Ligand Field Theory, Density Functional Theory and Molecular Mechanics: Adventures with d-electrons

Transcription

1 Ligand Field Theory, Density Functional Theory and Molecular Mechanics: Adventures with d-electrons Dr Rob Deeth Inorganic Computational Chemistry Group

2 Overview The Density Functional Theory revolution Practical applications Beyond DFT: Classical modelling for TM systems and smart approaches LFT v. CFT LFT v. DFT Acknowledgements

3 DFT The Density Functional Theorem (Hohenberg-Kohn, 1964) the ground state total energy, E 0, is a unique functional of the electron density, ρ. E 0 = E[ρ] The theorem includes ALL electron correlation (Quantum Mechanics).

4 Pre-1988 Slater exchange-only Xα model V x ρ 1/3 Fast, accurate electronic structure o automatic geometry optimisation [CuCl 4 ] 2-, [VOCl 2 (urea) 2 ] d-d transitions energies molecular orbitals charge distributions

5 Energy Gradients and Functionals Versluis and Ziegler: J Chem Phys, 1988 Exact DFT solution for a Uniform Electron Gas Slater exchange plus fitted correlation LOCAL DESITY APPROXIMATIO LDA overbinds GEERALISED GRADIET APPROXIMATIO (e.g. BP86, B3LYP) GGA includes ρ corrections

6 Structural Chemistry: 1994 O H H Tc O O H O [TcO 2 Pent(AO) 2 ] Overlay: Obs/Calc 1994 (RMS ~0.03 Å) 58 atoms 297 basis functions 10 hrs per geometry step on DEC 3000/700 workstation

7 Structural Chemistry: 2002 i Pr O Zr O Bz Bz i Pr atoms 586 basis functions 2 hrs per geometry step on 4 CPUs of Pentium III cluster Overlay: Obs/Calc (RMS ~0.04 Å) DFT gives ~ X-ray structure accuracy for TM complexes

8 Aziridination Cu * R * R' R = Ts R' = H, CO 2 Me Ts A Cu + -nitrene diimine is the proposed catalyst. o experimental structure it s a catalyst!! the structure must be computed.

9 Real Substrates: Cinnimates Only the ester group was modelled. Quadrant 2 system spontaneously gives a Cu-O=C interaction at 2.26 Å and a structure 20 kj mol -1 more stable than the comparable styrene complex. DFT predicts much better e.e.s (Obs. e.e. >95%) Obs. and calc. absolute configurations identical 2.26 Å

10 Mechanism DFT provides direct access to Transition States Pd

11 Activation barriers Exchange on d 8 centres: H 2 O, MeC, MeC, C 2 H 4, CO, C - Excellent correlation with H but GGA energies vital! Activation Energies Energy (kj/mole) LDA GC Exp Energy (kj/mole)

12 Oxo-Transfer Mechanism Energies in kj mol [Exp(PR 3 ) ~ 75] 0 kj mol Products: -72 MECHAISM OK

13 Conclusions: DFT DFT is the best QM model for TM systems. Excellent structures and direct access to Transition States Static DFT modelling a good starting point for catalyst design Functionals not specifically designed for TM systems (too covalent) so require validation DFT (or any QM method) is too slow for really big molecules, VHTS or MD

14 eed for Speed DFT is accurate but ALL QM methods, including DFT, are relatively slow QM poorly suited to: Conformational searching Virtual high-throughput screening Biomolecules Molecular Dynamics

15 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 Conventional MM has fundamental problems with Transition Metal systems

16 Challenges Coordination numbers > 4 Multiple oxidation states Multiple spin states Organometallic versus classical Werner complexes Electronic effects (Jahn-Teller)

17 Electronic Effects: d-electrons The d electrons are structurally and energetically noninnocent. The effect can be correlated with changes in the LIGAD FIELD STABILISATIO EERGY (LFSE) E.g.: d 9 [CuL 6 ]: E JT electronic driving force d x 2 -y 2 e g E JT E JT L d z 2 L Cu L -δ L L t 2g L +2δ

18 Extending MM to the d-block Many TM properties have a LFSE component ( double hump behaviour) Add LFSE directly to MM Ligand Field Molecular Mechanics (LFMM) E tot = ΣE str + ΣE bend + ΣE tor + ΣE vdw + ΣE C + LFSE LFMM captures d electronic effects directly Dr Veronica Paget (nee Burton)

19 Getting LF Parameters The LFSE is computed using the Angular Overlap Model (AOM). Each M-L bond described by LOCAL parameters e σ, e πx, e πy Values from d-d spectra: e.g. oct = 3e σ -4e π Fit to general expression: e λ = a 0 + a 1 r + a 2 r -2 + a 3 r -3 + a 4 r -4 + a 5 r -5 + a 6 r -6 L Z L L M X M M Y d z 2 e σ d xz d yz d d e πx d e πy

20 LFSE Gradients Ε = tr(w ) W = Q VQ T + QV Q T + QVQ T δε δv = tr(q Q T ) δx (λκ) δx (λκ) i i LFSE includes σ and π parameters and d-s mixing effects Dr Dave Foulis

21 Parameter Fitting Cannot simply take existing TM FF parameters Bond length, r, is a balance of conventional MM terms (e.g. Morse function D 0, α and r 0 ) and LFSE Low spin d 6 has maximum LFSE: hence r < r 0 Energy r Morse r 0 CLFSE Total r = 1.93 Å r 0 = 2.11 Å -120 [Co(H 3 ) 6 ] 3+ Bond Length

22 Spectroscopic Accuracy Parameter a 0 a 1 e σ (Cl) e π (Cl) e ds (Cl) [CuCl 4 ] 2- Calc a (no π or d-s) Calc Obs Cu-Cl /Å d xy d x 2 -y d xz/yz d x 2 -y d z 2 d x 2 -y [CuCl 6 ] 4- Cu-Cl(eq) /Å Cu-Cl(ax) /Å d z 2 d x 2 -y d xy d x 2 -y d xz/yz d x 2 -y Morse parameters: D 0, r 0, α: 80.0 kcal mol -1, 2.50 Å, 0.30

23 LFMM: d 9 Cu(II) MOE parameters All Cu- 1.93Å Molecular Operating Environment DOMMIMOE Dr atalie Fey Ben Williams-Hubbard LFMM parameters (MMFF94-TM) Cu- ax 2.29Å (2.32) Cu- eq 2.05Å (2.06)

24 Auto J-T Effect: d H3 H3 H3 Cu H3 H3 H3 Cu Cu Cu- eq (av) Cu- ax (av) Cu Cu cis -Cu- (av) trans -Cu- (av) o other MM scheme gives J-T distortions automatically

25 High-spin/low-spin d 8 d x 2 -y 2 e g L d z 2 L i L The structures of d 8 i(ii) complexes are determined by the LFSE t 2g e g d x 2 -y 2 L L L L 2 E JT d z 2 L i L L L t 2g L

26 High and Low Spin States: d 8 H 3 H 3 i H 3 H 3 H 3 H 3 i i i i-(hs) ~2.1Å i-(ls) ~1.9Å i i i i i i RMS Errors i-: 0.01Å -i-: 0.6 JACS, 117, 8407, (1995) One set of M-L Force Field parameters handles widely different M-L bond lengths

27 Relative Energies Conventional MM has different parameters for each spin state. Cannot compare MM energies directly E.g.: MM cannot predict lowest energy spin state LFSE term in LFMM can model spin-states [CoF 6 ] 3- : 5 T 2g [Co(C) 6 ] 3- : 1 A 1g Test case: d 6 Co 3+ octahedral in high and low spin Ben Williams-Hubbard

28 Spin State Energies Both the LFSE and the interelectron repulsion needed. Theoretical d 6 spin-crossover point: d 6 Tanabe-Sugano 1 A2 5 E 1 T2, 1 E 3 E 3 T1 E(ls-hs) = 2 oct -(5F F 4 ) F 2 and F 4 are ier parameters E/B 1 I 1 T2 5 T2 5 T 2 1 T1 3 T2 The 5 T 2g - 1 A 1g splitting from DFT is ~2400 which is consistent with d-d spectroscopy and full LFT. 5 D 3 H 5 T2 3 T1 3 T1 1 A 1 /B

29 Getting Other Parameters: DFT to the Rescue Experimental data are not always available DFT can access actual and hypothetical systems with and without constrained geometries and/or spin states Use DFT to develop smart LFMM parameters DFT for high-symmetry ML 6 complexes very fast

30 DFT Protocol for Bond Lengths Optimised Bond lengths for [CoL 6 ] 3- Co-F Co-C LDA(hs) Exp LDA(ls) Exp Access to unobservables Experimental validation Can rapidly tune LFMM parameters to reproduce CoL 6 DFT data for BOTH spin states

31 The Results LFMM energies can be compared directly Parameters for homoleptic complexes applied unchanged to mixed-ligand systems - 10 for 2 [Co(C) n F 6-n ] 3-, spin crossover at n = F6C0 F5C1 F4C2cis F4C2trans F3C3fac F3C3mer F2C4cis F2C4mer F1C5 F0C Energy (kcal/mole) Energy (kcal/mole) DFT LFMM DFT(high) DFT(low) LFMM(high) LFMM(low)

32 Conclusions: LFMM A fast scheme is needed for TM systems which handles the important d-electron effects LFMM designed for TM systems for all those cases where LFSE important captures the essential physics around the metal and facilitates calculations which would otherwise require full-blown QM approaches - smart parameters automatic Jahn-Teller distortions single parameter sets for multiple coordination numbers and spin states energies can be compared directly efficient enough for large scale simulations

33 Amines σ-bonding only LFT v. CFT AOM: no π bonding = degenerate t 2g = two d-d bands, CFT: electrostatic model = four bands in rhombic D 2h [Cu(dien) 2 ] 2+ : 8800, 9900, 15400, cm -1 AOM wrong? DFT to the rescue!?! AOM [M(H 3 ) 6 ] n+ : σ only Electrostatic CFT d x 2 -y 2 d x 2 -y 2 e g d z 2 'd π ' (d xy /d xz /d yz ) t 2g d z 2 d xy d yz d xz D 2h D 4h O h D 4h D 2h rhombic distortion tetragonal elongation tetragonal elongation rhombic distortion

34 [Cu(dien) 2 ] 2+ DFT optimised structure agrees with X-ray DFT d orbitals 1:3 pattern, EPR g-values too low DFT too covalent (SOMO: Calc 43% d, Exp (EPR) 65-70% d) Mostly ligand Mostly metal d lig d lig Wrong covalent/ionic balance Correct covalent/ionic balance Tune DFT g-values by optimising Cu nuclear charge - best q = SOMO now 69% d Good g-values - d orbitals still 1:3 pattern DFT agrees with AOM, not with CFT

35 ew Interpretation [Cu(dien) 2 ] 2+ has two possible elongation axes d-d bands arise from ~6:1 mixture of two complexes aligned at ~90 Exp. solid state structure obtained from DFT in vacuo geometry Even get rhombic equatorial geometry from superimposing asymmetric axial elongation Asymmetric axial elongation Cu Cu % + 15% = Obs Cu

36 LFT v. DFT DFT seems to be replacing LFT Lots of useful knowledge derived from Ligand Field Theory Would be a shame to lose it all Does the Ligand Field description of metal-ligand bonding map onto Density Functional Theory?

37 Tetragonal Distortion e g t 2g O h D 4h tetragonal elongation b 1g (d x 2 -y 2) b 2g (d xy ) e g (d xz /d yz ) a 1g (d z 2) Classical (point charge) CFT model predicts t 2g splitting Qualitative MO model for [PtCl 4 ] 2- concurs What about DFT?

38 x Planar [MCl 4 ] 2- y s b 2g * e g * b 2g d e g * b 2g * y z x M e g b 2g Cl M e g b2g Cl e g qualitative MO DFT Experiment places d xy above d xz /d yz for M= Cu/Pd/Pt DFT inverts energies of nominal d π orbitals Is DFT wrong?

39 Planar [M(H 3 ) 4 ] 2+ H 3 σ-bonding only, simple MO theory and CLF model predict degenerate t 2g d orbitals EHMO actually gives degenerate d xy /d xz /d yz Ground state DFT calculations for M=Cu/Pd place d xy ~4000 cm -1 lower than d xz /d yz DFT implies H 3 is a net π acceptor! Point charge model always splits t 2g set but d xy is always higher than d xz /d yz Is DFT wrong?

40 Can DFT really be wrong? DFT gives excellent description of ground state properties (geometries, frequencies, multipole moments etc.) Relative energies of bonding MOs imply M-Cl π donor DFT charge distributions reasonable But ground state DFT d-orbital sequence still looks wrong LFT treats both ground and excited d-d states so maybe it s an excited state issue DFT excited state energies are qualitatively correct (ADF multiplet states relative to AOCs) DFT is OK so where is the problem? [PdCl 4 ] 2- Exp. DFT 1 A 1g 1 A 2g A 1g 1 E g A 1g 1 B 1g [CuCl 4 ] 2- Exp. DFT 2 B 1g 2 B 2g B 1g 2 E g B 1g 2 A 1g

41 DFT is OK, but... Hoffmann and Baerends argue that Khon-Sham orbitals provide a good basis for discussing bonding LFT naturally focuses on the (anti-bonding) d orbitals and assumes their energies are mirrored by equal and opposite movements of the matching bonding functions - c.f. zero-overlap approximation - antibonding orbital increases by the same amount that the bonding MO decreases DFT is far more sophisticated and consequently we loose this simple relationship between antibonding d orbitals and their bonding counterparts Thus, ground state DFT d orbital energies cannot be interpreted in the usual way

42 Implications for LFMM Cannot use ground state DFT d orbital energies directly for FF development DFT includes d-d interelectron repulsion explicitly and within the full molecular symmetry LFT separates d orbitals from interelectron repulsion and treats the latter within a spherical central field approximation If we define an approximate spherical average configuration where each d orbital has roughly the same population - E.g.: t 2g 3.6 e g 2.4 for an octahedral d 6 complex - then LFT and DFT agree (.B. Software issues. Jaguar versus ADF)

43 Acknowledgements Inorganic Computational Chemistry Group Dr Veronica Paget (LFMM) now with Acelrys Dr David Foulis (LFMM development) Dr atalie Fey (LFMM/MOE, Diels-Alder) Ben Williams-Hubbard (LFMM/MOE,Co spin states and Cu proteins) icola Waite (acrylate polymers) Jack Smith (DFT and Heck reaction) Joanne Hanna (Binding energies) James Burnside (acrylate polymers) Peter Scott, Warwick Lars Ivar Elding, Lund Dominic Ryan, Millenium s EPSRC University of Warwick Chemical Computing Group