1

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:

a) LANL2DZ:6-31G(d) A popular standard choice

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

1.2 Density functional

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:

a) B3LYP

b) BP86

c) M06

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)

Phys. Chem. Chem. Phys. 2005, 7, 3297-3305 def2-QZVP

J. Chem. Phys. 2007, 126, 124101 new SDD

The LANL2TZ(f) basis set uses the f polarisation functions developed by Frenkings group: Chem. Phys. Lett. 1993, 208, 111-114.

The following paper by Jan Martin defines some augmented basis sets for SDD:

J. Am. Chem. Soc. 2004, 126, 11699-11710 aug-SDB-cc-pVDZ

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).

2

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:

a) LANL2TZ(f):6-311+G(2d,p)

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)

e) aug-SDB-cc-pVDZ

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. A 2006, 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. A 2007, 111, 10439-10452

Comprehensive Organometallic Chemistry III 2007, Vol. 1, p 639-669

3

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)

b) B3LYP (or B3LYP-D)

c) M06

4

Overall summary of recommended choices

Geometries Energies

Basis sets

Ligands 6-31G(d) 6-311+G(2d,p)

(or 6-31+G(d) )

Transition LANL2DZ LANL2TZ(f)

metals

SDD SDD Def2-QZVP

Density functionals

B3LYP B3LYP

M06 M06

5

3. Some notes from Cramer and Truhlar

The hierarchy of density functionals:

LSDA

Local spin density approximation

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

e.g. SVWN5

GGA

Generalised gradient approximation

Depends on the gradient of the spin densities.

e.g. BP86, BLYP, PBE

Meta functionals

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.

Hybrid meta GGA functionals

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

6

4. Example input files for geometry optimisation and single-point calculation

a) Geometry optimisation

%mem=4gb

%nproc=8

# b3lyp genecp opt

Title

(charge) (multiplicity)

Atomic coordinates

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

6-31G(d)

****

-Ru 0

SDD

****

-Ru 0

SDD

7

b) Single-point energy

%mem=4gb

%nproc=8

# M06 genecp (include scf=tight if Gaussian03 is used)

Title

(charge) (multiplicity)

Atomic coordinates

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

6-311+G(2d,p)

****

-Ru 0

S 3 1.00

15.000000000 0.40205707045

13.500000000 -0.59417167365

7.2130868530 0.12541032854

S 1 1.00

4.5405901225 1.0000000

S 1 1.00

1.1904973723 1.0000000

S 1 1.00

0.54307531590 1.0000000

S 1 1.00

0.13700563039 1.0000000

S 1 1.00

0.73396375028E-01 1.0000000

S 1 1.00

0.31250715458E-01 1.0000000

P 4 1.00

11.388100061 0.55871461629E-01

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

8

D 1 1.00

0.49787892886 1.0000000

D 1 1.00

0.21481968266 1.0000000

D 1 1.00

0.85666751170E-01 1.0000000

F 1 1.00

2.8246600 1.0000000

F 1 1.00

0.9431400 1.0000000

F 1 1.00

0.3149100 1.0000000

G 1 1.00

1.0093000 1.0000000

****

-Ru 0

SDD

9

4. Lanthanide calculations

(Written by Damien Stringer, former PhD student)

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.

10

An example input file for a problematic single point calculation in a lanthanide study is given

below:

%mem=4gb

%nproc=8

# ub3lyp genecp guess=core scf=(qc, maxcycles=512) stable=opt

Title

(charge) (multiplicity)

Atomic coordinates

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

3-21G(d)

****

-LN 0

MWB51

****

-LN 0

MWB51