Theoretical methods for transition metals and organometallic complexes

Professor Brian Yates

Brian.Yates@utas.edu.au

University of Tasmania

Friday 2 December 2011
1. Geometries
1.1 Basis set

Recommended possibilities:

b) SDD:6-31G(d) Probably better choice for metal

c) LANL2TZ:6-31G(d) See J. Chem. Theory Comput. 2008, 4, 1029-1031.
Also see the following link (EMSL Basis Set Exchange) for easy accessibility of basis sets:

https://bse.pnl.gov/bse/portal

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:

b) BP86

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:

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.

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:

e) aug-SDB-cc-pVDZ

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.

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.

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.

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.

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!

This is a very useful paper by Cramer and Truhlar which gives a good overview of DFT for transition metal chemistry.

b) B3LYP (or B3LYP-D)

c) M06

Overall summary of recommended choices
Geometries Energies
Basis sets
Ligands 6-31G(d) 6-311+G(2d,p)

(or 6-31+G(d) )

SDD SDD Def2-QZVP

B3LYP B3LYP

The hierarchy of density functionals:

Local spin density approximation

Depends only on spin densities (not their derivatives or orbitals).

e.g. SVWN5

Generalised gradient approximation

Depends on the gradient of the spin densities.

e.g. BP86, BLYP, PBE

Includes kinetic energy density to compensate for errors introduced by self-correlation in DFT.

e.g. TPSS
Hybrid functionals

Includes a portion of Hartree-Fock exchange to compensate for errors introduced by self-exchange in DFT.

e.g. B3LYP, B3PW91, PBE0 (=PBE1PBE)

In the period 1990-2006, 80% of all literature DFT references were to B3LYP.

Includes both HF exchange and kinetic energy density.

e.g. B1B95, TPSSh, M05 or M06.
Double hybrid methods

Add dependence on unoccupied spin orbitals.

e.g. B2PLYP
4. Example input files for geometry optimisation and single-point calculation
a) Geometry optimisation
%mem=4gb

%nproc=8

Atomic coordinates

…

…
-C -H -N -P -(all elements not using the effective core) 0

****

SDD

SDD
b) Single-point energy

%nproc=8

Atomic coordinates

…

…
-C -H -N -P -(all elements not using the effective core) 0

****

S 3 1.00

13.500000000 -0.59417167365

7.2130868530 0.12541032854

S 1 1.00

S 1 1.00

S 1 1.00

S 1 1.00

S 1 1.00

S 1 1.00

P 4 1.00

6.1591005666 -0.25808446847

1.7320431063 0.42924265341

1.0194857402 0.43313353048

P 1 1.00

0.58131419111 1.0000000

P 1 1.00

0.27290530268 1.0000000

P 1 1.00

0.66000000000E-01 1.0000000

P 1 1.00

0.22000000000E-01 1.0000000

D 4 1.00

18.598247778 0.31556859652E-02

6.7883773752 -0.34551060293E-01

2.2470797667 0.21708566158

1.0884195428 0.42834135307

D 1 1.00

D 1 1.00

D 1 1.00

F 1 1.00

F 1 1.00

F 1 1.00

G 1 1.00

****
-Ru 0

SDD
4. Lanthanide calculations

(Written by Damien Stringer, former PhD student)

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.

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.

%nproc=8

Atomic coordinates

…

…
-C -H -N -P -(all elements not using the effective core) 0

****

MWB51

MWB51