDD basis set where ## = number of electrons in the effective core. Typically this number is 28 for lanthanide calculations where f electrons are treated explicitly (core involves 1s – 3d electrons), but may be larger for calculations where f electrons are included in the core (e.g. MWB51 for Sm(III)). If a large core is used, the GUESS=CORE keyword must be specified in the initial single point calculation. Typically SCF convergence takes longer for lanthanide calculations and the default number of iterations is insufficient. Specify SCF=(maxcycles=512) to circumvent this problem.
A general basis set is also often employed. This allows the SDD (or similar) basis set to be used for the lanthanide and an alternative basis set for the remaining elements (e.g. 6-31G(d)). As an ECP is required we specify the general basis set with the GENECP keyword.
Undertake a low level single point calculation first:
In order to achieve SCF convergence, a lower level basis set should be used for the first single point calculation.
E.g. if you are aiming for a final level of theory of MWB28/6-31G(d,p), you might first carry out a single point calculation at MWB51/3-21G(d). The resulting wavefunction may then be used as a starting point for the single point calculation at the higher level using the GUESS=READ keyword.
Check you have obtained a stable wavefunction:
Due to the large number of similar energy-level molecular orbitals that result in lanthanide calculations, the resulting wavefunction may not be the true minimum, and may cause problems with further calculations (e.g. geometry optimisations). To ensure the wavefunction is correct, use the STABLE=OPT keyword. In the resulting output you will see the wavefunction check, and after the final cycle it should print “the wavefunction is already stable”. The stable wavefunction may then be used for geometry optimisations etc. using GUESS=READ.
If a large core ECP is used, SCF convergence is generally much easier. If problems remain after employing the above methods, the SCF=QC keyword may be used. This uses a quadratic convergence algorithm to achieve SCF convergence rather than the default method, and it is very reliable. This benefit however comes at a significantly greater computational expense.
An example input file for a problematic single point calculation in a lanthanide study is given below:
# ub3lyp genecp guess=core scf=(qc, maxcycles=512) stable=opt
-C -H -N -P -(all elements not using the effective core) 0