Heidelberg Molecular Modelling Summer School

The Challenges of Transition Metal Systems

Dr Rob DeethInorganic Computational Chemistry Group

University of WarwickUK

Overview

• Is molecular modelling of TM systems a challenge?– Certainly!– But compared to what?

• General features of Molecular Modelling• Specific features of Transition Metal

chemistry

General Issues• Quantum versus Classical• Quantum

– Generality

– Accuracy ?– Speed

• Classical

– Generality ?– Accuracy ?– Speed

Quantum MechanicsPaul A. M. Dirac — “The underlying physical laws necessary for the mathematical theory of a large part physics and the whole of chemistry are thus completely known....

HΨ = EΨ

and the difficulty is only that the exact application of these laws leads to equations much too complicated to be soluble”

Proc. Roy. Soc. A, 1929, 123, 714

QM: Practical ImplementationEXACT treatment

Relaivity

Nucl-Nucl QM exchange (Born-Oppenheimer)

Exact e--e- QM exchange

Average e--e- exchange(Hartree-Fock ApproximationThe first “ab initio” MO theory)

The Big HurdleThe Variational Principle states that the lower the energy, the more accurate the calculation.This places a fundamental limit on HF model.

eHF - E = ecorr

ecorr is the CORRELATION ENERGY

HF averages the instantaneous e--e- interactions which is a poor treatment of electron correlation.ecorr is small (ish) for light ‘organic’ atoms but ecorr is uncomfortably big for TM atoms.

Improving Hartree-FockHF is a single configuration model and will always have a correlation error.By including multiple configurations, the HF approximation can be progressively improved.These better methods are forms of

Configuration Interaction (CI)

CI reduces the correlation error but it is computationally expensive which severely reduces the size of system (~100 atoms).

DFT to the RescueThe Density Functional Theorem states that the ground state total energy, E, is a unique functional of the electron density, ρ.

E = F[ρ]

The theorem includes ALL the electron correlation.Practical DFT uses approximate functionals but it’s still faster and more accurate than HF.DFT is the best QM method for large TM systems.

Classical Methods

• Dispense with quantum effects• Treat molecule as set of balls connected by

springs - Molecular Mechanics• Mathematically simpler than QM

– Fast– Can treat very large systems (‘000s atoms)

• But– Parametric: The results are only as good

as the parameters

The Challenges

• The challenges of modelling TM systems can be put into context by comparing TM chemistry with organic chemistry

• Diversity• Structural complexity• Electronic complexity• Magnetic complexity

Diversity• Carbon is but one element• There are 30 transition elements

Structural Complexity: Coordination Number

• Carbon– Only three coordination numbers– Angles around carbon always the same for a

given hybridisation• TM

– Linear: MX, XMX, XMMX– Bent: MX2– Trigonal and pyramidal: MX3– Tetrahedral and planar: MX4– Square pyramidal and trigonal bipyramidal: MX5– Octahedral MX6– Higher coordination numbers…

Structural Complexity: Ligands

• TMs bind to many different elements including themselves

• Electronegative elements stabilise higher oxidation states - Werner type coordination complexes

• Carbon donors stabilise lower oxidation states - organometallic chemistry (Landis)

Electronic Complexity

• Most organic compounds are diamagnetic with large separation between ground and excited states

• Many TM systems are paramagnetic with small separations between ground and excited states

• Carbon has three formal oxidation states• TM centres can have many more• Jahn-Teller effects

Magnetic Complexity

• Paramagnetic TM complexes do not show free-radical behaviour

• Multiple spin states for same formal oxidation state

• Spin state affected by both coordination geometry and ligands

• Need to understand something about the electronic structure of metal complexes

Asymmetric Catalysis

• Catalytic selectivity much more subtle• Both pathways are feasible if e.e. < 100%,

one has a higher rate• High e.e. implies diastereomeric TSs only

differ by a few kcal mol-1

• Absolute QM resolution ~ 5 kcal mol-1

• QM still OK in principle due to cancellation of errors

• But…

Asymmetric Diels-Alder Reaction

O N

O

R

O

NO

R

O

O

C5H6

Cu2+

N

Cu

N

O

N

O

OO

O R''

RR

R' R'

N N

OO

R1R1

R2 R2

N N

OOR2 R2

N N

OOR2 R2

N N

OOn

Conformational Searching

• May be many energetically accessible TSswhich differ only in ligand conformations

• Need to be able to sample conformational space

• QM too slow

Molecular Mechanics

• Etot = ΣEstr + ΣEbend + ΣEtor + ΣEvdw + ΣECFast (big systems, dynamics)Accurate (experimental information built in to Force Field parameters)Works well for organics and TM complexes with “regular” coordination environments

• Can we use a “normal” approach?

Metal Contribution

N

Cu

N

O

N

O

OO

O R''

RR

R' R'

CuO

O

N

Nχ

Cu OO

NN

Planar catalyst

Cu

O

O

NN

Tetrahedral catalyst

MM Model

• Use Molecular Operating Environment (MOE)• Model twist via torsion around dummy bond

Twisting Potentials• Parameterise MM to match DFT profile

-2.00

-1.50

-1.00

-0.50

0.00

0.50

1.00

1.50

2.00

2.50

3.00

0 10 20 30 40 50 60

χ / °

rel.

ener

gy /

kcal

mol

-1

DFT MM difference MM, parameterised

Transition State

• MM parametric so cannot access TS• DFT to the rescue!

n1 n2

Modelling Strategy

• New MM parameters for Cu-L interactions• Torsional term around dummy bond based on

DFT energetics• C-C bonds from DFT TS constrained in MM• No electrostatics• Isolated molecules• Conformational space covered by 1000 step

stochastic search

Regiochemistry• Correctly predict endo isomer• Endo rationalised on electronic grounds but

MM has no electronic terms• Endo preference is steric

8082

84

8688

90

9294

96

98100

%

H (H) Me Et iPr iPr,expt.

tBu tBu,expt.

Ph Ph,expt.

ind ind,expt.

thn

exo endo

Enantioselectivity

• E.e.s correct sense but agreement with experiment patchy

010

20

3040

50

6070

80

90100

%

H (H) Me Et iPr iPr,expt.

tBu tBu,expt.

Ph Ph,expt.

ind ind,expt.

thn

n1 n2

Conclusions: Pure MM

• Relatively crude approach gave good results• Regiochemistry good, enantioselectivity less

good but at least model is not overly biased in favour of one direction of attack

• But, improvements needed– Metal: need to capture electronic effects at

Cu centre– More flexible treatment of TS geometry

(Norrby and Landis)– Include solvent/counter ion interactions

Electronic Effects• Problem: conventional MM requires

independent FF parameters for high spin d8

(octahedral) Ni-N 2.1Å versus low spin d8

(planar) Ni-N 1.9Å• Answer: add LFSE directly to MM

Ligand Field Molecular Mechanics (LFMM)

• LFMM should capture d electronic effects directly

d Orbitals• Many structural, electronic and magnetic

properties of TM species can be traced back to the behaviour of the d electrons.

• In octahedral symmetry, the five d orbitals split (remember what they look like?)

Mn+

Point charge q = ze

Free Mn+ ion

d

eg

t2g

10Dq

Mn+ in octehdral crystal field

∆oct

Octahedral [ML6]

Metal

3d

4s

4p

Ligands

σ

t2g

eg*

a1g*

t1u*

eg

a1g

t1u

Octahedral ML6

t2g

eg*eg* eg*

Ligands

π (filled)

Ligands

empty π*

σ only

π donor10Dq decreases

π acceptor10Dq increases

t2g

t2g

t2g*

t2g*

• σ-only ligand leaves t2gorbitals degenerate

• π donors decrease ∆oct

• π acceptors increase ∆oct

Jahn-Teller DistortionsThe d electrons are structurally and energetically non-innocent.The effect can be correlated with changes in the LIGAND FIELD STABILISATION ENERGY (LFSE)E.g.: d9 [CuL6]: ∆EJT electronic driving force

eg

t2g

∆EJT

∆EJT

L

CuL L

L

L

L+2δ

-δ

dx2-y2

dz2

Spin State Effects

eg

t2g

L

NiL L

L

L

L

dx2-y2

dz2

The structures of d8 Ni(II) complexes are determined by the LFSE

eg

t2g

2∆EJT

L

NiL L

L

L

L

dx2-y2

dz2

Ligand Field Molecular Mechanics

• Augment conventional MM• Etot = ΣEstr + ΣEbend + ΣEtor + ΣEvdw + ΣEC +

LFSE• Programming implications• Molecular Operating Environment (MOE)

– Full modelling package– GUI– Scientific Vector Language– Applications Programming Interface

LFMM: d9 Cu(II)

MOE parametersAll Cu-N 1.93Å

Molecular OperatingEnvironmentDOMMIMOE

LFMM parameters(MMFF94-TM)Cu-Nax 2.29Å (2.32)Cu-Neq 2.05Å (2.06)Dr Natalie Fey

Ben Williams-Hubbard

Conclusions

• DFT good but too slow• MM fast but needs parameters• TMs structurally/electronically and

magnetically complex• TMs a challenge for any modelling method