Magnetic Field (g-Value) Dependence of Proton Hyperfine Couplings

J. Phys. Chem. 1996, 100, 5235-5244

5235

Magnetic Field (g-Value) Dependence of Proton Hyperfine Couplings Obtained from ESEEM Measurements: Determination of the Orientation of the Magnetic Axes of Model Heme Complexes in Glassy Media Arnold M. Raitsimring,* Peter Borbat, Tatjana Kh. Shokhireva, and F. Ann Walker* Department of Chemistry, UniVersity of Arizona, Tucson, Arizona 85721 ReceiVed: August 28, 1995; In Final Form: NoVember 15, 1995X

Electron spin echo envelope modulation (ESEEM) studies were utilized to characterize the coupling between protons of axially bound pyrazole ligands (PzH) and the unpaired electron of low-spin tetraphenylporphyrinatoiron(III) chloride. Samples were prepared in mixed-solvent glasses to maximize the resolution of the electron paramagnetic resonance (EPR) signals. X-band two-pulse ESEEM experiments at 4.2 K in deuterated solvent glasses demonstrated that this coupling results in 0.2-0.7 MHz shifts of the νR + νβ proton sum combination peak from twice the Larmor frequency. These shifts have been investigated across most of the EPR absorption spectrum of [TPPFe(PzH)2]+Cl-. Two-pulse ESEEM spectra were simulated at different magnetic field positions. Combination peaks were observed from both distant protons (DP) (β-pyrrole, orthophenyl, and β-pyrazole) and near protons (NP) (R-H of the pyrazole ligands). For the simulations, the orientation of the nearest four protons of the pyrazole ligands with respect to the g-tensor of the complex, the FeIII-proton distance, and g-strain were taken as input parameters. Comparison of the experimental data and computer simulations, in terms of magnetic field dependence of both frequency and intensity data, allows for the determination of the orientation of the hyperfine coupling tensor of the protons in coordinates of the g-tensor principal axes. For the DP peak, the magnetic field dependence clearly shows that the maximum g-value is aligned with or close to the Fe-Nax vector perpendicular to the plane of the porphyrinate. For the NP doublet, the results show that the R-H atoms of the axial pyrazole ligands, and thus the planes of those ligands, are aligned with the gmin or gxx magnetic axis of the metal, and hence, the pπ orbital of the axial ligands are aligned with the gyy magnetic axis of low-spin FeIII. Thus, in spite of the fact that the “rhombicity” defined by Blumberg and Peisach is much greater than the theoretical value of 2/3, the magnetic axes of this model heme complex correspond to a “proper axis system”, with gzz > gyy > gxx.

Introduction Since the early work of Griffith,1 Blumberg and Peisach,2 Taylor,3 Bohan,4 Loew,5 and others, the detailed interpretation of the g-values of low-spin FeIII porphyrinates and heme proteins, in terms of the mixing of the d orbitals of the metal under the influence of spin-orbit coupling and the ligand field, has been used to predict the axial ligands of newly discovered heme proteins and to interpret the ligand field properties of the ligands of these systems and model hemes. The “truth diagrams” developed by Blumberg and Peisach, in which the ligand field parameters V/λ (defined as the rhombic splitting), ∆/λ (defined as the tetragonal splitting, or “tetragonality”), and the ratio of these, V/∆ (defined as the “rhombicity”) were calculated from the g-values:2

gxx gyy V + ) Eyz - Exz ) λ gzz + gyy gzz - gxx

(1)

gzz gxx ∆ 1V 1V + ) Eyz - Exy ) (2) λ 2 λ gzz + gyy gyy - gxx 2 λ and have been extremely valuable in defining, with excellent accuracy, the identity of the axial ligands of newly discovered heme proteins for many years. For calculating V/∆ and ∆/λ to construct the “truth diagrams”, these workers always assumed that the largest g-value was gzz, coincident with the molecular z-axis, and the smallest was gxx, and the unpaired electron was X

Abstract published in AdVance ACS Abstracts, March 1, 1996.

0022-3654/96/20100-5235$12.00/0

mainly localized in the dyz orbital.2 Such calculations produced large values of V/∆, sometimes greater than 1.0, especially for low-spin iron(III) chlorin-containing systems. Taylor later showed that the Rhombicity, V/∆, should not be greater than 2/ and that if it were, the assignment of g-values corresponded 3 to an “improper axis system”, whereas the “proper axis system” would have gxx, gyy > gzz, and the unpaired electron would be mainly localized in the dxy orbital in the plane of the porphyrinate ring.3 However, unless the crystal and molecular structures of the iron porphyrinate or heme protein are known and the orientation of the principal g-values is determined by single crystal electron paramagnetic resonance (EPR) spectroscopic techniques, as has been done in a few cases,6,7 the mere occurrence of a value of V/∆ > 2/3 is not absolute proof that the unpaired electron is mainly located in the dxy orbital. Since most EPR spectra of model hemes and heme proteins are obtained for frozen solution samples, the relationship between the molecular axes and the axis of the g-tensor of these lowspin FeIII systems cannot be assigned unambiguously. This impacts not only the interpretation of the ligand field effects of low-spin ferrihemes from the EPR point of view, but also the NMR spectroscopy of these paramagnetic systems, since gvalues are typically used to estimate the dipolar contribution to the isotropic shifts of the resonances.8 This laboratory has participated actively in using g-values to understand d orbital splitting patterns in low-spin ferriheme systems, first with a comprehensive study of the variations in g-values, V/λ, ∆/λ, and the orbital mixing coefficients a, b, and c for the dyz, dxz, and dxy orbitals, respectively, with a wide range © 1996 American Chemical Society

5236 J. Phys. Chem., Vol. 100, No. 13, 1996 of nitrogen-donor axial ligands (imidazoles, pyridines, pyrazoles, indazoles, triazoles, tetrazoles)9 and, more recently, with several detailed studies of the effect of axial ligand plane orientation10 and ligand basicity11 on the ligand field parameters V/λ and ∆/λ and the orbital-mixing coefficients. In particular, in our study of the g-values of a wide range of axial ligand complexes, we observed that pyrazoles, indazoles, and triazoles, when bound to model hemes such as tetraphenylporphyrinatoiron(III) chloride, TPPFeCl, exhibited g-values that led to calculated rhombicities of 1.0 or greater,9 and on the basis of the work of Taylor,3 we had since come to suspect that they, as in the case of low-basicity pyridine complexes of the same model heme,11b,c probably have reversed definitions of the g-values such that gxx > gyy > gzz, with the unpaired electron largely localized in the dxy orbital. However, this supposition is not supported by the NMR spectra of the same complexes,12 which show both pyrrole-H and meta-phenyl isotropic shifts and temperature dependences that are totally consistent with a (dxy)2(dxz, dyz)3 electronic configuration over the temperature range of the NMR measurements (-90 to +30 °C). We therefore sought a method for unambiguously determining the orientation of the g-tensor with respect to the molecular axis system in glassy or polycrystalline samples. Pulsed EPR techniques, such as electron spin echo envelope modulation (ESEEM),13 offer attractive methods for determining the magnetic field or g-value dependence of weak couplings between protons close to the metal center and the unpaired electron in glassy media. The protons closest to the metal center are the R-H of the axial ligands, at a distance of 3.1-3.3 Å. At greater distances are the β-H of the axial ligands and the pyrrole-H and ortho-phenyl protons of the TPP. At yet greater distances are any γ-H of the axial ligands and the meta- and para-H of the phenyl rings of the TPP. If the signals arising from these protons could be deconvoluted from the ESEEM spectra and the magnetic field dependence of their frequencies and intensities interpreted theoretically, we reasoned that it might be possible to utilize this magnetic field dependence to define the orientation of the axes of the g-tensor with respect to the molecular axis, which is usually defined with the z-axis as the normal to the plane of the porphyrinate ligand and with the x- and y-axes in the porphyrinate plane. We have found that it is indeed possible to deconvolute and interpret the ESEEM spectra and that the combination of frequency and intensity data allows for an unambiguous assignment of the orientation of the g-tensor with respect to the orientation of the planes of the (parallel) axial ligands. In this paper we report ESEEM studies of the proton interactions of two pyrazole ligands (PzH) axially coordinated to TPPFeIII. For most of these investigations we have exploited a two-pulse train and observed the primary echo signal. As is well known,13 for electron-proton interaction, the Fourier transform of the time domain primary echo yields a spectrum of four signals associated with the fundamental frequencies νR and νβ, their difference ν- ) νR - νβ, and their sum ν+ ) νR + νβ. All of these signals contain information about the electron-nucleon distance and mutual orientation, and each of them, in principle, may equally be used to calculate these parameters. However, for this particular case, the characteristic width of the highest-frequency signal in the ESEEM spectrum is an order of magnitude less than the three lower-frequency signals, which makes its intensity correspondingly an order of magnitude greater. In addition, the unpaired electron of lowspin FeIII also interacts with the nitrogen nuclei of the porphyrinate and pyrazole rings,14,15 giving rise to spectral features in the range 1-9 MHz. These spectral features may overlap with

Raitsimring et al. the proton spectra at the fundamental and difference combination frequencies and thus complicate the analysis of these proton spectra. However, the sum combination νR + νβ spectrum is located near twice the proton Larmor frequency, and it is thus far away from the spectral features caused by 14N-electron interactions. The advantages of using the proton sum combination peaks in such a situation have already been discussed by several authors.16-19 Therefore, in this paper we have utilized the proton spectrum at ν+, with intensity I(ν+), for the detection of ligand proton couplings. We have found that not only frequencies and line shapes but also signal intensities are extremely valuable in data interpretation, and we have extended the theoretical treatment of these quantities. Materials and Methods Samples of the pyrazole complex of TPPFeIII, [TPPFe(PzH)2]+Cl-, were prepared from [TPPFeCl] synthesized in this laboratory and from a fresh sample of pyrazole (Aldrich) by dissolving the two compounds in deuterated dichloromethane (Cambridge Isotopes, 99.9%) or CD2Cl2-toluene-d8 (Cambridge Isotopes, 99.6%) mixtures in the ratios 1:1, 1:2, and 1:5. The cw EPR spectra were obtained to determine which gave the sharpest, best-resolved rhombic spectrum. It was found that the 1:2 mixed solvent ratio produced the best spectral qualities, and thus, this mixture was used for all ESEEM spectra. The concentration of the complex used for electron spin echo (ESE) measurements was approximately 1 mM. Continuous wave EPR spectra were obtained on a Bruker ESP-300E spectrometer operating at the X-band. A SystronDonner microwave counter was used for measuring the frequency. The EPR measurements were performed at 4.2 K using an Oxford continuous flow cryostat, ESR 900. Pulsed EPR studies were performed on a home-built spectrometer that has been described previously.20 ESEEM measurements were done at 8.802 GHz using a reflecting cavity that mates with the Oxford cryostat. Two microwave pulses of equal amplitude and duration (25 ns) were used to generate the primary echo signal. The nominal angle of the resonant spin rotation was 2π/3. The pulse separation varied from 300 ns (the dead time for the chosen cavity) to 5300 ns, with 5 ns steps. The number of accumulations at each step depends on the signal amplitude, i.e., the field position of data collection, and was generally 1000-4000 at a boxcar gate width of 15 ns. To avoid signal saturation, the repetition rate was no more than 400 Hz. Such measurements were performed at various field positions of the EPR spectrum with steps of 40-200 G. ESEEM spectra were obtained by Fourier transformation (FT) of the experimental time domain data. Before the FT procedure an exponential fit was used to normalize the decaying time domain data to unity and a low-order polynomial fit was used to subtract the nonmodulated part of the spin-echo signal. With these experimental conditions, the accuracy of the measurements of the spectral peak position in the FT ESEEM spectra was (0.03 MHz. The normalized noise level (for unit signal) in the FT spectra was about (1.5 × 10-3; this value defines the accuracy of the amplitude measurements. Results The cw EPR spectrum of [TPPFe(PzH)2]+Cl- obtained in this work is identical to those reported previously,9 and is presented in Figure 1. This paramagnetic center is characterized by a rhombic g-tensor with principal values of 2.60, 2.38, and 1.73. Although no crystal structure has been published for this or a related bis-pyrazole complex, the observation of a rhombic

Magnetic Axes of Heme Complexes

J. Phys. Chem., Vol. 100, No. 13, 1996 5237

Figure 1. CW EPR spectrum of 10-3 M [TPPFe(PzH)2]+ in a 1:2 methylene chloride-d2:toluene-d8 glass at 4.2 K: microwave frequency, 9.5529 GHz; power, 0.1 mW. The insert shows the structure of the complex. Observation of a rhombic EPR spectrum indicates that the axial ligands are coplanar.9 Observed g-values are g1 ) 2.60, g2 ) 2.38, and g3 ) 1.73. Calculated values of V/λ and ∆/λ are 3.08 and 2.81, respectively, leading to a calculated rhombicity, V/∆, of 1.1.

g-tensor is strong indication that the axial pyrazole ligands are aligned in parallel planes10 in the glassy state. A representative example of the ESEEM time domain data is shown in Figure 2a. These data were collected at a magnetic field Bm of 2440 G. The modulus FT ESEEM spectrum, obtained from these time-domain data, is shown in Figure 2b (upper curve). The assignment of peaks in this spectrum is quite clear: The position of the sharp line at 1.57 MHz corresponds to the Larmor frequency of the deuteron and is caused by interaction of matrix deuterons of solvent molecules. The lines between 1 and 8 MHz are caused by interaction of the electron spin and the eight 14N of the porphyrinate and pyrazole rings. The peaks for which intensity and position are the subject of this investigation are seen at 20.8, 21.2, and 21.5 MHz in Figure 2b (upper trace). These are “sum combination peaks” with intensities I(ν+). The position of the first of these peaks, in the limit of experimental resolution, coincides with twice the proton Larmor frequency, 2νI ) 20.8 MHz for this chosen field. The absence of a detectable shift of this line from twice the proton frequency allows one to conclude that this peak is caused by interaction of the unpaired electron of FeIII with distant protons, those which are separated from the electron spin by a distance greater than 5 Å. In general, such a line arises from matrix protons. However, in this particular case, because deuterated solvent mixtures were used, matrix protons arising from the solvent are excluded from consideration. Thus, the only source for such distant protons is the molecule itself. Indeed, the porphyrinate ring contains eight nonexchangeable β-pyrrole protons and each pyrazole ring contains two protons, all at more than 5 Å from the Fe center. The phenyl rings of the porphyrinate also contain eight ortho protons and 12 meta and para protons at even greater distances. Therefore, interaction of FeIII with all these distant protons (DP) of the porphyrin pyrrole and phenyl rings and the pyrazole ligands is the origin of this line at 20.8 MHz. The other two peaks, a doublet, are caused by interaction of FeIII with the four nearest protons (NP) of the pyrazole rings. At the magnetic fields of the measurements shown in Figure 2b, these peaks are shifted from 2νI by ∆ ) ν+ - 2νI ) 0.42 and 0.7 MHz (the position of 2νI is shown by a thin line in Figure 2b). The relative and absolute amplitudes of all these peaks and also their shifts, ∆, from twice the Larmor frequency, were found to depend on the strength of the magnetic field,

Figure 2. (a) Two-pulse ESEEM time-domain data obtained for [TPPFe(PzH)2]+. Measurement conditions are T ) 4.2 K, Bm ) 2440 G, microwave frequency ) 8.802 GHz, pulse width ) 25 ns, and nominal rotation angle ) 2π/3. (b) FT-ESEEM spectra of the same complex obtained at various magnetic fields: (1) 2440 G; (2) 2680 G; (3) 3550 G. The low-frequency part of the second and third spectra has been removed in order to avoid overlap with the first. Thin lines show the position of twice the Larmor proton frequency in each case. The peaks at larger frequency than this are shown in this work to be due to the near protons (NP), the R-H of the axial pyrazole ligands. Open squares mark the expected position of fundamental frequencies for distant protons (DP).

Bm. To demonstrate this effect, the analogous spectrum at Bm ) 2680 G is also shown in Figure 2b (lower curve). The dependences of shifts and intensities were investigated across the entire EPR spectrum of FeIII, from Bm ) 2400 to 3550 G. However, because of decreasing signal amplitude at higher fields, the experiment time became too long to reach a reasonable intensity for the doublet/noise ratio. Therefore, we concentrated our experimental and following simulation efforts on the low-field part of the EPR spectrum, Bm < 2800 G, and performed only one long accumulation in the very high-field portion of the EPR spectrum, Bm ) 3550 G. This spectrum is also shown in Figure 2b (trace 3). As is evident from this spectrum at the high-field limit, the doublet is not resolved and the average shift appears to be about 0.25 MHz. Such a loss of resolution was the additional reason that ESEEM measurements were limited to magnetic fields Bm < 2800 G. Because the DP peak does not show a shift from 2νI in the limit of the experimental accuracy at all field positions, it is only possible to measure the dependence of intensity with magnetic field for these protons, as shown in Figure 3. As is evident in Figure 3, the amplitude of the DP peak varies by a factor of 3-4 over the magnetic field range of the measurements, and this dependence anticorrelates with that for the NP, as shown in Figure 5. The intensity reaches a maximum at

5238 J. Phys. Chem., Vol. 100, No. 13, 1996

Raitsimring et al. to obtain structural information. The method of analysis of the experimental data to obtain this information is described in the following sections. Theory Analysis of the magnetic field strength dependences of the frequency shifts and amplitudes is based on comparison of the experimental spectra to those simulated for particular ligand orientations. To explain the simulation procedure, we start with the well-known expression for two fundamental frequencies, νR and νβ, of a system that contains an electron spin S ) 1/2 and a nuclear spin I ) 1/2:21-24

νms ) |h B(|; B h ( ) -νIl + Figure 3. Experimental (bars) and calculated (solid lines) magnetic field strength dependences of the amplitudes of the DP ν+ peaks. Parameters used for calculations are (curves 1 and 2) gxx > gyy > gzz and (curves 3 and 4) gzz > gyy > gxx, and a equals 0 MHz for curves 2 and 4 and -1 MHz for curves 1 and 3. Calculations include eight equatorial β-pyrrole protons of the porphyrinate, eight ortho-phenyl protons, and four DP protons of the two pyrazole ligands. The planes of both pyrazole rings are aligned along the x-axis of the RCF.

Dgl m ge s

νms ) [(msA1 - νIl1)2 + (msA2 - νIl2)2 + (msA3 - νIl3)2]1/2 (3) where ms ) (1/2 for R or β electron spins, D is the tensor of the hyperfine interaction (HFI), g is the g-tensor, νI is the nuclear Larmor frequency at a given magnetic field Bm, and l is a unit vector that coincides with the direction of the external magnetic field Bm. The particular form of Ai depends on the reference coordinate frame (RCF) in which they are calculated. For systems where g-tensor anisotropy exceeds the anisotropy of the HFI, the convenient RCF is that in which the axes coincide with the principal axis of the g-tensor. In this RCF and HFI caused by dipolar (in the point-dipole approximation, PDA) and isotropic hyperfine interactions, the other terms of eq 3 are defined as:

l1 ) sin θ cos φ; l2 ) sin θ sin φ; l3 ) cos θ

(4)

A1 ) T × [g1l1(g1(3n21 - 1) + a/T) + 3g22l2n1n2 + 3g23l3n1n3]/ge Figure 4. Experimental (bars) and calculated (solid lines) magnetic field strength dependences of the shifts from twice the Larmor proton frequency of the ν+ peaks of the NP. Parameters used for calculations are gzz > gyy > gxx, Fe-proton distances r ) 3.05 Å , r-z-axis angle of (43° and r ) 3.3 Å, and r-z-axis angle of (37°. The planes of the pyrazole rings are parallel curves 2 and 4 and perpendicular curves 1 and 3 to the x magnetic axis. The isotropic hyperfine constant, a, used for the calculated spectra is -0.6 MHz for all NP. The experimental error margin is shown in top right-hand corner.

2600 G (2% of the normalized amplitude) and decreases at both lower and higher fields. Because the relative intensities of peaks in the doublet arising from the NP vary slightly with the magnetic field position, Bm, we chose, as an experimental measure of intensity, the average amplitude of these peaks. Figures 4 and 5 depict, respectively, the magnetic field dependences of the shift in frequency from 2νI, ∆, and the relative amplitudes of the NP peaks over the range 2400 < Bm < 2750 G. As is evident from Figure 4, the ∆ values for both peaks vary by only a factor of 1.3-1.4, while over the same field interval, the amplitude varies by approximately a factor of 5 (Figure 5). The amplitude reaches a maximum (∼3% of the normalized amplitude) at the extreme low-field position, Bm ) 2407 G, and a minimum (∼0.6% of the normalized amplitude) at B ) 2650-2700 G. Thus, the output of the experiments was the magnetic field dependences of the shifts ∆ and the amplitudes for the NP and DP. Because a particular field position selects only certain orientations of molecules, the observed dependences can be used

A2 ) T × [3g21l1n1n2 + g2l2(g2(3n22 - 1) + a/T) + 3g23l3n2n3]/ge A3 ) T × [3g21l1n1n3 + 3g22l2n2n3 + g3l3(g3(3n23 - 1) + a/T)]/ge (5) n1 ) sin θn cos φn; n2 ) sin θn sin φn; n3 ) cos θn where ni are the direction cosines of the radius-vector r connecting the electron and nuclear spins in the RCF, a is the isotropic hyperfine coupling constant, gi are the principal values of the electronic g-tensor with ge ) (∑(gili)2)1/2 being the effective electronic g-value for a given experiment, T ) -βeβngn/pr3, βe ) Bohr magneton, βn ) nuclear magneton, and r ) electron-nuclear distance. The modulation of the primary spin echo signal V(τ) for this spin system and for a particular orientation of electron and nuclear spins is described by the expression25

V(τ) ∝ 1 -

k 1 - cos 2πνRτ - cos 2πνβτ + 2 1 1 cos(2πν-τ) + cos(2πν+τ) (6) 2 2

[

]

If the system contains (i) nuclei,

V(τ) ) ∏V(i)(τ)

(7)

Magnetic Axes of Heme Complexes

J. Phys. Chem., Vol. 100, No. 13, 1996 5239

〈V(τ)〉 ∝ 1 - (I0 - ∑I(νw)cos 2πνwτ))

(12)

w

where νw is νR, νβ, ν+, or ν- and 〈...〉 means averaging over orientations. The frequency distribution of modulation amplitude, or by definition, the spectrum at a given frequency νk, I(νk) is

I(νk)|Bm )

Figure 5. Experimental (bars) and calculated (solid lines) magnetic field strength dependences of the average relative amplitudes of the NP ν+ peaks. For curve 1 the planes of the pyrazole ligands are parallel and for curve 2 perpendicular to the x magnetic axis. Parameters used for calculations are the same as for those shown in Figure 4.

This expression, for the case of a weak hyperfine interaction, i.e., T/νI < 1, may be rewritten as

V(τ) ∝ 1 - ∑

[

k(i)

(i)

2

]

1

1 (i) (i) τ) + cos(2πν+ τ) (8) cos(2πν2 2

As follows from eq 8, the modulation amplitude (or intensity of the FT ESEEM spectrum) is proportional to the parameter k. This parameter is the product of allowed and forbidden transition probabilities and, in the same approximation as was applied for deriving the fundamental frequencies, k ) sin2 η, where cos η is determined by the following expression:26

B h( )

[(

)(

A1 ( νIl1 , 2

B h +B h|h B+||h B-|

)(

A2 ( νIl2 , 2

A3 ( νIl3 2

)]

(9)

The explicit expression for k as derived from eq 9 is

k)

νi2

{[A1l2 - A2l1]2 + [A2l3 - A3l2]2 + [A1l3 - A3l1]2} ν2Rνβ2 (10)

For the case of an isotropic g-tensor, i.e., when g1 ) g2 ) g3, the RCF may be chosen as either the laboratory frame (l1 ) l2 ) 0, l3 ) 1 in eqs 5 and 10), or along the principal axis of the HFI tensor (n1 ) n2 ) 0, n3 ) 1 in eq 5) and eq 10 transforms to the well-known result often used for analysis of ESEEM spectra:

k)

νi2B2 ν2Rνβ2

; B ) 3gT sin θ cos θ; θ ) r∧l

∫dB∫dΩ f(Bm - B)

(13)

where the summation is performed over (i) protons, dΩ ) sin θ dθ dφ, f(Bm - B) is the individual line shape of the paramagnetic center at a particular orientation, and const ) 1/2 for νR or νβ and 1/4 for ν+ or ν-. For δ-function line shapes and k ) 1, eq 13 transforms to the expression used for simulation of orientationally selected electron nuclear double resonance (ENDOR) spectra.27 Equations 12 and 13 were straightforwardly used for the simulations that follow. Simulations

(i) 1 - cos 2πν(i) R τ - cos 2πνβ τ +

cos η )

dΩ const∫dB∑k(i)(li) f(Bm - B) dνk i

(11)

In a disordered system, each given magnetic field Bm represents not a unique but a set of orientations and, consequently, a set of fundamental, sum, and difference frequencies. Because the modulation amplitude also depends on orientation, eq 8 for this system must be rewritten as

1. Parameters. As follows from eq 10, calculation of I(ν+) requires as input parameters r(i), ni(i), ai (the constant for the isotropic hyperfine interaction for the (i) proton), the principal values of the g-tensor, Bm, the microwave frequency, and the individual line shape function, f(Bm - B). We start the discussion of the input parameters with the latter. There are three different sources that contribute to determining the individual line shapes of the FeIII signal: g-strain, unresolved hyperfine structure due to interaction of the unpaired electron with nitrogen nuclei and protons, and dipolar broadening. ENDOR measurements on TPPFeIII bis(imidazole), [TPPFe(ImH)2]+, performed by Scholes et al.28 have shown that the nitrogen hyperfine coupling constant is about 7 MHz and it is practically the same for porphyrinate and imidazole nitrogens. This FeIII-nitrogen interaction produces a Gaussian-like line shape, exp[-(x/σg)2] with σg ) 25 MHz. An additional 10 MHz broadening comes, we have evaluated, from FeIII-proton interaction. Therefore, in our simulations, the line shape due to the electron-nuclear hyperfine interaction was taken as Gaussian with σg ) 35 MHz. The dipolar interaction between paramagnetic centers observable in ESE is negligible and may be ignored. An estimation of the characteristic line width from the first derivative of the spin-echo detected EPR spectrum gives a value of 150-160 MHz. This means that the excess broadening of 110-120 MHz must be caused by g-strain. Therefore, in further simulations we used these values for the individual line width. The crystal structure of [TPPFe(PzH)2]+Cl- has not been reported, although after submission of this paper we learned that it has been determined.29 In the absence of the structural data, all of the following simulations were based on the distances obtained from the crystal structure of the similar molecule [TPPFe(ImH)2]+Cl-.30 In accord with this structure, the distances from FeIII to the NP of the axial ligand are, on average, 3.2 Å. In our simulations we have varied this distance from 3.05 to 3.3 Å. In the RCF, where the z-axis is perpendicular to the porphyrinate plane and the x and y axes are parallel and perpendicular to the planes of the axial ligands, respectively (or Vice Versa, the choice to be made on the basis of the results of this study), the angle between z and r is close to (40°, and the direction cosines in the xy plane were varied. The hyperfine

5240 J. Phys. Chem., Vol. 100, No. 13, 1996 constants for the NP of pyrazole have not been reported. However, for imidazole they have been evaluated as -0.9 and -0.3 MHz from ENDOR28 and NMR31 measurements on [TPPFe(ImH)2]+. The same magnitude of a-values is expected for pyrazole, and as will be shown below, such small a-values only slightly modify the field dependences of ∆ and the intensity. As already mentioned, there are different sets of DP: the β-H of the pyrazole rings and those of the pyrrole and phenyl rings of the porphyrinate The distance to the DP of pyrazole and the angles between the z-axis of the RCF and the radiusvector connecting the β-H of pyrazole are 5.2 Å and (5°, respectively.30 The isotropic hyperfine coupling constants are known for the DP of imidazole in [TPPFe(ImH)2]+ and are -0.25 and -0.4 MHz.28 We have used a similar range of values for the DP of pyrazole. Eight β-pyrrole protons are located symmetrically in the xy plane of the RCF each with an equal distance from FeIII of 5.27 Å. Two different isotropic hyperfine coupling constants are observed for these protons in [TPPFe(ImH)2]+, -0.2 and -0.9 MHz.28 As for the phenyl protons, we take into account only the ortho-H, whose distance from FeIII is 6.7 Å. Because the intensity of the DP is proportional to r-6, their contribution to the intensity of the DP proton line is about 1/3 that of the pyrrole protons. By the same reasoning, contributions from the phenyl meta- and para-H (r ) 8.5-8.8 Å) are negligible. The angle of deviation of the phenyl protons from the xy plane of the RCF was neglected. The isotropic hyperfine constant for phenyl protons is close to 0 MHz.28,32 For purposes of our calculations, the principal axis of the g-tensor in our calculations was set to coincide with that of the RCF. As for the order of principal g-values, simulations were carried out for both gzz > gyy > gxx and gxx < gyy < gzz. 2. Simulation Technique. The simulations have been carried out in the following manner. Evaluation of eq 13 was performed numerically in two stages. First, g-strain broadening was taken into account. There are a number of models describing broadening caused by g-strain.33,34 In our particular case we used a simplified model of g-strain, where each principal value of the g-tensor, gii, has been considered as a value uniformly distributed in range gii +(1 - 2ξ)κ, where ξ is a random number uniformly distributed between 0 and 1. The value of κ was chosen to be a constant, 2 × 10-2, to provide a g-strain broadening of 120 MHz. For integration of eq 13 the Monte Carlo method was used. At each trial, three values of gii and three values of li (cos θ ) 1 - 2ξ and φ ) 2πξ) were calculated. The trial was accepted if |(hν - geβBm)| < ω1/2 (where ω1 is the amplitude of the microwave pulses, 13 MHz in our experiment, and ge is defined by eq 5). If the trial was accepted, the values of ν+(i) and k(i) were then calculated from eqs 3 and 10. The spectrum I(ν+ ) was then constructed, with a resolution of 10 kHz, and the accumulation of the spectrum was continued until a reasonable signal/noise ratio was obtained. Usually, a reasonable accuracy was reached after 3 × 104 to 105 accumulations. The normalizing factor here is just the number of accepted trials. To include the second source of broadening, the hyperfine interaction, a set of I(ν+) was prepared and summed with corresponding weights in the vicinity of each chosen Bm with a step of (10 MHz. By use of I(ν+) calculated according to eq 13, time domain patterns were calculated with experimental values of the step in τ, the interval of τ, and the dead time. Then the same FFT procedure that was used in the treatment of the experimental data was applied to these time domain patterns, and the resulting spectra were used for calculations of

Raitsimring et al. shifts and intensities to be compared to the experimental data. Examples of I(ν+) and the resulting spectra are shown in Figures 6-8 below, and the resulting dependences are shown in Figures 3-5. Discussion In the following discussion we have assumed that the pointdipole approximation (PDA) is applicable for describing the anisotropic interaction of the DP and NP of the pyrazole ligands and the DP of the β-pyrrole protons of the porphyrinate as well. Analysis of ENDOR28 and NMR31,32 data for [FeTPP(ImH)2]+ has already proved that this assumption is valid for both kinds of DP. For the NP, Dikanov et al.19 recently showed that the PDA describes the CuII-NP interaction in [Cu(Im)4]2+ very well, where the spin-density on the ligands greatly exceeds that found for [FeTPP(ImH)2]+.28,31,32 Order of g-Values. We start this discussion with an analysis of the order of the g-values. For this purpose, we utilize the dependence of the intensity of the DP on the magnetic field. Let us start with a quantitative evaluation of this dependence. In the ideal case, without orientational distortion caused by g-strain and hyperfine broadening, for gzz > gyy > gxx the extreme low-field position corresponds to the direction of the external magnetic field along the z-axis, i.e., l3 ) 1 and l1 ) l2 ) 0. In accord with eq 8, the intensity of I(ν+) (or k) is proportional to (A2)2 + (A1)2. In their own turn (eq 3) for this orientation, A1 ) 3g3n1n3 and A2 ) 3g3n2n3. Because the DP of the pyrrole and phenyl rings are in or close to the xy plane (n3 ) 0), they do not contribute to I(ν+). For the DP of the pyrazole ring, they are directed practically along the z-axis (n1 ≈ n2 ≈ 0 and n3 ≈ 1) and also do not contribute to I(ν+). Therefore, the intensity of I(ν+) for this g-value order at the extreme low-field position should be close to zero and it will increase with increasing Bm. For the opposite situation, gxx > gyy > gzz, the extreme lowfield position corresponds to l1 ) 1 and l2 ) l3 ) 0. The dependence of intensity on the magnetic field in this case is more complicated than in the previous one. However, the general tendency in the vicinity of the low-field extreme may be tracked. Here, I(ν+) ∝ (A2)2 + (A3)2, with A3 ) 3g1n1n3 and A2 ) 3g1n1n2. Therefore, the expected contribution to I(ν+) from the DP of pyrazole is again close to zero (n1 ≈ n2 ≈ 0 and n3 ≈ 1). However, the value of (A2)2 is not zero for all xy plane protons, and the average may be evaluated as being proportional to 9(g1)2/8. Upon an increase of the magnetic field, this term will decrease (at least if |a/T| < 1) and so also will the amplitude of the signal. However, the amplitude due to the axial DP will increase as Bm is increased, and the balance would be difficult to predict if the number of protons were the same. However, because the number of pyrazole DP is only one-half the number of pyrrole protons at the same distance, we do not expect an overall increase in amplitude of the DP peak due to the increasing contribution to the intensity by DP pyrazole protons. Therefore, the gzz > gyy > gxx order of g-values will definitely lead to an increase in the amplitude of the DP line in the ESE spectrum with increasing magnetic field from the low-field extreme to higher magnitude; the opposite order of g-values likewise gives the opposite result. Indeed, the orientational uncertainty caused by line broadening might reduce the difference between these two cases, but it is unlikely that the trend will be completely destroyed. The experimental data (Figure 3) show increasing intensity of the DP line with increasing magnetic field, which corresponds to the assignment gzz > gyy > gxx, in line with the abovementioned discussion. To prove this reasoning quantitatively,

Magnetic Axes of Heme Complexes

J. Phys. Chem., Vol. 100, No. 13, 1996 5241

Figure 6. Simulated modulus FT spectra of the DP protons at sum (ν+) and fundamental (νR and νβ) frequencies. For curve 1 all a ) 0 MHz. For curve 2 a is -0.9 and -0.3 MHz for two types of pyrrole protons, -0.25 and -0.45 MHz for two types of pyrazole protons, and 0 MHz for phenyl protons, with gzz > gyy > gxx, Bm ) 2680 G, deadtime ) 300 ns, step ) 5 ns, and time sweep interval ) 5300 ns.

we calculated the dependences of the DP line intensity on magnetic field for gzz > gxx> gyy and also the inverse order of g-values, with two values of the isotropic hyperfine constant, a ) 0 and a ) -1 MHz. These values of a overlap the possible values of the isotropic hyperfine interactions for the DP (00.9 MHz), which was discussed in the Parameters section. As can be seen from Figure 3, introducing a hyperfine coupling constant of -1 MHz does not change the general behavior of the dependences for a given order of g-values. This result is expected because I(ν+) is not sensitive to the small isotropic hyperfine interaction.13 Thus, for the case of gzz > gyy > gxx, the intensity increases from the low-extreme field, reaches a maximum at 2500-2600 G, and decreases again at higher field values. The opposite behavior is observed for gxx > gyy > gzz. The intensity is maximal in the vicinity of the low-extreme field and minimal at ∼2550 G. The comparison of these calculated dependences to the experimental data (Figure 3) allows us to unambiguously assign the order of g-Walues as gzz > gyy > gxx. This order of g-values is used below for determining the assignment of g-tensor axes relative to the planes of the pyrazole rings. To complete this discussion, we must mention one peculiarity in the spectrum of the DP-FeIII interaction: In none of the measurements did we observe clearly the I(νR) and I(νβ) lines. For instance, in Figure 2b, at a magnetic field of 2680 G (curve 2), one can see only a featureless broad line in the vicinity of the expected positions (11.5 MHz) of I(νR) and I(νβ) and a weak broad line in the vicinity of 15 MHz for measurements at 3550 G (curve 3). The intensity of this line is smaller than or comparable to I(ν+) for the DP, although for such distant protons the intensities of lines evaluated at the fundamental should be greater than those of the sum combination line. The direct simulation of these lines, performed with a ) 0 and shown in Figure 6 (curve 1), confirmed this evaluation. As one can see in Figure 6, because of a small value of T, the I(νR) and I(νβ) lines merge and their combined intensities exceed that of I(ν+). However, if the isotropic hyperfine constants (see Parameters section) are included in the calculations, this situation immediately reverses (Figure 6 (curve 2)) and makes the calculated and experimental intensities very similar. The intensity of the lines at the fundamental frequencies becomes one-third that at ν+. Therefore, spin-echo data implicitly confirm the ENDOR data that showed that the protons of the pyrrole rings have

Figure 7. Simulation of I(ν+) for the NP of pyrazole at Bm ) 2440 G, gzz > gyy > gxx, and r-z-axis angle of ( 40°, with the plane of pyrazole ring parallel to the x-axis of the g-tensor: (a) r ) 3.1 Å, a ) 0 MHz for curve 1, a ) -1 MHz for curve 2; (b) a ) -1 MHz, (1) r ) 3.3 Å, (2) r ) 3.1 Å.

different isotropic constants,28 which also differ from the isotropic hyperfine coupling constant of the DP of pyrazole. Alignment of the Pyrazole Ligands with the g-Tensor. For the discussion of this point, we start by considering the origin of the doublet line shape observed for the NP of pyrazole, shown in Figure 2b. As already mentioned, the doublet, with approximately equal intensity peaks, was observed throughout the magnetic field range of 2400-2800 G (between gzz and gyy). In principle, a doublet line shape may be caused by (i) different distances from FeIII to the two NP of pyrazole or (ii) different isotropic hyperfine coupling constants for the two NP protons. Figure 7a demonstrates the calculated line shapes for the NP protons at a particular field and fixed distances and two values of a: 0.0 and -1 MHz. The latter is the maximum magnitude expected for a for the NP. As one can see, the difference between peak positions for this case is 20 kHz, which is less than the experimental resolution. Therefore, as we already mentioned, the I(ν+) line shape is not sensitive to the small isotropic hyperfine interaction for small values of a. At the same time, it is sensitive to small distance variation because of the r-6 dependence of shifts of the peaks from 2νI. Actually, to satisfy the experimental results, for example, those shown in Figure 2b, it is enough to assume that the NP have slightly different distances from FeIII of 3.1 and 3.3 Å. Variation of 6% in distance leads to approximately a 40% difference in shifts. Figure 7b depicts the calculated I(ν+) for NP at 3.1 and 3.3 Å. To reproduce the experimental spectra, which include the contributions of both NP and DP, we varied the distances and

5242 J. Phys. Chem., Vol. 100, No. 13, 1996

Figure 8. (a,b) Experimental (upper curve) and simulation (lower) modulus FT proton spectra at ν+. The experimental spectra is an enlarged part of spectrum 1 of Figure 2b (part a: Bm ) 2440 G) and spectrum 2 (part b: Bm ) 2680 G). Parameters used for the simulation are the following. For the four NP, they were the same as those used for the simulations of Figure 4, and the plane of pyrazole ring was parallel to the x-axis of the g-tensor. For the four DP of the two pyrazole rings, the r-z-axis angle is ( 5°, r ) 5.2 Å, and the isotropic hyperfine constant a ) -0.3 MHz. For the eight β-pyrrole protons, n1,2, n2,1 ) (((0.3), (0.954 and n3 ) 0, a ) -0.2 and -0.9 MHz, and r ) 5.27 Å. For the eight ortho-phenyl protons uniformly distributed in the xy plane, r ) 6.7 Å, a ) 0.0, deadtime ) 300 ns, step ) 5 ns, and the time sweep interval ) 5300 ns.

r-z-axis angle of the NP slightly. Figure 8 demonstrates the appearance of the sum of these lines in the ESEEM spectrum and also in the experimental spectra. Good agreement between these data support the assumption that the NP are two sets of two protons with a slight difference in distance.29 Figure 4 shows the experimental data and the calculated magnetic field dependences of the shifts of these two peaks, ∆, for two ligand orientations: (curves 1 and 3) with the ligand planes, and thus the NP of the pyrazoles, perpendicular to and (curves 2 and 4) parallel to the x magnetic axis. As can be seen, in the limits of the accuracy of determination of ∆,35 one ligand orientation is not obviously distinguished from the other. Therefore, we have utilized the second set of experimental data, the magnetic field dependence of the amplitude of I(ν+). Figure 5 depicts these dependences, calculated with one particular value of a () -0.6 MHz) for ligand orientations perpendicular and parallel to the x magnetic axis, along with the experimental data. We also performed calculations for a ) 0.0 to -1.0 MHz, and as in the cases discussed above, the isotropic hyperfine interaction changes these dependences only in detail, leaving a general similarity. For ligand orientation parallel to the x

Raitsimring et al. magnetic axis, the amplitude I(ν+) decreases monotonically with increasing field and shows only a very shallow minimum (or leveling) in the vicinity of 2700 G. For ligands oriented perpendicular to the x magnetic axis, the amplitude I(ν+) shows a deep minimum in the vicinity of 2500-2600 G. The difference in these intensity dependences substantially exceeds the experimental uncertainty for the intensity determination. Therefore, we can conclude that the pyrazole ligands are oriented with their NP parallel or nearly parallel to the x-direction of the RCF or the x-axis of the g-tensor (in our calculation we chose the direction of the principal axes of the g-tensor and the RCF to coincide). In accord with our evaluation, the deviation of the R-protons of the ligands from the x-axis of the g-tensor should not exceed 30°. To complete this part of the discussion, we wish to mention that the absolute amplitudes of the spectra in the simulations exceed by a factor of 1.7-1.9 (depending on the parameters chosen) the absolute experimental amplitudes. Such differences have been observed previously and have already been discussed.19 In our case, the major part of this difference is caused by partial excitation of the proton frequencies. Therefore, we have divided the absolute amplitudes of the simulated spectra by 1.8 for comparison to the experimental spectra of Figure 8. Combination of Results to Define the Orientation of the g-Tensor with Respect to the Plane of the Axial Ligands. In the first part of the Discussion section, we have shown that the maximum g-value is aligned near the normal to the plane of the porphyrinate and may thus be identified as gzz. In the second part we showed that the pyrazole ligands are oriented with their R-H close to the minimum g-value, which we have defined as gxx. Therefore, gyy is oriented perpendicular to the plane of the pyrazole ligands, along the direction of the pπ orbitals of the two (parallel) pyrazole ligands. Thus, although the rhombicity, V/λ, calcuated from the g-values is greater than 1.0,9 the complex [TPPFe(PzH)2]+ conforms to the “proper axis system” observed for bis(imidazole) complexes.2 Comparison of these results to those from single crystal EPR spectroscopy provides mixed results. Single crystal EPR studies of ferricytochrome c have shown that gxx is aligned along the methionine S-CH3 vector, and thus, gyy is aligned along the direction of the π-symmetry orbital of the methionine sulfur.7 Although no reports of single crystal EPR spectral analyses have been reported for pyrazole complexes of model hemes, there have been several reports for bis(imidazole) complexes that are relevant to this work. For the bis(imidazole) complexes of both [TPPFe(cis-methylurocanate)2]+ 6b and [TPPFe(ImH)2]+,6c the directions of gxx were found to coincide closely with the plane of the parallel axial imidazole ligands for the molecules having those ligand planes oriented close to the N1-Fe-N3 vector in the porphyrinate plane (φ ) 5-15°), but for the molecules having the imidazole planes oriented at nearly 45° to that vector, the counterintuitive situation was observed in which the in-plane magnetic axes were rotated counterclockwise to the direction of rotation of the axial ligands. In the cases reported,6b,c the direction of gyy was rotated by nearly 90°, placing the direction of gyy in the plane of the imidazole ligands. It is not clear whether crystal-packing forces or other factors may be responsible for this observed rotation of the in-plane magnetic axes for molecules with large φ or whether this is a frequently observed phenomenon. From the present study of [TPPFe(PzH)2]+ in glassy media, we cannot define the relationship between the axial ligand planes and the porphyrinate nitrogen vectors. For use of these data for NMR studies of paramagnetic ferriheme complexes with pyrazole molecules as axial ligands,

Magnetic Axes of Heme Complexes the axial magnetic anisotropy gzz2 - 1/2(gxx2 + gyy2) is positive, whereas the rhombic or in-plane magnetic anisotropy gxx2 gyy2, is negative, as is believed to be true for bis(imidazole) complexes.8 To our knowledge, this is the first case where the orientation of the g-tensor with respect to the planes of the axial ligands of model heme complexes has been unambiguously defined for model heme complexes in glassy media. Furthermore, it is clear that the unpaired electron of the low-spin FeIII porphyrinate is aligned at least approximately with the pπ orbital of the axial ligands, as has been suggested previously on the basis of NMR data.8,37 Such an alignment is expected to direct the nodal plane of the e(π) orbital of the porphyrinate ring that is preferred for the spin delocalization that gives rise to the NMR contact shift to be coincident with the plane of the (parallel) axial ligands and suggests, as we have pointed out previously, that the in-plane magnetic axes that give rise to the rhombic dipolar shift should be aligned with gxx in the nodal plane of the axial ligand(s).36,37 We have observed this to be the case in a model heme complex having a bulky tris(3,5-dimethylpyrazolyl)boratooxomolybdenum(V) group appended to the ortho position of one phenyl ring, where the nodal plane of the fixed axial ligand is coincident with both the nodal plane of the e(π) orbital preferred for spin delocalization and the direction of gxx.37 We have also shown that odd-electron thermal population of the other e(π) orbital, whose nodal plane is oriented perpendicular to the nodal plane of the axial ligand, may cause a “twisting” of the in-plane magnetic axes and a diminution of both the in-plane magnetic anisotropy and the spread of the contact shifts as the temperature is raised.36 Such “twisting” could occur in heme proteins, where axial ligands are fixed in orientation and the energy difference between the two nondegenerate “e(π)” orbitals is several times kBT at the temperatures of the NMR measurements.36 However, in agreement with the findings of the present work, for cytochrome c, the direction of both the nodal plane of the e(π) orbital that defines the contact shift pattern and the x-axis of the g-tensor, obtained from fitting the dipolar (pseudocontact) shifts of protein residues, are approximately aligned with the S-methyl vector of the methionine ligand, and thus, gyy is approximately aligned along the π-symmetry p orbital of the sulfur,38 in agreement with the single crystal EPR findings7 and with our predictions, based upon the ESEEM data for the bis(pyrazole) complex. For two cyanoferriheme proteins having a histidine as the planar axial ligand, sperm whale cyanometmyoglobin39,40 and horseradish peroxidase,41 both the nodal plane of the e(π) orbital that defines the contact shift pattern and gxx have also been found to be approximately aligned with the nodal plane of the histidine imidazole in each case, placing gyy approximately coincident with the direction of the pπ orbital of that ligand. In contrast, the alignment of the g-tensor with gyy close to the orientation of the nodal plane of the two histidine ligands of cytochrome b5 was found by Keller and Wu¨thrich,42 Williams and coworkers,43 and La Mar and co-workers44 from analysis of the dipolar (pseudocontact) shifts of protein residues, while the pattern of contact shifts of the heme resonances shows that the e(π) orbital preferred for spin delocalization has its nodal plane approximately coincident with the average nodal plane of the axial histidines. More recent studies of the two heme rotational isomeric forms of rat microsomal cytochrome b5 40 are in general agreement with the earlier work and show that although the nodal plane of the e(π) orbital is approximately aligned with that of His-63, the direction of χyy is approximately in the nodal plane of His-63, in contradiction to our predictions. Thus, at least in the majority of cases reported thus far (except for cytochrome b5), both EPR and NMR studies have shown that

J. Phys. Chem., Vol. 100, No. 13, 1996 5243 the nodal plane of the axial ligand is aligned with the minor in-plane magnetic axis χxx or gxx as we have found in this study. Additional studies of the cytochrome b5 system should be carried out in order to determine why this protein does not appear to follow these predictions. Acknowledgment. The support of the National Institutes of Health Grant DK 31038 (F.A.W.), the University of Arizona Materials Characterization Program (F.A.W.), and the National Science Foundation Grants DIR-9016385 for purchase of the cw EPR spectrometer and BIR-9224431 for funds to construct the pulsed EPR spectrometer are gratefully acknowledged. We also thank Professor W. R. Scheidt for communicating the structural information for [TPPFe(PzH)2]+ given in footnote 29 before publication. References and Notes (1) Griffith, J. S. Proc. R. Soc. London, Ser. A 1956, 235A, 23. Griffith, J. S. Mol. Phys. 1971, 21, 135. (2) (a) Blumberg, W. E.; Peisach, J. In Structure and Bonding of Macromolecules and Membranes; Chance, B., Yonetani, T., Eds.; Academic: New York, 1971; p 215. (b) Peisach, J.; Blumberg, W. E.; Adler, A. D. Ann. N. Y. Acad. Sci. 1973, 206, 310. (3) Taylor, C. P. S. Biochim. Biophys. Acta 1977, 491, 137. (4) Bohan, T. L. J. Magn. Reson. 1977, 26, 109. (5) Loew, G. M. H. Biophys. J. 1970, 10, 196-212. (6) (a) Byrn, M. P.; Katz, B. A.; Keder, N. L.; Levan, K. R.; Magurany, C. J.; Miller, K. M.; Pritt, J. W.; Strouse, C. E. J. Am. Chem. Soc. 1983, 105, 4916. (b) Quinn, R.; Valentine, J. S.; Byrn, M. P.; Strouse, C. E. J. Am. Chem. Soc. 1987, 109, 3301. (c) Soltis, S. M.; Strouse, C. E. J. Am. Chem. Soc. 1988, 110, 2824. (d) Innis, D.; Soltis, S. M.; Strouse, C. E. J. Am. Chem. Soc. 1988, 110, 5644. (7) Mailer, C.; Taylor, C. P. S. Can. J. Biochem. 1972, 50, 1048. (8) Walker, F. A.; Simonis, U. In Biological Magnetic Resonance, Vol. 12: NMR of Paramagnetic Molecules; Berliner, L. J., Reuben, J., Eds.; Plenum: New York, 1993; pp 133-274. (9) Walker, F. A.; Reis, D.; Balke, V. L. J. Am. Chem. Soc. 1984, 106, 6888. (10) Walker, F. A.; Huynh, B. H.; Scheidt, W. R.; Osvath, S. R. J. Am. Chem. Soc. 1986, 108, 5288. (11) (a) Safo, M. K.; Gupta, G. P.; Walker, F. A.; Scheidt, W. R. J. Am. Chem. Soc. 1991, 113, 5497. (b) Safo, M. K.; Gupta, G. P.; Watson, C. T.; Simonis, U.; Walker, F. A.; Scheidt, W. R. J. Am. Chem. Soc. 1992, 114, 7066. (c) Safo, M. K.; Walker, F. A.; Raitsimring, A. M.; Walters, W. P.; Dolata, D. P.; Debrunner, P. G.; Scheidt, W. R. J. Am. Chem. Soc. 1994, 116, 7760. (12) Simonis, U. Unpublished results. (13) (a) Kevan, L. In Modern Pulsed and Continuous-WaVe Electron Spin Resonance; Kevan, L., Bowman, M. K., Eds.; John Wiley and Sons: New York, 1990; Chapter 5. (b) Dikanov, S. A.; Tsvetkov, Yu. D. Electron Spin Echo EnVelope Modulation (ESEEM) Spectroscopy; CRC Press: Boca Raton, FL, 1992; Chapter 1. (14) Peisach, J.; Mims, W. B.; Davis, J. L. J. Biol. Chem. 1979, 254, 12379. (15) Flanagan, H. L.; Gerfen, G. J.; Lai, A.; Singel, D. J. J. Chem. Phys. 1988, 88, 2162. (16) Reijerse, E. J.; Dikanov, S. A. J. Chem. Phys. 1991, 95, 836. (17) McCracken, J.; Freidenberg, S. J. Phys. Chem. 1994, 98, 467. (18) Lee, H.; McCracken, J. J. Phys. Chem. 1994, 98, 12861. (19) Dikanov, S. A.; Spoyalov, A. P.; Hu¨ttermann, J. J. Chem. Phys. 1994, 100, 7973. (20) Borbat, P.; Raitsimring, A. New Pulse EPR Spectrometer at the University of Arizona. Abstracts of 36th Rocky Mountain Conference on Analytical Chemistry, Denver, CO, July 31-August 5, 1994; p 94. (21) Hurst, J. C.; Henderson, T. A.; Kreilick, R. W. J. Am. Chem. Soc. 1985, 107, 7294. (22) Iwasaki, M.; Toriyama, K. In Electronic Magnetic Resonance of the Solid State; Weil, J. A., Bowman, M. K., Morton, J. R., Preston, K. F., Eds.; Canadian Society of Chemistry: Ottawa, 1987; p 545. (23) Hutchinson, C. A.; McKay, D. B. J. Chem. Phys. 1977, 66, 3311. (24) Henderson, T. A.; Hurst, J. C.; Kreilick, R. W. J. Am. Chem. Soc. 1985, 107, 7299. (25) Mims, W. B. Phys. ReV. B 1972, 5, 2409. (26) Carrington, A.; McLachlan, A. D. Introduction to Magnetic Resonance with Application to Chemistry and Chemical Physics; Harper and Row: New York, 1967; Chapter 7. (27) Hoffmann, B. M.; Martinsen, J.; Venters, R. A. J. Magn. Reson. 1984, 110, 59.

5244 J. Phys. Chem., Vol. 100, No. 13, 1996 (28) Scholes, C. P.; Falkowski, K. M.; Chen, S.; Bank, J. J. Am. Chem. Soc. 1986, 108, 1660. (29) Scheidt, W. R. Personal communication. The pyrazole ligands of [OEPFe(PzH)2]+ are parallel to each other, while those of [TPPFe(PzH)2]+ have dihedral angles of the pyrazole ligand planes of 45° and 54° for the two independent molecules in the unit cell. For the latter molecule, the calculated Fe-H(C) (pyrazole) distances are 3.20, 3.20, 3.23, and 3.25 Å and the Fe-H(N) distances are 3.08, 3.09, 3.06, and 3.07 Å, in excellent agreement with the values taken from the [TPPFe(ImH)2]+ structure, as revised by the best simulations of the ESEEM spectra of this study. Whether or not the pyrazole ligands are, in fact, at the crystallographically observed dihedral angles or in parallel planes in the frozen glasses used for our ESEEM studies cannot be determined from our data; we had stated, before knowing the X-ray structural data, that the deviation of the R-H of the pyrazole ligand from the gxx magnetic axis should not be greater than (30°, which is within the range found by Scheidt’s group for the two independent molecules in crystals of [TPPFe(PzH)2]+. (30) Collins, D. M.; Countryman, R.; Hoard, J. L. J. Am. Chem. Soc. 1972, 94, 2066. (31) (a) Satterlee, J. D.; La Mar, G. N. J. Am. Chem. Soc. 1976, 98, 2804. (b) Chacko, V. P.; La Mar, G. N. J. Am. Chem. Soc. 1982, 104, 7002. (32) (a) La Mar, G. N.; Walker, F. A. J. Am. Chem. Soc. 1973, 95, 1782. (b) La Mar, G. N.; Walker, F. A. In The Porphyrins; Dolphin, D., Ed.; Academic Press: New York, 1979; Vol. IV, pp 57-161. (33) Hagen, W. R.; Hearshen, D. O.; Sands, R. H.; Dunham, W. R. J. Magn. Reson. 1985, 61, 220.

Raitsimring et al. (34) Pilbrow, J. R. Transition Ion Electron Paramagnetic Resonance; Clarendon Press: Oxford, 1990; Chapter 5. (35) The positions of the peaks in the simulation also have an uncertainty of 0.025 MHz because of the FFT. (36) Shokhirev, N. V.; Walker, F. A. J. Phys. Chem. 1995, 99, 17795. (37) Basu, P.; Shokhirev, N. V.; Enemark, J. H.; Walker, F. A. J. Am. Chem. Soc. 1995, 117, 9042. (38) (a) Keller, R. M.; Wu¨thrich, K. Biochem. Biophys. Res. Commun. 1978, 83, 1132. (b) Senn, H.; Keller, R. M. Wu¨thrich Biochem. Biophys. Res. Commun. 1980, 92, 1362. (c) Williams, G.; Clayden, N. J.; Moore, G. R.; Williams, R. J. P. J. Mol. Biol. 1985, 183, 447. (d) Feng, Y.; Roder, H.; Englander, S. W. Biochemistry 1990, 29, 3494. (39) Emerson, S. D.; La Mar, G. N. Biochemistry 1990, 29, 1556. (40) Banci, L.; Pierattelli, R.; Turner, D. L. Eur. J. Biochem. 1995, 232, 522-527. (41) La Mar, G. N.; Chen, Z.; Vyas, K.; McPherson, A. D. J. Am. Chem. Soc. 1995, 117, 411. (42) Keller, R. M.; Wu¨thrich, K. Biochim. Biophys. Acta 1972, 285, 326. (43) (a) Williams, G.; Clayden, N. J.; Moore, G. R.; Williams, R. J. P. J. Mol. Biol. 1985, 183, 447. (b) Veitch, N. G.; Whitford, D.; Williams, R. J. P. FEBS Lett. 1990, 269, 297. (44) McLachlan, S. J.; La Mar, G. N.; Lee, K.-B. Biochim. Biophys. Acta 1988, 957, 430.

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