EPR Spectra and Electron Spin Relaxation of O₂

Abstract

It has been known from the pioneering and approximately simultaneous work of Freed and Frankel, Hausser and Deguchi (1959 −1960) that collisions with O₂ in fluid solutions broaden the electron paramagnetic resonance (EPR) spectra of free radicals. Freed showed Hausser the effect of degassing solutions on the hyperfine of DPPH. Hausser and Deguchi published spectra illustrating the effect. The effect of O₂ on CW EPR spectra and on relaxation times have been applied to the problem of measuring O₂ concentration in vivo. Various aspects of the effect of O₂ on biological EPR and on the biological systems have been studied. A large literature has developed about in vivo O₂ measurements using nitroxyl radicals, triarylmethyl radicals (trityl, TAM), carbon particles, and analogues of lithium phthalocyanine (LiPc). All of these measurements correctly assume that the O₂ electron spin relaxation time is short relative to the relaxation time of the sensor molecules. There has been no prior review of the EPR spectra and electron spin relaxation of O₂ in the gas phase, dissolved in fluid solution, and in frozen solutions. A summary of the relevant literature is presented here as a resource for the O₂ measurement community.

1. Overview

It was shown by the pioneering and approximately simultaneous work of Freed and Frankel in 1959 [1], Hausser [2, 3] and Deguchi [4] that collisions with O₂ in fluid solutions broadens the electron paramagnetic resonance (EPR) spectra of free radicals. Freed showed Hausser the effect of degassing solutions on hyperfine of DPPH. Hausser and Deguchi published spectra illustrating the effect. Several aspects of the effect of O₂ on biological EPR and on the biological systems studied were discussed [5, 6].

Electron spin relaxation times of O₂ are strongly influenced by the environment of the O₂. Estimates are available for gas phase O₂, O₂ in fluid solution, and O₂ in various solids. The spectra are complex because there is coupling between rotational angular momentum, orbital angular momentum, and electron spin angular momentum in O₂. In the gas phase, rotational angular momentum is not quenched. In condensed phases, the rotational angular momentum is quenched to varying degrees, and in fluid solutions the spin-lattice relaxation times are of the order of magnitude of the molecular collision times. The small, fast-relaxing O₂ molecule reduces the relaxation time of other paramagnetic species with which it interacts. In fluid solution, O₂ diffuses rapidly and collisions with other species provide a means of measuring the [O₂]. A major application is in vivo oximetry using trityl [7], nitroxyl [8], carbon particles such as in India ink [9], or analogues of LiPc as the monitor of [O₂] [10].

All of these measurements correctly assume that the O₂ electron spin relaxation time is short relative to the relaxation time of the sensor molecules. Estimates of T₁ for O₂ are based on CW EPR line shapes, effect on NMR relaxation times, or are based on limits inferred from experimental parameters such as temperature effects, field scan rates, etc. There have been no direct, time-domain, measurements of T₁ of O₂.

2. Background – rotational spectroscopy

Crucial to the understanding of the EPR spectra of O₂ is the rotation of diatomic molecules. Transitions are usually found in the microwave region of the electromagnetic spectrum. The gas-phase “EPR” spectra of diatomic molecules are a mix of rotational transitions and electronic dipole transitions. Quenching of rotational angular momentum has a major effect on relaxation times. The molecule must have a dipole moment for the rotational transitions to be observed. Since O₂ does not have an electric dipole moment, the EPR transitions are all due to electron spin modified by spin-orbital interactions.

Rotational and vibrational spectroscopy of diatomic molecules in the gas phase is often introduced in undergraduate physical chemistry courses to demonstrate quantization of energy [11]. For a diatomic molecule, the rotational energy is [11]:

$$E_{rot}=\frac{J(J+1){\hslash }^2}{2\mu r^2}$$ (1)

Where μ is the reduced mass and r is the internuclear distance. The average rotational energy of a gaseous diatomic molecule is k_BT, which is 4.x10⁻²¹ J. For O₂ at room temperature the average period of rotation for the ensemble of occupied rotational states is 9.7 × 10⁻¹³ s. In condensed phases the motions are slowed, but we know from nitroxyl studies that tumbling correlation times in low-viscosity solvents at room temperature are of the order of 1 to 10 ps.

3. EPR Spectra and Relaxation of O₂ in the Gas Phase

Some of the early EPR studies of O₂ are described by Bleaney’s review of gas phase EPR [12]. Beringer and Castle [13] recorded about 40 lines of the room temperature X-band spectrum of O₂ at 4 mm Hg from 3000 to 9000 G. Although it is not stated in the paper, the dots in the spectrum are manually recorded (pencil and paper) galvanometer readings [14]. They observed that the half width of the Lorentzian line was dependent on gas pressure, and was about 2 MHz (slightly less than 1 G) per mm of O₂ pressure. This would correspond to T₂ ≈ 6×10⁻⁸ s. It seems reasonable to assume T₁ = T₂ in these gases.

The earliest high-resolution gas-phase EPR spectrum of O₂ at low concentration was recorded from 2.5 kG to 9.5 kG at X-band and is reproduced in [15]. Marshall et al. [16] reported more than 100 lines over a 9000 G range in the spectrum of O₂ at 9.45 GHz. The gas pressure was “a few tenths of a millimeter of mercury” and the resonator was immersed in liquid N₂. A line width of 1.6 G was observed for a transition at 6350 G, which corresponds to T₂ ~ 1×10⁻⁷ s. A modern Q-band CW EPR spectrum of O₂ in air at 1.6×10⁻² mbar, with 100 mG resolution exhibited EPR linewidths of 300 – 500 mG (Figure 1). These linewidths correspond to T₁ ≈ 1.3×10⁻⁷ to 2.2 ×10⁻⁷ s.

Figure 1.

X-band CW EPR spectrum of O₂ in air at ~1 mbar. A) Full spectrum. B) Expansion of smaller region show the resolution of the lines. Spectra recorded by Ralph Weber, Bruker BioSpin.

Tinkham and Strandberg [17] interpreted the gas-phase EPR spectrum of O₂ in terms of (i) electron spin magnetic moment, (ii) spin-orbit coupling (about a 0.1% or 7 G correction), and (iii) the rotation-induced magnetic moment of the molecule (ca. 1 G correction). One hundred twenty X-band and 78 S-band lines were observed. The theory presented in this paper is basis for all subsequent work. Some refinements were made by Bowers et al. [18] to achieve agreement with experiment within 6 ppm. The ratio of g for O₂ to the free electron g value is 1 – (147±10) × 10⁻⁶. The entire gas-phase EPR spectrum of O₂ was measured between 23 and 29 T at 730.5 GHz at 120 K [19]. The Tinkham and Strandberg theory explains the spectrum [17].

The g = 2.17 peak in the EPR spectrum of O₂ in normal air was used as the signal-to-noise test for Varian Q-band spectrometers. The intensity and shapes of the peaks are strongly dependent on the gas pressure, but for the purpose of understanding the effect of O₂ on relaxation of other species it is sufficient to note that there are O₂ peaks of significant intensity from about g = 2.8 to 1.0, with the major intensities at g = 2.17 and g = 1.22.

Other gas-phase spectra are reviewed by Krupenie [20].

4. Relaxation of O₂ in Fluid Solution near Room Temperature

4.1. NMRD measurements

NMR measurements of the relaxation of O₂ are performed as a function of the NMR Larmor frequency. If the frequency range studied is wide enough, there is a dispersion in the nuclear relaxation rate vs. frequency plot (this is why the method is called NMR dispersion – NMRD). The dispersion occurs at a frequency at which some dynamic aspect of the system becomes dominant. In the O₂ experiments, the dispersion is interpreted in terms of electron spin relaxation and translational diffusion of the molecules. Analogous plots are used to characterize MRI contrast agents.

The earliest estimate of O₂ T₁ in solution was by Hausser and Noack [21]. The magnetic interaction between the electronic magnetic dipole moment of molecular O₂ dissolved in water and protons of H₂O was investigated by measuring the proton nuclear relaxation times and their dependence on O₂ pressure (10⁻²-200 atm), on the proton Larmor frequency over the range 0.45–160 MHz (NMR dispersion), and on temperature (20–300°). The dipolar interaction, which is dominant, appears to be modulated in time mainly by the correlation time, T₁, (called t_s in the original paper) of the O₂ electron spin. At 25°, T₁ = (1 ± 0.4) × 10⁻¹¹ s. The effective distance of nearest approach between electron and proton spin, d = 2.87 ± 0.15 Å. The value for the translational correlation time, t_D ≥1.3 × 10⁻¹¹ sec. at 25°, was somewhat larger than in pure water, and might suggest a weak, short-lived bonding between O and H₂O.

Delpuech et al. [22] derived 0.9 ± 0.4×10⁻¹¹ s for T₁ of O₂ from the relaxation of benzene. Interpretation of hexafluorobenzene relaxation due to O₂ was more complicated, and it was suggested that the O₂ diffusion was discontinuous with short residence times in “privileged positions.” Other measurements of nuclear relaxation caused by dissolved O₂ by Hamza, et al., were interpreted using T₁ of O₂ = 0.9×10⁻¹¹s [23].

The relaxation time of O₂ dissolved in solution was estimated by Bryant and coworkers by NMRD [24]. Electron T₁ and translational correlation times were the primary contributor to dependence on NMR Larmor frequency. Water, methanol, benzene, DMSO, acetone, acetonitrile, and 1:1 water:glycerol were studied at room temperature. The T₁ value was largely independent of solvent, with a range of 5×10⁻¹² to 1×10⁻¹¹ ps. Extrapolation based on molecular translational correlation time gave an intercept of 7.5×10⁻¹² s for T₁. This was stated to be similar to literature values for fluorinated solvents. Teng et al. [24] noted that the electron T₁ was close to the translational correlation times for the solutions, so the τ was expressed in terms of both times. They observed that T₁ of O₂ is very nearly independent of solvent.

4.2. Relaxation of a nitroxyl or trityl by O₂

In an air-saturated aqueous solution of a nitroxyl or trityl radical, with the normal sub-millimolar radical concentration, the oxygen concentration will also be roughly 220 μM [25], about the same as the radical concentration. The problem can be approximated as a two-site exchange. The O₂ relaxation (ca. 7.5×10⁻¹² s) is very much faster than the nitroxyl relaxation (ca. 0.5×10⁻⁶ s). The relaxation mechanism is Heisenberg exchange. Each collision results in relaxation of the nitroxyl by the O₂. This model has been well-established by the work of the Hyde lab [25, 26]. The approximate equation for the collision frequency, ω is:

$$\omega =4\pi p{r}_0{D}_{0}C$$ (2)

where

pr₀ = 4.5 Å (4.5×10⁻⁸ cm)

D₀ = 2×10⁻⁵ cm²s⁻¹

C(O₂) = 0.2 mM = 1.2×10¹⁷ molecules cm⁻³

from which ω = 1.3×10⁶ s⁻¹.

This collision rate may change by more than an order of magnitude depending on the viscosity of the environment and the concentrations of the nitroxyl and the O₂. The change in T₁⁻¹ due to O₂ is (2/3)pω, where p is a probability to allow for some collisions not being effective. Thus, approximately, T₁⁻¹ = ω. The same arguments apply to trityls. Pulsed EPR measurements of trityl T₁ provide absolute measurements of O₂ concentration [27].

Diakova and Bryant [28] concluded that the local concentration of O₂ in water sensed by nitroxyls may be a factor of 2 higher than “that associated with a free diffusion hard sphere limit.” This is attributed to a hydrophobic effect, which “increases the local concentration of oxygen in the nonpolar portions of solute molecules.” The conclusion is based on the assumption that hydroxylamines are very similar to nitroxyls in their interaction with O₂.

When the collisions are infrequent (small diffusion-concentration product D₀C), there is small but observable broadening of the EPR spectrum of the nitroxyl. However, if the collision rate increases by a factor of 10³ the ca. 100 mG CTPO nitroxide lines would be 100 G wide. To find the total integral value, it is necessary to integrate over a spectral width many times the peak-to-peak width [29]. Thus, in a “normal” 200 G scan of a nitroxyl radical, much of the intensity would be missed if the concentration were high.

4.3. Application to observations using fluorocarbon solvents

Solubility of O₂ in fluorocarbons has been studied extensively because of potential clinical use as heme substitutes. O₂ is about 100 times more soluble in fluorocarbons than in water. A mole fraction of ca. 4×10⁻³ has been reported for O₂ in some fluorocarbons [30, 31]. Another study reported an average solubility of 48 mL O₂ per 100 mL of fluorocarbon liquid, which is about 20 mM O₂ [32]. The Turro lab studied the effect of dissolved O₂ on EPR spectra of nitroxyl radicals in fluorocarbon solvents [33]. The solutions were described as “oxygen purged” which could result in O₂ concentrations as much as 500 times that in air-saturated water solutions. Because of the high O₂ concentrations, the large frequency difference between the O₂ transitions and the nitroxyl transitions, and the very fast relaxation of the O₂, exchange can both broaden the nitroxyl spectrum beyond detection limits and shift intensity away from the g values of the nitroxyl spectrum (toward the O₂ lines). In the usual oximetry applications, the intensity change is negligibly small, but in the presence of large concentrations of O₂ in air- or oxygen-saturated fluorocarbons, the effect on the apparent spin concentration could be very large. Another part of the interpretation is why some of the nitroxyl intensity is still observed. The O₂ spectra extend over the entire magnetic field range, so some of the nitroxyls are interacting with O₂ at the nearly the same magnetic field as the nitroxyl, and the resultant exchange-averaged spectrum is not shifted. There is some discussion in the literature of specific interaction of O₂ with CF₃ groups. It is conceivable that there could be multiple environments of nitroxyl and O₂ such that some of the nitroxyl is not interacting with O₂ as much as other nitroxyls. Finally, one should note that at the very high O₂ concentrations, the O₂-O₂ collisions will change the intensity and location of O₂ transitions in a temperature-dependent way.

5. Spectra and Relaxation of O₂ in Condensed Phases at Low Temperature

Several papers report spectra of O₂ in condensed phases. The spectra are fit with g = 2 and zero field splitting (ZFS) D = 3.57 to 3.96 cm⁻¹. Usually, temperatures below 10 K are required, depending on the matrix, because the relaxation times are so fast. In most of these studies there is no mention of spin relaxation. Kon observed the EPR of O₂ in several matrices below 10 K [34]. A sharp (25 G peak-to-peak) X-band line at 8.928 GHz, 11,465 G, was observed for < 30 ppm of O₂ in N₂ (Figure 2) and a broader line was observed in CO. Other matrices gave very broad lines (Ar) or no observable signal (H₂, Xe, CO₂). The spectra were interpreted in terms of D = 3.96 cm⁻¹. Calculations suggest that the spectra for a range of orientations of the O₂ molecule would extend about 10,000 G. Breyberg [35] created O₂ by UV radiation of single crystals of KBrO₄ and measured the EPR spectra at 9.3 and 35 GHz at 30 K. The g values were close to 2 with D larger than the EPR quantum. The EPR spectrum was attributed to O₂ based on comparison of spectral parameters.

Figure 2.

The effect of temperature on the EPR absorption spectrum of molecular O₂ in a N₂ matrix. The signal position and the linewidth remain the same below 5.5 K. Above ~ 13K the signal is not observable due to broadening. The spectrometer gain was increased by the ratio 1:2:2:4 as the temperature was increased. Figure reproduced, with permission, from [34].

Pardi et al. [36] observed that 94 and 328 GHz spectra of solid air at 5 K reveal 3 and 4, respectively, turning points in the derivative spectra. They described these spectra of O₂ as “typical S = 1 paramagnets.” Spectra were obtained up to 550 GHz, and were fitted with g = 2 and D = 3.572 cm⁻¹. Figure 3 and 4 are from Pardi et al. [36]. These spectra demonstrate the power of high field/high frequency EPR for characterizing species with large zero field splittings.

Figure 3.

328 GHZ EPR spectrum of O₂ in solid air at 5 K. Top, experimental, bottom, simulation. Simulation parameters, S = 1 with D = 3.572 cm⁻¹ and g = 2.000. The single crystal linewidths used in the powder simulation were 20 mT (perpendicular peaks) and 10 mT (parallel peaks). The amplitude of the features labeled as B_z1 and B_x2 were amplified by a factor of 10. Figure reproduced, with permission, from [36].

Figure 4.

Frequency vs. magnetic field plot of the transition fields observed in the high-field, high-frequency EPR spectra of O₂ in solid air in the 94 – 550 GHz frequency range. The squares are the experimental points: empty squares indicate the high precision data used in the fitting procedure. The lines are calculated for a triplet state with D = 3.572(3) cm⁻¹ and g = 2.000. Figure reproduced, with permission, from [36].

The EPR spectrum of O₂ diluted in N₂ was observed below 25 K using 40 to 200 GHz sources. Spectra were fit with g = 2 and D = 3.497 cm⁻¹ [37]. Figure 5 shows the temperature dependence of the 285 GHz EPR signal from 4% O₂ diluted in N₂ [37]. The ZFS decreases and the intensity decreases at the temperature increases. The spectrum is not observable above about 25 K. The authors interpret these observations as showing that the rigid magnetic triplet ground state of O₂ is not stable in this host matrix. An alternative interpretation considers the dynamics of the frozen N₂ matrix, and the high concentration of O₂ in the N_2. Pangilinan et al. [38] showed that there is a transition between the low-temperature ordered cubic α phase of N₂ to a hcp β phase at 35.6 K, and partial relaxation of orientational ordering approximately 10 K below the transition temperature. This is the temperature region in which van der Horst and Bentrum observed large changes in the O₂ spectrum.

Figure 5.

Temperature dependence of the low (a) and high (b) field signal of 4% O₂ diluted in N₂. The decrease in signal intensity and the shift in resonance position are evident. Reproduced, with permission, from [37].

In frozen Xe at liquid He temperatures the nuclear relaxation is due almost entirely to O₂ present as an impurity (or purposely added). The Xe nuclear relaxation measurements were interpreted as showing an O₂ T_1e ≈ 1.4×10⁻⁸ s at 2.3 K and 0.96 T [39].

A molecule of O₂ can be trapped in a cage of β-quinol clathrate. Below 4 K the O₂ is in a hindered rotational state. The most highly-resolved spectra were obtained with crystals grown under N₂ containing small concentrations of O₂. Pulsed fields were used for some studies. From the time intervals between passing through resonance and relative intensities, the authors estimated that T₁ was less than 50 μs at 1.5 K [40]. This is an opportunity for measurement with modern spectrometers.

The O₂ effect on T₁ and T₂ of nitroxyl-spin-labeled polystyrene as a function of temperature (77 – 295 K), [O₂], and time of exposure was interpreted in terms of the O₂ T₁ [41]. The O₂ T₁ was described as not known, but the results “imply T₁ (O₂) < 10⁻⁸ s at 77K and T₁ (O₂) < 2×10⁻¹¹ s for all temperatures” above the nitroxyl T₁ minimum. The latter phrase means the T₁ minimum of the spin label in the presence of O₂. This limiting value is consistent with the values determined by Bryant in fluid solution. T₁ of spin labels on polystyrene decrease with decreasing temperature below ca. 200K. For samples in vacuum, T₁ increased monotonically with decrease in temperature. For various concentrations of O₂, T₁ reached a minimum at different temperatures, and then increased again at lower temperatures. The minimum in T₁ as a function of temperature was interpreted by Brown as indication of a time-dependent dipolar interaction between O₂ and the nitroxyl radical.

Sutin et al. [42] used O₂ “gas” at 77 K to change the relaxation time of H^. atoms produced by irradiating silica gel in the presence of H₂ gas. They used two models for the effect of the O₂. If they assumed that the O₂ was distributed through the volume, they estimate T₁ = 4×10⁻¹² s, and if they assumed the O₂ was uniformly distributed on the surface, they estimated T₁ = 0.6×10⁻¹² s. “We thus get T₁ as about 10⁻¹² s.” They claim that T₁ in the gas is shorter than that on the surface. They saw no effect on line width (T₂), but only on T₁ of the H atoms, up to about 1 mm Hg pressure of O₂. Then, the line broadened rapidly, and then less rapidly at higher O₂ pressures.

5.1. Other observations of O₂ EPR

In our laboratory we have, from time-to-time observed broad peaks in EPR spectra at g > 2 that we attribute to O₂ trapped in frost on the outside of sample tubes. Removing the frost without melting the sample removed the peak from the spectrum. In some samples of protein solutions stored in open EPR tubes in a −80° C freezer, the EPR spectra contained strong lines that disappeared upon thawing or upon preparing the same protein samples and sealing so that they were not exposed to air. One sample that was prepared by the usual freeze-pump-thaw cycle contained a small residual O₂ in the gas phase above the frozen solution that contributed sharp lines to the CW EPR spectrum (Figure 6).

Figure 6.

X-band spectrum of residual O₂ gas in a nominally ‘degassed’ sample at 60 K, obtained by Joseph McPeak (University of Denver) in 2018 with 2 G modulation amplitude at 100 kHz.

6. Singlet O₂

Singlet O₂ was measured in the gas phase by Yagi et al. [43] and by Hasegawa et al. [44]. They achieved about 30% singlet O₂ in the gas phase by photoexcitation using octafluoronaphthalene as the sensitizer. X-band spectra of the triplet and singlet O₂ are compared in Figure 7, from [43].

Figure 7.

EPR spectra of O₂ (¹Δ_g) and O₂ (³Σ_g⁻) observed at 0.20 torr with the microwave frequency of 8.873 GHz. (a) EPR spectrum of O₂ (³Σ_g⁻) before excitation. (b) EPR spectrum of O₂ (¹Δ_g) and O₂ (³Σ_g⁻) under excitation. Reproduced, with permission, from [43].

7. Summary of the relaxation times estimated in the articles cited above.

The few cases in the literature for which values are reported for T₁ of O₂ are summarized in Table 1. Electron spin relaxation of O₂ in the gas phase is strongly dependent on concentration of O₂. Lines are very broad in normal air and narrow as the pressure is decreased. At a few tenths of a mm of Hg, the EPR line width corresponded to ca. 1×10⁻⁷ s. At the other temperature extreme, O₂ trapped in a lattice at 1.5 K was estimated to have a relaxation time < 5×10⁻⁵ at 1.5 K. In fluid solutions of low-viscosity solvents such as water, at room temperature, T₁ for O₂ is about 10⁻¹¹ s.

Table 1.

Estimates of T₁

condition	T1 (s)	comment	Ref.
gas phase	10−7	line width extrapolated to low pressure	[16]
	6×10−8	assuming T1 = T2 from line width	[13]
fluid solution	5–10×10−12	in water, room temperature	[24]
	(1 ± 0.4) × 10−11	in water, 25 °C	[21]
	9.1×10−12	in benzene	[22]
solid at low temperature	<5 ×10−5	1.5 K in a cage of β-quinol clathrate	[40]
	1.4×10−8	frozen Xe, 2.3 K, 0.96T	[39]
	< 10−8 s at 77 K and < 2×10−11 s at higher temperatures	in spin-labeled polystyrene	[41]
	about 10−12	silica gel at 77 K	[42]