J . Phys. Chem. 1984, 88, 3159-3162 (azU)(0.3 eV for HF, 0.4 for DVM-Xa, and 0.5 eV from photoemission data). It is important to note that muffin-tin calculations with many different combinations of basis sets and sphere radii could not obtain the spectroscopic level ~ r d e r i n g . The ~ DV-Xa method, because of its better representation of the potential, differentiates between the ionization relaxation of d vs. a distributions. Also, these first-principles DV-Xa results are at least as accurate as the results of semiempirical SPINDO and CNDO calculations, despite the extensive parametrization of those methods. Even when the CNDO results are shifted by a constant energy, as is suggested in ref l l b , the DV-Xa values better correspond to observations. Table I1 presents the DV-Xa results for p-xylene obtained with the transition-state method. Results from CNDO" and HF13 calculations and the ionization potentials obtained from photoelectron spectroscopy are also listed for comparison. The DV-Xa method obtains the same level order as the HF calculations, except where the experimental spectrum itself is unclear. Indeed, on the basis of our calculations we feel that some uncertainties in the original photoemission orbital assignment^'^ may be clarified. In particular, the peak at 11.34 eV is more probably assigned to alg than to bl,, that at 13.40 is due to the bl, orbital, with the b3,, more probably contributing to the peak at 12.70 eV. The computational time required for the present study was much less than that for the necessarily large basis HF calculation.
Remarks The level ordering and ionization energies calculated here are generally in good agreement with experiment. The substantial improvement over results using the self-consistent-charge version of DVM-Xa with identical basis sets indicates that, not surprisingly, the density must be represented more accurately than by a sum of spherical charge clouds if an accurate molecular electronic SCF potential is to be obtained for anisotropic systems. The substantial improvement over multiple scattering results again is due to the better (variational) treatment of the potential. The potential corrections suggested by Delley and Ellis4 are apparently satisfactory, even for dealing with the fairly complicated cr/a structure of p-xylene. When the transition-state method is used, the X a technique, with the DVM representation of potential and wave function, is thus capable of accurately assigning photoelectron (13) Palmer, M. H.; Mayes, W.; Spiers, M.; Ridyard, J. N. A. J . Mol. Struct. 1978, 49, 105.
3159
TABLE II: p-Xylene Ionization Potentials (eV)
CNDO/ Dlhr C 2 2 b b,g, b, (n)
obsd' 8.44
Xold 8.90 (P)
HFC C N D O / S ~ ~ s3f
8.98 9.60 2.94 3.12
3.43
8.45 8.99 11.09 11.14 12.78
8.33 9.00 1.10
1.16 1.91
4.21
13.4 13.81 13.81 14.83
12.65 13.49 13.88 (n)
14.02 (n) 15.57 (a)
14.87 (u)
4.92 15.15 15.75 16.08 16.08 16.9
"The correct point group symmetry is C2". bThe orbital character (in parentheses) and level ordering are those of ref 13 from HF calculations. CReference13. Experimental peaks were assigned by using the HF calculation (also ref 13), and regions of unclear spectroscopic resolution were assigned an average IP. dPresent calculation; rc-c = 1.39 A, rCxHJ = 1.51 A,.I;!& = 1.08 A, = 1.00 A. In regions of unclear spectroscopic assignments (see footnote C), this work reassigns the order of some levels. eReference lla. These values have been shifted by 1.0 eV to align CNDO results with experimental observations. fReference 1la. Here the shift is taken as 0.9 eV. spectra for typical conjugated and substituted hydrocarbons. The accuracy of the present calculations, plus striking results in accompanying studies on the [2.2] paracyclophane m ~ l e c u l e , ' ~ indicates that our local-density method is of the requisite power for subunit calculations on conductive polymer^'^ based on aromatic subunits; such studies are now in progress.
Acknowledgment. We are grateful to the Chemistry Division of the NSF, the Office of Naval Research, and to the NSF-MRL Division for support of this research, the latter through the Northwestern MRC (Grant DMR-79-23345). We thank Frank Kutzler for very valuable help in these calculations. Registry No. Benzene, 71-43-2;p-xylene, 106-42-3. ~~
(14) Doris, K. A.; Ellis, D. E.; Marks, T. J.; Ratner, M. A. J . Am. Chem. SOC.1984, 106, 2491. (15) (a) Pietro, W.; Ellis, D. E.; Ratner, M. A.; Marks, T. J. Mol. Cryst. Liq. Cryst. 1984, 105, 273. (b) Ciliberto, E.; Doris, K. A,; Pietro, W. J.; Reisner, G.M.; Ellis, D. E.; Fragall, I.; Herbstein, F. H.; Ratner, M. A,; Marks, T. J., submitted for publication.
Picosecond Kinetics by Exchange Broadening in the Infrared and Raman. 2. Acetyiacetone Benyamin Cohen and Shmuel Weiss* Department of Chemistry, Ben-Gurion University, Beer-Sheva 84105, Israel (Received: May 5, 1983; In Final Form: October 26, 1983)
Spectra of acetylacetone, CH3COCH2COCH3,and its partially deuterated analogue, CH3COCD2COCH3,in the region of the C=O and C = C stretches were taken over a wide temperature range. The results could be interpreted on the assumption that the cis enolic modification of acetylacetone exists in two different, rapidly interconverting forms. The kinetics of the interconversion, in the picosecond range, were investigated and rate constants and energies and entropies of activation determined. The nature of the two forms of the cis enol is discussed.
Introduction The structure of the cis enolic form of acetylacetone, like that of other P-diketones, is not entirely clear. For one thing, the controversy as to whether the cis enolic'form is of C2, symmetry with the enolic hydrogen located midway between the oxygens and both C-0 distances and ring C-C distances equal, respec0022-3654/84/2088-3 159$01.50/0
tively, to one another, or whether the enol is of C, symmetry with the hydrogen in a double minkmm Potential, is not Yet settled. Electron diffraction seems to support the C2, structure' whereas (1) A. H. Lowrey, C. George, P. D'Antonio, and J. Karle, J . Am. Chem. 93, 6399 (1971).
SOC.,
0 1984 American Chemical Society
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The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
Cohen and Weiss
N M R and IR results have been interpreted as indicating the existence of a double minimum potential and a C, s t r u c t ~ r e . ~ - ~ For another, there is evidence that the cis enol exists in more than one form. Thus it has been observed that the chemical shift of W the enolic hydrogen is temperature dependent with AS/AT in0 sensitive to concentration. According to a model that has been z U proposed4 the observation is due to the enolic form existing in two m (or more) rapidly interconverting forms, with different chemical LT shifts, the equilibrium between which changes with temperature. 0 The OH stretching modes of acetylacetone are extremely broad cn and featureless and do not seem likely to yield much new inform mation. On the other hand, it seemed that the broad line at 1623 U cm-' which is made up of the C 4 stretch and the C=C stretch (plus C H in-plane bending3) might reveal structure when the temperature is sufficiently lowered. Such structure of bond vibrations, the forms of which are at issue, could shed new light on the problem. Furthermore, if it turned out that the band does indeed contain features which are broadened at room temperature and the broadening is of kinetic origin then the kinetics might 1500 I600 1700 cm-1 be elucidated in the manner discussed in part 1.5 New information Figure 1. Spectra of CH,COCH2COCH, in n-hexane. For convenience which has an obvious bearing on the above-mentioned problems of presentation all spectra were normalized to the same height. would thus be gained.
,
Experimental Section Spectra were taken on a Perkin-Elmer 225 spectrometer with a resolution of 0.6-0.7 cm-'. Samples were contained in a RIIC variable-temperature cell. The temperature range spanned in this study was -85 to +27 OC. Acetylacetone was in solution in n-hexane at a concentration of 0.1 M. CH3COCDzCOCH3was dissolved in n-octane also at a concentration of 0.1 M. The optical path was 0.05 mm. Results are reported as absorbances.
A
W
102 OC Results and Discussion Both the do, CH3COCHzCOCH3,and the dz,CH3COCD2COCH,, analogues were studied. Representative spectra of the do analogue are reproduced in Figure 1 and those of d2 in Figure 2. The do spectrum splits at low temperature into three components. When analyzed it is found that the intensity of the middle component varies with temperature (increases) relative to the two outward components, the intensity ratio of which remains constant. The d2 spectrum, on the other hand, reveals two components at all temperatures. The intensity ratio of these also changes with temperature, the intensity of the low-frequency component increasing with temperature relative to that of the high-frequency one. Both components broaden with temperature. The first explanation of the do splitting which comes to mind is that it is a manifestation of the splitting of the vibrational levels of the proton caused by its tunneling through the barrier separating the two minima in a double minimum potential. Tayyari et aL2 did indeed search for (but did not find) a splitting of this origin in the internal modes of the chelate ring of acetylacetone. However, such an explanation cannot account for the variation of the intensity ratio with temperature. Model calculations6 indicate clearly that if the ground level is split sufficiently for the temperature to have a noticeable effect on the thermal distribution (2) S . F. Tayyari, Th. Zeegers-Huyskens, and J. L. Wood, Spectrochim. Acta, Part A , 35, 125, 1289 (1979). (3) H. Ogoshi and K. Nakamoto, J . Chem. Phys., 45, 3113 (1966). (4) W. Egan, G. Gunnarsson, T. E. Bull, and S.Forsen, J . Am. Chem. SOC.,99,4568 (1976). The references cited in this article summarize the debate till 1976. (5) B. Cohen and S . Weiss, J . Phys. Chem., 87, 3606 (1983). (6) R.. L. Somorjai and F. Hornig, J . Chem. Phys., 36, 1980 (1962).
73°C
2 7°C I
I
I
I
I500 1600 1700c m- 1 Figure 2. Spectra of CH,COCD2COCH3in n-octane. For convenience of presentation all spectra were normalized to the same height. then the first excited level will be split enormously which is certainly not the case here. (For example, a typical calculation showed that if the ground level is split by 56 cm-' the first excited level is split by 1041 cm-I.) We are thus led to believe that, as quoted in the Introduction, the cis enolic acetylacetone exists in two different forms. While we shall postpone the discussion of the nature of these two forms till somewhat later we may mention at this point that these forms do not involve the trans enol, the concentration of which is known to be very small,2 nor the keto form, all the vibrations of which are accounted for. We think that the change of line shape with temperature in the spectra of both the do and d2 analogue is caused by fast interconversion, on the subpicosecond scale, between the two forms of the cis enol. This fast reaction affects the spectra in a manner similar to that described in our previous papers5 We shall see below
T h e Journal of Physical Chemistry, Vol. 88, No. 14, 1984 3161
Picosecond Kinetics by IR Exchange Broadening Ink
I
TABLE I: Activation Energies and Entropies and Enthalpy Differences for the Two Forms of Cis Enolic Acetylacetone
cal/mol
I \
-- 1
I
AHaacal/mol
AS*.' eu
\
\
form A form B
3050 f 45 1500 f 30
9.8 f 0.2 3.2 f 0.2
1590
form A form B
3400 f 20
5.1 f 0.1
1570
7o
aError limits are standard deviations.
45t 3
4 +XlOOO
Figure 3. Plots of In k vs. l/T:(O) doform A; ( 0 )doform B; (X) d2 form
Wn(1.K)
II
P
A.
that comparison of the results obtained for the doand d2analogues supports this interpretation. We point out also that in the do spectrum we have an example not only of line broadening but also, at the highest temperatures, of line narrowing. Designating, for the time being, the two forms as A and B, we assign the outward components of the do spectrum and the high-frequency peak and part of the low-frequency peak of the d2spectrum to form A and the middle feature of the do band and the other part of the low-frequency peak of d2 to the B form. Analysis results in relative absorption coefficients of 1, 2.65, and 2.4 for the components of the doband, starting with the feature at the low frequency. The intensity coefficients of the features of the form A then relate to those of form B as 3.4:2.65 or as 1.28:1. In other words, the intensity coefficients for both forms are similar. For dz the relative absorption coefficients of the features of forms A and B could not be determined but there is no reason to believe the ratio is very different from that found for do. The necessity of assuming that the low-frequency peak of d2 actually consists of contributions from both forms follows from the need to obtain a AH-for the transition between the two forms-which is in line with that for do. We further assume that the single feature assigned to the form B, in both the do and d2 spectra, is actually a doublet like the features of form A, though degenerate or nearly degenerate. The two components of the doublet, for either form, are probably the C=O stretch and the C=C stretch (plus CH in-plane bending) as indicated by the normal-mode a n a l y ~ i s . ~ With the above assumptions it is possible to analyze the spectra with the Bloch equations as described in our previous paper5 and by taking all of the temperature-dependent width to be of kinetic origin. We were able to analyze in this way all but the lowfrequency feature of d2 which, according to our assumptions, consists of contributions of both forms, the exact positions and widths of which could not be ascertained. The rate constants obtained were in the range of (0.5-1 1.3) X 10l2 SKIfor do and (0.8-2.6) X 1Ol2 for dz. Plots of In k vs. 1 / T are reproduced in Figure 3. From these plots activation energies were calculated. Also, calculating AG* from each rate constant and plotting it vs. T,we obtained values of AS*,All these values are collected in Table I. Also shown in this table are values of AH for the difference between the two forms. For do these were determined from the temperature dependence of the intensity ratio of the features of the two forms in a straightforward manner. For the d2 spectrum, where only one feature could be analyzed, a somewhat more complicated procedure was required. Denoting the composite low-frequency peak as 1 and the other as 2 we have and I2 = tA&A were the for the intensities I, = tA1XA tdB meaning of the symbols is obvious. Then Zl/Z2= tAI/tM + tB/tMK and In (ZIIZ2 - tAI/tN) = In tB/tM + In K = - A H / R T + constant. It is therefore necessary to adjust tAl/tA2 until a plot of the
+
1 .o
0.5
1.5
Figure 4. Plot of w(K + 1) vs. K (for do).
K
left-hand side vs. 1 / T yields a straight line. In practice it was found that the tAl/tA2 of the do analogue (112.4) satisfied the condition. AH was then obtained from the slope. The agreement between the AH values and the corresponding differences of E , values is seen to be within experimental errors. Attention is also drawn to the fact that E, for form A is somewhat higher for d2 than for do as would be expected (since the levels of the deuterated analogue are lower lying). When two expressions for the equilibrium constant of the do form are compared, K = kA/kBand k = (tA/tB)(IB/IA),where t A and tB are the absorption coefficient of all A features and all B features, respectively, and ZA and ZB are the corresponding intensities, it is possible to extract tA/tB. The intensity coefficients ratio for the two features of the A form is, of course, simply the ratio of the intensities of the two features. In this way were determined the relative intensity coefficients of the do analogue mentioned above. As has been pointed out in the literature the temperature dependence of the chemical shift of the enolic hydrogen is readily explained in terms of a rapid equilibrium between two different forms. Let the chemical shifts be w A and wB and the equilibrium constant be defined as K = x B / x A where the X ' s are the corresponding mole fractions. Then the observed chemical shift will 1)) + wB(K/(K + be given by w = WAXA w&YB = wA(l/(K 1)) or w(K + 1) = W A + wBK. Plotting o(K + 1) vs. K should then yield a straight line. In Figure 4 we reproduce such a plot were the w values were taken from the literature4 and the K values are ours. The excellent straight line obtained certainly supports
+
+
3162 The Journal of Physical Chemistry, Vol. 88, No. 14, 1984
the two-form model and gives us some confidence in our analysis. Finally, we now address the question of the nature of the two forms of the cis enol. One possibility, suggested by Egan et a1.: is that the two forms are the ground state and a low-lying excited vibrational state. With AH, the energy difference between the two forms, now known we are in a position to identify the vibration in question. The list of normal modes3 reveals a ring deformation at 515 cm-' for do and at 500 cm-' for d,; these correspond to 1474 and 1431 cal/mol, respectively. Our AH values of 1590 cal/mol for do and 1570 cal/mol for d, agree very well with these values; no other normal mode is close and surely a ring deformation is a suitable candidate for a mode that is to affect the enolic hydrogen and the C=O and c=C vibrations. On the other hand, the difference in AS+A,4.7 eu, between do and d,, which corresponds to a frequency factor ratio of 10.7, strongly suggests tunneling of the enolic proton in do. This is difficult to visualize though by no means ruled out, on the basis of a transition from the ground state to an excited vibrational state. It is therefore tempting to cosider another possibility-that the enolic hydrogen moves in a symmetric triple minimum potential such that the central minimum is at a higher energy then the two outer minima. The role of tunneling is intuitively clear in this model as are the meanings of the activation energies. One may also speculate that the uncertainty regarding the position of the enolic hydrogen stems from the simultaneous existence of C,, and C, molecules. While the two models appear to be quite different from one another this is not necessarily so. Thus if, in the first model, the ground state has a double minimum potential for the enolic hydrogen and in the excited state these two minima have come appreciably closer (or, in the extreme case, coalesced to a single minimum) then the two models are not really so dissimilar. Summary In this work we tried to show that the temperature variation of spectra of do and d2 acetylacetone is consistent with the assumption that the enolic modification of this molecule actually exists in two different, rapidly interconverting, forms. Equilibrium constants, determined in this work at various temperatures, combined with NMR results reported in the literature yieid a
Cohen and Weiss consistent interpretation of the results. Ultrafast kinetics, on the picosecond time scale, provide a relaxation mechanism in addition to rotational and vibrational relaxation.' In favorable cases the temperature variation of line widths caused by the kinetics is large enough to allow separation, at least approximately, from the effects due to vibrational and rotational relaxation. (In the present case, the half-width at half-height changes by tens of wavenumbers, according to the Bloch line shape analysis, for do and by about 10 cm-' for d2.) As we have pointed out previously5 it is important, whenever kinetic line broadening is claimed, to find instances in which the reaction is completely arrested or at least considerable slowed down so that it is possible to assess which part of the broadening and, particularly, its temperature dependence is indeed due to the kinetics. In the present case the kinetic isotope effect brought about by deuteration serves this purpose. For the d2 analogue line-width variation with temperature is indeed much less pronounced than for the do analogue (see above and Figure 3). The difference between activation energies, 1550 cal/mol, is in very satisfactory agreement with the AH of 1590 cal/mol. As would be expected the activation energy for the d2 analogue is somewhat higher than that for the do analogue (3400 cal/mol vs. 3050 cal/mol) and AS* for do is considerably larger than for d, corresponding to a frequency factor ratio of 10.7 and consistent with proton tunneling in do. On the whole then a self-consistent picture is obtained.
Acknowledgment. This work was supported by a grant from the Fund for Basic Research administered by the Israel Academy of Sciences and Humanities. Registry No. CH3COCH2COCH3,123-54-6; CH3COCD2COCH3, 10225-30-6; CH,COCH,COCH, enol, 1522-20-9; CH3COCD2COCH3 enol, 14180-56-4; deuterium, 7782-39-0. (7) Recently vibrational relaxation has been very intensively studied. An account of recent work, as well as references to earlier work on both vibrational and rotational relaxation, is given by D. W. Oxtoby, Adu. Chem. Phys., 40, 1 (1979). For still more recent work see K. S . Schweitzer and D. Chandler, J. Chem. Phys., 76,2296 (1982); S . M. George, H. Auweter, and C. B. Harris, ibid., 73, 5573 (1980).
