Introduction
The heme group is in the active centre of a number of relevant proteins as the oxygen (O 2) transport
proteins haemoglobin (Hb) and myoglobin (Mb) [1,2], as well as enzymes involved in catabolism as peroxidases
[3], catalases, oxidases [4] and cytochromes [5]. The replacement of Fe by Mg in heme leads to chlorophyll [6],
and the replacement of Fe by other transition metals coupled with modifications in the aromatic ring leads to
species as vitamin B12 [7] and cofactor F-430 [8]. The study of heme models was a focal point of experimental
bioinorganic chemistry [9].
Rohmer and co-workers characterized the electronic state of Fe(P) ( P  porphyrin) complexes [10-12]
and predicted an electronic structure that was later proved by experiment [13]. Another theoretical studies are the
real position of the CO group in Fe(P)(Im)(CO) ( Im  imidazole) complexes [14,15], the position of the CN
group in Fe(mdi)2(py)(CN) complexes [16], the role of distal and proximal histidines (His) on the binding of O 2
in Hb [17-20], and structural aspects of the binding of O 2 and other ligands to heme [21-27]. The amount of
information obtained from the calculations is seriously limited by the size of the heme group itself, which has
allowed only recently the appearance of theoretical studies on reactivity [28-33].
The coordination of O2 to the Fe(P)(Im) 5-coordinate species leads to 6-coordinate species with
octahedral geometry: the biomimetic forms of Mb–O2 and Hb–O2. X-ray data were reported only on two
complexes, viz. Fe(TpivPP)[1-(Me)Im](O2) [34] and Fe(TpivPP)[2-(Me)Im](O2) [35]. Both complexes are quite
similar, sharing the same porphyrin T pivPP, which is meso-tetrakis(,,,-o-pivalamidophenyl)porphyrin.
Maseras and co-workers published the optimized geometry of Fe(T pivPP)[1-(Me)Im](O2) with the hybrid
quantum mechanics/molecular mechanics (QM/MM) method IMOMM(DFT-B3LYP:MM3) [36] and pure QM
DFT-B3LYP [37]. Ghosh and Bocian carried out density functional theory (DFT) geometry optimization on
Fe(Por)(Im)(CO) [38]. Salzmann et al. performed DFT-B3LYP constrained geometry optimization of a
Fe(TpivPP)[1-(Me)Im](CO) model [39]. Han et al. studied a heme model–CO system employing the ab initio
pseudopotential method with local density approximation (LDA) exchange correlation [40].
The reversibe binding of O2 and carbon monoxide (CO) played a central role in studies of heme-protein
structure and function. As a result, numerous encumbered Fe II porphyrin models were synthesized in an effort to
elucidate the structural details of small ligand binding. The steric bulk of certain axial ligands bonded to
synthetic FeII porphyrins provided model compounds of reduced O2 and CO affinity, and models of the so-called
tense (T) state of hemoproteins. Unfortunatelly, thus far there was only one single-crystal X-ray structure
determination on such a complex [41]. There was much discussion on the mechanistic basis of the variation of
1
affinity values in heme proteins and model compounds. This focused on the nature of the axial ligand, distal
steric effects, distal polar effects, and enforced doming and ruffling of the porphyrin skeleton.
In previous papers, both non-interacting and interacting induced dipoles (NID and ID) polarization
models were implemented in the program molecular mechanics (MM2) [42]. The new polarizing force field for
proteins (MMID2) was described elsewhere [43]. MMID2 calculation of the N-formylglycinamide
(For-Gly-NH2) backbone was reported [44,45]. MMID2 was improved to include terms specific for five- and
six-coordination [46,47]. In this work, the force field has been parametrized to include terms specific for
transition metal complexes. The new program is called MMIDX. The next section presents the computational
method. Following that, the improvements in the force field are described. Next, the calculation results are
discussed. The last section summarizes the conclusions.
2
Computational Method
Molecular polarizabilities has been calculated with the method of Applequist et al. [48]. One considers
the molecule as being made up of N atoms (i, j, k,…), each of which responds to an electric field only by the
induction of a dipole moment, which is a linear function of the local field. If a Cartesian component of the field
due to the permanent multipoles is Ea , then the induced moment a in atom i is:
i

N

j ( i)

i
 Tabij bj
i
ia   i 
Ea 

(1)
ij
ij is the field gradient tensor,
where i is the polarizability of atom i and Tab
Tab
 1 e ia Ebj , e is the charge of
the proton. Equation (1) can be expressed:


   I E  T    I E   T
where I is the 3N  3 N -dimensional unit matrix. The equation can be solved as

  I T
  E  AE
1
Here the symmetrical many-body polarizability matrix A is introduced:

A I T

1
The compact matrix equation   AE is equivalent to the N matrix equations:
i
 
N

A
ij
E
j
j 1
j
If the molecule is in a uniform applied field ( E  E ), this equation becomes
 N
ij 
   A E  
i

j
eff ,i


1
E
The coefficient of E is the effective polarizability of i, 

mol
N

 N
N
ij 
 N
     A E  
i

i 1 j
i1
1


i 1
eff ,i
. The total induced  is:
eff ,i 
E

from which it is seen that the molecular polarizability tensor 

mol
N
N
A
i 1 j 1
ij
N
 
eff ,i
i 1
Force-Field Modifications
3
mol
is:
(2)
1,3-Interactions between atoms bonded to a common atom are not specifically included in Equation (3)
in the MM2+polarization approach because they are effectively already included in the bond length and bond
angle strainless parameters.
Esteri c 
 Estr   Ebend   Etors   Enb
(3)
However, for five-coordinate structures, there is a need to consider the effect of 1,3-interactions because an
energy term is needed for ligand–ligand repulsion (1) to account for the stability difference of various geometries
possible and (2) to account for structural effects due to the variation of ligand electronegativity.
Since the geometries of the methylfluorophosphoranes (CH 3)nPF5-n ( n  0  3 ) have been qualitatively
correlated with Gillespie’s VSEPR theory, VSEPR was adopted as a model for the present approach. Bond
electron-pair repulsion (EPR) terms were introduced via the non-bonded term Enb of Equation (3) modified to
express EPR effects for atoms bonded to penta or hexacoordinated atoms (1,3-bond EPR terms).
The unmodified non-bonded energy term for non-bonded interactions is

1



5
  2.25 P 6 
Enb(AB )   8.28 10 exp 
 0.0736 P 



(4)

where P  rVDW(A)  rVDW(B) rAB , rVDW is the van der Waals radius of the specific atom, and rAB is the
non-bonded distance between A and B for a given molecular configuration;    A B 
12
where A and B are
parameters specific to atoms A and B, and are related to the hardness of the atoms. Hill evaluated the constants
in Equation (4), which give the energy Enb(AB) in units of kilocalories per mole [49].
The modification of Equation (4) to express 1,3-bond EPR terms is [50]

1



5
  2.25 P *6 
E1,3 AB  D   8.28  10 exp 
 0.0736 P* 


(5)
The addition of a scaling factor D, to obtain a suitable balance between the energy of this 1,3-interaction term
and the other energy terms in Equation (3), and the replacement of P

with P*
(where

P*  rVDW(A)  rVDW(B) r *AB and r* is the distance between atoms A and B calculated from modified bond
AB
lengths, d*CA and d*CB, between the central atom C and either atom A or B), provide the necessary adjustments
to quantitatively reproduce the (CH3)nPF5-n structures [51].
The variation in ligand electronegativity is introduced by a distance factor RA (or RB) in the relation
d * CA  dCA RA (or d * CB  dCB RB ). The magnitude of R is inversely related to the electronegativity difference
between atoms C and A (or B). The R factors are the means of including the concept of bond EPR between
atoms A and B. If the electronegativity difference XCA is large, the bonding electron pair can be considered to
4
move away from atom C, thus decreasing the bond electron-pair repulsion between the C–A and C–B bonds.
When  XCA  X CA' , the repulsion term E(1,3)AB  E(1,3)A' B even when the actual bond lengths are equal.
A set of distance factors R may be obtained from the bond ionic character I,
 1
2 
I  1  exp  XCA  
 4

(6)
and using the relation
R
I  rA  rC
rA  rC
(7)
where rA and rC are covalent radii of atoms A and C.
Calculation Results and Discussion
The structure of heme(-His)-O2 is shown in Figure 1. Heme is the prostetic group of Hb. The van der
Waals parameters for the iron atom have been taken from the UFF force field [52], and the torsional
contributions involving dihedral angles with the metal atom and the bending terms involving Fe in central
position have been set to zero. The dipole moment increases, in general, with the oxidation state of Fe [46].
Thus, the dipole moment of FeIII heme(-His)-O2 and -CN results large due to the polar Fe+–O–O- and Fe+–C–
N- complexes, respectively [47]. The binding of His in heme and of CN in heme–His increase the dipole
moment.
The 4-Coordinate Fe(P) System
The heme group has little direct application in biochemistry, but it is a natural starting point for both
experimental and theoretical studies. The crystal structures of a number of heme derivatives were reported, with
different substituents in the ring. The simplest model, with all substituents being H atoms, was not provided.
Because of this, comparison will be made with a species containing some substituents. In particular, Fe(TPP)
( TPP  meso-tetraphenylporphyrin) has been chosen. Its electronic state is well known experimentally to
correspond to a low spin triplet ( S  1 ).
Selected structural parameters are collected in Table I. The agreement in bond angles between both
MM2/MMX+polarization geometries and the X-ray structure is good, with discrepancies always smaller than 5°.
Discrepancies in bond distances are larger in a number of cases. Some of them were, however, to be expected.
This is the case of the C-Cbridge, C-C’ and C’-C’’ distances. These distances have values of 1.395Å, 1.439Å and
1.365Å, respectively, in X-ray, ca. 1.336Å, 1.340Å and 1.332Å, respectively, in MM2/MMX+polarization.
5
Agreement between experiment and MM2/MMX+polarization is good (ca. 0.06Å). All these atoms are in part
purely described with the MM2 method, and the optimized MM2/MMX+polarization values are close to the
optimal bond distance for these types of atoms in the applied force field, which is 1.337Å. A modification of the
force field would undoubtedly correct this result. However, to keep the fairness of the test, the introduction of
experimental parameters in the calculation has been kept to a minimum.
Another discrepancy in the geometries appears in the Fe–N distance. This is more puzzling, because the
calculated distance 1.877  1.881 Å is smaller than the experimental value of 1.966Å.
The 5-Coordinate Fe(P)(Im) System
Coordination of an imidazole ligand to the heme group leads to a 5-coordinate species with a square
pyramidal geometry. These compounds are good biomimetic models of Mb and Hb, the imidazole replacing the
proximal His of the biological systems. The need to avoid both the dimerization and the formation of the
6-coordinate species with two axial ligands poses serious restrictions on the nature of the porphyrins able to give
this
kind
of
complexes.
For
this
study,
the
species
Fe(Piv2C8)[1-(Me)Im]
(Piv2C8
=
,,5,15-[2,2’-(octanediamido)diphenyl]-,,10,20-bis(o-pivalamidophenyl)pophyrin) has been chosen. This
species has the advantage of having 1-methylimidazole as axial ligand, in constrast with the more common
2-methylimidazole, which is more sterically demanding. Unfortunately, neither for [Fe(Piv2C8)[1-(Me)Im] nor
for other 5-coordinate derivatives of heme the electronic state is experimentally known. Electronic spectroscopy,
magnetic susceptibility and Mössbauer measurements are conclusive in identifying it as high spin ( S  2 ).
Selected parameters are resumed in Table II. The F–Nporphyrin distances are longer by ca. 0.06Å (MMX)
than those in the 4-coordinate system. This trend is in agreement with the reference values. This result is fully
consistent with the shift from low spin to high spin in the metal. Most data in Table II focus on the description of
the imidazole ligand. Overall agreement in the geometric parameters is correct. Moreover, one has to take with
some suspicion the X-ray parameters of the imidazole ligand, which would make the N=C double bond N Im–CIm
of imidazole longer than the N–C single bond NIm–C’Im. However, the MMX+polarization calculations are, in
general, in agreement with the QM/MM reference, which provides the expected result.
The sharper discrepancy shown in Table II concerns the Nporphyrin–Fe–NIm–CIm dihedral angle. This
angle measures the rotation around the Fe–NIm single bond, and rules the placement of the imidazole plane with
respect to the porphyrin ring. Its sign is arbitrary, because the x and y directions are equivalent in absence of
axial ligand. In this work, a positive sign has been chosen for consistence with data on the 6-coordinate
6
complexes presented below. An angle of 90° (like in the pure QM reference) means that the imidazole plane is
eclipsing one of the Fe–Nporphyrin bonds, while an angle of 135° (ca. the 133.8° found in the MMX calculation)
indicates a staggered orientation of the imidazole with respect to the Fe–Nporphyrin bonds. Therefore, both pure
QM and MMX reference values are just opposite with the experimental value (126.0°) lying in between,
although closer to the MMX value. The MMX+polarization results lie, in general, in the range 90 –133 ° of the
reference results. The only exception results the MMX value, which is close to the QM/MM reference. The
importance of the large discrepancy between different values is, however, arguable, because there is also a large
dispersion in different experimental 5-coordinate derivatives of heme, as well as in experimental reports of Mb
and Hb. It seems, therefore, that the rotation around this single bond has a very low barrier.
The 6-Coordinate Fe(P)(Im)(ligand) Systems
Coordination of O2 to the 5-coordinate heme–His species leads to 6-coordinate species with an
octahedral geometry. These compounds are the biomimetic forms of Mb–O2 and Hb–O2. Despite their large
interest, X-ray data
were reported only on two complexes,
viz. Fe(TpivPP)[1-(Me)Im](O2) and
Fe(TpivPP)[2-(Me)Im](O2). Both complexes are quite similar, sharing the same porphyrin T pivPP, which is
meso-tetrakis(,,,-o-pivalamidophenyl)porphyrin. The Fe(T pivPP)[1-(Me)Im](O2) complex, containing the
less sterically demanding 1-methylimidazole ligand has been chosen for comparison. The state of this system is a
low spin open-shell singlet ( S  1 ) resulting in a FeIII–O2- system.
Selected parameters are reported in Table III. The parameters concerning the coordination of O 2, which
are probably the most critical for the biochemical activity of Hb, are well reproduced. The computed values for
the Fe–O distance, 1.8 1.9 Å, are close to the experimental value of 1.746Å. The calculated values ( 1.2  1.3 Å)
for the O–O distance are far from the experimental report of 1.163Å. However, the experimental value (even
shorter than the value of 1.21Å for free O2) is suspect, because of the disorder on the placement of the second O
atom within the crystal, as admitted by the authors of the X-ray experiment themselves [34]. The O–O
interatomic distance increases from 1.21Å in free O2 to 1.326Å (MMX+ID), suggesting that electronic charge is
transferred from FeP to O2. This is in agreement with the experimental result that the Fe–O2 bond can be
formally described as FeIII–O2- [9].
A similar reasoning can be used for the Fe–O–O bond angles, which are, nevertheless, in all cases
indicative of a bent 1 coordination mode, where only one O atom is directly attached to the metal. The
7
orientation of the Fe–O–O plane with respect to the Fe–Nporphyrin axis is staggered ca. 35° (MMX and
MMX+NID). This value is of the same order of magnitude as the experiment (42.4°) and calculation references.
The sharper discrepancy shown in Table 6 concerns the N porphyrin–Fe–O–O dihedral angle. This angle
measures the rotation around the Fe–O single bond, and rules the placement of the Fe–O–O plane with respect to
the porphyrin ring. An angle of 0° (ca. the 3.3° in the MM2 calculation) means that the Fe–O–O plane is
eclipsing one of the Fe–Nporphyrin bonds, while an angle of 45° (ca. the 44.6° in the pure QM reference) indicates
a staggered orientation of the O2 with respect to the Fe–Nporphyrin bonds. The MMX/MMX+NID results lie near
the range 42 – 45 ° of the reference results.
For the binding of CO to heme–His, a linear FeII–CO binding model is proposed. For heme(-His)-CN,
the C–N distance increases from 1.147Å (calculated with AM1 [53]) in free CN to 1.16  1.28 Å, suggesting that
electronic charge is transferred from FeP to CN. This is in agreement with the experimental result that the Fe–
CN bond can be formally described as FeIII–CN- [9]. A linear FeIII–CN- binding model is proposed.
Conclusions
From the preceding results the following conclusions can be drawn.
1. For the heme-IX adducts, the NID or ID polarization energy represents 74% of the total energy
MM2+polarization energy. The EPR energy corresponds to 48% of the total energy MMX+polarization.
2. The model system takes into account the structural differences of the fixing centre in the Hb subunits.
That is why the customary proximal His is added. The macrocycle hemo IX is wholly considered in the model.
The calculations show that certain conformations are much more favourable that others for fixing O2.
3. Three different Fe-binding models are proposed for O2, CO and CN: bent superoxide FeIII–O2-, linear
FeII–CO and linear FeIII–CN-. The nature of O2 binding in Hb, Mb and simple Fe–porphyrin models is
becomming clear. When O2 is bound as a bent, rather than a triangular, ligand, it is best described as bound
superoxide. This bent geometry may be critical to biological functioning because it allows the discrimination
between O2 and CO.
Acknowledgement
The author acknowledges financial support of the Spanish MCT (Plan Nacional I+D+I, Project No.
BQU2001-2935-C02-01).
8
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11
Figure Caption
FIGURE 1. Structure of heme(-His)-O2. Heme is the prostetic group of haemoglobin.
12