Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Electronic Effects and Ligand Field Theory Dr Rob Deeth Inorganic Computational Chemistry Group University of Warwick UK Overview • • • • • • • • • Introduction Electronic effects in TM chemistry Classical v. Organometallic compounds Ligand Field Stabilisation Energy d orbitals Spin states and Jahn-Teller effects Generalised ligand field theory Ligand Field Molecular Mechanics DommiMOE Electronic Effects • Geometric preferences • Obvious ones: – Jahn-Teller effect = distorted, especially Cu(II) – four short, two long • Less obvious ones: – Low-spin d8 = planar, especially Pd(II), Pt(II), Rh(I) – Low-spin d6 = octahedral, Co(III) • First row TMs particularly complicated Plasticity • M-L bonds weaker than C-C • Higher coordination numbers • More flexible geometry – angular variations – [CuCl4]2– High spin NiL4 – tetrahedral – Low spin NiL4 – planar – Five coordination – small energy difference between square pyramidal and trigonal bipyramidal Classical v. Organometallic • Werner-type: – Relatively ionic – Electronic effects focussed on d orbitals – IONS • Organometallic – Relatively covalent – More general electronic effects – spndm – Neutral or +-1 • For classical coordination complexes, need to consider d orbitals d orbitals Z Z Z Y Y Y X X dx2-y2 X d2z2-x2-y2 dxz Y X X Z Z Y dxy dyz d Orbital splittings • In octahedral symmetry, the five d orbitals split • Barycentre relative to average d orbital energy eg +3/5 n+ M 10Dq d -2/5 n+ Free M t2g ion n+ M in octehdral crystal field Point charge q = ze ∆oct Ligand Field Stabilisation Energy • Structural preferences and Jahn-Teller instabilities can be traced to LFSE • LFSE d0: 0 d1: -2/5∆oct d2: -4/5∆oct d3: -6/5∆oct d4: -3/5∆oct d5: 0 ∆Hhyd Ca Sc Ti V Cr Mn Fe Co Ni Cu Zn Spin States • • • For dn configurations with 2 ≤ n ≤ 8, multiple spin states are possible Spin depends on symmetry and ligands Consider octahedral complexes – Spin state a balance between d orbital splitting and spin pairing energy S=2 4 S = 1/2 S=1 S = 3/2 d 1 d S=1 S = 5/2 2 4 3 d 5 d d d high low high S = 1/2 5 d low S = 3/2 5 d intermediate π Bonding Affects ∆oct • σ-only ligand leaves t2g orbitals degenerate • π donors decrease ∆oct • π acceptors increase ∆oct t1u* t2g* 4p a1g* empty π* 4s Ligands eg* eg* eg* eg* t2g* 3d t2g t2g π (filled) t2g Metal σ σ only t2g eg a1g Ligands t1u Octahedral ML6 Ligands π acceptor π donor 10Dq increases 10Dq decreases Jahn-Teller Effect • The d electrons are structurally and energetically non-innocent. • Complexes with a ground state orbital degeneracy unstable with respect to a vibration which removes the degeneracy - Jahn-Teller theorem dx2-y2 ∆EJT eg ∆EJT dz2 L L L -δ Cu L L L t2g +2δ Molecular Mechanics • Etot = ΣEstr + ΣEbend + ΣEtor + ΣEvdw + ΣEC 9 Fast (big systems, dynamics) 9 Accurate (experimental information built in to Force Field parameters) 8 Parameterised 9 Works well for organics and TM complexes with “regular” coordination environments 8 Problems with “plastic” systems 8 Problems with electronic effects Extending MM to the d-block • 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 captures d electronic effects directly • Etot = ΣEstr + ΣEbend + ΣEtor + ΣEvdw + ΣEC + LFSE d-orbital energies • Crystal Field Theory is global symmetry approach – all ligands simultaneously • MM is bond centred • Need to express d orbital energies as function of individual bonds • Angular Overlap Model describes each bond´s contribution to the total ligand field potential Getting LF Parameters • Each M-L bond is described by up to three parameters — eσ, eπx, eπy. L L L M M Z M X Y dz2 dxz eσ d d dyz eπx d eπy Angular variations • d orbital energies for linear ligator M-L Z dz2 y x eσ(L) L Y z M Effect of moving ligand Fσ(dz2) = 1/4(1+3cos2θ) E(dz2) = eσ F(dz2) = 1/16 eσ (1 + 3cos2θ)2 _ d X θ = 0° Z L eπ(L) dxy,dx2-y2 Z Z θ = 25° L θ = 54.7° θ = 90° L M M M M . 1.00 0.75 Fraction of e(sigma) • • • dxz,dyz 0.50 0.25 0.00 0 30 60 90 θ 120 150 180 L Other motions Z θ = 0° θ = 25° L L χσ θ = 45° θ = 90° L M M X M M dxz 1.00 Fraction of e(sigma) 0.75 0.50 0.25 0.00 0 30 60 90 θ 120 150 180 L Octahedral symmetry Angular Coordinates Z y ψ θ z M N Y φ X Z x Ligand θ φ 1 90 0 2 90 90 3 0 0 4 90 180 5 90 270 6 180 0 L3 L4 Y L2 M L5 L1 L6 X d orbital energies • The energy of each d function will consist of the sum of all possible symmetry contributions (σ, πx, πy) from each ligand. For N ligands, this will in general correspond to a sum of 3N terms. • E(dz2) = ¼eσ(L1) + ¼ eσ(L2) + eσ (L3) + ¼ eσ (L4) + ¼ eσ (L5) + eσ (L6) = 3eσ (L) • E(dx2-y2) = ¾ eσ(L1) + ¾ eσ(L2) + 0eσ (L3) + ¾ eσ (L4) + ¾ eσ (L5) + 0eσ (L6) d ,d = 3eσ (L) ∆ 3e • AOM automatically recovers correct symmetry d ,d ,d oct 4eπ 'mean' d z2 x2-y2 xz yz σ xy Strategy and Examples • Only develop parameters for metal-ligand bonds • Use existing force fields for ´spinach´ • [CoF6]3– High spin d6 • [Co(CN)6]3– Low spin d6 • [CuCl4]2• Ammonia and amine complexes DFT Protocol for Bond Lengths • Optimised Bond lengths for [CoL6]3complexes Co-F Co-CN DFT(hs) 1.97 2.12* Exp 1.94 DFT(ls) Exp 1.88* - 1.88 1.89 • We can use the bond lengths for high-spin [Co(CN)6]3- and low-spin [CoF6]3- to design better LFMM parameters. Adding Chemical Unrealism: LFSE-free • MM uses separate energy terms so it is feasible to pose questions like “What is the M-L distance in the absence of LFSE?” • LFSE = 0 if all d orbitals equally occpied • For d6 Co(III), this corresponds to t2g3.6eg2.4 • DFT gives approximate LFSE-free bond length Adding Chemical Realism: π Bonding Both F- and CN- can form π bonds. Averaged configuration DFT calculations on hypothetical CoL4 species yields ‘d’ orbital energies which can be fitted to standard AOM expressions to determine eπ to eσ ratio. Co-F: ~0.3 Co-CN: ~0.1 (CN π donor!) Parameter Fitting • In general, we want to be able to handle large M-L bond length changes: use Morse function. • Angular geometry determined by 1,3-ligand-ligand (POS, VSEPR) interaction (plus LFSE contribution). • The required bond length, r, is a balance of Morse function (D0, α and r0) with the LFSE and POS. NB: r0 > r • CAN´T USE METAL PARAMETERS FROM OTHER FFs 160 Morse 120 CLFSE Energy 80 Total 40 0 1.50 -40 1.70 1.90 2.10 -80 -120 Bond Length 2.30 2.50 MOE • Scientific Vector Language • LFSE and derivatives: code written in C • Connect LFSE code to MOE via API and SVL communication routine function __LFMM_potential [x, args] // (nf) *********************************************************************** local function LFMM_potential; local [f,g] = LFMM_potential [lfmm_vector, x, args, 1]; // type 1 = optimisation, type2 = single point //*************************************************************************** return [f,g]; endfunction DommiMOE •D-orbitals in molecular mechnics in inoragnics in MOE