J. Phys. Chem. 1983, 87, 3017-3019
the dynamics of 2-pyridone in toluene and methanol should reveal that the same dimer I remains stable whatever the solvent polarity. However, closer inspection of carbon-13 and nitrogen-14 chemical shiftsl8 (Tables I) as well as literature results15 disagrees with such an assumption. Moreover, by similar arguments, the T I / T ~ ratio accommodates the stable twice solvated species I11 as the reorienting compound in methanol. (18) 6(14N) = -137.92 in toluene and -138.57 in methanol from the atmospheric N2. Values are bulk magnetic susceptibility corrected and positively downfield, under the same experimental conditions as carbon-13 measurements.
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This study has demonstrated that 2-pyridones and methanol form stable complexes whose lifetimes are by far below the NMR chemical shift time scale-lower than 10-4-10-5 s-but clearly greater than the rotational correlation time scale-10-11-10-12 s. It is likely that pyrimidinic nucleic bases such as thymine, uracil, and cytosine behave similarly. The exact magnitude of these lifetimes, outside of the NMR capabilities, remains open to question and their accurate determination calls for other spectrokinetic techniques. Registry No. 2(1H)-Pyridinone, 142-08-5; l-methyl-2pyridinone, 694-85-9.
Calculation of the Missing Mode Effect Frequencies from Raman Intensities Lee Tutt,” Davld Tannor,lb John SchIndler,la Erlc J. Heller,*lb and Jeffrey I. Zlnk*la Lbpartment of Chemlstry and Blochemisby, Unlverslfy of Californla-Los Angebs, Los Angeles, Callfornla 90024, and Theoretical Division, Los Alamos Natlonal Laboratory, Los Alamos, New Mexlco 87544 (Received May 2, 1983)
Regularly spaced vibronic structure in the luminescence spectra of large molecules often does not correspond to any ground-state normal-mode vibration of the molecule. This “missing mode effect” (MIME) is explained in terms of the time-dependent picture of electronic transitions. Simple equations from which the MIME frequency can be calculated are derived. The parameters which are needed to calculate the MIME frequency are independently determined by using preresonance Raman spectroscopy. Good agreement between the experimental spectrum and the spectrum calculated by using the independently determined parameters is observed. The normal modes contributing to the MIME frequency are identified and discussed.
Recent spectroscopic advances made possible by lasers and supersonic jet expansion techniques have resulted in ultrahigh resolution of vibronic structure of molecules. However, most spectra of perturbed polyatomic molecules are not fully resolved. Although instrumental resolution may be a few wavenumbers, the spectra show no structure on a scale of less than tens or even hundreds of wavenumbers. This low apparent resolution occurs because a polyatomic molecule may have a high density of vibrational levels with significant interactions. The effect of the medium is to broaden each level enough to smooth the spectrum. For example, a typical emission spectrum of a large organometallic molecule in the condensed phase at 10 K, that of W(CO)5(py),is shown in Figure 1. The main spectral features are spaced by 550 cm-l although the instrumental resolution is 2 orders of magnitude higher.2 Much as we might wish to have resolved individual vibronic lines, this spectrum is typical of what one sees without heroic efforts to get these molecules into a collision-free environment at 0 K. The following question then arises: what is the correct interpretation of the information in this spectrum? The natural tendency would be to interpret the progression in terms of a 550-cm-l frequency in the ground state which is displaced relative to the excited state. In the case of this molecule and many others,3i4 (1) (a) University of California-Los Angeles. (b) Los Alamos National Laboratory. (2) Tutt, L.; Tannor, D.; Heller, E. J.; Zink, J. I. Inorg. Chem. 1982, 21., 3858. (3) Yersin, H.; Otto, H.; Zink, J. I.; Gliemann, G. J . Am. Chem. SOC. 1980,102,951. (4) Eyring, G.; Schmidtke, H. H. Ber. Bunsenges. Phys. Chem. 1981, 85, 597.
this “rational” explanation is far from the truth. There is no 550-cm-’ mode in the ground ~ t a t e . ~In, ~an earlier paper, we showed that it is possible to reproduce the regular 550-cm-l spacing with simultaneous displacements in two modes of very different frequencies.2 We call this effect the “missing mode effect”, or MIME, because the “mode” which appears to be present in the spectrum is actually nonexistent in the molecule. The dual purposes of this paper are the following: to derive a simple expression from which the MIME frequency can be calculated, and to use the simple expression in conjunction with vibrational frequencies and normalmode displacements independently determined by preresonance Raman spectroscopy to interpret the spectrum. An expression for the direct calculation of the MIME frequency as a function of both the normal-mode vibrational frequencies and their relative displacements is derived. The preresonance Raman spectrum is used to independently determine the frequencies and displacements. The calculated MIME frequency and the luminescence spectrum are in good agreement with the experiment. Formula for the MIME Frequency Here we derive simple expressions for the value of the MIME frequency. Under the assumptions that we shall make (separable harmonic oscillators in both electronic states,normal modes the same in both states, no frequency changes in each of the normal modes) it is possible to give a simple formula for the wave packet overlap ( @ l @ ( t ) )
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0022-3654/83/2087-3017$01.50/0
(5) Brown, R. A.; Dobson, G. R. Inorg. Chim. Acta 1972, 6, 65. (6) English, A. M.; Plowman, K. R.; Butler, I. S. Inorg. Chem. 1981, 20, 2553.
0 1983 Amerlcan Chemical Society
The Journal of Physical Chemistty, Vol. 87, No. 16, 1983
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