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Electronic Effects andLigand Field Theory
Dr Rob DeethInorganic Computational Chemistry Group
University of WarwickUK
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, especiallyCu(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
dx2-y2
Z
Y
X X
Y
Z
d2z2-x2-y2
X
Y
Z
dxz
Y
Z
X
dxy
Z
X
Y
dyz
d Orbital splittings
• In octahedral symmetry, the five d orbitals split
• Barycentre relative to average d orbital energy
Mn+
Point charge q = ze
Free Mn+ ion
d
eg
t2g
10Dq
Mn+ in octehdral crystal field
+3/5
-2/5
∆oct
Ligand Field Stabilisation Energy
• Structural preferences and Jahn-Teller instabilities can be traced to LFSE
• LFSEd0: 0 d1: -2/5∆oct
d2: -4/5∆oct
d3: -6/5∆oct
d4: -3/5∆oct
d5: 0
∆Hhyd
Ca Mn ZnV NiSc Ti Cr Fe Co Cu
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
d1 d2 d3
d4 d4 d5 d5 d5
S = 1/2 S = 1 S = 3/2
S = 2 S = 1 S = 5/2 S = 1/2 S = 3/2
high low high low intermediate
π Bonding Affects ∆oct
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 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
eg
t2g
∆EJT
∆EJT
L
CuL L
L
L
L+2δ
-δ
dx2-y2
dz2
Molecular Mechanics• Etot = ΣEstr + ΣEbend + ΣEtor + ΣEvdw + ΣEC
Fast (big systems, dynamics)Accurate (experimental information built in to Force Field parameters)ParameterisedWorks well for organics and TM complexes with “regular” coordination environmentsProblems with “plastic” systemsProblems 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 symmetryapproach – 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 fieldpotential
Getting LF Parameters• Each M-L bond is described by up to three parameters — eσ, eπx, eπy.
L
eσ
dz2
deπx
dxz
deπyd
L
M
L
MM X
Y
Z
dyz
Angular variations
_d
dz2
eσ(L)dxz,dyz
dxy,dx2-y2M
L
eπ(L)z
xy
X
Y
Z
L
M
L
M
L
M LM
θ = 0° θ = 25°θ = 54.7°
θ = 90°
.
Z Z Z
0.00
0.25
0.50
0.75
1.00
Frac
tion
of e
(sig
ma)
0 30 60 90 120 150 180 θ
• d orbital energies for linear ligatorM-L
• Effect of moving ligand• Fσ(dz2) = 1/4(1+3cos2θ)• E(dz2) = eσ F(dz2)
= 1/16 eσ (1 + 3cos2θ)2
Other motionsL
M
L
M
L
M LM
θ = 0° θ = 25°θ = 45°
θ = 90°χσ
dxz
Z
X
0.00
0.25
0.50
0.75
1.00
Frac
tion
of e
(sig
ma)
0 30 60 90 120 150 180 θ
Octahedral symmetryAngular Coordinates
L3
ML4 L2
L1L5
L6X
Y
Z
Ligand θ φ
1 90 0
2 90 90
3 0 0
4 90 180
5 90 270
6 180 0
M Nθ
φX
Y
Z
ψy
x
z
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)= 3eσ (L)
• AOM automatically recoverscorrect symmetry
3eσ
4eπ
∆oct
dz2, dx2-y2
dxz, dyz, dxy
'mean' d
Strategy and Examples
• Only develop parameters for metal-ligandbonds
• 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]3-
complexesCo-F Co-CN
DFT(hs) 1.97 2.12*Exp 1.94 -
DFT(ls) 1.88* 1.88Exp - 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 t2g
3.6eg2.4
• 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: ~0.3Co-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
-120
-80
-40
0
40
80
120
160
1.50 1.70 1.90 2.10 2.30 2.50
Bond Length
Ene
rgy
MorseCLFSETotal
MOE
• Scientific Vector Language• LFSE and derivatives: code written in C• Connect LFSE code to MOE via API and SVL
communication routinefunction __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 molecularmechnics in inoragnics inMOE