Cepstral and Direct Analysis of ESR Spectra
however, that the effect of electron gain or loss on the barrier to inversion of 9,lO-dihydrophenanthreneis likely t o be small. Experimentally we observe for the tetramethoxydihydrophenanthrene cation radical (IIa’) a barrier considerably larger than those reported for the 9,lO-dihydrophenanthreneanion radical. This result may be due to the presence of the methoxy substituents which undoubtedly cause a considerable redistribution of spin density as shown by the averaged P-methylene splitting of 1.48 G for the 9,lO-dihydrophenanthreneanion and 5.20 for IIa’. Unfortunately, neither the 9,lO-dihydrophenanthrene cation radical or IIa- have been prepared for direct comparison.
Acknowledgment. We gratefully acknowledge support for this research by Grant No. CHE76-04166 from the National Science Foundation. References and Notes (1) Preliminary report presented at the 173rd National Meeting of the American Chemical Society, New Orleans, La., March, 1977. (2) P. D. Sullivan and J. Y. Fong, Cbem. Pbys. Lett., 38, 555 (1976). (3) P. D. Sullivan and J. Y. Fong, J . Pbys. Cbem., 81, 71 (1977). (4) D. H. Whiffen, Mol. Pbys., 6, 223 (1963). (5) D. H. Miles, J. Bhattacharyya, N. V. Mody, J. L. Atwood, S. Black, and P. A. Hedin, J . Am. Chem. SOC.,99, 618 (1977). (6) S. M. Kupchan, R. W. Britton, M. F. Ziegler, C. J. Gilmore, R. J. ReSrNO, and R. F. Bryan, J . Am. Cbem. SOC.,95, 1335 (1973).
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(7) R. F. Homer, G. C. Mees, and T. E. Tomlinson, J . Sci. Food Agric., 11, 309 (1960). (8) F. M. Ashton and A. S. Crofts, “Mode of Action of Herbicides”, Wiley, New York, N.Y., 1973. (9) A. Ronlan, 0. Hammerich, and V. D. Parker, J . Am. Cbem. SOC., 95, 7132 (1973). (10) I. C. Calder and W. H. F. Sasse, Aust. J . Cbem., 18, 1819 (1965). (11) P. D. Sullivan and M. L. Williams, J . Am. Chem. SOC.,98, 1711 (1976). (12) J. Heinzer, Mol. Pbys., 22, 167 (1971). (13) P. D. Sullivan, J . Phys. Cbem., 74, 2563 (1970). (14) I. C. Cakier, T. M. Spotswood, and W. H. F. Sasse, TetrahedronLeft., No. 95 (1963). (15) F. C. Adam, Can. J . Cbem., 49, 3524 (1971). (16) J. Vander Kooj, C. Cooijer, N. H. Velthorst, and C. Maclean, Red. Trav. Cbim. Pays-Bas, 90, 732 (1971). (17) M. Iwaizumi, T. Matsuzaki, and T. Isobe, Bull. Chem. SOC. Jpn., 45, 1030 (1972). (18) P. D. Sullivan and J. R. Bolton, Adv. Magn. Reson., 4, 39 (1970). (19) D. H. Levy and R. J. Myers, J . Cbem. Pbys., 43, 3063 (1965). (20) E. T. Strom, E. G. Janzen, and J. L. Gerlock, Mol. Pbys., 19, 577 (1970). (21) P. J. Krusic, J. P. Jesson, and J. K. Kochi, J . Am. Cbem. SOC., 91, 4566 (1969). (22) C. Elschenbroich, F. Gerson, and V. Boekelheide, Helv. Cbim. Acta, 58, 1245 (1975). (23) M. B. Yim and D. E. Wood, J . Am. Chem. SOC.,97, 1004 (1975). (24) H. Tylli, Fin. Kemisfsamf. Medd., 81, 113 (1972). (25) P. D. Sullivan and J. R. Bolton, J . Magn. Reson., 1, 356 (1969). (26) M. Oki, H. Iwamura, and N. Hayakawa, Bull. Cbem. SOC.Jpn., 38, 1452 (1963). (27) K. Mislow, M. A. W. Glass, H. B. Hopps, E. Simon, and G. H. Wahl, J . Am. Cbem. SOC.,86, 1710(1964).
Cepstral and Direct Analysis of Electron Spin Resonance Spectra of Substituted Triarylaminium Cation Radicals. Correlation of Spin Distribution with Substituent Constants Gerald A. Pearson,‘ Martin Rocek, and Robert I. Walter” Department of Chemistry, University of Illinois at Chicago Circle, Chicago, Illinois 60680 (Received September 12, 1977)
Hyperfine coupling constants have been determined for a series of 4,4’,4’’-trisubstituted triphenylaminium cation radicals with a variety of substituents in the three para positions. For many of these compounds, these parameters can be evaluated in the conventional manner from the ESR spectra. They also have been determined independently by the method of cepstral analysis of Kirmse, and an assessment is given of the value of Kirmse’s method. Proton coupling constants are available in a few cases from NMR contact shift studies. Agreement among the parameters assigned by these different methods is generally good, and the results appear not to be highly solvent or concentration dependent. These data, together with values from the literature for two compounds not reported here, cover 14 cation radicals of this series. The central nitrogen and the ortho hydrogen hyperfine coupling constants show an acceptable correlation with the Hammett u’ parameters for donor substituents, but the acceptor substituents fail to fit this (partial) correlation.
Introduction Hyperfine coupling constants from the ESR spectra of the tri-para-substituted triphenylaminium cation radicals have been reported in a number of publication^.^-^ In spite of this substantial effort, spectra have been fully analyzed in only six cases (including the unsubstituted radical from triphenylamine), and there are serious disagreements in the literature about the assignments for three of these. A scheme has been proposed for classification of substituent effects on some properties of free radicals; in this scheme, class S radicals have been defined2 as those in which both donor and acceptor substituents on aromatic rings directly bonded to the atom which carries the major spin density alter properties in the same direction. Only a few types 0022-3654/78/2082-1185$01.OO/O
of free radicals meet the structural criterion2 for assignment to class s, and of these the triarylaminium cations are the most suitable on stability grounds for study by conventional methods. Some reservations have been expressed8 over the validity of the assignment of these radicals to class S, in view of the small number of cases for which data have been available. Thus it is desirable to have reliable assignments of hyperfine coupling constants for enough substituents in this series of radicals to establish firmly the effects of substitution on spin distribution. In particular, more data for radical cations substituted by electron acceptor groups are needed to verify the assignment of these radicals to class S. If possible, the hyperfine parameters should be verified by
0 1978 American
Chemical Society
1186
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
assigning them by several independent procedures. Analysis of the ESR spectra of some of the triarylaminium cations presents special problems. The coupling of electron spin to the 14Nnucleus of the central nitrogen atom divides the spectra into three sections which always overlap due to additional coupling with the large numbers of protons in these radicals. Furthermore, there is solventand temperature-dependent line broadening in the outer sections of the spectra which originates with the I = f l spin states of this nitrogen. The consequence is that lines in the wings of all three spectrum sections are lost either by line broadening or by overlap with lines from the central section, for which IN= 0. These characteristics limit the amount of information which can be extracted from direct examination of these spectra, particularly when the experimental spectrum has a poor signal-to-noise ratio, proton coupling constants whose ratios are close to integers, or accidental line overlap. Thus one becomes dependent upon trial-and-error methods of analysis which can be misleading since more than one set of coupling constants often can produce a reasonable fit of a calculated to the incomplete observed spectrum. In this paper, we compare parameters assigned by a conventional scheme with those assigned independently by the method of cepstral analysis of Kirmseag In some cases, it is also possible to compare them with parameters determined from NMR contact shift studies.lOJ1 These new results, together with literature data for the u n s u b ~ t i t u t e d and ~ , ~ the trinitro-substituted7 radicals, permit a test of the substituent effects in these radicals for a total of 14 substituents.
Experimental Section Preparation of most of the triarylamines required for this study has already been described.11-14 Tris(paminopheny1)amine was prepared by reduction of the trinitro compound. 4,4’,4”-Tri(tert-butylphenyl)amine. This compound was prepared by the Ullmann reaction1* using p-tert-butylaniline (freshly distilled from zinc dust under vacuum) and p-brorno-tert-butylbenzenel5 in DMF solution. Crude solid (10 g) recovered from the reaction mixture after washing with 6 M hydrochloric acid was decolorized by extracting over night (Soxhlet) with pentane. Purification by twofold recrystallization from benzene-acetonitrile and twofold sublimation gave product in 3.7% yield. It sublimes above 210 “C, and melts at 289.0-290.5 “C. Anal. (C30H39N)C, H, N. 4,4”4”-Tricyanotriphenylamine. The modification by Friedman and SchechterlGof the Rosemund-von Braun reaction was used for this preparation. Tris(p-bromophenyl)amine13 (24.1 g, 0.05 mol) was dissolved in 100 mL of DMF, 16 g (0.18 mol) of CuCN was added, and the mixture was stirred under reflux for 5.5 h. It was then poured on ice, solid material recovered, and shaken with 300 mL of 30% NaCN solution. Filtration gave creamcolored solids; the weight after washing was 15.5 g. This sample contained a significant amount of 4-brom0-4’,4”-dicyanotriphenylamine (identified by mass spectrum and qualitative test for Br), which has nearly the same sublimation and chromatographic properties as the desired tricyano compound. Separation was carried out inelegantly by repeated fractional sublimation (product sublimes more slowly), Soxhlet extraction into chloroform, and chromatography on silica gel from benzene. This gave 8.2 g of product which gives a negative Beilstein test for halogen, sublimes above 250 “C, and melts at 340-342 “C. Anal. (C21H12N.4) c, H, N. Preparation of the Radicals. Amines substituted by
G. A. Pearson, M. Rocek, and R. I. Walter
electron-donating substituents were converted to the crystalline aminium perchlorates with silver perchlorate and iodine in ether.12 Amines which contain electronwithdrawing substituents are not fully oxidized by this procedure. Instead, they were oxidized with P b 0 2 in ca. M solutions in the solvent in which they were to be studied. Excess oxidant (which must be completely eliminated, since the radicals are less stable in its presence) was removed by successive centrifugation and filtration. The solvent for most of the ESR studies was reagent-grade trifluoroacetic acid (TFAA), to which was added 5-10% of the anhydride. Radical solutions at 3-5 X M concentration were degassed by successive freezepump-melt cycles and sealed for the ESR measurements. Equipment. Most of the ESR spectra were recorded at the Chemistry Division, Argonne National Laboratory. The spectrometer is a Varian E-9 linked through a Nicolet 1074 Fabritek digitizer-computer which was on line in time-sharing mode to the Chemistry Division Sigma 5 c ~ m p u t e r . ’ ~Spectra were initially stored on disk, then transferred to cards for manipulation at UICC. The arrangement permits accumulation of digital spectra consisting of 4000 data points over a 40-G field scan, and makes it possible to time-average successive scans. Analysis of Spectra. Since most ESR spectrometers now in operation give only spectrum plots, parameter fitting has required the exercise of a fair amount of intuition, and goodness of fit has been a matter of judgment not subject to any quantitative criterion. Well-resolved spectra present no great problem, but spectra with many lines which overlap or are lost in noise give decidedly more ambiguous results. The scheme we have used for the assignment of hyperfine coupling constants from an experimental derivative spectrum involves the following steps: (1) Generate a stick plot from the experimental spectrum. (2) Make tentative assignments of coupling constants based upon prominent line intervals in the stick plot, aided by expectations based upon analogy to accepted assignments in related radicals and/or the results of calculations. (3) Check by computing a stick plot from the assigned parameters; optimize by least-squares fit of line positions to the experimental stick plot. (4) Generate a derivative spectrum from these tentative parameters; refine by optimizing fit to the experimental spectrum. This refinement is carried out both by direct visual comparison of the two derivative spectra, and by comparison of the stick plots generated from the experimental and computed derivative spectra. It should be noted that this scheme places heavy reliance upon the mechanical precision of the plotter which generates the stick and derivative spectra. We observe a variation of up to 2% in line separations measured on spectra generated from the same data over several years time by our Calcomp Model 663 drum plotter. For proton couplings, this error is 20.03 G; for nitrogen couplings, it ranges up to 0.2 G. The error for the x-axis stepping motor operating within specifications is 50.03 G. Possibly the remaining variation is due to changes in paper dimensions which result from changes in humidity at the time plots are made, and during subsequent storage. Variations between plots made within a short time span are within the error of the stepping motor. Computer Programs for Direct Analysis o f ESR Spectra. A conventional program which plots derivative
The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
Cepstral and Direct Analysis of ESR Spectra
ESR spectra computed from an assumed set of coupling constants was used. Another Fortran program generates a stick plot from a digital derivative spectrum by determining the vertical separation between extremum points and the midpoint between them, for each peak in the derivative spectrum. It can be used to generate a stick plot either from an experimental spectrum or from one computed with a trial set of coupling constants. Noise in experimental spectra is converted into additional sticks which can be suppressed on the basis of a minimum intensity criterion. The appearance of stick plots so generated is often quite sensitive to small changes in the coupling constants used to compute the simulated derivative spectrum. Apparent intensities of symmetrically placed lines can differ, and occasionally the sections of the spectrum defined by different I N values switch from apparent even to odd symmetry. Evidently this is due to changes in the phases of overlapping lines, which can add or cancel their contributions to the stick representation. Stick plots generated in this way were used for comparison with the stick plots (prepared in the same manner) from experimental spectra. A third program generates a stick plot from an assumed set of coupling constants and compares it with the experimental stick plot. This is particularly useful for initial determination of rough values for the coupling constants. Computer Program for Cepstral Analysis. The cepstrum of an ESR spectrum, taken as a continuous function S of time or (at constant scan rate) of magnetic field, is given by
cepstrum = ~ - ‘ [ l nIs(S)12]
(1)
Here, 3 is the Fourier transformation operator and 5-1its inverse. The raw spectrum is prepared for the calculation of the cepstrum by successive removal of noise spikes, cubic polynomial smoothing,18 linear baseline correction, and scaling the data to avoid overflow-underflow problems. The program then calculates In lS(S)12;this introduces new noise spikes which originate in the values close to zero produced by the Fourier transformation. These are removed and another linear baseline correction is applied in order to minimize the size of the lineshape-function spike at the origin of the final cepstrum. Multiplication by an exponential decay (which smooths and broadens cepstral lines) prepares the array for the inverse Fourier transform. The real part of this is plotted. The interval used for the cubic polynomial smooth is equal to the distance between derivative extrema of the sharpest ESR line in the spectrum; this choice minimizes line distortion and line broadening. The exponential decay constant is chosen to produce approximately optimum smoothing of the cepstrum. The consequent broadening by all exponential smooths in the cepstrum program is 5.73 data point intervals, or 0.06 G. (The cubic polynomial smooths introduce no line broadening, but do distort the lines.) The noise spike removal subroutine operates in the following manner. Successive seven-point array element averages are computed, along with the corresponding standard deviations. If one of the central three points of this array of seven deviates from the average by more than 2.1 standard deviations, it is deemed to be a “noise spike”. Each such “noise spike” is replaced by the value of a cubic polynomial evaluated for that point, where the cubic polynomial is least-squares fitted to the six nearest “good” points. With this procedure, probability that a random “good” point will be mislabeled as a “noise spike” by the criterion described is ca. 0.036 for baseline regions, and
1107
TABLE I: Summary of ESR Parameters for the Tri-p-tolylaminium Ion Solvent“
XC XC CH,Cl, CH,Cl,
Data fromb ESR CEPS ESR CEPS
aN
ao
9.65
2.11 2.11 2.07 2.06
9.78?
9.51 9.46
am 1.06 1.06 1.04 1.03
%
3.87 3.85 3.89 3.89
a Data for this radical in trifluoroacetic acid (TFAA) Data sources are solution are in Table 11, sample 3. This solvent was 0.5 M ESR, cepstra (CEPS), or NMR. TFlAA in acetonitrile.
much less for rapidly changing spectral regions.
Results Our best-resolved spectra were obtained for the tri-ptolylaminium cation. Values for the coupling constants in two solvents are collected in Table I; the values for TFAA solution are in Table 11, entry 3. The total width of these spectra exceeds the 40-G limit of the computer-controlled spectrometer sweep, so full spectra were obtained by joining two baseline- and amplitude-corrected part-spectra recorded separately, or else the truncated center 40 G spectrum was used alone. It appears that, for a given solvent, the ESR and cepstrum results agree within 1%for the proton hyperfine couplings, and within 2% for the 14Ncouplings. Solvent effects are small for this radical, but it is probable that they are significantly greater than the errors in their determination, since they were measured on plots recorded within a short period of time. The values reported in Table I generally agree well with those in the literat~re.”~-~ In TFAA solution, the ESR and NMR results agree within 4%; the precision of the NMR data is lower than that of the ESR results. It should be noted that these spectra were obtained with solutions which really are not alike: that for ESR studies was slightly contaminated solvent at ca. 3 X M radical, while the sample for NMR was ca. 1.5 M, and contained of the order of 50% (by weight) solute. We conclude that within the error range of the NMR data, the ESR and NMR results are identical, and solvent effects are negligible. Some plots of the ESR spectra of this radical show an additional feature. It is not possible to fit both halves of these spectra equally well with a single 14N coupling constant. The two optimum values differ by 0.04 G, and in all cases the upfield value is larger. We interpret this as a second-order effect on the nitrogen hyperfine splitting;19 its magnitude is in good agreement with the estimated value, 0.03 G. Unfortunately, not all of the plots show this feature, so it is possible that it is an artifact produced by the plotter. Since there is little uncertainty about the values of the hyperfine parameters for this radical, we use it to illustrate certain properties of the cepstra calculated with our computer program. Figure 1 shows (top) the cepstrum calculated from the experimental ESR spectrum of this radical in TFAA solution. The three cepstra below this are calculated from simulated noise-free spectra at 0.16-, 0.07-, and 0.02-G line widths. (The line widths in the experimental spectrum are close to 0.07 G.) It can be seen that all of the cepstra have peaks at separations from the zero abscissa which correspond well with the proton coupling constants given by the vertical lines marked m, 0, p. This is not true for the nitrogen coupling; here, there is only a weak peak, hardly above the noise, in the proper region of the cepstrum computed from the experimental ESR spectrum. The strongest peak close to the value for
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The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
G. A. Pearson, M. Rocek, and R. I. Walter
TABLE I1 : Hyperfine Coupling Constants for Triarylaminium Cation Radicals Sample no., substituent, and solventa,b 1. -NH, in ACN 2. -OCH, in TFAA
3. -CH, in TFAA
Line width, G
Hyperfine coupling constants assigned,d G
0.04 0.25 0.07
4 . -t-Bu in TFAA
0.04
5 . -H in TFAA 6. -SO,^ in TFAA
0.08 0.12
7 . -COOMe in TFAA
0.08
8. -COMe in TFAA
0.30
9. -CN in TFAA
0.23
12. -C1 in TFAA
? ?
14. -C,H, in TFAA
?
a0
7.9 (7.89)f 9.05
1.38 1.38
CEP ESRm ESR NMR ESR NMR ESR NMR ESR NMR
0.18
13. -Br in TFAA
aN
ESR CEP ESR NMR ESR CEP NMR ESR CEP ESR~ ESR CEP ESR CEP ESR CEP
ESR‘
10. -NO, in TFAA
11. -F in TFAA
Method‘
9.63’ 9.60 9.62 9.52 10.19 9.75 9.76 9.73 9.72 ? 9.69 9.67 9.72 9.76 10.05 9.80
g -1.80 2.09 2.10 - 2.02 2.13 ? (2.1 O)f 2.26 2.26 2.27 2.28 2.29 2.26 2.31 2.30 2.28
am (0.14)e (0. 14)e 0.60 t 0.60h
1.05
+
1.05 1.05 1.05 1.05 1.22 1.25 1.26 1.14 1.32 1.35 1.33 1.38 1.35
2.23
1.00
- 2.08
t 1.00
UP
? (2.73d 0.60 t 0.65h 3.87 3.87 3.82 0.14 ? (0.29)f 3.27
+
0.175 0.18
k k 0.46 0.49 8.51
Unresolved
9.8 ?? -2.12
t 1.07
Unresolved -1.99
+ 1.10 + 0.93
Unresolved
8.7 ??
- 1.81
n
a The same substituent is present on all three para positions. Solvent symbols are: trifluoroacetic acid, TFAA; acetonitrile, ACN. c Assignments are made by optimizing a simulated ESR spectrum (ESR), by analysis of the cepstrum computed from the digital ESR spectrum (CEP), or from NMR contact shift data (NMR). Algebraic signs are given only when directly determined. e Assignment uncertain; this is the smallest line separation in the ESR spectrum. f Assignment of cepstrum Rough value from.an NMR spectrum with line is uncertain. g The ESR spectrum is fitted equally well by 1.20 or by 1.80. very broad lines; see discussion in ref 11. Average value; second-order splitting observed; see text. J Data from ref 7; almost identical values determined in liquid SO, solution are reported in ref 4. lZ N o splitting by the para acetyl protons is obValue from ref 7. Values for the secserved in the ESR spectrum. Wing line sets are severely broadened in TFAA. ond ring, from NMR contact shifts, ref 10, are as follows: ortho’ = -0.59; meta’ = + 0 . 2 3 ; para’ = -0.60 G.
’
U N is at 9.60 G. Cepstra computed from simulated spectra do not have an intense peak near the correct position until line widths in the simulated spectra are below 0.05 G, when it appears at 9.63 G. The spectrum is best simulated with the average value for aN = 9.63 G. We conclude from this and other cases that cepstrum lines for coupling constants less than 4 G should be relatively intense and correctly positioned. For larger coupling constants, the lines are often not much above noise, and they may not be located a t the correct positions. This empirical analysis of line width and noise effects on the cepstrum can profitably be compared with the brief analytical discussion given by Bieber and Goughe20 Figure 1 also illustrates other characteristics of cepstra generated by our program. Both Kirmse’s cepstra9 and ours display an intense positive or negative spike very near the origin which originates in the line shape function and scale factor introduced by the computer programs. Kirmse published only cepstra generated from selected noise-free ESR spectra. In these, each coupling constant is represented by a single dominant line whose separation (on the magnetic field axis) from the origin is equal to the magnitude of that constant, followed by a pattern of weaker positive or negative lines separated by integral multiples of that magnitude. The pattern of the overtone lines can be used to determine the spin of the nucleus which produces each line in the cepstrum. Cepstra generated by our computer program from both experimental and simulated (noise-free) ESR spectra are rather different. No overtone pattern can be identified in any of the cepstra derived from our experimental ESR spectra, so the spin information in these is lost. The overtone pattern does appear, in part,
in cepstra generated from noise-free simulated ESR spectra of radicals with relatively few nuclei coupled to the electron spin, such as the triphenylaminium-4,4’,4”-trisulfonate cation. Noise spikes appear throughout our cepstra, although the highest-frequency noise appears only in the cepstra generated from experimental ESR spectra, and is absent from cepstra generated from noise-free simulated spectra. Cepstrum line intensity diminishes along the magnetic field axis, so large coupling constants (e.g., those for the central nitrogen in these radicals) may be represented by lines which are not much above neighboring noise, as we have already seen in Figure 1. When the noise spikes are broadened by the exponential smoothing routine used, they may completely conceal the weakest lines of the cepstrum. Finally, intense combination lines appear a t positions which correspond to various sum and difference values (a, f ai)of the coupling constants. The intensities of these sum and difference peaks are higher relative to the “real” peaks in the cepstra generated from the experimental spectra than they are in cepstra from noise-free simulated spectra. Furthermore, their intensity pattern changes drastically with small changes in the coupling constants assumed for the derivative spectrum simulation. All of the intense peaks in the top cepstrum of Figure 1located less than 5 G from the origin and not assigned as 0 , m, or p couplings can be accounted for as combination peaks. Note that the addition of any nontrivial function to either the raw spectrum or its Fourier transform is a potential source for generating combination bands in that cepstrum. This added function might be a baseline correction or even spectral noise. Our computer program was designed to
Cepsfral and Direct Analysis of
ESR Spectra
1i
The Journal of F'hysical Chemistry, Vol. 82, No. 10. 1978 1189
E
i iI I
c .16
I
I
11
I1
I
10
1
I
I
I
20
-COOCH3
I
I
G
30
Figure 2. Experimental (heavier line) and simulated (lighter line) ESR derivative spectra fw 4,4',4"-fricarbomethoxytriphenylaminiumcation in TFAA solubbn. The experimental spechum is an average of 32 scans. The downfield halves of the stick plots derived from the experimental ard simulated specba are shown at W lower kft,ard the cepsba (ottset 3 G from the center line for clarity) at the lower fight. The heavy vertical line marks the centers of these spectra, and the horizontal magnetic field scale is shown.
I
I
O P
N
Flgure 1. Cepstra generated from (top to bottom) the experimental ESR spectrum for Isi-p-tolylaminium cation In TFAA solutwn, and from spectra simulated with a. = 2.09, a, = 1.05, a, = 3.87. and a, = 9.63 G, at 0.16.0.07-, and 0.026 line widms. The magnitudes of the am0,meta. para, and n-n coupling constams used in W simulaMns are marked by the vertical lines.
minimize all of these problems insofar as possible. We cannot analyze in detail differences between our cepstra and those reported by Kirmse hecause we have no detailed information on his computer program for this calculation. For example, some of these differences may arise from different conventions for the truncation of the Fourier series in the two programs. Figure 2 gives the ESR spectrum, stick plot (downfield half), and cepstrum for the 4,4',4"-tricarhomethoxytriphenylaminium cation. These are shown as heavy lines and are marked E the lighter lines are the simulated
derivative spectrum and the stick plot and cepstrum generated from it, marked C. In this case, the spectrum is very well resolved, hut it is not possible t o select unambiguous intervals for a, or aNfrom the experimental spectrum. In fact, ow choice for the meta proton coupling from the ESR spectrum was 1.13 G; the cepstrum shows a stronger peak a t 1.32 G, and this value gives a better fit for the simulated spectrum. The two regions where the three sections of this experimental spectrum overlap look rather different; we believe this could result from the second-order contribution to the nitrogen coupling, if separation of the upfield section of the spectrum from the center section is 0.04G larger than that of the downfield third. This produces differences in the phase relationships of lines at the downfield overlap region where intensities reinforce, and the upfield overlap region, where intensities cancel. A case in which unambiguous analysis of the spectrum is impossible is illustrated in Figure 3, which gives the spectra for 4,4',4"-tricyanotriphenylaminium ion. The outer line sets in this ESR spectrum display a severe and strongly solvent-dependent distortion which we ascribe to broadeningz1of unresolved components of each line which corresponds to IN = *l for the central nitrogen atom. Possibly this arises from a slow tumbling rate in solution
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The Journal of Physical Chemistry, Vol. 82, No. 10, 1978
G. A. Pearson, M. Rocek, and R. I. Waiter
I
-6N
I
in Table 11. These spectra were run in TFAA except for the first entry, which was run in acetonitrile solution. (We failed to find any single solvent which gave superior spectra for all substituents.) Solvent effects on the coupling constants appear to be small for these radicals (see also data in Table I), but probably are greater than the error limits in the assignment of parameters. Precision of the assignments varies with the substituent studied because of the variation in signal/noise ratio and resolution of the spectra, and is decreased when ratios of coupling constants approach integers.
I
I
4
10
1
I
20
0
Flgure 3. Experimental (heavier line) and simulated (lighter line) ESR spectra for 4,4f,4f’-tricyanotriphenylaminiumcation in TFAA solution. The experimental spectrum is an average of 16 scans. The downfield halves of the stick plots derived from these spectra are shown at the lower left, and the cepstra (offset 5 G from the center line for clarity) at the lower right. The heavy vertical line marks the centers of these spectra, and the horizontal magnetic field scale is shown.
produced by the projecting linear cyano groups. Furthermore, this is a “deceptively simple” ESR spectrum, in which each observed line must be made up of a number of unresolved components. This requires that the ratios of the coupling constants (with the exception of that for the central nitrogen) be close to small integers. In this case, the spectrum does not even afford an unambiguous choice for the 14N coupling constants for the central nitrogen atom. It was analyzed by assuming that a, 2a,, as in other radicals of this series, and that the values for these parameters should be close to those for the other acceptor-substituted radicals. However, ambiguities still remain in the assignments of the nitrogen coupling constants for the para cyano groups, and these are not removed by examination of the cepstrum. The ESR spectrum in Figure 3 was recorded in TFAA solution. The spectrum in solvent X (0.5 M TFAA in acetonitrile) looks very different; the wing line sections are then more than twice as intense relative to lines in the center section, and intensities of adjacent lines vary more within the line sets. It appears that these changes do not require coupling constants greatly different than those for TFAA solution; they can be accommodated by reducing the coupling constant for the nitrogen atoms in the para cyano groups by about 10%. The parameters produced by analysis of our ESR spectra and the cepstra produced from them are collected
-
Discussion The ESR spectra of the radicals in Table 11fall into four sets from the standpoint of reliability of the assigned coupling constants. Radicals 6 and 8, substituted by sulfonate or acetyl groups, show no coupling by the para substituents. (Coupling by the methyl protons in 8 is unresolved, but it does broaden the observed ESR lines.) Analysis of these uncomplicated spectra is trivial. Radicals 3, 5, and 11, with the substituents methyl, hydrogen, or fluorine, have relatively complex but well-resolved spectra without a great number of overlapping lines. There are some problems in achieving reasonably close initial guesses for the coupling constants, particularly for the para substituents. However, once these have been attained, the spectra are sufficiently distinctive that trial simulations lead to a good fit to each experimental spectrum. The cepstra were not of much use to us in assigning coupling constants for these radicals. Data for 5 are quoted from the literature. The ESR spectra of 3 were fully analyzed before we attempted to use cepstra for this purpose, and deficiencies in the digital spectra for 11, substituted by fluorine atoms, have made it impossible to calculate the cepstrum in this case. There are two sets of compounds whose analysis is relatively difficult. Spectra of radicals 4 and 7 not only contain many lines, but line spacings are fairly uniform, and several values of one or more of the coupling constants will produce a respectable fit to the experimental spectra. The use of the cepstrum to select the value for the meta coupling for compound 7 has already been mentioned. Compound 4, substituted by tert-butyl groups, has given relatively poor spectra with a low signal/noise ratio, so it is not possible to select the para coupling unambiguously. The cepstrum suggests the value 0.28 G, but 0.14 G has been necessary to give a simulated spectrum with the closely spaced lines (0.14 G ) observed. The fourth category of ESR spectra is given by samples 1,2, and 9, for which the spectra contain lines arising from proton hyperfine splittings which still contain many unresolved components. Problems in the analysis of the spectrum of 9, shown in Figure 3, have already been considered. They are much the same for the trianisylaminium cation, 2. In this case, Neugebauer and coworkers7 have based their revision of the ortho coupling on a perceptive analysis of the ESR spectrum. We have determined it directly, and established that (as assumed previously) the meta and para coupling constants are nearly equal, by proton contact shift studies of deuterium-labeled samples of this radical.l’ Radical 1,substituted by amino groups, gives a clearly resolved spectrum which cannot be unambiguously interpreted. It is likely that both aNand a, are correct within one or two times the smallest line separation (0.14 G). The ESR spectrum gives no indication of the correct coupling constants for the amino groups. The cepstrum has intense lines a t 2.73 and 5.60 G. The latter value cannot be used for any coupling constant because the simulated spectra are then too broad.
Cepstral and Direct Analysis of ESR Spectra
Assignment of 2.73 for the hydrogen atoms and 0.28 for the nitrogen atoms of the amino groups gives a fair simulation of the experimental spectrum. However, these cannot be regarded as reliable assignments for this spectrum; these will require ENDOR data or successful NMR contact shift studies. A fifth set of triarylaminium cation radicals, 12, 13, and 14, substituted by chlorine, bromine, or phenyl groups, in our hands gave ESR spectra with no resolvable proton couplings. We are uncertain whether the values for the central nitrogen coupling constants are affected by this unresolved hyperfine structure at low modulation amplitudes. Resolution of the proton splittings in radical 12 has been reported by two group^,^,^ but their assigned proton coupling constants are not in agreement, nor do they agree with our NMR data. In view of the remarks of Mobius and co-workers22on the problems of resolving chlorine hyperfine splittings, it would be no great surprise if resolution beyond the nitrogen splitting proved impossible. The case is similar for sample 13, substituted by bromine atoms with isotopes which have mass numbers 79 and 81; the magnetogyric ratios of these nuclei differ by about l o % , and consequently they produce lines at somewhat different positions in the ESR spectrum. In addition, both nuclei have a nuclear quadrupole moment which would broaden the ESR lines. In the case of the phenyl-substituted compound, there are five unrelated proton coupling constants, and the ESR spectrum is too thickly populated by lines for separation a t our best resolving power. Our data on the proton coupling constants in each of these radicals were obtained from proton NMR contact shift studies.1° Many of the ambiguities in the coupling constants already discussed could be removed by data from NMR contact shift spectra. We have tried to obtain these, but we have been unable to resolve NMR spectra for solutions of the aminium cation radicals 6 , 7 , 8, or 9, which contain sulfonate, carbomethoxy, acetyl, or cyano groups. These NMR samples were prepared by oxidation of the amines with Tl(II1) solution, and the electron-withdrawing substituents increase the difficulty of oxidation of the amines. In the absence of resolved spectra, we have no basis to judge whether oxidation was complete. In any case, complete oxidation would be expected of compounds 1 and 4, with amino or tert-butyl substituents, and we have no adequate explanation for the failure of the measurements in these cases. ESR studies show that spin exchange is slower than average for 4. We speculate that the bulky tert-butyl groups slow down Heisenberg spin exchange by hindering close approach and good overlap of the ir systems of the radicals, so that the NMR lines may remain too broad to resolve at the radical concentration used. Our ESR spectrum simulations were optimized by visual comparison of experimental and simulated spectra, and of the corresponding stick plots. It should in principle be possible to carry out the optimization of these digital spectra on a computer. We have made some unsuccessful attempts to do so with the program E S R C O N . ~ ~We suspect that failure was due to broadening of lines in the wing sections of the spectra, since point-by-point comparison necessarily will give large intensity errors in the absence of elaborate line width corrections. Possibly this difficulty could be circumvented by use of a program such as that reported by PlatoZ4which operates on a digitized segment of the spectrum. However, the most significant optimization of our spectra, at least for the central nitrogen and the larger para coupling constants, would be obtained in the regions where the spectrum sktions which arise from
The Journal of Physical Chemistry, Vol. 8.2,No. IO, 1978 1191
different IN values overlap. This would again introduce problems with line width variation and poor intensity match. We have not tried the autocorrelation technique for recording and analysis of spectra. This gave excellent results for the anthracene cation.20 We would expect problems in its application to our spectra with varying line widths, since peak-to-peak intensity relations in the lines in the wing sections become badly distorted. Some of the nitrogen coupling constants reported here are larger than those given earlier by one of US.^ Most of these differences are due to overmodulation of the magnetic field sweep deliberately introduced in the earlier spectra to simplify the determination of these parameters. However, the largest difference among the two sets of values arises for the amino-substituted radical, where the change (increase by 1.0 G) is due to reassignment of the centers of the spectrum segments which correspond to 1, = fl for the central nitrogen. The new assignment appears to be confirmed by the cepstrum and by spectrum simulation, but it is not completely certain because of the poor resolution of the lines in the wings of this spectrum. Note that the overall pattern of 14N coupling constants through the series of radicals is not altered by elimination of overmodulation. We have tried to carry out the conventional analysis of these ESR spectra separately from the cepstral analysis, in order to evaluate the relative merits of the two methods. Indeed, most of our direct analysis of the spectra was complete before our cepstrum program was available. The cepstra have been useful in optimizing the analysis of a number of spectra, particularly in the choice among alternate values of proton coupling constants which seemed to give equally good spectrum simulations. On the other hand, the cepstrum values for aNoften differ from those which give the optimum fit of simulated spectra. More generally, a well-resolved ESR spectrum with little line overlap will give an unambiguous cepstrum with significant lines far more intense than the noise. On the other hand, the cepstrum of an ambiguous ESR spectrum will contain combination lines as intense (or more so!) than the lines which represent coupling constants, as in Figure 3, so it becomes impossible to select unambiguously the correct ones. Thus, the cepstrum does not provide more information than the ESR spectrum from which it is derived. It is a useful aid in the analysis of spectra; in particular, it suggests coupling constants (but not their assignments) which should be tried in the simulation of a difficult spectrum. We have never tried the least-squares optimization of the Fourier transforms of the simulated and experimental ESR spectra which was suggested by Silsbee,25 and applied to the difficult case of the l-picryl2,2-diphenylhydrazyl radical by Gubanov and co-workers.26 We turn now to the often-discussed question of linear free energy correlations for various coupling constants in these radicals. The question has assumed some importance because the triarylaminium cations are the only chemically stable type of radical assigned to class S (donor and acceptor substituents affect radical properties in the same direction2),and because all assignments to class S have been questioned on grounds of insufficient evidencee8 A Hammett plot of I4N (for the central nitrogen atom) and lH (for the ortho positions) coupling constants27against u’ is given in Figure 4. The pattern is essentially that reported earlier;2*7 that is, there is an acceptable correlation of a, or a, with u+ for donor substituents, but no correlation for acceptors.28 We conclude that the effects of substitution on spin distribution in the triarylaminium cations cannot be described as a “Hammett correlation”.
1192
The Journal of Physical Chemistry, Vol. 82, No. 70, 1978
Weltner et ai.
References and Notes
1
..
B
2.01
1"
1.5CA
I*
I
I
-1.0
-0.5
d
7
0.0
0.5
d*
Figure 4. Plot of nitrogen (open circles with estimated error bars, and scale on the right ordinate) and ortho proton (solid dots, and scale on the left ordinate) hyperfine coupling constants vs. Hammett u+ parameters for the triarylaminium cation radicals. The substituents represented by the vertical pairs of points and identified by the letters are (from left to right): A, -NH,; B, -OCH3; C, -CH,; D,-t-Bu; E, -F; F, -H; G, -SO3-; H, -COOCH3; I, -COCH,; J, -CN; and K, -NO2.
Our original proposal for class S radicals was based in part upon the expectation, which goes back to the early work of Pauling and Wheland29on the stabilization of free radicals by electron delocalization, that both donor and acceptor substituents should be capable of delocalizing an unpaired electron. This appears not to be correct for the triarylaminium cations, where donor substituents appear to delocalize spin effectively but acceptor substituents do not seem to have much more effect than the para hydrogen atoms in the triphenylaminium cation. We can offer no explanation of this which is consistent with all of the facts for these and other types of free radicals. Acknowledgment. Financial support for this work was provided by Grant No. GP33518X from the National Science Foundation. Dr. J. J. Katz of the Chemistry Division, Argonne National Laboratory, generously gave permission to use the computer-linked ESR equipment in his laboratory. Dr. James R. Norris provided willing advice and help with that equipment. Preliminary analyses of some of the ESR spectra were carried out by Miss S. J. G. Linkletter and Drs. Robert Schwartz and H. Andriessen. Computing services were provided by the Computer Center of UICC. Dr. L. Singer offered helpful comments during several conversations on the method of cepstral analysis. All of this assistance is gratefully acknowledged.
(1) Present address: Chemistry Department, Universlty of Iowa, Iowa City, Iowa 52242. (2) R. I.Walter, J. Am. Chem. Soc., 88, 1923-1930 (1966). (3) E. T. Seo, R. F. Nelson, J. N. Fritsch, L. S. Marcoux, D. W. Leedy, and R. N. Adams, J . Am. Chem. Soc., 88, 3498-3503 (1966). (4) H. van Willigen, J . Am. Chem. Soc., 89, 2229-2230 (1967). (5) M. Mohammad and B. R. Sundheim, Theor. Chim. Acta, 10, 222-230 (1968). (6) S. P. Sorensen and W. H. Eruning, J. Am. Chem. SOC., 95, 2445-2451 (1973). (7) F. A. Neugebauer, S. Bamberger, and W. R. Groh, Chem. Ber., 108, 2406-24 15 (1975). (8) E. G. Janzen, Acc. Chem. Res., 2, 279-388 (1969). ' (9) D. W. Kirmse, J . Magn. Reson., 11, 1-8 (1973). (10) G. A. Pearson and R. I.Walter, J. Am. Chem. Soc., 99, 5262-5268 (1977). (11) S. J. G. Linkletter, G. A. Pearson, and R. I. Walter, J. Am. Chem. SOC., 99, 5269-5272 (1977). (12) R. I.Walter, J . Am. Chem. Soc., 77, 5999-6002 (1955). (13) T. N. Baker, 111, W. P. Doherty, Jr., W. S. Kelley, W. Newmeyer, J. E. Rogers, R. E. Spalding, and R. I.Walter, J . Org. Chem., 30, 3714-371 8 (1965). (14) R. I.Walter, J . Am. Chem. Soc., 75, 2771-2772 (1953). (15) C. S.Marvel, H. W. Johnston, J. W. Meier, T. W. Martin, J. Whitson, and C. M. Himel, J . Am. Chem. Soc., 66, 916 (1944). (16) L. Friedman and H. Schechter, J . Org. Chem., 26, 2522-2524 (1961). (17) J. R. Norris and H. L. Crespi, Chem. Phys. Lett., 16, 543 (1972). (18) A. Savitzkv and M. J. E. Golav. Anal. Chem.. 36. 1627-1639 (19641. (19) K. Scheffier and R. H. B. Stegmann, "Elektronenspinresonanz';, Sprlnger-Verlag, Berlin, 1970, pp 53-56. (20) K. D. Bieber and T. E. Gough, J. Magn. Reson., 21, 285-293 (1976). A referee kindly called this publication to our attention. (21) The theory of line broadenlng and many of the mechanisms whlch produce it are reviewed by G. K. Fraenkel, J . fhys. Chem., 71, 139-171 (1967). (22) K. Mobius, K. Hoffmann, and M. Plato, 2. Naturforsch. A , 23, 1209-1 213 (1968). (23) ESRCON is program No. 197 from the Quantum chemistry Program Exchange, Indiana University. I t is designed for least-squares optimization of spectra of up to 2500 lines. The author of the program, Dr. J. Heinzer of the EidgenossicheTechnische Hochschule, Zurich, kindly furnished a copy of a revised program ESRCON IIB for our work. (24) M. Plato, Z. Naturforsch. A , 22, 119-129 (1966). (25) R. Silsbee, J . Chem. fhys., 45, 1710-1714 (1966). (26) V. A. Gubanov, V. I.Koraykov, and A. K. Chirkov, J. Magn. Reson., 11, 326-334 (19731. (27) The use of a, vs. u In Hammett-type plots has been rationalized by Janzen, p 282 of ref 8. (28) Captions for the figures in ref 2 were not printed. The Hammett-type plot given there as Figure 4 actually shows the relationship between the position of the longest-wavelengthband in the optical absorption spectra and u or.'rc These data were used rather than the I4N coupling constants because the estimated precision in the latter was lower. (29) L. Pauling and G. W. Wheland, J. Chem. fhys., 1, 362-274 (1933); 2, 482 (1934).
Electron Spin Resonance of the Ytterbium Fluoride Molecule at 4 K I?. J. Van Zee, M. L. Seely, T. C. DeVore, and W. Weltner, Jr." Department of Chemistry, University of Florida, Gainesviiie, Florida 326 11 (Received August 4, 1977) Publication costs assisted by the Air Force Office of Scientific Research and the National Science Foundation
The electron spin resonance spectrum of the YbF(?Z+)molecule matrix-isolatedin solid argon has been observed at 4 K. g tensor and hyperfine tensor components have been measured: g, = 1.9954(5),gll = 1.9975(5),AiI(F) = 220(2) MHz, A,(F) = 134(2)MHz, All[171Yb(l = 1/2)] = 7822(5) MHz, A,[171Yb(l = 1/2)] = 7513(5) MHz. The hyperfine splittings indicate that the spin density on fluorine is only about 2%, indicating that the molecule is essentially an ion pair, Yb+F-. About 80% of the spin is in a Yb+ 6su orbital and the remainder in 5du and 6pc on the metal ion. From Ag,, the spin-rotation constant is estimated to be +0.0034 cm-l.
Introduction Barrow and Chojnickil have recently observed the optical spectrum of the gaseous YbF molecule and analyzed the rotational and vibrational structure in the ground ( 2 ~ + )and two excited states. From the chemiluminescent 0022-3654/78/2082-1192$01 .OO/O
reaction of ytterbium atoms with fluorine, Lee and Zare2 have also observed the spectrum of YbF and have confirmed and extended the vibrational analysis of Barrow and Chojnicki. From its spin-orbit coupling constant and dissociation energy (via a relationship of Hildenbrand),3
0 1978 American
Chemical Society
