A Practical Strategy for Determination of Proton Hyperfine Interaction

A practical strategy is outlined for the determination of proton hyperfine parameters in paramagnetic transition metal ion complexes in disordered sys...
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J. Phys. Chem. 1996, 100, 3387-3394

3387

A Practical Strategy for Determination of Proton Hyperfine Interaction Parameters in Paramagnetic Transition Metal Ion Complexes by Two-Dimensional HYSCORE Electron Spin Resonance Spectroscopy in Disordered Systems Andreas Po1 ppl and Larry Kevan* Department of Chemistry, UniVersity of Houston, Houston, Texas 77204-5641 ReceiVed: September 5, 1995X

A practical strategy is outlined for the determination of proton hyperfine parameters in paramagnetic transition metal ion complexes in disordered systems from a single two-dimensional hyperfine sublevel correlation spectroscopy (2D HYSCORE) electron spin resonance experiment. Both dipolar and isotropic hyperfine interaction parameters can directly be determined from the cross peak ridges in the HYSCORE spectrum in the limit of the point dipole approximation. This approach is justified by spectral simulations for isotropic and axially symmetric g tensors. If the HYSCORE spectrum is measured at the g⊥ spectral region of the electron spin resonance powder spectrum, the orientation of the hyperfine interaction tensor with respect to the g tensor frame can also be deduced from the shape of the cross peak ridges in many cases. Two experimental examples are presented. Using this approach, the hyperfine interaction parameters for protons in [Cu(H2O)6]2+ and in [Cu(C5H5N)4]2+ complexes, both incorporated into mesoporous (L)Cu-MCM-41 silica tube material, are determined from a single 2D HYSCORE spectrum. The parameters are in good agreement with independent measurements by electron spin echo modulation spectroscopy.

Introduction In transition metal ion complexes hyperfine interactions between paramagnetic ions and ligand nuclei carry important information about the structure of the complex and the distribution of electron spin density within the complex. The dipolar hyperfine interaction T⊥ can be regarded as a measure of the distance between the transition metal ion and ligand nuclei in many cases and contains information about the coordination geometry of the complex. This interaction is often approximated by a classical magnetic dipole-dipole interaction. The degree of overlap between the metal ion and ligand orbitals can be derived from the distribution of the electron spin density measured by the isotropic hyperfine interaction Aiso. Unfortunately, hyperfine interactions between the transition metal ion and the ligand nuclei are often very weak and contribute only to inhomogeneous broadening of the electron spin resonance (ESR) signal. However, these weak hyperfine interactions can be resolved by electron nuclear double resonance (ENDOR)1,2 or electron spin echo modulation (ESEM)3 techniques. In single crystals most investigations of paramagnetic transition metal ion complexes have been performed by ENDOR spectroscopy.2 ESEM techniques have been proven to be powerful tools in the investigation of disordered materials such as metal oxide surfaces and biological systems.3b Different electron spin echo modulation methods have been developed to determine the hyperfine interactions of ligand nuclei in transition metal ion complexes in disordered systems. Two- and four-pulse sum peak electron spin echo experiments allow the determination of the dipolar hyperfine interaction from the shift of the sum combination harmonics ωR + ωβ of the basic ENDOR frequencies ωR and ωβ from a S ) 1/2, I ) 1/2 spin system with respect to the double nuclear Larmor frequency 2ωI in Fourier transformed (FT) electron spin echo spectra.4-6 For an anisotropic electron g tensor the coordination geometry of the complex can be derived from orientation selective sum peak ESEM spectra in many cases.6-8 However, sum peak X

Abstract published in AdVance ACS Abstracts, January 15, 1996.

0022-3654/96/20100-3387$12.00/0

ESEM spectra provide only restricted information about Aiso as the combination harmonics are mainly determined by T⊥. This restriction is overcome in the present method. Another powerful approach is the direct analysis of the time domain ESEM pattern usually measured by two- or three-pulse sequences.9 Using a spherical averaging approximation,10 the number of interacting ligand nuclei and their dipolar hyperfine interaction can be evaluated by a simulation of the time domain ESEM spectra with high accuracy as shown in a variety of studies of transition metal ion complexes on metal oxide surfaces.11 Most of these investigations have been performed on complexes with deuterated ligands since the modulation depth at X-band frequencies is considerably higher for I ) 1 nuclei than for I ) 1/2 nuclei such as protons. However, this approach does not allow direct determination of the coordination geometry of the nuclei from ESEM spectra since geometrical correlations between the interacting nuclei are not included by the spherical averaging approximation used to analyze powder spectra. The analysis of the basic modulation frequencies ωR and ωβ in FT-ESEM spectra of disordered solids suffers from different limitations such as line-shape distortions due to spectrometer deadtime, disappearing spectral intensities near the canonical orientations of the hyperfine tensor, and blind spots in threeand four-pulse ESEM experiments.12 Recently, Ponti and Schweiger13 suggested an experiment based on the detection of nuclear coherence transfer echoes in a four-pulse ESEM sequence which provides spectra free from deadtime distortions. However, in the case of small dipolar and isotropic hyperfine interactions, 2πT⊥/ωI < 0.5 and 2πAiso/ωI < 0.8, which is often the case in transition metal ion complexes, the ENDOR signals ωR and ωβ from both electron spin manifolds overlap in the powder spectra and provide a rather featureless broad signal near ωI. This poorly structured signal often prevents a direct determination of T⊥ and Aiso from the experimental FT-ESEM spectrum. Two-dimensional (2D) electron spin resonance experiments such as the 2D four-pulse or HYSCORE (hyperfine sublevel © 1996 American Chemical Society

3388 J. Phys. Chem., Vol. 100, No. 9, 1996 correlation spectroscopy)14 sequence offer potential to overcome these disadvantages of ESEM spectroscopy as the second frequency domain enhances the spectral resolution.15 In the HYSCORE experiment (π/2-τ-π/2-t1-π-t2-π/2-τ-echo) the mixing π-pulse creates correlations between the nuclear coherences of the two different electron spin (Ms) manifolds of a S ) 1/2, I ) 1/2 spin system. The symmetric nuclear coherence transfer pathways ωR-ωβ and ωβ-ωR during the evolution period t1-π-t2 lead to cross peaks (ωR,ωβ) (ωβ,ωR) in the 2D spectra, where ωR and ωβ are the nuclear transition frequencies in the two different Ms states. In disordered systems the anisotropic hyperfine interaction results in a spread of the ωR and ωβ frequencies which leads, together with the correlations between ωR and ωβ, to two different ridges for the two nuclear coherence transfer pathways in the 2D spectrum. These ridges are directed perpendicular to the frequency diagonal ω1 ) ω2 in the case of small hyperfine, 2πT⊥ + πAiso < ωI.12,15 The shape of the two ridges and their degree of separation depend on the dipolar hyperfine magnitude. Basically, the principal values of the hyperfine tensor can be estimated from the end positions of the ridges.12 But an exact determination of these end positions is often difficult since the end positions of the cross peak ridges correspond to the canonical orientations of the hyperfine tensor where the echo signal intensity drops to zero. Furthermore, both end positions can often not be observed in a single HYSCORE experiment due to a suppression effect depending on the first pulse delay τ.12,14 Recently, a 3D version of the HYSCORE sequence and detection of the HYSCORE echo by a remote echo sequence were suggested to observe suppression-free line shapes in disordered systems.12 But these experiments result in long measurement times for systems with weak echoes as often observed for transition metal ion complexes. In this study we develop a simple and practical approach to determine directly both the dipolar and isotropic hyperfine interactions of protons with an axially symmetric hyperfine tensor from a single 2D HYSCORE spectrum in the limit of small hyperfine interaction. Spectral simulations for different anisotropic and isotropic hyperfine interactions as well as for isotropic and axially symmetric g tensors are presented which demonstrate the practical utility of the method. The influence of the orientation of the dipolar hyperfine tensor with respect to the g tensor principal axis on the spectral features in the 2D spectra is also demonstrated. Two experimental examples involving transition metal ions are presented which demonstrate the practical utility of the method. HYSCORE measurements are shown to enable determination of the hyperfine interaction parameters of the equatorial protons of a [Cu(H2O)6]2+ complex formed in the mesoporous Cu-MCM-41 silica tube material. Also, the hyperfine interaction parameters of protons in a [Cu(C5H5N)4]2+ complex likewise incorporated into Cu-MCM41 are successfully measured by HYSCORE spectroscopy.

Theory and Simulations The theoretical expressions for the modulation in the 2D HYSCORE experiment in the case of a S ) 1/2, I ) 1/2 spin system have been derived by Gemperle et al.,16 and some sign corrections have been noted by Tyryshkin et al.6 For simplicity, we retain only those parts of the time domain modulation formula which give rise to cross peaks in the 2D FT-ESEM

Po¨ppl and Kevan spectrum. The corrected modulation formula is then given by

Emod(τ,t1,t2) ) 1 - (k/4)Cτ[c2 cos(ωRt1 + ωβt2 + (ωR + ωβ)τ/2) + c2 cos(ωβt1 + ωRt2 + (ωR + ωβ)τ/2) s2 cos(ωRt1 - ωβt2 + (ωR - ωβ)τ/2) s2 cos(ωβt1 - ωRt2 - (ωR - ωβ)τ/2)] (1) where the τ suppression effect is described by the factor

Cτ ) -2 sin(ωRτ/2) sin(ωβτ/2)

(2)

The intensity of the cross peaks is determined by

K ) 4s2c2

(3)

where

s2 )

|ωI2 - 1/4(ωR + ωβ)2| ωRωβ

c2 )

|ωI2 - 1/4(ωR - ωβ)2| ωRωβ

(4)

In general, ESR spectra of transition metal ion complexes show a large g tensor anisotropy. Here we restrict ourselves to an axially symmetric g tensor which is commonly observed in cupric complexes. If we describe the dipolar hyperfine interaction by a point dipole approximation, the nuclear transition frequencies ωR and ωβ are then given by17,18

ωR ) [(ωI - A/2)2 + (B/2)2]1/2 ωβ ) [(ωI + A/2)2 + (B/2)2]1/2

(5)

with

A ) 2πT⊥[(3/g2)(g|2 cos θ0 cos θI + g⊥2 sin θ0 sin θI cos φI) × (cos θ0 cos θI + sin θ0 sin θI cos φI) - 1] - 2πAiso (6) B2 ) B′2 + C′2

(7)

B′ ) 2πT⊥[(3/g2)(g|2 cos θ0 cos θI + g⊥2 sin θ0 sin θI cos φI)(cos θ0 sin θI cos φI sin θ0 cos θI) + (Aiso/T⊥ - 1)(g⊥2 - g|2)/g2 sin θ0 cos θ0] (8) C′ ) 2πT⊥[(3/g2)(g|2 cos θ0 cos θI + g⊥2 sin2 θ0 sin θI cos φI)(sin θI sin φI)] (9) and

g2 ) g|2 cos2 θ0 + g⊥2 sin2 θ0

(10)

T⊥ ) ggnββn/hr3

(11)

Here, the principal values of the dipolar hyperfine tensor T are (-T⊥,-T⊥,2T⊥). The quantity ωI is the Larmor frequency of the coupled nucleus, and g| and g⊥ are the principal values of the g tensor. The other terms in the above equations are defined as illustrated in Figure 1. A coordinate system was chosen such that g| lies along z and θ0 is the angle between the external magnetic H0 and the g| direction. The x and y axes are chosen

Paramagnetic Transition Metal Ion Complexes

J. Phys. Chem., Vol. 100, No. 9, 1996 3389

Figure 1. Vector diagram showing the relationship between the external field H0 and the vector r joining the electron spin and the nucleus. The xyz coordinate frame corresponds to the g tensor frame.

so that the vector r joining the electron spin and the nucleus lies in the xz plane at an angle θI to the z axes. φI is the azimuthal angle from z between the zx plane and the zH0 plane. All other symbols have their usual meaning. Isotropic g Tensor. After defining the nuclear transition frequencies, the properties of the HYSCORE spectrum can be derived from expressions 1-11. As we deal with small hyperfine interaction, A < 2ωI, the relation s2 , c2 ∼ 1 holds.12 A 2D FT of eq 1 results then in cross peaks at (ωR,ωβ) and (ωβ,ωR) in a single-crystal HYSCORE spectrum. To illustrate the influence of the dipolar hyperfine parameter T⊥, we first consider a single-crystal HYSCORE spectrum with an isotropic g tensor. In this case we can choose the xyz axis frame in such a way that r points along z (θI ) 0). The parameters in eq 5 then become

A ) 2πT⊥(3 cos2 θ0 - 1) + 2πAiso B ) 2πT⊥3 cos θ0 sin θ0

(12)

For B ) 0, meaning that the hyperfine interaction is solely isotropic, the nuclear transition frequencies are symmetric with respect to the nuclear Larmor frequency, ω°R,β ) ωI ( 1/2A. The cross peaks (ω°R,ω°β) and (ω°β,ω°R) are situated on an axis ω1 ) -ω2 in the 2D spectrum that cuts the frequency diagonal ω1 ) -ω2 at (ωI,ωI). In the presence of dipolar hyperfine interaction, B * 0, the frequencies (ωR,ωβ) are not symmetric with respect to ωI and are shifted toward higher frequency due to the term (B/2)2 in eq 5. This frequency shift

∆ωsR,β ) [(ωI - A/2)2 + (B/2)2]1/2 - (ωI - A/2) (13) can be evaluated in the weak coupling limit (ωI - A/2) . |B/ 2| by expanding the square root in eq 13 to obtain

∆ωsR ) B2[8(ωI - A/2)]-1

∆ωsβ ) B2[8(ωI + A/2)]-1 (14)

The cross peaks are shifted away from the ω1 ) -ω2 axes to the positions (ω°R + ∆ωsR, ω°β + ∆ωsβ) and (ω°β + ∆ωsβ, ω°R + ∆ωsR). This effect is illustrated in Figure 2 where a simulation of a single-crystal HYSCORE spectrum is presented. If we assume ωI . A/2, we can directly determine the parameter B from the vertical distance ∆ωs between the cross peaks and the ω1 ) -ω2 axis according to

B ) [8∆ωsωI/(2)1/2]1/2

(15)

We expect the maximum value ∆ωsmax for θ0 ) 45°. In a powder system all possible orientations of r with respect to H0 (0 e θ0 e 180°) are present. Thus, the pairs of cross peaks observed in the single-crystal spectrum turn into two different ridges in a powder spectrum.12 The ridges extend from ωI -

Figure 2. Simulated single-crystal HYSCORE spectrum for an axially symmetric g tensor. The simulation parameters are ωI/2π ) 14.5 MHz, T⊥ ) 5 MHz, Aiso ) 0, θ0 ) 45°, and τ ) 104 ns. The spectrum illustrates the vertical shift ∆ωs of the cross peaks from the ω1 ) -ω2 axes due to the dipolar hyperfine interaction. The insert shows an expanded view of the cross peak at (13.1, 16.9) MHz.

π(2T⊥ + Aiso), ωI ( π(2T⊥ + Aiso) to ωI - π(-T⊥ + Aiso), ωI ( π(-T⊥ + Aiso) corresponding to the two canonical orientations of the hyperfine tensor θ0 ) 0 and θ0 ) 90°. At an orientation θ0 ) 45° the ridges show the maximum vertical shift ∆ωsmax from the ω1 ) -ω2 axes. The maximum shift is measured from the midpoint between the lines from the highest contour level. The dipolar hyperfine parameter T⊥ can be calculated from ∆ωsmax using eqs 12 and 15 to obtain eq 16.

T⊥ ) (2/3)[(8∆ωsmaxωI)/(21/24π2)]1/2

(16)

After T⊥ is determined from ∆ωsmax, the isotropic hyperfine parameter Aiso can be calculated from the θ0 ) 0° or θ0 ) 90° positions of the ridges where they meet the ω1 ) -ω2 axes using eq 5 and 12. This is illustrated by simulated HYSCORE powder spectra for different values of T⊥ in the limit of an isotropic g tensor. The simulations are shown in Figure 3. The powder spectra were calculated in the time domain using the expression

〈Emod〉 ) (1/2)∫0 Emod(θ0) sin θ0 dθ0 π

(17)

A 170 × 170 point 2D data set was calculated. An experimentally reasonable pulse delay of τ ) 104 ns was used in the simulations to avoid blind spots in the spectral region close to the proton nuclear Larmor frequency ωI/2π ) 14.5 MHz.12 Before FT the 2D data set was multiplied by an exponential decay function with a line width ∆ω12hom/2π ) 0.1 MHz (fwhh) to account for homogeneous broadening of the nuclear transition frequencies. The ridges are clearly resolved for values T⊥ g 5 MHz. (Figure 3a,b). The maximum vertical shift ∆ωsmax of the ridges from the ω1 ) -ω2 axis is marked by a line parallel to the ω1 ) -ω2 axis. For a small dipolar hyperfine interaction (T⊥ e 3 MHz) Figure 3c,d shows that the ridges collapse into a single spectral feature. But their maximum vertical shift ∆ωsmax from the ω1 ) -ω2 axes can still be

3390 J. Phys. Chem., Vol. 100, No. 9, 1996

Po¨ppl and Kevan

Figure 3. Simulated powder HYSCORE spectra for an isotropic g tensor showing the effect of the T⊥ magnitude. The simulation parameters are τ ) 104 ns, ωI/2π ) 14.5 MHz, and Aiso ) 0. (a) T⊥ ) 7 MHz, (b) T⊥ ) 5 MHz, (c) T⊥ ) 3 MHz, and (d) T⊥ ) 2 MHz. The maximum vertical shift ∆ωs from the ω1) -ω2 axes is illustrated by a solid line.

TABLE 1: Comparison between Simulation Parameters and Parameters Estimated from the Simulated HYSCORE Spectra simulation parameter

estimated parameter

T⊥ (MHz) Aiso (MHz) T⊥ (MHz)a Aiso (MHz)b isotropic g tensor

axially symmetric g tensor θI ) 90° θI ) 70° θI ) 45°

7.0 5.0 3.0 2.0 5.0 5.0 5.0 5.0

0.0 0.0 0.0 0.0 5.0 3.0 1.5 -1.5

7.0 5.1 3.1 2.2 5.2 5.0 5.1 5.1

0.3 0.1 0.2c 0.1c 4.8 3.1 1.5 -1.6

5.0 5.0 5.0

1.5 1.5 1.5

5.1 5.2 5.1

1.5 1.5 1.3c

a The error of T⊥ is determined by the resolution of the 2D spectra and is about (0.2 MHz. b The error of Aiso is about (0.2 MHz. c The error in Aiso is (0.4 MHz as the end position of the ridges are poorly resolved in the simulated 2D spectra.

resolved with satisfactory accuracy. The simulation parameters and the T⊥ values determined from the simulated spectra according to eq 16 are summarized in Table 1. We note that the end positions of the ridges for θ0 ) 0° are not observed with sufficient signal intensities in our simulated spectra. This is related to the suppression effect in the HYSCORE spectra which is caused by the τ-dependent term Cτ (eq 2) in the HYSCORE modulation formula. But the observation of the end positions of both ridges near θ0 ) 90° allows a direct determination of the isotropic hyperfine parameter Aiso from the 2D spectra and the T⊥ parameters. Of course, the determination of the ridge position at θ0 ) 90° has some uncertainty as the ridge intensity approaches zero at the canonical orientations of the hyperfine tensor. Only in the case of small values of T⊥ (Figure 3c,d) does the determination of the θ0 ) 90° positions seem vague.

Figure 4. Simulated powder HYSCORE spectra for an isotropic g tensor showing the effect of the Aiso magnitude. The simulation parameters are τ ) 104 ns, ωI/2π ) 14.5 MHz and T⊥ ) 5 MHz. (a) Aiso ) 5 MHz, (b) Aiso ) 3 MHz, (c) Aiso ) 1.5 MHz, and (d) Aiso ) -1.5 MHz. The maximum vertical shift ∆ωsmax from the ω1 ) -ω2 axes is illustrated by a solid line.

A series of simulated spectra for different Aiso parameters are presented in Figure 4. The 2D spectral features are very sensitve to changes of Aiso. An increase in Aiso results in a spreading of the total 2D pattern whereas the shape of the individual ridges is preserved. Again T⊥ can be determined by the vertical shift ∆ωsmax of the ridges from the ω1 ) -ω2 axis, and Aiso can then be calculated from the θ0 ) 90° positions of the ridges. All simulation parameters and the values of T⊥ and Aiso are summarized in Table 1. It is worth noting that according to our simulations the different 2D spectral features even allow one to distinguish between positive and negative isotropic hyperfine values. Axially Symmetric g Tensors. In this section we discuss HYSCORE spectra of a proton S ) 1/2, I ) 1/2 spin system in the case of an axially symmetric g tensor. This problem is strongly related to the subject of orientation selective ESEM spectra. In general, ESR spectra of transition metal ion complexes show a large g tensor anisotropy. For instance, the total anisotropic ESR line width of an axially symmetric Cu2+ species on metal oxide surfaces is about 600 G.18 However, the microwave pulses for an ESEM experiment, which are typically about 20 ns, cover only approximately 10 G of the ESR spectrum. Here we discuss only the case of irradiation in the g⊥ region of the spectrum, θ0 ) 90°, since it is the most usual experimental condition. For a general orientation of the vector r with respect to the g tensor frame the parameters in eq 5 become

A ) 2πT⊥(3 sin2 θI cos2 φI - 1) + 2πAiso B ) 2πT⊥(3 sin2 θI cos2 φI cos2 θI + sin4 θI cos2 φI sin2 φI)1/2 (18) For simulation of the powder spectra θ0 ) 90° is fixed and the

Paramagnetic Transition Metal Ion Complexes

J. Phys. Chem., Vol. 100, No. 9, 1996 3391 necessarily at φI ) 45°. The ∆ωsmax position corresponds to crystallite orientations with  ) 45°. Therefore, T⊥ can again be evaluated from ∆ωsmax by eq 16. Again, Aiso can then be determined by the inner end position of the ridges corresponding to φI ) 90°. The simulation parameters together with the T⊥ and Aiso values determined from the simulated spectra are summarized in Table 1. Surprisingly, the HYSCORE spectra are similar to the case of an isotropic g tensor for 90° g θI g 70°. The cross peak ridges only appear sensitive to changes in θI for 70° g θI g 45°. Case b. For θI < 45° only crystallites with min > 45° are excited by the microwave pulses. Therefore, the vertical shift ∆ωs of the ridges from the ω1 ) -ω2 axes that can be taken from the spectra is not equal to the maximum possible shift of ∆ωsmax corresponding to the orientation with  ) 45°. The measured value ∆ωs is observed for orientations with φ1 ) 0°. The parameter T⊥ cannot be determined directly from ∆ωs using eq 16 since ∆ωs is also a function of θI.

∆ωs ) (2)1/2[(6πT⊥ sin θI sin θI)]2/8ωI

Figure 5. Simulated powder HYSCORE spectra for an axially symmetric g tensor and microwave irradiation at g⊥(θ0d90°) showing the effect of the θI magnitude. The simulation parameters are τ ) 104 ns, ωi/2π ) 14.5 MHz, T⊥ ) 5 MHz, and Aiso ) 1.5 MHz. (a) θI ) 90°, (b) θI ) 70°, (c) θI ) 45°, and (d) θI ) 20°. The maximum vertical shift ∆ωsmax from the ω1 and -ω2 axes is illustrated by a solid line.

integration performed over φI

〈Emod〉 ) (1/Π)∫0 Emod(θ0,θI,φI) dφI π

(19)

In practice, the finite excitation range of the microwave pulses results in excitation of all crystallites with orientations θ0 - δ e θ0 e θ0 + δ with respect to H0. For instance, in the case of an axially symmetric Cu2+ ESR spectrum δ e 6°. It was found that varying δ between 0° and 6° had negligible effect on the simulated HYSCORE spectra. Therefore, an ideal excitation of the ESR spectrum at θ0 ) 90° was assumed in the simulation procedure. Figure 5 illustrates simulated HYSCORE spectra for different angles θI corresponding to different orientations of r with respect to the g tensor frame. Again, the maximum vertical shift ∆ωsmax of the ridges from the ω1 ) -ω2 axes is indicated by a line parallel to the ω1 ) -ω2 axes. The simulations show that we can distinguish two different cases: (a) 90° g θI g 45° and (b) 45° > θi g 0°. To simplify the discussion, we introduce a further angle  that measures the angle between r and H0. Case a. This situation is similar to HYSCORE spectra with an isotropic g tensor.12 The only difference is that with a decrease of θI from 90° to 45° the minimum achievable angle min increases from 0° to 45°. This means that crystallites with  < min are no longer excited by the microwave pulses, resulting in a narrowing of the ridges. The outer end positions of the ridges are no longer given by ωI - [2T⊥ + Aiso]π and ωI ( [2T⊥ + Aiso]. Now the ridges end at (ωeR,ωeβ), (ωeβ,ωeR) with

ωeR,β ) [(ωI - {2πT⊥(3 sin2 θI - 1) + 2πAiso}/2)2 + ({2πT⊥3 sin θI cos θI}/2)2]1/2 (20) corresponding to the orientation φI ) 0°. However, the maximum possible vertical shift ∆ωsmax of the ridges from the ω1 ) -ω2 axes is still observed in the spectra, but not

(21)

However, the ridges again meet the ω1 ) -ω2 axes at orientations with θI ) 90°. Together with the value of ∆ωs and the crosspeak positions at which ∆ωs is determined, the parameters T⊥, Aiso, and θI can be determined from eqs 5, 18, 20, and 21. The simulations show that the cross peak features of protons in powder HYSCORE spectra are very sensitive to changes in T⊥, Aiso, and θI. The hyperfine parameters T⊥ and Aiso can be directly determined from the HYSCORE spectra for θI g 45°. Besides T⊥ and Aiso, the orientation of the dipolar hyperfine tensor T with respect to the g tensor frame measured by θI has a strong influence on the shape of the ridges in the HYSCORE spectra for θI e 70°. Therefore, we see that HYSCORE spectra can provide information about the ligand coordination geometry of transition metal ion complexes eVen if only a single experiment is performed in the g⊥ region of the ESR spectrum. Finally, we address some problems that arise for excitation of the ESR spectrum at other positions than the g⊥ region (θ0 < 90°). Here the situation is more complicated as the spectral features depend on both θI and θ0. If for instance for a given θI the excitation region determined by θ0 is chosen such that min > 45°, the dipolar hyperfine parameter T⊥ cannot be determined from ∆ωsmax using eq 16. The situation is comparable to case b with excitation at g⊥ and θI < 45°. Otherwise, if we consider orientations of r corresponding to θI g 45° and irradiate a spectral region of the ESR spectrum that corresponds to orientations θ0 g 45° of the microcrystallites with respect to H0, min e 45° holds. This situation is then comparable to excitation at g⊥ and θI < 45°. Equation 16 is valid, and T⊥ can be determined from ∆ωsmax. Experimental Section Mesoporous MCM-41 material was synthesized in its siliceous form and calcined as described earlier.19 Cupric ions were exchanged into MCM-41 by a liquid state reaction using a Cu2+-ammonia solution to produce (L)Cu-MCM-41. After dehydration the ion-exchanged samples are exposed to H2O and C5H5N at their room temperature vapor pressure for 6 h to form [Cu(H2O)6]2+ and [Cu(C5H5N)4]2+ complexes. The HYSCORE experiments were performed on a Bruker ESP 380 FT-ESR spectrometer at 4.2 K. Pulse lengths of 24 ns for π/2 pulses and 48 ns for π pulses were used. A pulse delay of τ ) 104 ns was used to enhance signals near the proton nuclear Larmor frequency. A four-step phase cycle suggested by Gemperle et

3392 J. Phys. Chem., Vol. 100, No. 9, 1996

Figure 6. Experimental HYSCORE spectrum at 4.2 K of a [Cu(H2O)6]2+ complex in (L)Cu-MCM-41. The spectrum was obtained by irradiation of the g⊥ spectral region (θ0d90°) of the Cu2+ ESR spectrum. The proton Larmor frequency at the corresponding magnetic field is ωi/2π ) 14.5 MHz. The maximum vertical shift ∆ωs of the cross peak ridges from the ω1 ) -ω2 axes is illustrated by a solid line. The spectrum was measured with a pulse delay τ ) 104 ns.

al.16 was used to avoid interference with unwanted two- and three-pulse echoes. A 170 × 170 2D data matrix was sampled. The echo decay was eliminated by a third-order polynomial base line correction of the experimental data set in both time domains. Before 2D FT the data set was zero-filled to 512 × 512 points. Then 2D FT magnitude spectra were calculated and presented as contour plots. Experimental Examples and Discussion [Cu(H2O)6]2+ Complex. As a first experimental example, a [Cu(H2O)6]2+ complex in mesoporous MCM-41 material was chosen since the Cu2+ ESR spectrum of this complex shows a well-resolved axially symmetric powder spectrum. The Cu2+ g tensor values g| ) 2.400 and g⊥ ) 2.079 as well as the metal ion hyperfine splitting A| ) 0.0141 cm-1 were reported in a previous publication.19 Figure 6 illustrates the 2D HYSCORE spectrum of the [Cu(H2O)6]2+ complex. The spectrum was taken at the g⊥ spectral region of the Cu2+ ESR spectrum. The HYSCORE spectrum shows two ridges that are shifted from the ω1 ) -ω2 axes, indicating protons with substantial dipolar hyperfine coupling. Furthermore, a peak situated on the ω1 ) -ω2 axes with its center at (ωI,ωI) is observed. Such a peak is indicative of very weakly coupled protons. The peak at (15.5, 15.5) MHz is an artifact. The observed ridge pattern possesses a maximum vertical shift ∆ωsmax/2π ) 0.63. MHz from the ω1 ) -ω2 axes. The shape of the ridges are comparable to those of the simulated spectra in Figure 5a,b. Therefore, we conclude that θI > 45° holds for those protons giving rise to the ridge pattern. Consequently, the ridges are assigned to the equatorial protons of the [Cu(H2O)6]2+ complex. According to our theoretical discussion, a dipolar hyperfine parameter T⊥ ) 4.8 ( 0.03 MHz can be determined from ∆ωsmax using expression 16. The ridges meet the ω1 ) -ω2 axes at the positions (16.1, 12.8) and (12.8, 16.1) MHz corresponding to crystallite orientations with φI - 90°. From these ridge positions and the T⊥ parameter, Aiso ) 1.5 MHz is determined. Unfortunately, these inner end positions of the two ridges are to some

Po¨ppl and Kevan extent overlapped by the signal of weakly coupled protons at (14.5, 14.5) MHz. Thus, it seems more reasonable to give a range of Aiso between 1.2 and 2.2 MHz. The outer end positions of the ridges corresponding to orientations with φI ) 0° are not observed due to blind spots in the 2D spectrum related to the τ-dependent suppression effect.12 The hyperfine parameters of the equatorial protons estimated from the HYSCORE experiment can be compared with the deuterium hyperfine parameters determined by ESEM for a deuterated [Cu(D2O)6]2+ complex in (L)Cu-MCM-41. An analysis of the deuterium time domain three-pulse ESEM spectrum with the spherical averaging approximation10 revealed eight equatorial deuteriums with Aiso ) 0.27 MHz and a Cu2+-D distance of r ) 0.27 nm and four axial deuteriums with Aiso ) 0.26 MHz and a Cu2+-D distance r ) 0.33 nm.19 These values of the equatorial deuteriums translate into proton hyperfine parameters of Aiso ) 1.76 MHz and T⊥ ) 4.1 MHz, in good independent accordance with the parameters derived from the HYSCORE experiment. Probably the peak at (14.5, 14.5) MHz in the HYSCORE spectrum is due to the axial protons of the [Cu(H2O)6]2+ complex. For these protons φI e 16° holds. The width of their powder spectrum is then determined by the φI ) 90° orientation under the experimental condition θ0 ) 90°. Taking the ESEM values for the axial deuteriums of the [Cu(D2O)6]2+ complex,19 we get Aiso ) 1.7 MHz and T⊥ ) 2.2 MHz for the axial protons. From these hyperfine parameters and eqs 5 and 18, a width of the powder spectrum of the axial protons of ≈0.5 MHz is estimated in rough accordance with the actual spectral feature at (14.5, 14.5) MHz in the HYSCORE spectrum (Figure 6). We note that weakly coupled matrix protons from surrounding water molecules may also contribute to this peak. [Cu(C5H5N)4]2+ Complex. As a second example we investigated a copper-pyridine complex in (L)Cu-MCM-41. The previously reported Cu2+ ESR parameters g| ) 2.281, g⊥ ) 2.061, and A| ) 0.0182 cm-1 as well as the observation of five 15N superhyperfine signals indicated the formation of a squareplanar [Cu(C5H5N)5]2+ complex in (L)Cu-MCM-41 after pyridine adsorption.20 HYSCORE spectra were again taken at the g⊥ spectral region of the axially symmetric Cu2+ ESR spectrum. Figure 7a shows the HYSCORE spectrum measured with a pulse delay of τ ) 104 ns. Again, we can distinguish two ridges located approximately symmetric to the proton Larmor frequency at (14.5, 14.5) MHz in the 2D plot that extends from (14, 15) to about (11, 17) MHz and from (15, 14) to (17, 11) MHz. The ridges are overlapped in the spectral region near the proton Larmor frequency by signals from weakly coupled protons. The peak at (15.5, 15.5) MHz is again an artifact. Both ridges only show a small maximum shift ∆ωsmax/ 2π ) 0.19 MHz from the ω1 ) -ω2 axes. We assume from the square-planar [Cu(C5H5N)4]2+ complex geometry that both the g⊥ direction and the protons of the pyridine molecule are lying within the plane of the complex. Therefore, φI ) 90° holds, and a dipolar hyperfine parameter T⊥ ) 2.6 MHz can be determined from ∆ωsmax according to eq 16. From the inner end positions of the ridges we estimate Aiso ≈ 4 MHz. Of course, this Aiso is only a rough estimate as the inner end positions of the ridges are only poorly resolved. But the shape of the experimental ridge pattern in Figure 7a is very comparable to the spectrum simulated with T⊥ ) 5 MHz and Aiso ) 7 MHz (Figure 4a), indicating that Aiso > T⊥ holds for these pyridine protons. For such a large isotropic hyperfine coupling a considerable part of the ridge pattern is suppressed due to blind spots if a pulse delay of τ ) 104 ns is used.12 Therefore, a second spectrum was recorded with τ ) 136 ns (Figure 7b). In

Paramagnetic Transition Metal Ion Complexes

J. Phys. Chem., Vol. 100, No. 9, 1996 3393 the pyridine molecule, giving rise to the ridge pattern in the spectra of Figure 7. In the [Cu(C5H5N)4]2+ complex the pyridine molecule is bonded to the Cu2+ ion via the nitrogen atom where the C2 symmetry axes of the pyridine point toward the Cu2+. We can calculate from the known geometry of the pyridine molecule and an assumed Cu-N distance of 2.1 Å a distance of 3.05 Å between the Cu2+ and the two protons at the two carbon atoms that are directly bonded to the nitrogen in the pyridine. Therefore, it is natural to assign the ridge pattern in the HYSCORE spectra of the [Cu(C5H5N)4]2+ complex in (L)Cu-MCM-41 to a hyperfine interaction between the Cu2+ ion and these two protons. The other three protons of the pyridine with Cu2+-H distances of 5.2 and 6.0 Å presumably contribute to the peak at the proton Larmor frequency. The rather large value of Aiso ) 4.1 MHz is also reasonable as the spin density of the unpaired electron is delocalized over the [Cu(C5H5N)4]2+ complex as indicated by the large isotropic 15N superhyperfine splitting A ) 13 × 10-4 cm-1.20 ComN parable isotropic and dipolar hyperfine couplings of protons were measured by ENDOR on planar Cu(II)-bis(oxychinolate) complexes incorporated into different single-crystal hosts.2 These complexes also included a pyridine molecule. The protons in these complexes are likewise coupled to the Cu2+ via a carbonnitrogen bond. Conclusions

Figure 7. Experimental HYSCORE spectrum at 4.2 K of a [Cu(C5H5N)4]2+ complex in (L)Cu-MCM-41. The spectrum was obtained by irradiation of the g⊥ spectral region (θ0d90°) of the Cu2+ ESR spectrum. The proton nuclear Larmor frequency at the corresponding magnetic field is 14.5 MHz. The maximum vertical shift ∆ωsmax of the cross peak ridges from the ω1 ) -ω2 axes is illustrated by a solid line. Spectra were recorded with (a) τ ) 104 ns and (b) τ ) 135 ns.

this spectrum peaks at the proton Larmor frequency are suppressed, but the two ridges of the stronger protons are wellresolved. The strong peak at (15.5, 15.5) MHz is again an artifact. Both ridges show a small shift of ∆ωsmax/2π ) 0.2 MHz from the ω1 ) -ω2 axis. The ∆ωsmax value is comparable to that determined from the spectrum in Figure 7a and provides a dipolar hyperfine parameter of T⊥ ) 2.6 MHz. The two end positions of both ridges are fairly well-resolved. So Aiso ) 4.1 MHz can be determined from the points (9.7, 19.0), (19.0, 9.8) and (13.8, 15.0), (15.0, 13.8) MHz where the ridges approach the ω1 ) -ω2 axes. These points in the 2D ridge pattern correspond to orientations of the dipolar hyperfine tensor for φI ) 0° and φI - 90° with respect to H0. The dipolar hyperfine parameter T⊥ can also be obtained from the total width ∆ωr/2π ) 4.0 MHz of a ridge projected onto the ω1 or ω2 axes. If φI ) 90°,

∆ωr/2π ) 3/2T⊥

(22)

and we get T⊥ ) 2.7 MHz, in good accordance with the value determined from the ∆ωsmax shift of the ridges. We see that the T⊥ and Aiso parameters determined from both spectra with different pulse delays are the same. Therefore, the measurement of a single HYSCORE spectrum is sufficient for the determination of both T⊥ and Aiso in the case φI ) 90° if the maximum shift ∆ωsmax of the ridges from the ω1 and -ω2 axes and one end position of the ridges corresponding to orientations φI ) 0° or φI ) 90° of the hyperfine tensor can be observed in the 2D spectrum. Using the point dipole approximation (eq 11), we determine a distance r ) 3.1 Å between the Cu2+ ion and the protons of

Proton HYSCORE spectra of paramagnetic transition metal ion complexes including isotropic and axially symmetric g tensors are discussed for disordered systems. The simulated spectra show that the ridge pattern of the cross peaks observed in the powder HYSCORE spectra are very sensitive to changes in the dipolar and isotropic proton hyperfine interactions as well as to changes in the orientation of the hyperfine tensor with respect to the g tensor frame. A simple approach has been developed that allows direct determination of the dipolar and isotropic proton hyperfine parameters from the cross peak ridge pattern observed in a single HYSCORE spectrum. The method is especially suitable for isotropic hyperfine with 0 e |Aiso| e 5 MHz and dipolar hyperfine with 2 MHz e T⊥ e 7 MHz corresponding to distances between the transition metal ion and protons in the ligands in the range of 2.2 Å e r e 3.4 Å. In many practical cases the shape of the cross peak ridges in a HYSCORE spectrum taken at the g⊥ region of the ESR spectrum can be a sensitive tool for the determination of the proton orientation with respect to the g tensor frame. The practicality of the suggested approach is demonstrated by the two examples of [Cu(H2O)6]2+ and [Cu(C5H5N)4]2+ complexes incorporated into mesoporous (L)Cu-MCM-41 molecular sieve material. The proton hyperfine parameters in both complexes are in accordance with independent electron spin echo modulation results and the geometries of the complexes. The experimental results show the practical application of 2D HYSCORE spectroscopy for the determination of proton hyperfine parameters in paramagnetic transition metal ion complexes in disordered systems. Acknowledgment. This research was supported by the University of Houston Energy Laboratory and the National Science Foundation. A.P. thanks the Deutscher Akademischer Austauschdienst for support. References and Notes (1) Kavan, L.; Kispert, L. D. Electron Spin Double Resonance Spectroscopy; Wiley: New York, 1976. (2) Schweiger, A. Structure and Bonding 51; Springer: Berlin, 1982.

3394 J. Phys. Chem., Vol. 100, No. 9, 1996 (3) (a) Mims, W. B. In Electron Paramagnetic Resonance; Geschwind, S., Ed.; Plenum Press: New York, 1972; pp 263-352. (b) Kevan, L. In Modern Pulsed and Continuous-WaVe Electron Spin Resonance; Kevan, L., Bowman, M. K., Eds.; Wiley: New York, 1990; pp 231-266. (4) Schweiger, A. In Modern Pulsed and Continuous-WaVe Electron Spin Resonance; Kevan, L., Bowman, M. K., Eds.; Wiley: New York, 1990; pp 43-118. (5) Reijerse, E. J.; Dikanov, S. A. J. Chem. Phys. 1991, 95, 836. (6) Tyryshkin, A. M.; Dikanov, S. A.; Goldfarb, D. J. Magn. Reson., Ser. A 1993, 105, 271. (7) Tyryshkin, A. M.; Dikanov, S. A.; Evelo, R. G.; Hoff, A. J. J. Chem. Phys. 1992, 97, 42. (8) Lee, H.-I.; McCracken, J. J. Phys. Chem. 1994, 98, 12861. (9) Kevan, L. In Time Domain Electron Spin Resonance; Kevan, L., Schwartz, R. N., Eds.; Wiley: New York, 1979; Chapter 8. (10) Kevan, L.; Bowman, M. K.; Narayana, P. A.; Boeckman, R. K.; Yudanov, V. F.; Tsvetkov, Y. D. J. Chem. Phys. 1975, 63, 409.

Po¨ppl and Kevan (11) Kevan, L. Acc. Chem. Res. 1987, 20, 1. (12) Ho¨fer, P. J. Magn. Reson., Ser. A 1994, 111, 77. (13) Ponti, A.; Schweiger, A. J. Chem. Phys. 1995, 102, 5207. (14) Ho¨fer, P.; Grupp, A.; Nebenfu¨hr, H.; Mehring, M. Chem. Phys. Lett. 1986, 132, 279. (15) Shane, J. J.; Ho¨fer, P.; Reijerse, E. J.; de Boer, E. J. Magn. Reson. 1992, 99, 596. (16) Gemperle, C.; Aebli, G.; Schweiger, A.; Ernst, R. R. J. Magn. Reson. 1990, 88, 241. (17) Rowen, L. G.; Hahn, E. L.; Mims, W. B. Phys. ReV. 1965, 137, A61. (18) Anderson, M. W.; Kevan, L. J. Phys. Chem. 1986, 90, 6542. (19) Po¨ppl, A.; Newhouse, M.; Kevan, L. J. Phys. Chem. 1995, 99, 10019. (20) Po¨ppl, A.; Kevan, L. Langmuir 1995, 11, 4486.

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