J. Phys. Chem. 1983, 87,5367-5371
fective nuclear charges, qA and qB, and a bond charge q = - ( q ~ qB). In this model k&: turns out to be proportional to the product of the effective nuclear charges. But, as shown in Figure 7, k&R,3 correlates linearly with (a+ l)1/2. Thus (a 1)ll2must, within a colpair family, correlate linearly with q A q B . Moreover (a+ W2itself is linear with respect to X (see eq 4). Hence, within a colpair family, qAqB correlates linearly with = 1n (z~z~).l/~. This could provide an alternative means of parametrizing q A and qB in the SBC model.7 Implications for the PFD Model. In the perfectly following densities (PFD) model,s the electron density of the diatomic is written as P(r,R) = PA(r - RA) + - RB) + P d r , R ) where PAand PBare the R-independent perfectly following densities of atoms A and B respectively, and PNPF is the R-dependent nonperfectly following part of the density. Thus an approximate Poisson equation for molecular vibrations8 is obtained: V2W(R) = d2W/dR2 (2/R)dW/dR E ~TZAPB(RA RB) E ~TZBPA(RB - RA) I 4 ? f z ~ Z ~ f ( ER )F(R)
+
+
leads to a modified Hellman potential and the following expressions for the dimensionless parameters studied in this paper: a = qR,
0 = 3 + qR,
x
+
where RA and RB are the position vectors of the nuclei and R = IRA - RBI. An attempt has been made to extract the f(R) functions of the PFD model from known diatomic p0tentia1s.l~ However, little is known about the dependence of the PFD’s on the atomic numbers of the constituent atoms. Intuitively one may expect that the PFD’s of atoms in diatomics should depend on the partner. Reasonably accurate potential functions and spectroscopic constants have been obtaineds,20by modeling F(R). For example, the exponential decay F(R) = Gq exp(-qR)/R (19) R. G. Parr, J. M. Finlan, and G. W. Schnuelle, Chem. Phys. Lett., 14, 72 (1972).
(20) A. B. Anderson and R. G. Parr, J. Chem. Phys., 55,5490 (1971).
5387
y = 12
+ 4qR, + (vR,)~
The linear correlations between X = In ( 2 A 2 B ) 1 / 2 and a and 0 (see Figures 1and 3) imply that vR, should correlate linearly with In (ZAZB) within colpair families. This observation may be useful in alternative parameterizations of F(R). Concluding Remarks. Linear correlations between the dimensionless ratios a,0,and y of ground-state diatomic spectroscopicconstants and the logarithm of the geometric (and harmonic) average of the atomic numbers of the constituent atoms have been shown to hold with a fair degree of accuracy within a colpair family. These may be thought of as quantitative extensions of the suggestion6 that the Dunham constants al and u2 are constant within a colpair family. The KEN model using the T-normalized Rydberg representation of A T has been shown to predict the general form of these correlations. The model also provides a justification for a previously reported14correlation. Moreover it was used to derive some additional correlations. The correlations suggest alternative parameterizations for the SBC and PFD models. Acknowledgment. The main correlations of this work were inspired by a question posed to A.J.T. by Professor Neil Snider in 1976. R.F.N. thanks A.J.T. and his colleagues for their generous hospitality in Waterloo, and Professor Robert G. Parr for his hospitality in Chapel Hill in August 1982 where R.F.N.’s contribution to this work was concluded. This work was supported by grants from the Natural Sciences and Engineering Research Council of Canada, and the Institute of Low Temperatures and Structural Research, Wroclaw, Poland.
Infrared Flash Kinetic Spectroscopy: The v1 and v3 Spectra of Singlet Methylene HrvoJePetek,t David J. NesbItt,$Peter R. Ogllby,L and C. Bradley Moore” Department of Chemistry, Universlty of Callfornia, Berkeley, Callfornla 94720 (Received:June 2 1, 1983)
The transient infrared spectrum of singlet methylene (lCH2)produced by pulsed 308-nm laser photolysis of CH2C0has been observed by time-resolved absorption spectroscopy using a difference frequency infrared laser source. Single rotation-vibration transitions are observed in the 2740-2940-cm-l region with 0.0013-cm-’ instrumental resolution. Preliminary analysis of the 265 observed transitions yields vibrational frequencies v1 = 2805.9 f 0.1 cm-l and v3 = 2864.5 & 0.3 cm-l, and upper-state rotational constants A ’ = 19.8 f 0.2 cm-l, B’= 11.0 f 0.2, C’= 6.95 0.1, and A ’ = 19.3 0.6 cm-l, B’= 11.16 f 0.02 cm-’, and C’= 6.94 & 0.06 cm-l, for the symmetric and asymmetric stretch, respectively. This marks the first observation of lCH2in the infrared, and serves as an excellent test of this general technique for high-resolution infrared spectroscopy of even extremely reactive species. Introduction Infrared spectroscopy is the method of choice for determining molecular structure and force constants. The difficulty of generating broadly tunable, coherent infrared National Science Foundation Predoctoral Fellow. C. and Mary Sprague Miller Institute Fellow. Present address: Department of Chemistry, University of New Mexico, Albuquerque, N M 87131.
light, and the low sensitivity of infrared detectors for fast transient signals has made time-resolved spectroscopy of molecular radicals very difficult. Pimentel and co-workers1 used a carbon arc source and a rotating grating monochromator to record spectra of several radicals produced
3 Adolph
(1) K. C. Herr and G . C. Pimentel, Appl. Opt., 4, 25 (1965);L. Y. Tan, A. M. Winer, and G. C. Pimentel, J. Chem. Phys., 57, 4028 (1972).
0022-365418312087-5367$0 1.5010 @ 1983
American Chemical Society
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The Journal of Physical Chemistry, Vol. 87, No. 26, 1983
by flash photolysis. Time and frequency resolutions on the order of 10 ps and 1 cm-l were achieved. Sample pressures of -1 torr could be studied. Sorokin and collaborators2have produced a pulsed infrared laser source with a broad distribution of frequencies and recorded spectra photographically by upconversion to visible light. A time resolution of 10 ns has been achieved; however, spectral structure in the source has limited frequency resolution to -1 cm-l and absorption sensitivity to >5%. The recent development of tunable, difference-frequency infrared laser source3 (2.2-4.2 pm) with line widths of
