Heidelberg Molecular Modelling Summer School The Challenges of Transition Metal Systems Dr Rob Deeth Inorganic Computational Chemistry Group University of Warwick UK
verview 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 Mechanics Paul 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 Implementation EXACT treatment Relaivity ucl-ucl QM exchange (Born-ppenheimer) Exact e - -e - QM exchange Average e - -e - exchange (Hartree-Fock Approximation The first ab initio M theory)
The Big Hurdle The Variational Principle states that the lower the energy, the more accurate the calculation. This places a fundamental limit on HF model. e HF - E = e corr e corr is the CRREATI EERGY HF averages the instantaneous e - -e - interactions which is a poor treatment of electron correlation. e corr is small (ish) for light organic atoms but e corr is uncomfortably big for TM atoms.
Improving Hartree-Fock HF 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 Rescue The 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 A 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 But Fast Can treat very large systems ( 000s atoms) 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 umber Carbon nly three coordination numbers Angles around carbon always the same for a given hybridisation TM inear: MX, XMX, XMMX Bent: MX 2 Trigonal and pyramidal: MX 3 Tetrahedral and planar: MX 4 Square pyramidal and trigonal bipyramidal: MX 5 ctahedral MX 6 Higher coordination numbers
Structural Complexity: igands 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 (andis)
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 eed 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 K in principle due to cancellation of errors But
Asymmetric Diels-Alder Reaction R C 5 H 6 Cu 2+ R' R' R R Cu R R'' R 2 R 2 R 2 R 2 n R 2 R 2 R 1 R 1
Conformational Searching May be many energetically accessible TSs which differ only in ligand conformations eed to be able to sample conformational space QM too slow
Molecular Mechanics E tot = ΣE str + ΣE bend + ΣE tor + ΣE vdw + ΣE C Fast (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 R' R' R Cu R Cu χ R'' Cu Cu Planar catalyst Tetrahedral catalyst
MM Model Use Molecular perating Environment (ME) Model twist via torsion around dummy bond
Twisting Potentials Parameterise MM to match DFT profile rel. energy / kcal mol -1 3.00 2.50 2.00 1.50 1.00 0.50 0.00-0.50-1.00-1.50-2.00 0 10 20 30 40 50 60 χ / DFT MM difference MM, parameterised
Transition State MM parametric so cannot access TS DFT to the rescue! n1 n2
Modelling Strategy ew MM parameters for Cu- interactions Torsional term around dummy bond based on DFT energetics C-C bonds from DFT TS constrained in MM o 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 100 98 96 94 92 % 90 88 86 84 82 80 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 100 90 80 70 60 % 50 40 30 20 10 0 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 (orrby and andis) Include solvent/counter ion interactions
Electronic Effects Problem: conventional MM requires independent FF parameters for high spin d 8 (octahedral) i- 2.1Å versus low spin d 8 (planar) i- 1.9Å Answer: add FSE directly to MM igand Field Molecular Mechanics (FMM) FMM should capture d electronic effects directly
d rbitals 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?) e g M n+ d 10Dq oct Free M n+ ion t 2g Point charge q = ze M n+ in octehdral crystal field
ctahedral [M 6 ] σ-only ligand leaves t 2g orbitals degenerate π donors decrease oct π acceptors increase oct 4p 4s 3d Metal t 1u * a 1g * e g * t 2g e g a 1g igands empty π* σ igands t 2g * e g * e g * e g * t 2g t 2g π acceptor 10Dq increases σ only t 2g * t 2g π donor 10Dq decreases igands π (filled) t 1u ctahedral M 6
Jahn-Teller Distortions The d electrons are structurally and energetically non-innocent. The effect can be correlated with changes in the IGAD FIED STABIISATI EERGY (FSE) E.g.: d 9 [Cu 6 ]: E JT electronic driving force d x 2 -y 2 e g E JT E JT d z 2 Cu -δ t 2g +2δ
Spin State Effects d x 2 -y 2 e g The structures of d 8 i(ii) complexes are determined by the FSE t 2g d z 2 i d x 2 -y 2 e g 2 E JT d z 2 i t 2g
igand Field Molecular Mechanics Augment conventional MM E tot = ΣE str + ΣE bend + ΣE tor + ΣE vdw + ΣE C + FSE Programming implications Molecular perating Environment (ME) Full modelling package GUI Scientific Vector anguage Applications Programming Interface
FMM: d 9 Cu(II) ME parameters All Cu- 1.93Å Molecular perating Environment DMMIME Dr atalie Fey Ben Williams-Hubbard FMM parameters (MMFF94-TM) Cu- ax 2.29Å (2.32) Cu- eq 2.05Å (2.06)
Conclusions DFT good but too slow MM fast but needs parameters TMs structurally/electronically and magnetically complex TMs a challenge for any modelling method