Electron Paramagnetic Resonance Transition Probabilities of Gas

Jun 16, 1980 - Rockwell Internatbnal Science Center, Thousand Oaks, Callfornla 9 1360 and H. 0. Laeger. Rockefdyne Division, Rockweli Internatbnal ...
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J. Phys. Chem. 1980, 84, 3040-3045

Electron Paramagnetic Resonance Transition Probabilities of Gas-Phase Molecular Oxygen I. B. Goldberg" Rockwell Internatbnal Science Center, Thousand Oaks, Callfornla 9 1360

and H. 0. Laeger Rockefdyne Division, Rockweli Internatbnal Corporatbn, Canoga Park. California 9 1304 (Received: June 16, 1980; In Flnal Form: July 18, 1980)

Molecular oxygen has been used extensivelyto calibrate electron paramagnetic resonance (EPR) spectrometers for the quantitative measurement of gas-phase concentrations. Because of the large exchange interaction between the two unpaired electronsand the coupling of rotational states to electron spin states, calculationof the transition probabilities is not simple, as it is in the case of most atoms and diatomic molecules. The transition probabilities which are proportional to the square of the spin component perpendicular to the magnetic field, 41SJ2, and the conversion factor between frequency and magnetic field units, dv/dB, are dependent on the magnetic field. The only published values are approximate, they were calculated for magnetic fields which correspond to one resonance frequency, and they are not sufficiently accurate to permit optimum use of cuurrent EPR spectrometers. In this report, values for 41SJ2 and dv/dB are recalculated for 36 key absorption lines in the frequency range 8.5 to 9.6 GHz, commonly employed in EPR spectroscopy. Many of the values deviate significantly from the published values and show significant dependence on the magnetic field. Calculated EPR intensities were found to be in agreement with experimental ones with a precision of f3% or better.

Introduction The greatest advantage of using electron paramagnetic resonance (EPR) to determine concentrations of paramagnetic species is that any other paramagnetic material can be used as a standard, provided that the geometry of the sample and cavity and the dielectric properties remain unchanged throughout the series of measurements.112 Since these conditions are easily met in gas-phase experiments, O2was recommended3-I as a quantitative standard for atoms and nonpolar molecules because of its strong microwave absorption, its multitude of accessible lines, and its ease of preparing and measuring accurate concentrations. Since then, O2 has been used extensively for determining concentrations of atoms and molecules produced in microwave discharges and in gas-phase chemical reacMost recently, EPR has also been used extensively to measure yields of O2('A,) produced in various chemical


The major difficulty in using O2 as a quantitative standard is that the magnetic transition probabilities and, therefore, the absolute EPR signal intensities are not easily calculated, as they are for most atoms and diatomic molecules that have been measured. The theory of the spin-rotation and spin-spin interactions in ground-state oxygenlo and the interaction of oxygen with a magnetic field" were first described in detail in 1955. In ref 11, transition probabilities and EPR signal intensities for 17 lines were reported for one microwave frequency, 9.477 GHz. However, the range of frequencies typically used for quantitative gas-phase measurements is between 8.6 and 9.5 GHz, and the spin interactions are strongly dependent on the resonance condition. Furthermore, the calculations presented in ref 11 were done without the aid of a computer and were only accurate to within a few percent. Although this was sufficient to account for the EPR spectra of 02,modern EPR systems are capable of much greater precision.12 Consequently, it is important to ascertain the reliability of the calculation and to provide more accurate parameters with which to compute the signal intensity over a wide frequency range. In this work, 0022-3654/80/2084-3040$01.0010

we present values of the EPR intensities calculated for the X-band (8.4-9.6-GHz) frequency range and evaluate the precision of the theoretical calculation.

Experimental Section EPR data of lines of 02(3Eg) were obtained on a Varian E-9 spectrometer; the data were recorded on a NicoletInstrument Corp. Model 1072-instrument computer with a time base sweep unit (Model SW-718) and an A-D converter (Model SD-71B). Data acquisition was initiated by a trigger pulse from the r-y recorder on the EPR spectrometer. Spectra over magnetic field ranges of 10-40 Oe (1Oe = 0.1 mT) for 60-120 s were recorded by using 256 data points. At least four lines were recorded for each set of measurements. An oscilloscope was used to monitor the convergence of the integrals. Oxygen (Matheson, 99.95% purity) ws monitored by an MKS Baratron capacitance manometer. Typically, the pressure was approximately 70 Pa, measured with an accuracy of kO.2 Pa by using a Baratron capacitance manometer. Theory Interaction of O2 in a Magnetic Field. Although Tinkham and StrandberglOJl and TischeP provide detailed descriptions of the theoretical treatment of 02(32,-) interaction with a magnetic field, it is important to review the basis of the calculation and to state the approximations used. Because 02(31: -) is a homonuclear diatomic molecule with no orbital a n d a r momentum, the quantum number L is 0. Thus in the symmetric ground state, the rotational quantum numbers, K , must be odd. The spin quantum number S , which is equal to 1, can then couple with the rotation, so that the total quantum number J is given by J=K,Kkl (1) For most EPR measurements, the spin-spin interactions and the rotational energy level separations are much larger than the Zeeman splittings; therefore the only spin transitions detected are those in which the change of the spin 0 1980 Amerlcan Chemical Society

EPR of Gas-Phase Mollecular Oxygen

The Journal of Physical Chemistty, Vol. 84, No. 23, 1980 3041



zol “1

line. Transitlons

component in the field direction ASz = fl. From eq 1, this requires that AMJ = f l where MJ = -J, -J+l,...,J. Those transitions in which the change of the component of spin parallel to the magnetic field, ASz,is zero are weak, although several can bel detected. Typically for an EPR transition, AJ = fl or 0. However, for 02,transitions of A J = f l occur at frequencies close to that of the spin-spin splitting (fine structure splitting) which is approximately 59 GHz (see Figure l), and most of these transitions therefore occur outside of the usual magnetic fields used in EPR measurements at -9 GHz. Because of the mixing of states due to spin-rotation interactions and incomplete decoupling of the spin arid rotation by the magnetic field, transitions with AJ = 2 become allowed, and in many cases these are very intense. For the case J = K , the spin contribution to the state is very small, since S 0, so that the effective g factor is of the order of 2 / J ( J + 1). This is too small to observe transitions at reasonable magnetic fields at -9 GHz. One


exception to this occurs for the state J = K , M j = -J. Because of admixture of J = K + 1and J = K - 1states, the energy of the state decreases as the field is increased, while the energies of the other states increase and slowly diverge from each other. Thus, the transition (K,J = K , MJ = -4 (K, J =: K, MJ = -J + 11 can be observed. Since only the odd K states can exist, transitions with AK = f l cannot take place. As a result, the transitions that are observed by EPR are principally ( K , J = K f 1,MJI ( K , J K f l , hfj f 1) (AJ = 0, AMj = fl) (2)




= K f 1, MJI ---* ( K , J = K rl,kfj f 11

with the unique case ( K ,J = K , MJ = -JI --.* (K, J = K, MJ= -J f 11

(AJ = f2,AMJ

fl) (3)

(AJ = 0, AMj = +I) (4)


The Journal of Physical Chemistry, Vol. 84, No. 23, 1980

TABLE I: Values of Spin and Rotational Parameters of Parameters of 0,

symbol g factor


rotational g factor orbital g factor rotational constants, GHz

gr g1

Bo Bl

spin-spin coupling, GHz spin-rotation coupling, GHz


A1 p

value 2.002025 -0.000126 -0.002813 43.100518 -0.000145 59.501342 0.000058 -0.252586

ref 17 17 17 18 18 18 18 18

The energy of different J states as a function of magnetic field for K = 3 are shown in Figure 1. The details of the calculation of the interaction of 02(32;) in a magnetic field are described in ref 11 and need not be reiterated in detail. The method consists of the following: (1) calculating the ground-state wave function including rotational states and spin-spin, spin-orbit, and spin-rotation interactions in the absence of a magnetic field by using Hund’s case (a) basis set; (2) calculating the magnetic field interaction by second-order perturbation theory and determining the wave function; (3) transforming to Hund’s case (b) basis set; (4) calculating the spin projections parallel and perpendicular to the magnetic field. In the absence of a magnetic field, the Hamiltonian is given by

A = grot + Ei,, + Aso+ Hsr


described below. The rotational Hamiltonian is given by

fir,,= h(Bo + B1 1 P + KI)R2


where B1 represents the centrifugal distortion term. The difference between K and K‘ is that K may no longer be a good quantum number since it may contain a contribution from small residual orbital angular momentum. The spin-spin interaction Hamiltonian is given by

Has= 2/3(Xo and the spin-rotational, tions are given by

+ X11K1)(3SZ2- 9)


RBI,and spin-orbit, REO, interac-

Ha, + Hso = hpK.8


Values of the molecular constants used in the calculations presented here are given in Table I. Since the molecular parameters of Table I were used rather than the parameters determined by Tinkham and Strandberg,’l the transformation coefficients between case (a) and case (b) couplings were determined from the more accurate data of Tischer.13 The parameters bJ and d J in the notation of ref 10 is equivalent to U J and C J of ref 13. The relationship between transformation coefficients to change basis sets from case (a) to case (b)coupling is given by eq 55 of ref 10. Distortion of the molecule with rotational level can be neglected in second order because we only need to compute states of relatively low K. As a result, the second-order perturbation calculation is used for the ground-state vibrational and electronic energy levels. Thus the rotational Hamiltonian, including residual orbital angular momentum, becomes Hrot =

[email protected] - 2hBd.L

+ hBo(LX2+ L:)

where the last term of eq 8 is a constant and need not be considered. The solution of eq 4-9 gives the eigenvalues and eigenvectors for Hund’s case (a) coupling basis set. I t is relatively simple to convert the final eigenfunctions from Hund’s case (a) to case (b) by an appropriate transformation. Because there is no significant orbital angular momentum, Hund’s case (b) more closely represents the molecular coupling. It is simpler to represent O2 spin functions in case (a), since J. MJ,S, and S, are diagonal in the basis set, while for case (b), J, K , S, and MJ are diagonal. Although the calculations of the wave functions are carried out in case (a), the final states are described in terms of the more representative case (b) basis set. In solving the second-order perturbation calculations, it is also necessary to use the energies Y- and ut which are, respectively, E(J = K ) - E(J = K - 1) and E(J = K ) - E(J = K + 1). Values reported in ref 15 were used rather than the values of Tinkham and Strandberg. Once the eigenvalues and eigenvectors are determined, the perturbation of a magnetic field can be added to the calculation, eq 11, so that the spin transition porbability HB = gpBB.9 (11) can be calculated. The matrix involves terms of K and K f 1, with higher order terms. Since the Hamiltonian matrix includes three J states for each K state, and the energies of the rotational levels are large with respect to the Zeeman interaction, the principal elements of the Hamiltonian matrix lie along the diagonal in K. The magnetic interactions in each K state can be written as a 3 X 3 matrix in which second-order perturbation theory includes states of K - 2 and K + 2. These matrices are easily diagonalized for each magnetic field, giving the magnetic energy and the wave functions in terms of basis set K , K f 1 $J = UK-14K-1 + UK4K + [email protected]+l (12) Rather than include the orbital and rotational interactions with the magnetic field in the Hamiltonian equation, these are treated by perturbation theory on the wave functions. The rotational and orbital g factors are given in Table I. The wave function was not recalculated, since these energy terms are small and would not result in a significant change of the coefficients. The transition dipole matrix element I(K,’M,I&IK,Md)l2 between states i and J’ is equal to 4 ~ ( K ~ M j ~ ~ , ~ Kas’ M , ) ~ described in ref 16. These are calculated by computing the projection of S onto the axis of the oscillating field. It is important to change from Hund’s case (a) basis set coupling to the case (b) basis set coupling, since S, is only diagonal in a case (a) molecule. Since there is no significant orbital angular momentum that strongly couples with the electron spin, the effect of applying a magnetic field is to partially decouple the spin and rotational angular momenta. As a result, the wave functions and thus S, must be calculated for each applied field. EPR Intensities. Westenberg4p5p8has shown that the concentration, C, of a nonpolar gas-phase species undergoing a nondegenerate transition is given by


The spin-orbit and spin-spin terms can therefore be used in the second-order Hamiltonian

[email protected]) hA*L*S+ 2hBL.K

Goldberg and Laeger


where uo is the microwave field, Z is the partition function of the atom or molecule, Ei is the energy of the molecule in its electronic or rotational state, p i j is the transition probability, geffand D are defined below, and K I is an

The Journal of Physical Chemistry, Vol. 84, No. 23, 1980 3043

EPR of Gas-Phase Molecular Oxygen

TABLE E1 : Calculated Transition Probabilities of 0 2 ( 3 X g-) Magnetic Resonance Absorption Lines at 9.477 GHz calcd transition magnetic line field K J MJ dv/dBa 41S,Iz

instrumental constant. For O2

The effective g factor, geff,is defined as

and reflects the change from frequency units to the magnetic field units used here. Because of the strong dependence of the spin-rotation wave function on the magnetic field, both IS,( and geffmust be calculated for each magnetic field. The double integral of the first-derivativesignall is given by DI =

r" r E S dB'dB Jo J o AB,P1/2

where S is the EPR signal, A is the signal amplifier gain, B, is the modulation amplitude, and P is the microwave power incident in the cavity. In eq 13, only the term in square brackets is dependent on the molecule itself, so that it is convenient to define the parameter Q as h/kB(dv/dB)Z g241Lgzli? exp[-J(J + l)B/kT]



which is then equivalent to the parameters tabulated by Westenberg.* In the ?nighrotational temperature limit, the partition function of' 02(3Z;) approaches 3kT/2jBo. To improve the precision, we found that a better approximation of 2 is given by

The higher order expression fro the rotational energy, E,, = BJ(J 1) + BlJ2(J + 1)2,changes the partition function by less than 0.1% at 300 K. As a result, the second-order term was neglected. The temperature clependence of Q occurs only in the exponential and the partition function; it is easily shown that d(ln Q) 1 hB&J + 1) .(19) dT T kT2 This relationship is extremely convenient when making measurements over a temperature range of about 20 deg. It is also easily seen that the temperature dependence of Q is primarily a function of the rotation quantum number J.



Results a n d Discussion Tinkham and Strandbergll list 36 EPR transitions of 02(3Z;) measured a t 9.477 GHz. For ease in comparing their data with ours, we have numbered in consecutive order the transitions listed in Table I on p 958 of ref 11. Of these transitions, Westenberg4 selected seven lines as primary standards, with one additional line (transition 34) being used extensively for calibration when 02(lAg) is to be m e a s ~ r e d . ~ J ~ The energy levels of the J , MJ states for K = 3 are shown in Figure 1. The major contribution to the separation of states J = K f 3. from d = K i n the absence of a magnetic field arises from the spin-spin interaction, equivalent to 59.5 GHz. The smaller energy difference between states

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 a

1402.1 3 2342.8 3 3354.0 3 4 156.2 5 4503.5 7 5159.7 3 5265.8 2 5354.6 5 1 5584.8 5770.6 3 5987.4 3 5987.4 5 6088.8 1 6513.1 5 6685.9 7 6712.1 1 7021.6 11 7065.9 9 7256.1 1 7357.1 7 7522.7 3 7894.2 5 8038.0 13 8106.8 5 8273.7 5 8577.1 3 8642.1 '7 8707.3 '7 8731.5 5 8816.3 'I 8969.0 !3 9001.3 11 9033.3 9 3 9617.9 3 10460.0 1. 10715.9

2'4 2'4 4'2 6'4 8'6 4'2 2'4 4'6 1 2'4 4'2 6'4 2 6'4 8'6 2 10 1 2 8'10 2 6'8 2 4'6 12 + 14 4'6 4 4 8'6 6 6 8 8 12 10 4 3 1


2'3 1'2 - 3 '-2 -3 '-2 - 3 '-2 -1 '-2 1'0 1'2 -1 '0

1'0 - 2 '-1 -1 '-2 1 3 2 -2'-1 -2'-1

1'0 3'4 2'3 -1'0 l + 2 0 '-1 1'0 3'4 0'1 0 '-1 -1'0 -1'0 1'0 -1 + o

1'0 1'0 0'1 0'1 3'4 -3'-2 0'1

3.884 2.359 3.718 2.407 1.840 2.702 1.331 1.839 1.966 1.361 2.239 1.890 1.743 1.751 1.530 1.426 2.1 51 2.014 1.302 1.855 1.769 1.712 2.103 1.729 1.771 1.697 1.695 1.805 1.745 1.826 1.799 1.732 1.809 1.321 1.575 0.485

0.00719 0.03606 0.06819 0.1665 0.2269 0.04295 0.03471 0.4000 0.7468 0.5536 0.4891 0.07464 1.2125 0.6594 0.7154 1.485 0.7914 0.8362 1.259 0.9783 0.3750 0.2397 1.147 1.3288 0.34 21 1.4977 1.4604 0.3237 1.5180 1.5750 0.3445 1.6071 1.6412 0.9343 0.5808 0.2089

In units of MHz/Oe; for units of GHz/T, multiply by


J = K f 1and J = K - 1 - EJ+J at zero magnetic field is principally the result of spin-rotation and spinorbit interactions. This difference, expressed in frequency units, varies between -4.04 GHz for K = 3 and 6.6 GHz for K = 15, causes most of the A J = f 2 transitions to occur at smaller applied magnetic fields than the A J = f l transitions, as shown in Figure 1. This is also evident from the data in Table 11. Table I1 lists the 36 transitions of O2 with calculated values of dv/dB and 41S,li?. The calculated values of d v / U agree within *2.5% of those previously reported.ll However, of the 17 values of 41S,li? exp[-B(J)(J l ) ] reported,l' four (no, 7,10,11, and 36) differ by more than 5% from those Calculated here. The experimental consistency of the double integral values is shown in Figure 2, in which the product T(DI)Q/C should be constant. We find that of the 30 lines which we could measure without significant overlap with other lines, the standard deviation of the mean was 2.5% of the mean value. This is in contrast to the 21% previously reported. Lines 1 and 2 were not included in calculating the mean value because they were relatively weak, and double integrations were not reproducible to better then f5%. This also occurred for several other measurements which were not included in the average, but are shown in Figure 2. Several repeated series show that the range of double integral values falls in the range of f1.5% with several exceptions, so that it is not likely that the deviation of all of the data from the



The Journal of Physical Chemistry, Vol. 84, No. 23, 1980

Goldberg and Laeger


Figure 2. Values of T D Q / c for 31 transitions of O~('Z.J with line number based on the numbering of Table I of ref 11. Open circles indicate data not used in average: clrcied data points indicate primary lines.

TABLE 111: Frequency Dependence of Transition Probabilities and Resonant Field for the Principal 0, Standard Linesu ~

identification Ib 8 9 13 16 14 26 19 34











1 1


1 5 3





2 2 6'4 4 2 4

9.000 GHz

M 1'2

0'1 1' 2 0'1 - 2 + -1 -1'0

-1' 3'4





B,d Oe



5094 5343 5814 6393 6237 8293 6910 9242

1.817 1.945 1.727 1.429 1.730 1.660 1.297 1.294

0.3674 0.7354 1.2010 1.4862 0.6265 1.4868 1.2633 0.9217

A 4 IS, l a /



0.045 0.044 0.033

0.0666 0.0241 0.0242 -0.0021 0.0725 0.0238 -0,0091 0.0431

0.000 0.045 0.076 0.011 0.060

a Calculation valid to *1in last figure for resonant frequency from 8.5 to 9.6 GHz. Line number in Table I. 1 Oe = 0.1 mT. e MHz/Oe (1MHz/Oe = 0.1 GHz/T). f Changes in du/dB and 4 IS, la per W e ~ t e n b e r gassignment. ~?~ GHz in resonant frequency. g Commonly used for calibrating O,('A,) absorption (see ref 9 and 18).

mean is entirely experimental. This is reflected by the data of lines 5, 21, and 22 shown in Figure 2. Nevertheless, there appears to be no consistent trend in the value of T(DI)Q/C with values of K or whether AJ = 0 or f 2 . In some cases, weak absorptions or wings of nearby lines may influence the calculated value of the base line and thus alter the value of the double integral. Thus the magnetic field range over which the double integral is calculated and the pressure can slightly affect the result. Data for calculating the magnetic field dependence of seven of the eight lines recommended as primary standards4v5are given in Table 111. These are shown as circled points in Figure 1. In addition to du/dB and 4lS,lit, the changes of these values with microwave frequency are given so that Q can be calculated for any microwave frequency between 8.4 and 9.6 GHz. Experimental consistency of T(DI)Q/c is shown in Table IV. For these seven lines the relative standard deviation of the mean value was about 1%. Values of the resonant magnetic field, B,, for frequency v can be calculated by using both dv/dB and A(dvldB)lm by ( u - 9000) 1 (u - 9000)2 B, - B, = + (20) du/dB 2 [A(du/dB)/AB] where B, is the resonant field in Oe at 9000 MHz. This work provides accurate parameters which allow accurate calculation of EPR intensities of 02(3z2,-) in order to calibrate EPR spectrometers for gas-phase concentration measurements. These values are useful for microwave

TABLE IV: Calculated and Experimental Line Intensities at 25 "C and 8.85 GHz identification double integral T(DI)&/ P IIb Q calcd X loF6 u-&c x 10-'O

8 B 9 c 13 16 14 26 19 34


K c

240.93 103.75 56.66 37.64 133.15 46.44 40.10 58.94

0.5626 1.2630 2.332

0.9 0.4 0.3

3.845 3.905 3.910

inseparable lines 0.9951 2.783 3.182 2.191

0.4 0.6 0.4 0.5

3.863 3.869 3.804 3.870 mean 3.867 u 0.036 u/mean (0,009)

(25 lines) 3.880 0.096 0,024

Line number in Table I. Westenbergr5 assignment. Commonly used for calibrating O,(lA,) absorption (see Percent of mean value. ref 9 and 18).

frequencies nominally from 8.4 to 9.6 GHz. Lines that have previously been selected as primary standards appear most suitable for precise calibrations. The results of our measurements indicate that the theoretical intensities calculated from parameters determined from the method of Tinkham and Strandbergll can be accurate to better than f 2 % , but previously published values are not sufficiently accurate for the optimum utilization of EPR for concentration determinations. The values of du/dB and 41S,I2 presented in this paper permit accurate gas-phase

J. Phys. Chem. 1980, 84, 3045-3049

concentrations to be determined by EPR when 02(3Eg) is used as a calibration standard. Acknowledgment. The authors appreciate helpful discussions with Robert Coombe, the assistance of Richard Moore in carrying out experiments, and the editorial comments of Paula Cooper.

References and Notes (1) I. B. Qoldberg and A. J. Bard, "Analytical Applications of Electron Paramagnetic Resonance" in "Treatise on Analytical Chemistry," I. M. Kolthoff, P. J. Eiving, and M. M. Bursey, Ed., in press.

(2) 0. R. Eatan and SI.S. Eaton, Bull. Magn. Reson., 1, 130 (1980). (3) S. Krongelb and fv!, W. P. Strandberg, J. Chem. Phys., 31, 1196 (1958). (4) A. A. Westenberg rind N. de Haas, J. Chem. Phys., 40,3087 (1964). ( 5 ) A. A. Westenberg, J . Chem. Phys., 43, 1544 (1965).

(6) (7) (8) (9) 10) 11) 12) 13) .14)

(15) (16) (17) (18) (19)


K. M. Evenson and D. S. Burch, J. Chem. Phys., 44, 1715 (1965). C. J. Ultee, 4. Appl. Phys., 37, 1744 (1966). A. A. Westenberg, Prog. React. Kinet., 7, 23 (1973). D. J. Bernard and N. R. Pchelkln, Rev. Sci. Instrum., 49, 794 (1978). M. Tlnkham and M. W. P. Strandberg, Phys. Rev., 97, 937 (1955). M. Tinkham and M. W. P. Strandberg, Phys. Rev., 97, 951 (1955). I. 8. Goldberg, J. Magn. Reson., 32, 233 (1978). R. Tischer, 2.Naturforsch. A, 22, 1711 (1967). K. D. Bowers, R. A. Kamper, and C. D. Lustii, Rcc. R. Soc.London, Ser. A , 251, 565 (1959). P. H. Krupeniu, J . Phys. Chem. Ref. Data, 1, 423 (1972). J. E. Wertz and J. R. Bolton, "Electron Spin Resonance: Elementary Theory and Practical Applications", McGraw-Hill, New York, 1972, Appendix B. L. Tomuta, M. Mizushlma, C. J. Howard, and K. M. Evenson, Phys. Rev. A , 12, 974 (1975). W. M. Welch and M. Mizushima, Phys. Rev., 143, 31 (1966). A. M. Falick, Ph.D. Dissettatlon, The University of California, Berkeley, Calif., June 1967.

INDO Study of the Anion Radicals of Acetic Acid and Acetamide. Nonplanarlty and Barriers to Methyl Group Rotation D. Siuryanarayana and M. D. Sevllla" Depaitment of Chemlstty, Oakland University, Rochester, Michigan 48063 (Received: March 13, 1980; In Fhal Form: June 24, 1980)

The imion radicals of acetic acid and acetamidewere investigated by u h g the INDO method. Energy calculations suggest that the radical RC(Xl)(X2)(with R = CH3;XI = 0-!OH; XSl= OH and NH2)is pyramidal rather than planar with a nonplanar angle 9 = 27O in the case of R-C(0-)(OH). A comparison of the calculated and experimental &proton and 13C hyperfine splittings (hfs) suggests a dightly different value for 9 (~35'). This latter value is in reasonable agreement with the value of 40° calculated previously from experiment. INDO calculationsfor the remaining radicals gave similar values for 9. For nonplanar radical structures, it was found that the angular dependence of the INDO-calculated 0-proton hfs did not obey a simple cosine square rule. Instead the calculated splittings have been fit by using the relation asH = Blp" cos 8 + B2p" cos28 with Blp" = 8.8 and B,p" = 28.0 G for the acetic radical. The threefold barrier height (V3)as obtained from the INDO calculationswas found to increase monotonically with 4. This suggests that the relatively high activation energies (>2.5 kcal/mol) reported for acetic acid and acetamide anions in our previous work are therefore a consequence of pyramidal geometry at (Y carbon. In light of these results, our previously reported threefold potential barrier heights for CH3rotation in acetic acid and acetamide radicals, which were analyzed by using a simple cosine square relation, have been reevaluated. The present analysis of our previous experimental data, including nonplanarity, gives a better fit yielding activation energy parameters as 2.4-2.6 kcal/mol for these radicals. These values are slightly lower than those values previously reported (2.7-3.1 kcal/mol), where the effect of nonplanarity on the 0-proton splittings was not considered.

I. Introduction Irradiation of certain monocarboxylic acids,l" amino and analogue13~~~ have produced carbon-centered anion radicals of structure I where R = H, CH3, NH3+,etc., R-C(



\ x2


and X1and X2 represent electronegative groups such as 0-, OH, NH2,etc. A number of ESR (electron spin resonance) studies m well as theoretical calculations have been reported on the species I."*5 We previously reported the ESR spectra of radicals 11-IV in aqueous glasses containing n-