Extracting quantitative structural information from EPR g-tensors with density functional theory: applications to nitrosoiron(II) porphyrins - PowerPoint PPT Presentation

Title: Extracting quantitative structural information from EPR g-tensors with density functional theory: applications to nitrosoiron(II) porphyrins


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Extracting quantitative structural information
from EPR g-tensors with density functional
theory applications to nitrosoiron(II) porphyrins
I am on the Web http//www.cobalt.chem.ucalgary.
ca/ps/posters/EPR-FeP/
S. Patchkovskii and T. Ziegler
Department of Chemistry, University of Calgary,
2500 University Dr. NW, Calgary, Alberta, T2N 1N4
Canada
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Introduction.
Conclusions and outlook
Introduction
Iron-containing porphyrin complexes (hemes) serve
as prosthetic groups in many vitally important
enzymes1,2, such as hemoglobin. Because
oxy-hemoglobin possesses a singlet electronic
structure, it is not amenable to studies using
electron paramagnetic resonance (EPR).
Structurally similar heme nitrosyls have a
spatially non-degenerate spin-doublet ground
state, which is readily observable with
EPR. Experimental EPR spectra of nitrosylated
hemoglobins and myoglobins3,4, indicate the
presence of two distinct radical species rhombic
and axial. The rhombic ("Type I") species
exhibits three distinct principal components in
its EPR g tensor (g11.96-1.98, g22.00,
g32.06-2.08).
It has been assigned to a six-coordinated
structure, with NO coordinated in a bent end-on
orientation, and the second axial position filled
by an imidazole side chain. Despite extensive
investigations, the nature of the axial ("Type
II") species (g1.99-2.00, g?2.02-2.03) have
proven more elusive, and remains
controversial. In this work, we examine the
structure and EPR g-tensors of model porphyrins
with density functional theory (DFT). On the
basis of our calculations, we propose a new
structural model for the axial species.
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Theory I
Theory
Quasi-relativistic DFT formulation of the EPR
g-tensors used in this work distinguishes between
several contributions to the g-tensor5,6
free-electron g value (?2.0023)
diamagnetic term
paramagnetic term
Darwin term
Relativistic corrections
mass-velocity correction
kinetic energy correction
The paramagnetic term dominates deviation of g
from the free-electron value for complexes
considered here, and can be in turn separated
into several contributions
frozen core contributions
occupied-virtual coupling terms
occupied-occupied coupling terms
The occ-vir term is usually the most
qualitatively important contribution.
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Theory II
The contribution is given by
(atomic units)
? 0.00731
?-spin current
the effective potential
?-spin current due to unit magnetic field along
sx,y, or z
The form of the occupied-virtual paramagnetic
contribution the the EPR g-tensor is analogous to
the expression for the paramagnetic part of the
NMR shielding tensor for a nucleus N, given by
The similarity between the two quantities is
extremely useful both in the evaluation and in
analysis of g tensor, and is unique to our DFT
implementation.
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Theory III
The spin-current density for a spin ? arising due
to the coupling between occupied and virtual MOs
caused by the external magnetic field B0 is given
by
magnetic coupling coefficient
field strength in the direction s (x,y,z)
unperturbed occupied MO
unperturbed virtual MO
The principal contribution to the coupling
coefficient u is in turn given by
atomic orbitals (AOs)
applies to each AO ?
unperturbed orbital energies
unperturbed MO coefficients
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Methods
Methods
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ON-Fe(P) Coordination of NO
Conclusions and outlook
ON-Fe(P) Coordination of NO
Z

• The coordination of NO around iron gives rise to
  three key points on the PES of 1, namely
• the C4v structure 1a with the linearly
  coordinated NO ligand.This is a second-order
  saddle point, rather than a minimum.
• Cs structure 1b, with bent end-on coordination
  of the NO ligand, pointing towards one of the
  meso carbon atoms of the porphyrin ligand.
• a second Cs structure 1c, with the NO bond
  eclipsing one of the equatorial Fe-Np bonds.
• Given the isoenergetic 1a and 1b, the NO ligand
  in free five-coordinated heme nitrosyl should
  undergo free intramolecular rotation around the Z
  axis. A closer inspection of the optimised
  structures reveals that the rotation of the NO
  ligand is coupled to the distortion of the
  porphyrin ligand. As a consequence, hindering the
  distortion increases the barrier for NO rotation
  increases to about 1.2 kcal/mol.

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ON-Fe(P)-Im Coordination of imidazole
Conclusions and outlook
ON-Fe(P)-Im Coordination of imidazole
Dissociation of the imidazole was examined by
gradually increasing the iron-imidazole distance,
and optimizing the rest of the structure. The
resulting energy profile is exceptionally flat,
with variations in the Fe-N(Im) bond length in
the 2.05-2.50Å range changing energy by less than
1 kcal/mol. As a consequence, experimental bond
lengths are likely to be influenced by
substitution and environment effects. Although
the potential energy profile for the dissociation
of imidazole appears to indicate a presence of a
local minimum at ?2.4Å, g-tensors show no
qualitative changes in the vicinity of this
structure.
exp
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ON-Fe(P)-Im rotation of the axial ligands
Conclusions and outlook
In the six-coordinated complex, both axial
ligands preferentially appear in staggered
orientation (2a-2c). The local minima appear
within 0.3 kcal/mol of the global minimum (2c),
and will be substantially populated at non-zero
temperature. The orientations of NO and imidazole
in condensed phases are likely to be determined
by substituent effects and intermolecular
interactions. Free rotation of both axial
substituents may also be expected at room
temperature.
32
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Origin of g in C4v structure.
Conclusions and outlook
Origin of the g tensors C4v structure
Mulliken d-population on iron in 1 (?6.7) is
consistent with d7 electron count, formally
making 1 a complex of FeI and NO. The unpaired
electron is mostly on irons dz2 AO. The SOMO
vanishes upon action of the Mz operator, so that
all spin-restricted terms in the parallel
component ?g also vanish. If the magnetic field
is in the XY plane, the field-induced coupling
with ?-spin ? MOs (dxz, dyz-like), localised on
the Fe-NO fragment, results in a contribution of
-36 ppt to ?g?. This contribution is almost
identically cancelled by two ?-spin terms, (14
and 20 ppt)
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Origin of g in meso-Cs structure
Conclusions and outlook
Origin of the g tensors Cs structures
In the bent 1b, iron's dz2 AOs overlap with the
? orbitals of the NO ligand, tilting the
dz2-like contribution to the SOMO towards the
direction perpendicular to the NO bond. Such
orientation allows SOMO to interact with occupied
non-bonding dx2-y2 orbital n1. The SOMO?? and
SOMO?n terms exhibit a qualitatively different
dependence on the relative orientation of the NO
ligand and the porphyrin core, so that g-tensor
in bent 1 depends on the orientation of NO.
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Origin of g in ON-Fe(P)-Im
Conclusions and outlook
Origin of the g tensors ON-Fe(P)-Im
1b SOMO
2b SOMO

• Upon coordination of the imidazole, a weak ?
  interaction between an imidazole lone pair, and
  the dz2-like lobe of the SOMO, destabilises the
  SOMO by 0.9 eV. The Mulliken spin population on
  iron is also reduced, from 0.9 (1b) to 0.5 (2b).
• decrease in the d character of the SOMO reduces
  all spin-orbit coupling matrix elements,
  decreasing all ??g?s.

• a large NO ? contribution to the SOMO increases
  the magnitude of matrix elements of the M
  operator in ?-SOMO? ?-? terms.
• destabilisation of the SOMO increases ?-SOMO?
  ?-? terms, while decreasing ?-SOMO? ?-?
  contributions.

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Numerical results Principal components
Conclusions and outlook
Numerical results Principal components
g1 g2 g3
1a 2.008 2.003 2.003
1b 1.994 2.005 2.063
1c 1.997 2.024 2.033
ON-Fe(TPP) 2.010 2.064 2.102
2a 1.955 1.995 2.034
2d 1.967 2.000 2.012
ON-Fe(TPP)-Im 1.970 2.003 2.072
Mb(NO) 1.979 2.002 2.076
?-Hb(NO) 1.974 2.006 2.081
?-Hb(NO) 1.978 2.008 2.057
As expected from the qualitative analysis,
calculated principal g-tensor components in
ON-Fe(P) (1) are sensitive to both the Fe-NO
bond angle, and to the orientation of the NO
relative to the porphyrin (1a-1c). The values are
only in a broad qualitative agreement with
experiment, and appear to indicate an orientation
of the NO ligand intermediate between 1b and 1c.
Part of the error may be due to the neglect of
the environment effects. In ON-Fe(P)-Im (2),
g-tensor is again sensitive to the orientation of
NO, but is left unchanged by imidazole rotation.
Calculated magnitudes of the principal components
appear to be in a broad qualitative agreement
with experiment. The characteristic
g1ltg2(?ge)ltltg3 pattern is reasonably well
reproduced. At the same time, calculated values
are too small compared to experiment, by 20 to 50
ppt.
TPP tetraphenylporphyrinato2- Mb
myoglobin Hb hemoglobin
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Numerical results g-tensor orientations
Conclusions and outlook
Numerical results g tensor orientation
Theoretical orientations of the g-tensor
components in 2 are in a good agreement with
experiment for low-temperature "Type I" nitroso
myoglobin. At 77K, the principal components of
the g tensor in MbNO3 deviate from the
direction perpendicular to porphyrin plane (Z
axis) by, respectively, 632º (g1), 272º (g2),
and 882º (g3). The corresponding theoretical
values for free 2a are 58º, 32º, and 90º.
Comparison of the remaining experimental
direction cosines with the theoretical results
gives of approximately -70º. The good agreement
in the theoretical and experimental orientations
of the g-tensor indicated that the FeNO
fragment in MbNO is not substantially distorted
by the protein. The large g2 orientation has been
taken previously4 as an indication of the
Fe-N(NO) axial bond direction. As can be seen
from the SOMO plots, it in fact corresponds to
the direction of the dz2-like part of the SOMO,
which in turn deviates from the Fe-N(NO) bond by
almost 40º.
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Numerical results RFe-N(Im) and g-tensor
Conclusions and outlook
Numerical results RFe-N(Im) and g-tensor
Elongation of the Fe-N(Im) bond results in an
increase in all three principal components. The
free electron-like component (g2) increases by
only 8 ppt/Å in the 2.0-2.9 Å range. The other
two components, g1 and g3, increase at the rates
of, respectively, 45 and 36 ppt/Å. At the
separation of 2.9 Å or more, the calculated g
tensor becomes essentially identical to the
result for free five-coordinated species. If the
NO ligand rotates freely on the EPR time scale,
averaging results in g?gt g. The parallel
component increases the rate of 19 ppt/Å. g?
grows at 35 ppt/Å, so that the separation between
the rotationally averaged components increases
with dissociation of imidazole.
g tensor components
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Biological ON-Fe(P)-Im Models galore
Conclusions and outlook
Biological ON-Fe(P)-Im Models galore
Axial
Rhombic
Source
Model
P.E.S.
g-tensor
Axial structure is not a minimum axial g-tensor
components are wrong
linear- bent
?
?
3
Axial structure is not a minimum, and has
rhombic g-tensor
up- down
?
?
13
Rhombic structure is not a minimum Axial
structure has rhombic g-tensor.
inclined- straight
?
?
15
bound- dissociated
?
Axial structure has rhombic g-tensor.
?
16
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Biological ON-Fe(P)-Im rhombic species
Conclusions and outlook
Biological ON-Fe(P)-Im Rhombic species
The rhombic signal ("State I") exhibits a
characteristic pattern of gminltgfreeltltgmax. This
pattern appears to correspond to the
six-coordinated complex 2 with the internal
rotation of the NO ligand frozen on the EPR time
scale. Calculated orientations of the principal
components are in an excellent agreement with the
experimental result for nitrosylated myoglobin
(MbNO) single crystals. At low temperatures, the
direction of the g2 component in MbNO deviates by
?30º from the average normal to the porphyrin
plane. The value calculated at the theoretical
gas-phase geometry of the model complex 2 is 32º,
suggesting that the ON-Fe(P) fragment in MbNO is
not noticeably distorted by interactions with the
protein environment.
g11 g22 g33
Calculated 1.96 2.00 2.03
?-Hb(NO) 1.97 2.01 2.08
?-Hb(NO) 1.98 2.01 2.06
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Biological ON-Fe(P)-Im axial species
Conclusions and outlook
Biological ON-Fe(P)-Im Axial species
The axial (Type II) spectra are usually found
at higher temperatures. In the absence of a
satisfactory static model, it appears reasonable
to consider possible dynamical interpretations.
If the rotation of NO is unfreezed, averaging of
the g components leads to an axial spectrum. In
the model complex, imidazole has no additional
chemical bonds to the ON-Fe(P) fragment, and will
dissociate completely. In heme proteins, it is
provided by a histidine residue, and is tethered
to the backbone. The tethering may prevent a
complete dissociation, leading to smaller values
of g? and g. It also allows protein to switch
between Type I and Type II spectra at the same
temperature A conformational change in the
backbone can pull the imidazole from the rest of
the complex,
effectively causing its dissociation. This would,
in turn, lower the barrier for NO rotation, and
produce the change in the spectrum.
g g?
Calculated 2.00 2.03
?-Hb(NO) 2.00 2.02
?-Hb(NO) 2.00 2.03
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Summary
Conclusions and outlook
Summary

• Structure of ON-Fe(P)-Im
• In both five- and six-coordinated complexes, NO
  is preferably coordinated end-on, with a Fe-NO
  bond angle of approximately 140º.
• In the gas-phase five-coordinated complex, NO
  undergoes free rotation. Imidazole coordination
  in the second axial position increases the
  activation barrier
• Variations in Fe-N(Im) bond in the 2.05-2.5Å
  change energy by less than 1 kcal/mol.
• EPR g-tensors
• are sensitive to the orientation of NO and
  Fe-N(Im) bond length.
• are not sensitive to the orientation of the
  imidazole ligand
• orientation of the g-tensor component, showing
  the smallest deviation from the free-electron
  value, does not coincide with the direction of
  the axial Fe-N(NO) bond.
• Biological ON-Fe(P)-Im systems
• Rhombic ("Type I") EPR signal in nitrosoheme
  systems corresponds to a static structure with NO
  in a staggered orientation, and RFe-N(Im)?2.1Å.
  The ON-Fe(P) moiety is not noticeably distorted
  by the protein environment.
• The axial ("Type II") EPR signal is tentatively
  assigned to a partially dissociated species
  (RFe-N(Im)?2.5Å), with a freely rotating NO
  ligand.

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Acknowledgements
Acknowledgements
Acknowledgements
This work has been supported by the National
Sciences and Engineering Research Council of
Canada (NSERC), as well as by the donors of the
Petroleum Research Fund, administered by the
American Chemical Society (ACS-PRF No 31205-AC3).
Dr. Georg Schreckenbach is gratefully
acknowledged for making the GIAO-DFT
implementation of the EPR g tensors available to
the authors.
References