Transcript [Fe(NH 3 ) 6 ] 2+ Finding optimal parameters for spin

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c
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Finding optimal parameters for spin-state changes in Iron(II) amine complexes
in Ligand Field Molecular Mechanics
Prakash
1MOAC
1
Patel
, Rob
2
Deeth
Doctoral Training Centre, and the 2Inorganic Computational Chemistry Group, Department of Chemistry, University of Warwick.
Abstract
Iron(II) Hexammine [Fe(NH3)6]2+
The geometries and energies of six-coordinated amine complexes of Fe2+ at both spin states were explored using the DommiMOE
program. Then the model parameters were refined using simulated annealing to give the correct geometries and predict the
correct spin state of the metal, initially with [Fe(NH3)6]2+, then with three other amine complexes. The parameters found were
applied to about 80 imine complexes, and after a slight modification, approximated the geometries reasonably well and most of the
time predicted the correct spin state.
This is an octahedral high-spin complex where the Fe – N bond lengths are 2.20 Ǻ (from X-ray
crystallographic data). To obtain data on a hypothetical low-spin structure, QM techniques were used, which
predict that the Fe – N bond lengths are around 2.00 Ǻ. Also, an estimate of 11 kcal/mol was set on the
energetic favourability of the high spin state over the low spin state.
Introduction
The importance of metalloproteins in biochemistry has long been recognised. Metal centres are instrumental in many catalytic and
binding functions. Computer modelling can help probe their properties but few methods exist that model transition metalcontaining proteins effectively, either using quantum or classical mechanical methods. Here is outlined a very promising new
molecular modelling approach to deal with transition metal complexes which can be used to model biological macromolecules.
As with all MM-based methods, some model parameters have to be found which fit the required geometries
and energies. Parameters modified included the Morse function parameters (Fe–N bond length potential
was modelled by a Morse function), octahedral-field splitting term, the ligand-ligand repulsion term and
some electron-pairing energy terms. To measure the ‘fit’ of the parameters, a cost function was constructed
such that the smaller its value, the better the parameters fit the data.
Simulated Annealing
U total   ( Eb  E  E  Enb  E )
Markov chain
explores
distribution of
interest, with a
preference of
‘downhill’ steps if
the global
minimum is to be
found.
2
1.8
1.6
p(x)
where the terms correspond to the deviation from the reference bond lengths, bond angles, torsions, non-bonded interactions and
electrostatic interactions from those given by the a particular force field.
2.2
2.2
1.4
Modelling transition metals using conventional MM has always been difficult as they can have variable oxidation states, spin states
and electronic effects, and can coordinate from 4 to 12 different ligands in a complex. This has been addressed in Warwick by
developing the Ligand Field Molecular Mechanics model of dealing with transition metal centres using an approach called Ligand
Field Theory.
A bit of Ligand Field Theory
In a free transition metal ion, the preference of the d-electrons is
to occupy each of the five d-orbitals, and when there are more
than five d electrons, spin-pairing occurs. In an octahedrallycoordinated complex, the dxy, dyz and dxz orbitals become lower in
energy than the dx2-y2 and dz2 orbitals and are filled first.
Ligand Field Theory states that this is because the former orbitals
repel the ligand electron densities less than the latter (the dorbitals are mostly antibonding and repel ligand electron clouds).
Depending on the ligands (the so-called ligand field strength), the
d-electrons may desert the dx2-y2 and dz2 orbitals completely as the
electron pairing becomes energetically more favourable than the
electron repulsion of ligand bonding orbitals.
Low Spin
U
LFMM
total
1.8
1.6
1.4
2
4
6
8
10
x
12
14
16
18
20
7
6
5
4
3
2
0.8
0
Start at
current
minimum.
Markov
chain is
more
confined to
an area of
interest
8
1.2
Reduce T
1
1
0.8
The smallest
value
encountered
by the
Markov
chain is
noted.
2
0
2
4
6
8
10
x
12
14
16
18
20
1
0
0
2
4
6
8
10
x
12
14
16
18
20
In simulated annealing, the target distribution π(x) is changed to π(x)1/T (T is known as the ‘temperature’), which has the same
maxima and minima as π(x) but is rather ‘steeper’ as T decreases from 1 to 0, and this makes the Markov chain less likely to
escape local minima. If the temperature is carefully reduced, then (hopefully) at the end of the procedure the Markov chain will
reside near the global minimum.
1.
2.
Amine Complexes
Free Fe2+ ion (high spin)
(1) Low Ligand Field strength
(e.g. Cl-, I-, F-, H2O)
(2) High Ligand Field strength
(e.g. CN-, phenantroline)
(1) is known as the high-spin state of Fe2+ as the total
spin is greater than in (2), known as the low spin state.
The difference between low spin and high spin states is the metal-ligand bond lengths of low spin
states are much smaller than those of high spin. For example, the Fe – N bond length in low
spin and high spin amine complexes are about 2.00 and 2.20Ǻ respectively. This is because of
the smaller repulsion of the ligands from the d-electron cloud at low spin than at high spin.
High Spin
1.2
9
p(x)1/T
Molecular Mechanics (MM), or Force-Field (FF) methods, of finding molecular structures determine the relationship between the
energy and structure by application of empirical rules based on classical mechanics. To find an optimal structure in MM, we
optimise the total potential energy
MM
Simulated Annealing (SA) is a method of finding the maximum or minimum of a distribution π(x) by using Markov Chain Monte
Carlo (MCMC) to sample the parameter space, in this case the distribution needed to be minimised is the cost function. A Markov
chain (a ‘random walk’) is constructed whose limiting distribution is π(x) - the target distribution.
p(x)
Molecular Mechanics
Deeth summarised this effect by the Ligand Field Stabilisation Energy (LFSE), and incorporated
into the MM framework by adding to the MM equation:
 ( Eb  E  E  Enb  E  LFSE)
Deeth has implemented LFMM into the Molecular Operating Environment (MOE), a popular
modelling program, to form DommiMOE, which uses the MMFF94 FF for non-transition
metals. DommiMOE can optimise the geometry of a complex for a given spin state, and so
can give hypothetical structures of transition metal complexes for both spin states with the
same set of parameters.
The simulated annealing procedure yielded some good parameters for the iron hexaammine
complex, which were applied to three other amine complexes. From the bond lengths in their X-ray
crystallographic structures, (1) and (2) were low spin complexes, while (3) was a high spin complex,
which illustrates the sensitivity of the spin state of Fe2+ with nitrogen ligands. The parameters found
for [Fe(NH3)6]2+ were found to reproduce the geometry of the complexes very well in their native spin
states, and also the spin states of the complexes were correctly predicted.
3.
Imine Complexes
Can these parameters transfer to imine complexes? Unlike amine nitrogens, imine nitrogens are unsaturated, and most Fe 2+
imine complexes are low-spin. After further refinement of the parameters to account for p bonding, DommiMOE correctly
predicted the spin state for most of the complexes, although the geometries require more analysis.
The most striking result was the predicted spin states of the low spin complex [Fe(1-10-phenantroline)3]2+ and the high spin [Fe(2methyl-1-10-phenantroline)3]2+. Although the ligands in these complexes were very similar, DommiMOE correctly deduced their
spin states, which correspond to a large change in geometry.
Applications
The next step is to model iron porphyrins. The porphyrin is a symmetric planar ligand which
binds the metal via four aromatic nitrogens (chemically similar to imine nitrogens). An
important example of an iron porphyrin is the O2 -binding site for haemoglobin. Fe2+ in heme
changes from high spin to low spin when it binds to an oxygen molecule, which changes the
shape of the whole molecule. This change is important in the uptake and transport of oxygen.
It would be very interesting to find out if DommiMOE can model this ■
[Fe(1-10-phenantroline)3]2+
The author would like to thank Rob Deeth and the MOAC Doctoral Centre staff and colleagues for their help
and guidance and the Engineering and Physical Sciences Research Council Life Sciences Interface
Programme for their generous support.
[Fe(2-methyl-1-10phenantroline)3]2+