Download Ligand Field Theory in the New Millenium: Is there Life after DFT?

Electronic Effects and
Ligand Field Theory
Dr Rob Deeth
Inorganic Computational Chemistry Group
University of Warwick
UK
Overview
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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