9008
J. Phys. Chem. 1995, 99, 9008-9016
W-Band (95 GHz) EPR Spectroscopy of Nitroxide Radicals with Complex Proton Hyperfine Structure: Fast Motion Tatyana I. Smirnova,*yt Alex I. Smirnov,s R. B. Clarkson,"."and R. Linn Belford'" Illinois EPR Research Center and Departments of Chemistry, Veterinary Medicine, and Intemal Medicine, University of Illinois at Urbana-Champaign, 506 South Mathews Street, Urbana, Illinois 61801 Received: February 13, 1995@
Many dynamic processes in liquids fall into the rotational motion regime with correlation times of lo-" to s, which are difficult to probe by conventional electron paramagnetic resonance (EPR) spectroscopy (8.8-9.5 GHz, X-band). At 95 GHz (W-band), the range of rotational correlation times (TR) measured by EPR for the typical nitroxide radicals is extended by a factor of 7 toward short times, producing more pronounced motional effects on the line width at the same ZR. However, for protonated nitroxide spin probes, the inhomogeneous broadening caused by proton superhyperfine (shf) interactions still contributes significantly to motionally narrowed 95 GHz spectra, and this makes direct estimation of TR inaccurate. A multifrequency approach to solve this problem is reported. Information on proton hyperfine interactions can be obtained from X-band spectra. This significantly improves the accuracy of T2-I determination from W-band data without additional NMR or ENDOR experiments. The utility of this approach is demonstrated by two examples of nitroxide probes with complex superhyperfine structure: (i) 3-doxyl- 17P-hydroxy-5a-androstane(probe #1) and (ii) 3-maleimido-PROXYL (probe #2). EPR spectra of these probes at both X- and W-bands were studied. X-band EPR spectra from probe #1 revealed a well-resolved proton hyperfine structure; hyperfine coupling constants were determined by least-squares computer simulation. These hyperfine constants were used for successful simulations of the spectra at W-band, where proton hyperfine structure is not resolved. Another way to correct for inhomogeneous broadening is to use experimental X-band spectra measured near the limit of complete motional narrowing as an approximation of inhomogeneous envelope functions to fit experimental spectra obtained at W-band. This methodology can be especially useful when proton hyperfine structure at X-band is poorly resolved, as it is for probe #2. The spectra at both frequencies were analyzed with a computer program for inhomogeneous line width simulatiodfitting based on a fast convolution algorithm and a Levenberg-Marquardt optimization. Microwave phase effects present in W-band spectra were corrected directly by an adjustment of the microwave phase shift in the fitting algorithm. Results are analyzed in terms of anisotropic Brownian diffusion theory.
Introduction Studies of rotational dynamics of nitroxide spin probes benefit from the utility of very high frequency (VHF, ue > 90 GHz) EPR. This has been demonstrated in a variety of systems.'-3 The enhanced g-value resolution of VHF EPR allows accurate measurements of g- and A-tensors, which are necessary for motional analysis. The range of measurable correlation times is also extended, with increase of the resonance frequency, toward both fast and slow motion. For example, at 94 GHz the limit for measurable correlation time ZR for most nitroxide radicals is about one-seventhof that for traditional X-band (8.89.5 GHz) EPR spectroscopy. Since many dynamic processes in liquids fall into the 1O-Io to s range, VHF EPR appears to be suitable for probing molecular dynamics in such systems using a variety of known nitroxide spin probes or spin labels. In the fast-motion limit, the homogeneous line width (T2-I or ABL,-,) is a function of nitrogen nuclear spin number (mN):
* To whom correspondence should be addressed.
' Department of Chemistry, University of Illinois at Urbana-Champaign.
' Department of Intemal Medicine, Ufiiversity of Illinois at UrbanaChampaign. Department of Veterinary Medicine, University of Illinois at UrbanaChampaign. Abstract published in Advance ACS Abstracfs, May 15, 1995. @
0022-365419512099-9008$09.00/0
where A , B , and C are the line width parameters, which can be expressed in terms of spectral densities and also magnetic parameters of the radical and rotational diffusion t e n s ~ r . ~ . ~ . ' ~ Line widths, as directly measured in continuous wave (CW) EPR experiments, cannot be used in eq 1 because EPR spectra of nitroxides are subject to inhomogeneous broadening (even for deuterated nitroxides5). In VHF EPR experiments with single-channel detection the spectra may also be distorted by an admixture of dispersion contribution.2,6 EPR spectra can be additionally homogeneously broadened by nitroxide-nitroxide spin-exchange effects andlor spin-exchange broadening caused by oxygen for non-deoxygenated samples. While the spinexchange effects can be virtually eliminated by decreasing the nitroxide concentration and thorough sample deoxygenation, the main source of inaccuracy, inhomogeneous broadening, should be corrected during data processing. The main contributor to inhomogeneous broadening of nitroxide lines is the hyperfine interactions with protons (or deuterons for deuterated probes). In most cases, the proton hyperfine coupling constant aHisois small compared to the nitrogen coupling constant aNiso(aHisJaNiso 0.0257);thus, the line width dependence on mH can be neglected. Additional reasons for the broadening are inhomogeneities in magnetic field
0 1995 American Chemical Society
EPR Spectroscopy of Nitroxide Radicals and the hyperfine interactions with I3C and 14Nisotopes present in the radical molecule in natural abundance. Correction for inhomogeneous broadening, especially for poorly resolved proton hyperfine structure (or superhyperfine-shf), is a challenging task in EPR spe~troscopy.~ One approach is to measure the proton hyperfine coupling constant by NMR or ENDOR.598 Assignment from NMR spectra of numbers of nuclei with a given hyperfine constant is not easy, since they are usually not well resolved, and is even more difficult in the case of ENDOR experiment^.^ After the assignment, these constants are usually adjusted to fit the experimental EPR spectrum if the proton hyperfine structure is resolved. Since the proton coupling constants are also temperature-dependent, the analysis should be performed over the whole temperature range of the EPR experiment. When the coupling constants are much smaller than the homogeneous line width, the correction for inhomogeneous broadening can be simplified significantly, since the inhomogeneous line shape can be modeled by a Gaussian envelope f ~ n c t i o n . ~ One way to increase the accuracy of rotational correlation time measurements is to perform the experiments in such a way as to increase motional contributions to the overall line width compared to the inhomogeneous line width for the same sample at the same ZR. This condition is naturally satisfied at EPR frequencies higher than traditional X-band, for example, at 94 GHz (W-band). Although W-band nitroxide spectra are often more sensitive to the rotational modulation of the g-tensor, inhomogeneous broadening still contributes significantly to the overall line width, making the direct estimation of T2-I inaccurate. In this presentation we propose to use the shf information from X-band spectra in order to improve the accuracy of T2-I determination from W-band data without additional NMR or ENDOR experiments. The utility of our approach is demonstrated by two examples of nitroxide probes with complex superhyperfine structure: (i) 3-doxyl-17P-hydroxy-5a-androstane (probe #1) and (ii) 3-maleimido-PROXYL (probe #2). EPR spectra of these probes at both X- and W-bands were studied. X-band EPR spectra from probe #1 revealed a well-resolved proton hyperfine structure, which allowed determination of temperature-dependenthyperfine coupling constants via computer simulation. Then, these known hyperfine constants were used for successful simulations of the spectra at W-band, when proton hyperfine structure was not resolved. We propose another, simpler way of correcting for inhomogeneous broadening that is often useful. In this method, the experimental spectrum measured at X-band near the limit of complete motional narrowing can be used as an approximation of an inhomogeneous envelope function to fit experimental spectra obtained at W-band. This methodology can be especially useful when proton hyperfine structure at X-band is poorly resolved, as it is for probe #2. The proposed methodology allowed us to fit experimental W-band spectra without knowledge of proton hyperfine constants and assigning the hyperfine structure to groups of protons. The spectra at both frequencies were analyzed with a computer program for inhomogeneous line width simulatiodfitting based on a fast convolution algorithm and a Levenberg-Marquardt optimization.6 Microwave phase effects present in W-band spectra were corrected directly by an adjustment of the microwave phase shift in the fitting algorithm. Results are analyzed in terms of anisotropic Brownian diffusion theory.
Experimental Section Sample Preparation. Solutions of 3-doxyl- 17P-hydroxySa-androstane (henceforthreferred to as probe #I; concentration
J. Phys. Chem., Vol. 99, No. 22, 1995 9009
0.5 mM) and 3-maleimido-PROXYL (henceforth referred to as probe #2; concentration 0.3 mM) in o-xylene were prepared. Spin probes were purchased from Sigma and were used without further purification. The solvent was obtained from Aldrich and additionally distilled. Quartz capillaries (i.d. = 0.7 mm, 0.d. = 0.87 mm, length = 10 cm, Vitro Dynamics, Inc., Rockaway, NJ) were custom bent ("L-shape") to fit the experimental setup and sealed at the short end. Solutions were drawn into the capillaries, deoxygenated by the freeze-thaw technique (5 cycles), and then sealed with a torch at the other end. Solutions for X-band measurements were deoxygenated in the quartz tubes (id. = 3 mm, 0.d. = 5 mm) by the same technique. X-Band EPR Spectroscopy. EPR spectra at X-band were taken with a Varian (Palo Alto, CA) Century Series E-112 spectrometer equipped with a TE102 cavity and Varian temperature controller (Model 906790). The magnetic field was measured by a tracking NMR Gaussmeter (Varian, Model 92980102P). A small T-type (copper-constantan) thermocouple (Omega Engineering, Stamford, CT) was placed just outside the EPR-sensitive region of the cavity. Temperature was measured with an Omega Engineering (Model 410AlA) digital temperature indicator. During the measurement, the temperature readings were stable and reproducible within f 0 . 2 "C; however, the accuracy of temperature measurements at the sample site was estimated to be f0.5 "C because of possible temperature gradients within the dewar i n ~ e r t .After ~ temperature stabilization, spectra were continuously recorded until no changes in line shape were observed. At each temperature, the last spectrum in this sequence was saved for further analysis. Data acqusition was carried out by means of an IBM personal computer with an IBM analog-digital card, running a commercial software package (Scientific Software Services, Bloomington, IL). W-Band EPR Spectroscopy. The W-band (94 GHz) spectrometer constructed at the University of Illinois EPR Research Center is described elsewhere.I0 The magnetic field was supplied by a Varian (Palo Alto, CA) XL-200 superconductive magnet. The magnetic field was scanned with a roomtemperature air-cooled solenoid coil placed inside the roomtemperature bore of the magnet. The scan and the center of the magnetic field were calibrated with a Metrolab precision NMR teslameter PT 2025 (GMW Associates, Redwood City, CA). At low temperature, the validity of the scan calibration was controlled by monitoring the electric current in the scanning coils. The homogeneity of the magnetic field over the sample region is estimated to be better than 20 mG. The microwave frequency is assured with a source-locking microwave counter (Model 578, IEP Microwave Inc., San Jose, CA). The cavity was a cylindrical type (n = 2 or 3 depending upon tuning). The quality factor of the unloaded cavity is 4000. The cavity is fixed inside a bass waveguide block which provides excellent mechanical and thermal stability. Microwave detection is provided by a tunable Shottky diode (Hughes Aircraft Company, Microwave Products Division, Torrance, CA) with a low-noise preamplifier and bias current supply. Lock-in amplifier SR530 (Stanford Research Systems, Inc., Sunyvale, CA) was used for phase-sensitivedetection at 100 kHz magnetic field modulation. The sample temperature was monitored by two Fluke digital thermometers (Model 5 1, Fluke, Palatine, IL) equipped with K-type (aluminum-nickel alloy) thermocouples fixed inside the upper and lower parts of the microwave cavity block. For measurements above room temperature, air flow was directed through the heater into the bore of the magnet to heat the whole cavity assembly. By adjusting the heating element
mln
9010 J. Phys. Chem., Vol. 99, No. 22, 1995
Smimova et al. TABLE 1: Magnetic Parameters Measured from Rigid-Limit Samples at 94 GHz for 3-Doxyl-17~-hydroxy-5a-androstane (Probe #1) in o-Xylene 94.3 GHz
** *
2.00913 3 x 2.0061 3 x 2.00231 f 3 x 10-j 2.00585 5 x 2.00584 5.3 0.2 4.9 0.2 32.4 0.2 14.2 & 0.3 14.3
** *
33450
33500
33550
33600
33650
33700
33750
Magnetic Field ( G )
Figure 1. Rigid limit ( T = -135 "C) 94.3 GHz spectrum of 3-doxyl-
+ +
(g) = (gr g, gJ13. Measured from fast-motion spectra at 94.3 GHz. y e is the magnetogyric ratio of the free electron. (A) = A, A, A,)/3.
+ +
17P-hydroxy-5a-androstane (probe # I ) in o-xylene (solid line) and the best least-squares simulation (dashed line) with magnetic parameters given in Table 1.
voltage, we varied the cavity temperature. To cool the system below room temperature, the flow of nitrogen gas was passed through a heat-exchanger placed in a dewar with liquid nitrogen and then through an insulated line into the bore of the superconductive magnet to cool the whole cavity assembly. The temperature was considered stable if the readings of both thermometers were the same within the measurement accuracy, f 0 . 1 "C. The stability of the resonance frequency during the experiment also reflects the temperature stability. As in the X-band experiments, EPR spectra were taken until no changes were observed; the last spectrum in each sequence was saved for analyses. The quartz capillary with sample was coaxial with the cavity and did not change significantly the resonator quality factor. To avoid possible distortion of narrow EPR signals from nitroxides at fast motion by the automatic frequency control (AFC) system, the AFC circuit was switched off" after careful tuning to resonance frequency. In this mode, the microwave frequency stability was monitored with the EIP 578 microwave counter and was better than 1 ppm during the measurement time. Typical spectrometer settings for fast motion spectra were as follows: modulation amplitude, 0.09 G; microwave attenuation, 10 dB; scan width, 50.4 G; number of data points, 2048.
Results and Discussion Magnetic Parameters. Rotational motion of the nitroxide radicals can be analyzed if their magnetic parameters are measured accurately, for example, from the rigid limit (or "powder pattern") spectrum. As was shown,I2 these measurements are more accurate at very high EPR frequencies ('90 GHz) because of the enhanced g-value resolution. Canonical components of both A- and g-tensors for 3-DOXYL-17Phydroxy-5a-androstane (probe #1) in o-xylene were measured from the 94.3 GHz near-rigid-limit spectra at -150 "C (Figure 1). The initial correction for the observed microwave phase shift was accomplished in a similar way to that described by Budil et aL3 Then the spectrum was simulated with the SIMPOW programI3 (Illinois Research Center). The g- and A-tensor canonical components and the anisotropic line width were defined by a SIMPLEX least-squares optimization procedure. The resulting least-squares fit of the data is shown in Figure 1, and the corresponding magnetic parameters are listed in Table 1. Fast-Motional Data Analysis at 9.0 GHz. At temperatures from -50 to +50 "C, the motion of both EPR probes studied in this work falls into the fast-motional regime at both 94.3
3370
3380
3390
3400
3410
Magnetic Field (G)
Figure 2. X-band (9.05 GHz) experimental spectrum from 0.5 mM deoxygenated solution of 3-doxyl- 17P-hydroxy-5a-androstane (probe #1) in o-xylene at 9 "C corresponding to fast-motional regime.
and 9.0 GHz. The contribution to the homogeneous line width arising from the probe rotational motion is usually small at X-band ('0.1 G at 9 "C for ml = 0) and is difficult to measure for protonated nitroxide probes without computer modeling. For example, the X-band spectrum from probe #1 at T = 9 "C (Figure 2) demonstrates only small amplitude differences between m1 = 1 and m1 = 0 nitrogen hyperfine components. In order to obtain better digital resolution, we used 10 G scan ranges and 1000 data points to record separately the spectra from each of three nitrogen hyperfine components. Probe #1 exhibited a well-resolved proton superhyperfine structure within -50 "C < T < f 5 0 "C. Using the least-square simulation program,6 we found that the spectra can be described by an inhomogeneous line shape model that includes two types of nonequivalent protons. The fitting function for each of the nitrogen hyperfine components was written as follows:
where pl(B,BG,-,) is a Gaussian envelope of width ABG,-,; p2(B,allso,a2iso) is a proton hyperfine envelope with two coupling constants a'iso and a2iso;m(B,a,) is a Lorentzian line shape function (ajare the line-shape parameters such as isotropic g-value, Lorentzian width ABL,-,, and intensity); klB ko is included to describe a linear baseline with coefficients kl and b;and * represents a convolution operator:
+
J. Phys. Chem., Vol. 99, No. 22, I995 9011
EPR Spectroscopy of Nitroxide Radicals
A C
I
m
I
600 -v1 .1
3200
3201
3202
3203
3204
3205
c,
Magnetic Field ( G )
500
Figure 3. (A) Central nitrogen hyperfine component (" = 0) of X-band experimental spectrum from 0.5 mM solution of 3-doxyl-17Phydroxy-5a-androstane (probe #1) in o-xylene probe at T = 9 O C superimposed on results of least-squares fit shown as a dashed line (fit and experiment are almost identical). (B) Difference between experimental and simulated spectra (residual).
The merit function for the least-squares fit was constructed assuming the same standard deviations (a2(&) = 1) for all N data points of the experimental EPR spectrum Y(B): N
x2 = C [ Y ( B , )- F(4)l2
(4)
i= I
The following parameters were independently adjusted for each nitrogen hyperfine component during the Levenberg -Marquardt optimization: isotropic g-value; two different isotropic proton j = 1, 2); inhomogeneous broadening coupling constants (disO, parameter ABG,-, (same for all proton superhyperfhe components, measured as peak-to-peak); homogeneous line width, ABL,-, (same for all proton superhyperfhe components, measured as peak-to-peak); signal intensity; and the coefficients of the linear baseline. The initial simulation parameters were entered by the operator. The iterations were stopped after the of the previous value for a values of x2 are improved by second time. Since the spectra changed gradually with temperature, they fitted automatically into a sequential mode: the best of each spectrum was used as a first approximation for the next spectrum in the sequence. The best-fit results for the central (mN = 0) nitrogen hyperfine component are superimposed on the experimental spectrum in Figure 3A; curve 3B is the residual. Figure 3 demonstrates the good fit between experiment and simulation, with the residual showing only small oscillative deviations at the center of the signal. These deviations may be caused by a small instability in the magnetic field (about 3 mG is stability specified by the manufacturer) and/or by the effects of poorly resolved hyperfine interactions with remote protons, which were modeled as a Gaussian envelope. Figure 4 shows the variation of isotropic proton coupling constants and Gaussian line width derived independently for all three nitrogen hyperfine components in the temperature range studied (the data points for all components are superimposed on the plot). The estimated experimental errors (68% confidence intervals) are less than the size of the plot points. The temperature dependencies of both proton coupling constants and Gaussian line width are almost identical for different nitrogen hyperfine components and can be well approximated by linear functions (Figure 4). At temperatures T > 10 "C, the X-band spectra of probe #1 fall into the extreme narrowing regime: the homogeneous line
Q,
c
z
r"
1 I
C
B
1/ I
400c
,
,
,
,
,
.
,
250
Temperature
, 300
,
,
,
,
4 350
(KO)
Figure 4. Temperature dependence of proton hyperfine constants (V and 0 , hyperfine constants for two types of protons) and width of Gaussian envelope (0)for 0.5 mM solution of 3-doxyl-17P-hydroxySa-androstane in o-xylene (probe #1) as derived from X-band experiment. Fitting results for all three nitrogen hyperfine components (WZN) are superimposed on the same plot. Proton hyperfine constants for different m~ are almost identical. The estimated experimental errors (68% confidence interval) are less than the size of the plot symbols. Linear regressions shown as solid lines.
width extracted by spectral fitting was inaccurate and negligible compared to the width of the Gaussian envelope. At T -43 "C the resolution between proton hyperfiie components becomes insufficient to extract accurately all fitting parameters. At ABL,-, 2 1 G the proton hyperfine structure is not resolved and the fit based on eq 2 is not unique. Moreover, at T % -60 "C and below, an additional signal with ABL,-, % 5 G appeared; it may be related to the aggregation of probe #1 into small domains (similar to that observed by Smimov et ~ 1 . ' ~ ) . Therefore, the homogeneous line width ABL,-, was extracted by fitting function 2 only in the temperature range from -43 to 10 "C, although the nitrogen hyperfine splittings were measured at temperatures to f 6 4 "C. The estimated 68% confidence intervals for the homogeneous line width (ABL,-,) measured from X-band spectra were found to be large (up to 6-7%) because of a relatively large line width contribution from inhomogeneous broadening modeled as a Gaussian envelope (up to 95% of the overall line width for mN = 0 and T = 9 "C). Since both Gaussian and Lorentzian widths contribute to the observed line width, the accuracy in the ABL,-, determination can be improved significantly if the ABG,-, parameter is frozen during the fit. We have used the result of linear regression of ABG,-, data (Figure 4) to calculate the parameter hBGP-,(T) as a function of temperature. The reduced values of ABGP-,(T) were frozen during the next sequential fitting of the same data. As was expected, the values and the accuracy of the proton coupling constants were improved insignificantly, while the accuracy of the ABL,-, determination was improved at least sixfold. Line width parameters A , B, and C were calculated from the measured ABL,-, values and are shown in Figure 5 as a function of log(v/T) (empirical dependence = v(T) was taken from Viswanath et ~ 1 . ' ~ ) . Fast-Motional Data Analysis at 94.3 GHz. A typical 94.3 GHz EPR spectrum from probe #1 in o-xylene is shown in Figure 6 (T = 9.6 "C). Although the rotational motion of the
9012 J. Phys. Chem., Vol. 99, No. 22, 1995 h
t
4 e,
,
I
a
Smimova et al.
lo-'
1 t
4
e,
E
t
m
*9.0 C9.0
-2.6
-2.2
-2.4
-2.0
Figure 5. Line width parameters Ago, Bgo, and C ~measured O at 9.05 GHz for 0.5 mM solution of 3-doxyl- 17/3-hydroxy-5a-androstane (probe #1) in o-xylene as functions of log(vlT). Linear regressions shown as solid lines.
B
-
C
D 33580
33590
33600
33610
33620
M a g n e t i c Field ( G ) Figure 6. (A) Experimental W-band (94.3 GHz) spectrum from deoxygenated 0.5 mM solution of 3-doxyl- 17P-hydroxy-5a-androstane (probe #1) in o-xylene (T = 9 "C) fitted to different line shape models as described in the text. Corresponding residuals shown as B , C, and D.
probe is still falling into the fast-motion regime, the contribution to the homogeneous line width ABLp-parising from rotational motion is larger than that at X-band, and the proton superhyperfine structure is not resolved (compare to Figure 2 showing the X-band spectrum at the same temperature). To provide the necessary digital resolution for data analysis, we collected 2048 experimental points for each spectrum. A small modulation amplitude, 0.09 G, prevented line shape distortion. The spectra collected at 94.3 GHz (e.g., see Figure 6) are asymmetric because of an admixture of the dispersion signal which is usually present in high-frequency EPR In order to account for this dispersion contribution, the expression for the first derivative homogeneous line shape used in the fitting function (eq 2 ) was modified as follows:
8(B, - B ) cos A q
+ [4(Bo- B)2- ( B L 1 / J 2sin] Aq
AB^,,,)* + 4
( ~-, ~
1'1~
(5)
where A B L ~ / 2is a Lorentzian broadening, measured as line width
at half height of a signal, A is the area under the resonance absorption curve or the intensity of a signal, Bo is a resonance field, and Ag, is a phase shift ( A q = 0 corresponds to the absorption line). Initially, three line shape models were used to fit the experimental 94 GHz fast-motion EPR spectra from probe #l. In model 1 , the proton superhyperfine structure was modeled as a Gaussian envelope, and different homogeneous broadening ABL112(m~)was assigned to each of the nitrogen hyperfine components ". Although the ratio of the merit function x2 at the minimum to the square norm of the experimental signal was small (x'= x2/cp(B,) = 1.57 x the residual shown in Figure 6B revealed some significant deviations between the experiment and the fit. This model was rejected as unacceptable. In the next model ( 2 ) , we have included I3C satellite lines arising from two sets of nonequivalent I3Cnuclei (corresponding hyperfine constants were estimated from fitting of low-noise X-band spectra) as an additional nonadjustable envelope function pcl3(B) convoluted with the Gaussian envelope and the homogeneous line shape in the form of eq 5. The norm of the residual was improved significantly (x'= 0.86 x or by 45% compared to that of model l ) , although the deviations were still noticeable, especially near the my = 1 transition (residual shown in Figure 6C). In model 3, the fitting function was constructed by use of the temperature-dependent proton hyperfine constants, d,,,( r), j = 1, 2, measured in X-band experiments. The nonadjustable I3C satellite lines were included as in model 2. During the fitting procedure, the following parameters were adjusted: Lorentzian for each nitrogen component mK; line width, ABLl/z(m~) Gaussian envelope function, A B G 1 / 2 (to account for an additional broadening, e.g., inhomogeneities of magnetic field, etc.); microwave phase shift, Aq; signal intensity, A ; and the coefficients for the linear baseline, ki and ko. The best fit is superimposed on the experimental spectra in Figure 8A. The residual norm (Figure 6D) was further significantly improved ( y= 0.41 x The ratio of the merit function (eq 4 ) to the estimated standard deviations of the amplitude noise 02(B,) (the same 02(B,) were assumed for each of the spectral data points) at its minimum ~ 2 m l n /eu z2370) was close to the number of degrees of freedom (Y = 2038), assuring a "moderately" good fit.I6 The value of (xZmln/u2) depends on the estimates o2of the spectrometer noise as well as on assumptions that the errors u2(B,) in the signal intensity are normally distributed. In continuous-wave EPR some sources of experimental errors other than detector noise can be present, such as instabilities in magnetic field and/or frequency. This may explain why the standard deviation of the residual (fit using model 3 ) estimated over the region of the my = 1 line is larger than those measured for other parts of the spectrum. Another reason for this is a differential error in field calibration between X-band and W-band spectrometers; this would result in errors in the proton hyperfine and I3Chyperfine constants, since those were determined in the X-band experiment. The proton and I3Chyperfine constants cannot be measured from the W-band spectra because the corresponding spectral lines are not resolved (fitting with adjusting of these parameters will result in a nonunique fit). In spite of relatively large values of (x2,,,,,,/02) compared to degrees of freedom, model 3 seems to be the most suitable for fitting the W-band spectra from probe #1 at 9.6 "C. With decreasing temperature, the contribution from the homogeneous line width to the spectrum will further increase, and this will gradually eliminate all remaining features of the proton superhyperfine structure. Eventually, model 2 is ex-
J. Phys. Chem., Vol. 99, No. 22, 1995 9013
EPR Spectroscopy of Nitroxide Radicals
F ( B , B O , M , ~= J ~ ~ o ~ ~ ~ * ~ + ~ k,B ~ +, k,~ o , ~ L (6)
2.5 h
r?a -1
a 2.0
5
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4
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a
a
5 2
0.5
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.4
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0.0'' 0.0
'
'
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0.5
Linewidth parameter B ( A H
L
'
1.0
C) P-P' Figure 7. Comparison between A94 and B94 line width parameters for 0.5 mM solution of 3-doxyl- 17P-hydroxy-5a-androstane(probe #1) extracted using models 2 ( 0 )and 3 (0)from experimental 94.3 GHz EPR spectra over the temperature range -49 "C < T < 63 "C. The fitting models are described in the text. Solid line: linear regression of model 3 data over the whole temperature range (slope A94/B94 = 2.00, intercept A' = 0.24 G). Dashed line: linear regression of model 2 data over the interval of apparent linearity (slope A94/Bg4 = 2.16, intercept A' = -0.04 G).
where m(B,B0,ABLl/2,A~) is given by eq 5 . If only the absorption signal is measured, then A ~ I 0. The envelope function Fo(B) for probe #1 can be well approximated from the X-band measurements. Indeed, at X-band and T > 10 "C the main contribution to the homogeneous line width of probe #1 is the frequency-independent line width. The middle mN = 0 component of the X-band spectrum is the narrowest and can be taken as an approximation of the envelope function. The second-order effects on the proton hyperfine constants are estimated to be less than 1 mG and can be neglected. Then each of the nitrogen hyperfine components of the W-band spectrum at the same temperature can be approximated by eq 6, where the frequency-dependent part of the homogeneous broadening is included in m(B,Bo,ABL,/2 (mN),hqI). Frequency-independenthomogeneous broadening is already included in function Fo(B). (Convolution of two Lorentzian functions gives a Lorentzian function with the width equal.to the sum of the initial widths.) When this model was applied in the fitting of the W-band spectra, we found that, to account for the effects of small inhomogeneities of the magnetic field and g-strain, it was necessary to include an additional Gaussian envelope p1(B,ABG1,2) in the fitting functions as follows:
W , B 0 , h B L , , 2 )= pected to fit the experimental spectrum as well as model 3. However, at temperatures higher than 9.6 "C, the information on proton superhyperfine coupling can be crucial for extracting the correct line-width parameters. As a comparison, we have used both models to fit the W-band spectra over the whole temperature range. The line width parameters A94, B94, and C94 were computed from the extracted homogeneous line width ABL,-p (eq 1). Plots of A94 vs B94 in the temperature range -49 "C < T < 63 "C computed from both data sets are shown in Figure 7. The A94 and B94 parameters derived with the use of model 3 can be well fitted to a straight line with a slope of 2.00 and an intercept of 0.24 G (arising from the frequencyindependent contribution to the parameter A). According to the theory, the ratio A9dB94 is temperature-independent, as is observed in Figure 7. In contrast, the values of A94 obtained under the fitting model 2 all lie lower than those of model 3, and the A94 vs B94 data deviate from the linear dependence at temperatures above 10 "C. Although A94 vs B94 data points (model 2) at temperatures below 10 "C are apparently linear, the linear regression of these data points gave a slope of 2.16 with an intercept of -0.04 G. This shows that neglecting the proton hyperfine structure can significantly alter the apparent a94 vs B94 slope, and this may cause an error in the determination of rotational anisotropy. The estimated frequency-independent line width (A' = -0.04 G) is obviously incorrect. At T > 10 "C the line width A and B parameters obtained with model 2 clearly contradict the motion theory. Although model 3 was found to be the most accurate, it does require time-consuming measurements of the proton and CI3 hyperfine constants and the assignment of these constants to the nuclei. The measurements of the homogeneous line width, A B L 1 / 2 , can be significantly simplified if the whole inhomogeneous envelope function Fo(B) is known. Then, for a given homogeneous line width, ABL1/2,the mixed absorptioddispersion EPR spectrum can be written as
[ ~ , ( B ) * p , ( B , h B G , / , ) * ~ ( ~ , ~ 0 , ~ L 1+ / 2k,B , A ~+) 1ko (7) The introduction of a Gaussian envelope can also be helpful for modeling the W-band spectra in a broader temperaturerange. For probe #1, both proton hyperfine constants decrease slightly with temperature (Figure 4; less than 30 mG per 100 "C), and an additional Gaussian width may "compensate" for such temperature variations. The fitting function (eq 7) also accounts for any I3C satellite lines (since they are present in the X-band spectrum Fo(B)) without actual measurements of the corresponding hyperfine constants and assignments of them to the nuclei. When eq 7 was applied for fitting of the W-band spectrum at 9.6 "C (Figure 6; Fo(B) taken as the mN = 0 component of the X-band measured at T = 61 "C), the residual norm (P= 0.40 x was about the same as that for the best fit under That no significant deviations model 3 (X2 = 0.41 x between the fit and the residual were found demonstrates an acceptable fit. Since Fo(B) in model 4 is taken from the X-band experiment, the magnetic field at both X- and W-band must be accurately calibrated. Additionally, the samples for both frequencies should be equally deoxygenated, and the concentration should be kept the same, since the frequency-independent line width and the proton hyperfine constants vary with the concentration (mainly because of the spin-exchangebetween identical species; this interaction between identical radicals is frequencyindependent). The same requirements are necessary for model 3 as well. Model 4, based on eq 7, was further tested by fitting the same set of W-band spectra over the whole temperature range. A comparison between A94 and B94 parameters extracted with models 4 and 3 is shown in Figure 8. The data obtained with model 4 can be well approximated by a straight line with a slope of 2.05, which is close to that found with model 3 (2.00). The intercept of 0.036 G is close to zero, as it should be, since the frequency-independent line width A' was already accounted
9014 J. Phys. Chem., Vol. 99, No. 22, 1995
Smimova et al.
h
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Figure 8. Comparison between A94 and B94 line width parameters for 0.5 mM 3-doxyl- 17/3-hydroxy-5a-androstane(probe #l). Parameters extracted under the most accurate line shape models (3) (0)and (4) (A)from the experimental 94.3 GHz EPR spectra over the temperature range -49 "C < T < 63 "C. The fitting models are described in the text. Estimated experimental errors ( 6 8 8 confidence interval) are less than the size of the plot symbols. Linear regression of two data sets over all temperatures gave very similar slopes (A94/B94 = 2.00 for model 3, A94/B94 = 2.05 for model 4). The intercept for model 4 was close to 0 (A' = 0.036 G), as it should be, since the frequency-independent line width was already subtracted from A94 during the fitting.
Figure 10. (A) Experimental W-band (94.3 GHz) spectrum from deoxygenated 0.3 mM solution of 3-maleimido-PROXYL (probe #2) in o-xylene (T = 9 "C) was fitted to line shape models 4 and 2, as described in the text. Corresponding residuals shown as B and C.
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Figure 11. Line width parameters A94, B94, and C94, measured at 94.3 GHz for 0.3 mM solution of 3-maleimido-PROXYL (probe #2) as a function of log(q/n?.
3202
3204
3206
3208
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Magnetic Field ( G ) Figure 9. Central nitrogen hyperfine component ( m =~0) of X-band experimental spectrum from deoxygenated 0.3 mM solution of 3-maleimido-PROXYL (probe #2) in o-xylene at T = 9 "C in the fast-motional limit. Poor resolution between proton superhyperfine lines complicates the hyperfine and dynamic analysis.
for in the function Fo(B). Figure 8 also shows that the A94/B94 data obtained with model 4 are linear over the whole temperature range; this is in good agreement with theory. Model 4 can be especially useful when detailed information on the proton hyperfine coupling is difficult to obtain. One example is probe #2, for which an X-band spectrum (mN = 0 component) is given in Figure 9. In the fast-motional regime, the EPR spectrum of this probe is also subject to a substantial inhomogeneous broadening, although the proton hyperfine structure is resolved only at T > -5 "C. The resolution is poor, complicating the fitting of the spectrum and proton hyperfine analysis. Therefore, for this probe, information on the rotational dynamics may not be determined reliably from the X-band data. The W-band spectrum of probe #2 (Figure 10A) can be well fitted using model 4 and the experimental X-band spectrum; the residual is shown in Figure 10B. Model 2, in which the proton hyperfine structure was approximated by a Gaussian
envelope, failed to give a satisfactory fit (corresponding residual shown in Figure 1OC). The W-band EPR spectra of probe #2 were measured in the same range as for probe #1 and least-squares-fitted under model 4. Calculated line width parameters A, B, and C are given in Figure 11 on a logarithmic scale as a function of log(q/T). A plot of parameter A94 vs B94 for this probe can be well fitted by a straight line over the whole temperature range (-50 "C < T < 73 "C) with a slope of 2.27 and an intercept of 0.066 G (Figure 12). Independence of the slope of A94 vs B94 from the temperature and good linearity of the line width parameters in the log(q/T) scale at the lower temperatures are both in agreement with theory. The example of probe #2 further demonstrates that model 4, in conjunction with the multifrequency EPR measurements, can be very useful for characterization of the fast rotational motion of the nitroxides even if their proton superhyperfine structure is unknown. Rotational Diffusion Anisotropy of Probe #1. Line width parameters A, B, and C (eq 1) determined from the EPR experiment can be used to derive the anisotropy of rotational Brownian diffusion of the probe. When nonsecular densities are neglected but secular/pseudosecular reduced spectral densities are retained, then the A , B, and C line width parameters are proportional to the rotational correlation time t ~ The . ratios of these parameters impose the linear constraints on the anisotropy parameters which may be expressed in the form of allowed. ' ~ was shown recently, A and value equations ( A V E ' S ) . * , ~ As
J. Phys. Chem., Vol. 99, No. 22, 1995 9015
EPR Spectroscopy of Nitroxide Radicals h
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B parameters dominate over C at 250 G H Z . ~ At , ~ this EPR frequency, the nonsecular densities reach maxima at ZR RZ 0.64 ps (Le.,in the limit of extreme narrowing) and can be neglected for the slower rotations-those with ZR t 1.O ps. For rotations with ZR t 1.O ps the AIB ratio imposes a key constraint on the principal values Ri of the diffusion tensor R through the following AVE:
Figure 13. Determination of anisotropy parameters ex and e,, for 3-doxyl- 17P-hydroxy-5a-androstane(probe #1) in o-xylene using allowed-value equations calculated from line width parameters measured at 94.3 GHz (solid line, A9dB94 = 2.05; long-dashed line, A9dB94 = 2.00) and C90 and B9o line-width parameters at 9.0 GHz. Anisotropy parameters derived from the intersections of these lines: ex = 1.6 f 0.5, er = 5.8 f 1.0. h
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where ex = RJR,, eu = R,/R,, and the constants a and /3 are the functions of AIB, principal values of the A- and g-tensors, and the magnetic field as described by Budil et aL3 At 94 GHz, the A and B parameters still prevail over C. For a nitroxide radical with typical magnetic and anisotropy parameters, the nonsecular terms can be neglected for ZR t 20 ps, which corresponds to parameter B t 0.10 G. Most of the line width parameters measured for probe #1 satisfy this condition. Using the magnetic parameters of probe #1 listed in Table 1 and two slightly different AIB ratios obtained under fitting models 3 and 4, we have obtained the two AVE lines shown in Figure 13. Another independent constraint on the anisotropy parameters can be obtained from the X-band measurements-specifically from the c9,&9,0 ratio. The plot of C vs B line width parameters measured for probe #1 in the fast-motional regime is shown in Figure 14. All these parameters were measured for the interval 0.3 x lo-* -= q1T < 1.0 x lop2(cPK-I), where the contribution of the nonsecular spectral densities may become important and the apparent c9,0/B9.0 ratio may not be used for calculation of A V E ' S . ~ . 'The ~ measurements at higher qlT were complicated by the appearance of an additional exchange-narrowed signal possibly explained by aggregation of the probe species. We have used the apparent C9.0 vs B9,o slope to calculate a first approximation of the AVE and the anisotropy parameters (e,, er). Then the spectral parameters B and C were computed through the program developed by Budills for a set of (e,, er) values chosen in the vicinity of the approximated (e,, ey)values. The following reduced nonsecular spectral densities were used:
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L mG) P-P' Figure 14. C9 0 and B9 0 line width parameters measured for 0.5 mM solution of 3-doxyl- 17p-hydroxy-5a-androstane(probe #1) in o-xylene at 9.0 GHz (C9.dB9.0 = 1.50). Theoretical curve, which includes the contribution from reduced nonsecular spectral densities, is shown as a solid line.
3
Linewidth parameter B (AH
where the empirical parameter E was set to 1.0 (Brownian rotational diffusion). This allowed us to derive a numerical approximation of an apparent C9 dB9 0 slope within the studied temperature interval vs the anisotropy parameters. This approximation was used to correct C9 dB9 0 data for the nonsecular spectral densities (theoretical C9 0 vs B9 0 curve shown in Figure 14 as a solid line) and then to derive the AVE line shown in Figure 13. Intersections of AVE's occur at ex = 1.77, e, = 6.14 (AIB = 2.05); and ex = 1.48, = 5.54 (AIB = 2.00). Relative variations of these parameters from the average (ex= 1.6, er = 5.8) are 18% for ex and 10% for e,. The analysis shows that these errors are comparable with the other sources of errors affecting (@,,e,)such as, for example, uncertainties in the magnetic parameters. Using the estimates of parameter uncertainties, we arrived at the following average anisotropy parameters: ex = 1.6 f 0.5, = 5.8 f 1.0. This shows that probe #1 is experiencing a significant degree of rotational anisotropy and that the fastest rotation occurs about the y magnetic axis, which corresponds most closely to the longest axis of the molecule.
9016 J. Phys. Chem., Vol. 99, No. 22, 1995
Smimova et al.
As was pointed out by Freed and c o - w o r k e r ~ , ~high,~ frequency EPR spectra are more sensitive to the rotational anisotropy than 9.0 GHz spectra. In principle, if the line width parameter C is measured from high-frequency spectra with sufficient accuracy, then the C/B ratio can be used as an independent constraint for the rotational diffusion t e n ~ o r .Since, ~ at 250 and 95 GHz, parameter C is calculated as a difference between large line widths, the error in C and therefore in the ratio CIB can be large. For example, for probe #1, the ratio C94/B94 is 0.16 f 0.02. This value is close to the theoretical C94/B94 = 0.144 calculated for the chosen anisotropy parameters (ex = 1.6, ey = 5.8). The question of whether the anisotropy parameters can be accurately determined from the low-noise W-band spectra alone remains to be studied. The self-consistency of X-band and W-band data (and therefore the accuracy of our fitting technique) is also provided by a comparison of parameters B measured at the same v/T. When the nonsecular spectral densities can be neglected (v/T 2 1.0 x cPK-I), then the ratio B9.dB94 is equal to the ratio of the magnetic fields (=0.0960). The B9.dB94 ratio estimated from the data points near v/T = cPK-' was 0.0952 i 0.0038 (model 3) and 0.0979 f 0.0039 (model 4). Therefore, both fitting models are in excellent agreement with theory. Moreover, at lower v/T both models give slightly higher B9.dB9.4ratios (0.1034 and 0.1002), reflecting the contributions of nonsecular spectral densities at X-band.
groups of protons. The I3C satellite lines are also accounted for automatically in this model. The line-width parameters measured at two frequencies were used to estimate the anisotropy of rotational diffusion for probe #1. Comparison of linewidth parameters shows agreement with the theory of fully anisotropic Brownian diffusion. The spectral fitting technique developed here, based on both X- and W-band measurements, may be used for an accurate analysis of the fast rotational dynamics of the probes without direct assignment of the proton superhyperfine structure (such as probe #2). This additionally demonstrates the advantages of the multifrequency approach in rotational dynamics studies.
Conclusions
References and Notes
The motion-narrowed EPR spectra from solutions of the two nitroxide probes 3-doxyl- 17/3-hydroxy-Sa-androstane and 3-maleimido-PROXYL in o-xylene have been studied at 9.0 and 94.3 GHz. Using a very accurate spectral simulation algorithm,6 we demonstrate that the X-band spectra from the first probe fall into the regime of extreme narrowing at T 2 10 "C, and dynamics information cannot be derived by fitting of continuous wave spectra. Although the frequency-dependent homogeneous line width for a given ZR at 94.3 GHz is about sevenfold larger than that at 9.0 GHz, its determination for probe #1 is complicated by unresolved proton superhyperfine structure and a large extent of inhomogeneous broadening. This problem can be solved by using the information on the superhyperfine splitting obtained at the X-band frequency. We have tested several fitting models for the W-band spectra. A satisfactory agreement between the experimental and the simulated spectrum was achieved with two fitting models. One model was designed to use the 13C and temperature-dependent proton hyperfine constants measured in X-band experiment. Another model (model 4 in the text) was based on approximating the inhomogeneous envelope function by the experimental X-band spectrum measured in the regime of extreme motional narrowing. Similar residual norms were observed for both models. Line-width parameters extracted with these two models were only slightly different. For example, the A94B94 ratios differed by less than 3%. The use of the proposed model 4 for fitting of high-frequency EPR spectra may be advantageous because it requires neither the values of proton hyperfine constants nor assigning the hyperfine structure to the
Acknowledgment. This research used the facilities of the Illinois EPR Research Center (National Institutes of Health Biomedical Research Technology Program), supported by NIH Grant P41RR01811. This work was in part supported by NIH Grant GM-42208. The authors thank Prof. David E. Budil (Northeastern University, Boston) for kindly providing code of the ANDEN program and Dr. Mark J. Nilges (University of Illinois) for discussions of rigid-limit spectral simulations and the SIMPOW program. We also thank Prof. G. B. Schuster's research group for providing compounds and for stimulating part of this work in the context of applications to photochemical properties and relaxation mechanisms of dye molecules (supported by NIH Grant GM28190).
(1) Lebedev, Ya. S. In Modern Pulsed and Continuous-Wave Electron Spin Resonance; Kevan, L., Bowman, M. K., Eds.: John Wiley & Sons: New York, 1990; Chapter 8. (2) Earle, K. A,; Budil, D. E.: Freed, J. H. J . P h y . Chem. 1993, 97, 13289. (3) Budil, D. E.; Earle, K. A.; Freed, J. H. J . Phjs. Chem. 1993, 97, 1294. (4) Freed, J. H. J . Chem. Phys. 1964, 41, 2077. ( 5 ) Bales, B. L. In Biological Magnetic Resonance; Berliner, L. J., Reuben, J., Eds.; Plenum Press: New York, 1989; Vol. 8, Chapter 2. (6) Smimov. A. I.; Belford, R. L. J . Magn. Reson. 1995. 113, 67-73. (7) Jolicoeur, C.; Friedman, H. L. Ber. Bunsen-Ges. Phys. Chem. 1971, 75, 248. (8) Ottaviani, M. F. J . Phys. Chem. 1987, 91, 779. (9) Morse, P. D., 11; Magin, R. L.; Swartz. H. M. Rev. Sci. Instrum. 1985, 56. 94. (10) Wang, W.; Belford, R. L.; Clarkson, R. B.; Davis, P. H.; Forrer, J.; Nilges, M. J.; Timken, M. D.; Watczak, T.; Thumauer, M. C.; Norris, J. R.; Morris, A. L.; Zwang, Y. Appl. Magn. Reson. 1994, 6 , 195. (11) Smirnov, A. I.; Norby, S.-W.: Walczak, T.; Liu. K. J.; Swartz. H. M. J. Magn. Reson. 1994, B103, 95. (12) Ondar, M. A.; Grinberg, 0. Ya.; Dubinskii, A. A,; Lebedev, Ya. S. Sov. J . Chem. Phys. 1985, 3, 781. (13) Nilges, M. J. Ph.D. Thesis, University of Illinois, 1979. (14) Smirnov. A. I.: Poluectov. 0. G.: Lebedev, Ya. S. J . Magn. Reson. 1992, 97. 1. ( 1 5 ) Viswanath, D. S.; Natarajan, G. Data Book on the Viscosig of Liquids; Hemisphere Publishing Corporation: New York, 1989. (16) Press. W. H.: Teukolski, S. A.: Vetterling, W. T.; Flannery, B. P. Numerical Recipes in Fortran, 2nd ed.; Cambridge University Press: Cambridge, U.K., 1986; p 655. (17) Kovert, B. A. J . P h y . Chem. 1981, 85, 229. (18) Budil, D. E. ANDEN Program for calculating line width parameters which takes into account the possibility of a completely anisotropic diffusion tensor.
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