Analysis of Microwave Fast-Passage Effects in Optically Detected Magnetic Resonance Spectra

JOURNAL OF MAGNETIC RESONANCE, ARTICLE NO.

Series A 119, 82–89 (1996)

0054

Analysis of Microwave Fast-Passage Effects in Optically Detected Magnetic Resonance Spectra JIE Q. WU, ANDRZEJ OZAROWSKI,

AND

AUGUST H. MAKI

Department of Chemistry, University of California, Davis, California 95616 Received October 30, 1995

Optically detected magnetic resonance (ODMR) transitions of photo-excited triplet states in zero magnetic field usually are not measured under slow-passage conditions. At a typical temperature of about 1.2 K, spin–lattice relaxation is largely quenched; return to steady-state sublevel populations occurs primarily by electronic decay and optical pumping via the ground state. This process is often slower than the microwave passage time through the homogeneous line, leading to fast-passage effects observable in the inhomogeneously broadened ODMR band. These include a sweep-ratedependent shift of the peak frequency and distortion of the band shape. A mathematical model that predicts the spectrum of phosphorescence-detected ODMR as a function of microwave sweep rate is presented. The independent variables are band center, band shape and width, sublevel decay constants, and radiative decayconstant ratio. The model is applied to the ÉDÉ 0 ÉEÉ, and 2ÉEÉ transitions of tryptophan in lysozyme, and to the 4.36 GHz transition of 1-methyl-2-thiouracil. Nonlinear least-squares fitting of the spectra to the model produces consistent band center frequencies and widths, independent of microwave sweep rate. The reliability of a decay constant increases with its radiative quantum yield. The peak frequency shift with sweep rate is very nonlinear; its determination by extrapolation to zero rate is not reliable. q 1996

lattice relaxation, SLR, is effectively quenched, and the populations of the magnetic sublevels are governed by the kinetics of optical pumping and decay to the electronic ground state. The reestablishment of the initial stationary-state sublevel populations after they have been modified by microwave saturation relies on these processes rather than on SLR as it does in ordinary EPR. The correct ‘‘slow-passage’’ ODMR lineshape of a homogeneously broadened line is only achieved in the limit of an infinitely slow microwave sweep rate, but an acceptable approximation of the lineshape is nonetheless achieved provided that dn /(d n /dt) @ ti ,

where ti is the largest sublevel lifetime, i Å x, y, or z, dn is the homogeneous linewidth, and d n /dt is the microwave sweep rate. A large number of ODMR studies have been carried out on biological samples such as proteins, whose chromophores are subjected to inhomogeneous broadening of both the optical spectra and the ODMR spectra (3–6). These are the result of heterogeneity of the microenvironments that are frozen out at cryogenic temperatures. Microwave hole-burning measurements carried out on the ODMR lines of tryptophan in typical proteins suggest a homogeneous linewidth £5 MHz (7–9), although the inhomogeneously broadened band is typically on the order of 100 MHz or greater in width. Since the condition of slow passage (Eq. [1]) refers to the homogeneous linewidth, it is clear that very long experimental sweep times would be required to obtain an undistorted shape for a typical inhomogeneously broadened band of tryptophan. Since ti É 10 s, and assuming dn É 1 MHz, it is easy to see that durations on the order of 10 4 s would be required to approximate slow passage through a band with a width of 100 MHz. Since the relatively small signal level of tryptophan typically requires several cycles of signal averaging, it is clear that such sweep times are totally impractical. In practice, sweep rates less than about 10 MHz/s have been rarely employed for practical reasons. Thus, none of the tryptophan ODMR spectra that have been

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INTRODUCTION

In carrying out optically detected magnetic resonance spectroscopy (ODMR) of photo-excited triplet states (1, 2), EPR is frequently monitored via the phosphorescence intensity of the sample during continuous optical pumping. In many cases, ODMR is carried out in zero applied field; the microwave frequency is swept through the magnetic resonance line. The zero field splittings, ZFS, are then obtained directly from the frequencies of the observed phosphorescence responses. This optical method of detecting EPR, however, leads to difficulties in the experimental determination of magnetic resonance frequencies and lineshapes that do not occur in the typical EPR absorption or dispersion measurement. These problems arise from the usual conditions under which triplet-state ODMR is carried out, temperatures in the liquid helium range (typically 1–4 K) at which spin– 82

1064-1858/96 $18.00 Copyright q 1996 by Academic Press, Inc. All rights of reproduction in any form reserved.

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[1]

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reported are slow-passage spectra; they are distorted by fastpassage effects. These passage effects have been recognized for some time but an analysis of their effect on the shape of the inhomogeneously broadened ODMR transition has not been given. The peak frequency of the hypothetical slowpassage transition has been approximated either by averaging the peak frequencies of the signals produced by equal sweep rates in opposite directions (10) or by extrapolation of the peak frequency to zero sweep rate (11). Neither method produces the actual lineshape. In this paper, we present an analysis of the effects of microwave fast passage on an inhomogeneously broadened ODMR band. The analysis allows one to obtain the correct peak frequency and width of an idealized slow-passage ODMR band by curve fitting of the experimental response. Kinetic and radiative parameters also obtained therefrom can be compared with those obtained from traditional transient ODMR measurements (12–14). Specifically, we find that a plot of the observed peak frequency vs microwave sweep rate is very nonlinear. Thus, extrapolation to zero sweep rate is not a reliable method for obtaining the correct peak frequency of the inhomogeneous band.

each isochromat; the passage time, dn /(d n /dt), is assumed to be negligible. Furthermore, I ijn (tn õ 0) Å 0. The validity of Eq. [3] assumes that SLR rate constants are negligible relative to the ki and kj , and that optical pumping does not significantly deplete the ground-state population in the photostationary state (5, 6). It will be advantageous for the purpose of later computer simulation to treat the isochromats as discrete population bunches, each of which produces a response following the instant of fast passage that is given by Eq. [3]. ‘‘Slowpassage’’ ODMR spectra are normally plotted on a linear microwave frequency scale, so that for the purposes of fitting this type of data, we now change the tn variable in Eq. [3] to frequency, n. For simplicity in later calculation, we assume that the isochromats are separated by a constant frequency interval, Dn. The sweep rate, R, is given by

THEORETICAL MODEL

tn Å ( n 0 n Dn )/R,

We begin with the assumption that the inhomogeneously broadened band is composed of a distribution of unresolved, homogeneous contributions whose magnetic resonance frequencies are determined by details of the local solvent configuration. The homogeneous linewidth is referred to as dn. We refer to all of the triplet states having the same ODMR frequency within dn as an isochromat. The nth isochromat has frequency nn , and a population gn . The contribution of the nth isochromat to the signal intensity is proportional to gn . We are interested in predicting the observed lineshape of an inhomogeneous distribution of isochromats under the condition that a zero-field ODMR transition of any isochromat, say Ti } Tj , undergoes fast passage. The fast-passage condition is dn /(d n /dt) õ ti , tj

i, j Å x, y, z,

[2]

where t is a sublevel lifetime. The phosphorescence response of the nth isochromat to fast passage is given (12) by I ijn (t) Å Cgn[k (i r ) exp( 0ki tn ) 0 k (j r ) exp( 0kj tn )],

[3]

R Å NDn /T,

[4]

where T is the total sweep time, and N is the number of equally spaced isochromats in the data set. In terms of R, tn is given by [5]

where n § n Dn. In terms of index p, where p § n, tn Å (p 0 n) Dn /R.

[6]

Introducing R from Eq. [4], tn Å (p 0 n)T/N.

[7]

Note that the time variable is independent of the value chosen for Dn. The intensity of the phosphorescence response at a frequency corresponding to index p, n Å p Dn, will contain contributions from all frequencies n Dn, where n £ p. The intensity observed at n Å p Dn will be I(p Dn ) Å C ∑ gn {k (i r ) exp[ 0ki (p 0 n)T/N] n£p

0 k (j r ) exp[ 0kj ( p 0 n)T/N]}.

[8]

Equation [8] can be simplified to I(p Dn ) Å C * ∑ gn{exp [ 0 ki (p 0 n)] n£p

where C is a proportionality constant that depends on the spin alignment and on the experimental arrangement. In Eq. [3], ki and kj are the decay rate constants of the Ti and Tj sublevels, respectively, while k (i r ) and k (j r ) are their radiative rate constants. Also, in Eq. [3], tn is the time measured after passage through the nth isochromat. Thus, t Å 0 varies with

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0 Rj i exp [ 0 kj ( p 0 n)]},

[9]

where ki , j Å ki , j T/N, Rj i Å k (j r ) /k (i r ) , and C * Å Ck (i r ) . Thus far, we have not specified the form of gn which determines the population distribution of the isochromats. Normally, we would expect this distribution to resemble a

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symmetrical bell-shaped one, especially if the distribution is random and its frequency width greatly exceeds the homogeneous linewidth. In the following sections where we will compare experimental data with the predictions of this theoretical model, we have assumed that the lineshape is Gaussian and have tested Eq. [9] with gn Å exp( 0 G 2n 2 ) Å exp[ 0 ( n 0 n0 ) 2 ln 2/ n 21 / 2 ]

[10]

where G 2 Å ( Dn ) 2 ln 2/ n 21 / 2 , and n1 / 2 is the half-width of the distribution at half-height. For this distribution, n0 is the peak frequency. EXPERIMENTAL

To test the theoretical model described above, typical slowpassage phosphorescence-detected ODMR (PDODMR) experiments were performed using a range of microwave sweep rates on samples whose triplet state properties, measured by ODMR, have been reported previously. Hen egg white lysozyme (31 recrystallized) was purchased from Sigma, dissolved in 0.1 M phosphate buffer, pH 7.0, to which was added an equal volume of ethylene glycol (EG). The final enzyme concentration was about 1 mM. 1-Methyl-2-thiouracil (1-Me-s 2U) cocrystallized with isomorphous 1-methyl uracil (1-Me-U) was also measured. These compounds were synthesized and purified as described previously (15). Mixed crystals were grown in the dark by slow evaporation of an ethanol solution of 1-Me-U containing 0.75 mol% 1-Me-s 2U in a desiccator over P2O5 . The optical excitation source was a 100 W Hg high-pressure short-arc lamp. The excitation wavelength was selected by a 0.1 m grating monochromator (Instruments, SA, Inc.) using 16 nm bandpass. For the lysozyme solution, a 1 mm i.d. Suprasil quartz sample tube was used, while, for the crystalline sample of 1-Me-s 2U/1-Me-U, a 1.5 mm tube was chosen. The sample tube was placed within a copper helix that terminated a section of 50 V coaxial transmission line. The latter was immersed in a cryostat (Janis, Inc., Model 8DT) fitted with an optical tail in which the sample could be maintained either at about 77 K for phosphorescence measurements or at the temperature of pumped liquid helium, about 1.2 K, for slow-passage ODMR, microwaveinduced delayed phosphorescence (MIDP) (14) measurements, and measurement of microwave-induced phosphorescence transients (MIPT) (12). Emission from the sample was monitored at a right angle with respect to excitation and was focused upon the entrance slit of a 1 m grating monochromator (McPherson, Inc., Model 2051) with a dispersion of 3.2 nm/mm. For phosphorescence spectra and ODMR measurements of lysozyme during optical pumping, fluorescence was suppressed by a rotating sector. The 1-Me-s 2U sample emitted only phosphorescence. A 345 nm cutoff filter was placed in the emission

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path to minimize scattered light. The optical signals were detected by a cooled photomultiplier (EMI, Inc., Model 6256). The photomultiplier output was amplified by a fast preampifier and an amplifier-discriminator (Ortec, Inc., Models 9301 and 9302, respectively). The NIM standard negative current pulses from the discrimintator were applied to a low-noise current amplifier (Keithley, Inc., Model 428). The integrated output of the Keithley was transfered to an A/D converter board (Keithley, Inc., Model DAS 40) and signal-averaged by a 486 PC. Future acquisition of a multichannel scaler board will allow the elimination of the current amplifier and A/D converter. The signal-to-noise ratio was improved significantly by amplifying the uniform discriminator output pulses rather than the photomultiplier output pulses directly as had been our practice in the past. The principal source of noise eliminated by this change appears to be that caused by the extremely uneven photomultiplier gain for individual photons. In the measurement of individual slow-passage PDODMR transitions, the data sets consisted of 1024 data points separated by equal time intervals. A downward-sloping baseline due to slow photolysis of the lysozyme sample was compensated by subtraction of data sets collected in the absence of microwave power. The resulting data were fitted to Eqs. [9] and [10] using a Marquardt–Levenberg nonlinear leastsquares ( x 2 ) minimization procedure. In this procedure, there are five unknown parameters to be determined. These are the band center ( n0 ) and half-width at half-height ( n1 / 2 ) of the (assumed) Gaussian band shape, the decay constants of the sublevels undergoing magnetic resonance ( ki , kj ), and the ratio of the radiative rate constants (Rj i ). In order to simplify the calculation, the total number of equally spaced isochromats (N) was chosen to equal the total number of experimental points in a data set. The program was written in C language and was run on a 586 PC. RESULTS

The phosphorescence spectrum of lysozyme at 1.2 K has vibronic structure characteristic of tryptophan. The well-resolved 0–0 band occurs at 414.7 nm. The emission originates mainly from a single tryptophan residue at position 108 (16). Only two slow-passage PDODMR transitions are readily observed, É DÉ 0 É EÉ (about 1.55 GHz) and 2É EÉ (about 2.75 GHz), since only the Tx (intermediate energy) sublevel is strongly phosphorescent (4, 5). In Fig. 1, we plot the PDODMR spectra of the 2É EÉ transition of lysozyme measured at varying microwave sweep rates at 1.2 K. It is apparent that the band shape and maximum peak position depend strongly on the microwave sweep rate. The superimposed noiseless solid lines represent a direct fitting of nonlinear least-squares ( x 2 ) minimization (Levenberg–Marquardt method) to the experimental data sets based on Eqs. [9] and [10]. We found that in the fitting

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TABLE 1 Zero-Field Splitting and Kinetic Parameters for 2ÉEÉ Transition of Lysozyme in EG-Buffer at 1.2 K Sweep rate (MHz/s) 200 100 50 25 Averagec MIDPc MIPTc Literature

n0 (GHz)

n1/2 (MHz)a

Ryx

kx (s01)

ky (s01)

2.746 2.740 2.742 2.741

57.0 55.6 59.6 58.2

0.070 0.066 0.071 0.062

0.53 0.51 0.53 0.55

0.07b 0.07b 0.07b 0.07b

2.742 (3) — — 2.718d 2.724 f

57.6 (17) — — 44.5d 58 f

0.067 (4) — 0.083 (4) — —

0.53 (2) 0.48 (3) 0.55 (8) 0.293e —

0.07 0.07 (1) 0.09 (2) 0.113e —

a

Half of the line width at half-maximum. Fixed at value obtained from MIDP. c The standard deviation (s) in last digit given in brackets. d Reference (9). e Reference (18). Values are from microwave-saturated phosphorescence decay measurements, thus eliminating SLR effects. f Reference (19). b

FIG. 1. PDODMR spectra of the 2ÉEÉ transition of lysozyme in EGbuffer at 1.2 K. A total of 50 scans were collected for each spectrum using 10 mW of incident microwave power with a sweep rate of (a) 200, (b) 100, (c) 50, and (d) 25 MHz/s. The phosphorescence 0–0 band of lysozyme at 414.7 nm was monitored throughout, and the sample was excited at 295 nm. The solid lines represent the best fit of each experimental spectrum based on Eqs. [9] and [10]; best-fit parameters appear in Table 1. The dashed vertical line indicates the average calculated n0 value (2.742 GHz, cf. Table 1).

of both lysozyme signals, the best-fit value of the smaller of the decay constants, ky for the 2É EÉ transition and kz for the É DÉ 0 É EÉ transition (see below), did not converge properly on a unique value. Because of the small size of Rj i , the data are quite insensitive to variation of the smaller of the decay constants. For this reason, the smaller decay constant was fixed in the least-squares analysis at the value obtained from MIDP measurements. Independent of the initial values of the four remaining parameters, fits converged to the results shown as noiseless traces totally contained within the noise pattern of the experimental data in Fig. 1. Each iteration required about 20 seconds, and convergence was normally obtained after about 30 iterations. The bestfit parameters of zero-field splitting, Gaussian linewidth, and kinetics for each individual spectrum are given in Table 1. Ideally, each data set should be fitted with the same set of parameters. The mean value of each best-fit parameter also is given along with its standard deviation. For comparison, the apparent sublevel decay constants obtained from MIDP (14) and MIPT measurements (12) also are given, as well as the value of Ryx obtained by the latter method. In Fig. 2, slow-passage ODMR spectra are presented for the É DÉ 0

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FIG. 2. PDODMR spectra of the É DÉ 0 É EÉ transition of lysozyme in EG-buffer. The conditions are the same as described in the legend to Fig. 1. The microwave frequency is swept to only 2 GHz, and spurious output at the 2É EÉ frequency is suppressed by a 2 GHz low-pass filter. The sweep rate is (a) 200, (b) 100, (c) 50, and (d) 25 MHz/s. The superimposed solid lines represent the calculated best fit of each experimental spectrum; the values of the parameters appear in Table 2. The dashed vertical line indicates the average n0 value (1.585 GHz, cf. Table 2).

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TABLE 2 Zero-Field Splitting and Kinetic Parameters for ÉDÉ 0 ÉEÉ Transition of Lysozyme in EG-Buffer at 1.2 K Sweep rate (MHz/s) 200 100 50 25 Averagec MIDPc MIPTc Literature

n0 (GHz)

n1/2 (MHz)a

1.589 1.587 1.584 1.582

39.9 40.6 40.7 40.4

1.585 (3) — — 1.545d 1.571 f

40.4 (4) — — 44d 41.5 f

kx (s01)

kz (s01)

0.048 0.050 0.064 0.045

0.48 0.54 0.50 0.49

0.07b 0.07b 0.07b 0.07b

0.052 (8) — 0.05 (3) — —

0.50 (2) 0.48 (3) 0.55 (8) 0.293e —

0.07 0.07 (1) 0.05 (3) 0.054e —

Rzx

a

Half of the linewidth at half-maximum. Fixed at value obtained from MIDP. c The standard deviation (s) in last digit given in brackets. d Reference (9). e Reference (18). Values are from microwave-saturated phosphorescence decay measurements thus eliminating SLR effects. f Reference (19). b

É EÉ transition of lysozyme with the best-fit spectra superimposed. The data were analyzed as described above for the 2É EÉ transition; the best-fit parameters are listed in Table 2 along with data obtained from MIDP and MIPT measurements. In Fig. 3, we present some calculated band shapes of the 2É EÉ transition of lysozyme for a microwave sweep rate of 100 MHz/s. Responses were calculated for several deviations of the parameters from the best-fit values of Table 1 in order to demonstrate their effect on the predicted band shape. Included in this figure are the experimental data superimposed on the response calculated from the best-fit parameter values from Table 1. Figures 4 and 5 are plots of Dnmax å nmax 0 n0 vs microwave sweep rate for the 2É EÉ and É DÉ 0 É EÉ transitions of lysozyme, respectively. nmax is the measured peak frequency of the slow-passage spectrum and n0 is the average of the calculated best-fit peak frequencies of the data set based on an assumed Gaussian lineshape taken from Tables 1 and 2. Thus, Dnmax is the deviation of the experimental peak frequency from the global best-fit center frequency. The PDODMR spectra of polycrystalline 1-Me-s 2Udoped 1-Me-U obtained over a range of microwave sweep rates are shown in Fig. 6, along with the superimposed bestfit calculated spectra based on Eqs. [9] and [10]. The band observed is n1 , the lowest frequency ODMR transition of the three exhibited by this sample (15, 17). In this case, all five parameters were included in the analysis. The best-fit parameters are listed in Table 3, which also includes results from previous work (15). Figure 7 shows plots of Dnmax vs

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microwave sweep rate for this transition along with calculated values for various sets of parameters, including that from the global best-fit. The sensitivity of the calculated spectra to variations in the fitting parameters is shown in Fig. 8 for a sweep rate of 100 MHz/s. DISCUSSION

The PDODMR responses to microwave passage are fitted very well by the theoretical expression, Eq. [9], assuming a Gaussian lineshape, Eq. [10], over a wide range of sweep rates. The response curves predicted by the best-fit parameters fall within the noise level of the experimental ones in every case, as can be seen from examining Figs. 1–3 and 6. The only nonrandom deviations visible occur in the 1Me-s 2U data shown in Fig. 6 near the low-frequency edge of the signal. They are due most likely to a non-Gaussiasn distribution of isochromat frequencies in the crystalline sample that becomes visible as a result of the extremely narrow inhomogeneous bandwidth. Noticeable deviations from a Gaussian lineshape are not found in the lysozyme spectra where the inhomogeneous breadth is 20-fold larger. A comparison of the best-fit least-squares parameters for the various sweep rates in Tables 1–3 reveals that the smallest standard deviation occurs in n0 , and n1 / 2 . The standard deviation in n0 is less than 10% of n1 / 2 . The standard deviation

FIG. 3. Demonstration of the effect on the PDODMR spectrum of varying single parameters in Eqs. [9] and [10]. This is the 2É EÉ transition of lysozyme; the sweep rate is 100 Mhz/s. The upper points are experimental with calculated response from best-fit values of parameters (Table 1, second row) superimposed. Below are a set of calculated responses. Solid curve uses the best-fit parameters. In the dashed curve, n1 / 2 is changed to 80 MHz. In the dotted curve, kx is changed to 1.1 s 01 . In the dot–dashed curve, ky is changed to 0.7 s 01 .

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87

FIG. 4. The microwave sweep-rate dependence of Dnmax (defined in text) for the 2 É EÉ transition of lysozyme; points are experimental; (a) calculated based on Eqs. [9] and [10] using the average values in Table 1; (b) same as (a), except n1 / 2 Å 100 MHz; (c) same as (a), except kx Å 1.1 s 01 .

in n1 / 2 is a few percent at most. The methods presented here appear to be particularly well suited for obtaining these quantities. The ratio of radiative rate constants, Rj i , is in general

FIG. 5. The microwave sweep-rate dependence of Dnmax (defined in text) for the É DÉ 0 É EÉ transition of lysozyme. Points are experimental. (a) Calculated from Eqs. [9] and [10] by applying the average values in Table 2; (b) same as (a), except n1 / 2 Å 81 MHz; (c) same as (a), except kx Å 0.25 s 01 .

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FIG. 6. PDODMR spectra for low-frequency n1 transition of polycrystalline 1-Me-s 2U in 1-Me-U host at 1.2 K. A total of 500 scans were collected for each spectrum using 100 mW of applied microwave power with a sweep rate of (a) 400, (b) 200, (c) 100, (d) 50, (e) 25, and (f ) 10 MHz/s. The phosphorescence 0–0 band at 391.5 nm was monitored throughout, with the sample excited at 312 nm. The solid lines represent the best fit of each experimental spectrum based on Eqs. [9] and [10]. The best-fit parameters are given in Table 3. The dashed vertical line indicates the average n0 value (4.3656 GHz, cf. Table 3).

agreement with the MIPT results. Values obtained from varying sweep rates, however, reveal a relatively large standard deviation, particularly for 1-Me-s 2U. The apparent kinetic rate constants, ki , j , are obtained during optical pumping. Their values are influenced by the optical pumping kinetics and only assume validity in the limit of a negligible optical pumping rate (5, 6). Even then, they may be influenced by SLR, if it is not effectively quenched. The effects of optical pumping on the apparent values of ki , j could be large for tryptophan which has a long-lived triplet state, but can be neglected for 1-Me-s 2U. The values of kx obtained for lysozyme by the present analysis of slow-passage responses are in good agreement with those obtained from MIPT (12); the MIPT measurements were carried out using the same optical pumping conditions as for the slowpassage measurements. The effects of optical pumping are absent from the decay constants produced by the MIDP method (14); the smaller value of kx produced by MIDP relative to MIPT (Tables 1 and 2) could reflect a small influence of optical pumping on the decay kinetics. The

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TABLE 3 Zero-Field Splitting and Kinetic Parameters for n1 Transitions of Polycrystalline 1-Me-s2U in 1-Me-U Host at 1.2 K Sweep rate (MHz/s) 400 200 100 50 25 10 Averageb Literaturec

n0 (GHz)

n1/2 (MHz)a

Rji

ki (s01)

kj (s01)

4.3654 4.3657 4.3654 4.3653 4.3658 4.3657

2.55 2.58 2.47 2.22 2.15 2.08

0.41 0.39 0.38 0.45 0.16 0.33

18.5 16.9 16.0 13.8 28.5 13.4

6.5 5.1 4.9 5.4 2.7 3.7

4.3656 (2) 4.365

2.3 (2) 2

0.35 (10) 0.26

18 (6) 23.4

5 (1) 5.4

a

Half of the linewidth at half-maximum. The standard deviation (s) in last digit given in brackets. c Reference (15). b

apparent kx obtained in these measurements appears to be influenced significantly by SLR, since microwave-saturated phosphorescence decay analysis (18) which allows separation of the actual ki from the SLR rate constants, yields a smaller value for kx (Tables 1 and 2). The validity of the expression on which our treatment is based, Eq. [3], rests on the assumption that the fast-passage condition, Eq. [2], is fulfilled in the measurements. For lysozyme at the slowest sweep rate used, 25 MHz/s, the

FIG. 7. The microwave sweep-rate dependence of Dnmax (defined in text) for the n1 transition of 1-Me-s 2U at 1.2 K. Points are experimental. (a) Calculated using Eqs. [9] and [10], applying the average values in Table 3; (b) same as (a), except n1 / 2 Å 4.5 MHz; (c) same as (a), except Rj i Å 0.19; (d) same as (a), except ki Å 32 s 01 .

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FIG. 8. Demonstration of the effect of varying individual parameters in Eqs. [9] and [10] on the calculated band shapes of the n1 ODMR transition of 1-Me-s 2U. (a) Best fit of experimental spectrum of 1-Me-s 2U at a sweep rate of 100 MHz/s (Fig. 6c; Table 3, row 3); (b) same as (a), except ki Å 25 s 01 ; (c) same as (a), except Rj i Å 0.25; (d) same as (a), except n1 / 2 Å 5 MHz.

fast-passage condition is fulfilled provided dn õ 40 MHz. Since microwave hole-burning measurements on tryptophan in proteins produce holes in the ODMR bands that are about 5 MHz in width, we believe that the fast-passage condition is satisfied in this case. In the case of 1-Me-s 2U, the slowest sweep rate used was 10 MHz/s, and the corresponding condition for fast passage is dn õ 0.6 MHz. There are no holeburning data for this sample, and it is possible that we have not fulfilled the fast-passage condition at the slowest sweep rates used. Deviations of the lineshape from that predicted by our theory are not observed, however, at the slowest sweep rates, suggesting that we still approximate the fastpassage regime. The signal intensity of 1-Me-s 2U is very much less at low sweep rates than is observed at higher sweep rates, suggesting that we may be approaching slowpassage conditions. In slow passage, the signal intensity varies as the difference in radiative quantum yields (Qi Å k (i r ) /ki ) of the sublevels that are in resonance (3–6). From the data in Table 3, we can calculate that the radiative quantum yields of the resonant sublevels are similar: Qj /Qi Å 1.2. Since this ratio is greater than 1, while Rj i õ 1, an actual slow-passage PDODMR band should have negative polarity, i.e., represent a decrease in phosphorescence intensity. The consistency in the value of n0 obtained over a range of microwave sweep rates enabled us to define and calculate the deviation of the experimental maximum from this value, Dnmax , with some confidence. Plots of this quantity vs the microwave sweep rate, shown in Figs. 4, 5, and 7, are accu-

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FAST-PASSAGE EFFECTS ON ODMR SPECTRA

rately represented by the calculated plots obtained from Eqs. [9] and [10] when the global best-fit parameters are employed. These data and calculations reveal clearly that the behavior of the deviation of the experimental maximum from its value in a true slow-passage measurement is quite complicated, and its variation with microwave sweep rate is far from linear. For large values of Rj i , unusual ODMR band shapes are found at the slower sweep rates (e.g., Figs. 6e, 6f), and Dnmax even can become negative (Fig. 7). We conclude that extrapolation of the peak frequency of an ODMR response to zero sweep rate can not be carried out with confidence and that some method such as that developed in this work must be used to obtain n0 and n1 / 2 . ACKNOWLEDGMENT

6. A. J. Hoff, in ‘‘Advanced EPR with Applications to Biology and Biochemistry’’ (A. J. Hoff, Ed.), p. 633, Elsevier, Amsterdam, 1989; Methods Enzymol. 227, 290 (1994). 7. J. Zuclich, J. U. von Schu¨tz, and A. H. Maki, J. Am. Chem. Soc. 96, 710 (1974). 8. K. W. Rousslang, J. B. A. Ross, D. A. Deranleau, and A. L. Kwiram, Biochemistry 17, 1087 (1978). 9. M. V. Hershberger, A. H. Maki, and W. C. Galley, Biochemistry 19, 2204 (1980). 10. J. B. A. Ross, K. W. Rousslang, D. A. Deranleau, and A. L. Kwiram, Biochemistry 16, 5398 (1977). 11. D. H. H. Tsao, J. R. Casas-Finet, A. H. Maki, and J. W. Chase, Biophys. J. 55, 927 (1989). 13. A. L. Shain and M. Sharnoff, J. Chem. Phys. 59, 2335 (1973). 14. J. Schmidt, D. Antheunis, and J. H. van der Waals, Mol. Phys. 22, 1 (1971). 15. M.-R. Taherian and A. H. Maki, Chem. Phys. 55, 85 (1981).

REFERENCES 1. A. L. Kwiram, Chem. Phys. Lett. 1, 272 (1967). 2. M. Sharnoff, J. Chem. Phys. 46, 3263 (1967). 3. R. H. Clarke (Ed.), ‘‘Triplet State ODMR Spectroscopy,’’ Wiley– Interscience, New York, 1982. 4. A. L. Kwiram and J. B. A. Ross, Annu. Rev. Biophys. Bioeng. 11, 223 (1982).

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5. A. H. Maki, in ‘‘Biological Magnetic Resonance’’ (L. J. Berliner, and J. Reuben, Eds.), Vol. 6, p. 187, Plenum, New York, 1984; Methods Enzymol. 246, 610 (1995).

12. C. J. Winscom and A. H. Maki, Chem. Phys. Lett. 12, 264 (1971).

This publication was made possible by Grant ES-02662 from the National Institute of Environmental Health Sciences, NIH.

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16. K. W. Rousslang, J. M. Thomasson, J. B. A. Ross, and A. L. Kwiram, Biochemistry 18, 2296 (1979). 17. C. A. Smith and A. H. Maki, Chem. Phys. Lett. 179, 497 (1991). 18. J. Zuclich, J. U. von Schu¨tz, and A. H. Maki, Mol. Phys. 28, 33 (1971). 19. J. B. A. Ross, K. W. Rousslang, and A. L. Kwiram, Biochemistry 19, 876 (1980).

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