4922 The Journal of Physical Chemistry, Vol. 95, No. 12, I991
perature and below, where exact results are available for compari~on?.~ (Adiabatic-bending treatments of the three-atom internal angular motion in reactive scattering are quite well deIt has been pointed out that veloped and extensively used.I*") in the adiabatic-bend approximation, for reactions with a linear transition state, D is also the uibrationaI angular moment~m.'~*'~ It is the dual role of D as projection quantum number of j and vibrational angular momentum that can be used as follows to explain the experimental result mentioned above. In the harmonic approximation for the transition-state bending motion, 52 (the vibrational angular momentum) is restricted to the range -nb I D Inb in steps of 2, where nb is the bending quantum number, in terms of which the bending energy is given by hub*(,, l), where %*is the bend frequency. Thus, for the ground bend state, nb = 0 and 52 = 0. Similarly, 52 = f l corresponds to odd bending quantum states, n b = 1, 3, .... The important point is that the lowest energy bending state correlating with D = f 1 is the first excited bending state. Thus, for j = 1, only the projection quantum number D = 0 correlates with the
+
(9) For a review of accurate and approximate theoretical rate coeftlcients for H + HI, see: Schatz, G. C. Annu. Reu. Phys. Chem. 1W, 39, 317. (IO) (a) Bowman, J. M. Adu. Chem. Phys. 1985,6/, 115. (b) Bowman, J. M.; Wagner, A. F. In The Theory of Chemical Reaction Dynamics; Clary, *D.C., Ed.;Reidel: Dordrecht, 1986; p 47. (1 I ) Walker, R. 8.;Hayes, E. F. In The Theory of Chemical Reaction Dynamics; Clary, D. C.. Ed.; Reidel: Boston, 1986; p 10s. (12) Truhlar, D.0 . ; Iaaamn, A. D.; Garrett, 9. C. In The Theory of Chemical Reaction Dynamics; Baer, M., Ed.;CRC: Boca Raton, FL, 1985; Vol. IV, Chapter 2. (13) Ohsaki, A.; Nakamura, H. Phys. Rep. 1990, 187, 1. (14) Bowman, J. M. J. Phys. Chem., in press. (1 5) (a) Bowman, J. M. Int. J. Quantum Chem., Quantum Chem. Symp. 1986,20,681. (b) Colton, M. C.; Schatz, G. C. Chem. Phys. k t t . 1986,124, 256. (c) Bowman, J. M. Chem. Phys. k t r . 1986,124,260. (d) Colton, M. C.; Schatz, 0.C. Inr. J. Chem. Kinef. 1986, 18, 961. (e) H i p , P. G.; Kuppermann, A. Chem. Phys. k t t . 1987, J33, 1. (f) Sun, Q.; Bowman, J. M. J . Phys. Chem. 1990, 94, 718. (g) Sun, Q.;Bowman, J. M.; Schatz, G. C.; Sharp, J. R.; Connor, J. N. L. J. Chem. Phys. 1990, 92, 1677.
Additions and Corrections ground bending state of the H3transition state; the other two projection quantum numbers D = f 1 correlate with the first and higher excited bending states. For H + H2the difference in energy between the ground and first excited bending energies at the transition state (which at 4.2 K, I assume, is the saddle point) equals 2.6 k ~ a l / m o l , ~which ~J~ corresponds to a temperature of 1308 K. Thus, at 4.2 K it is reasonable to assume that the rate coefficient for states correlating with nb = 1 are much smaller than those correlating with nb = be orders of magnitude smaller than
Thus, the prediction based on these arguments, and eq 2, is that in agreement with the experimental results. Acknowledgment. Support from the Department of Energy (DE-FG05-86ER13568) is gratefully acknowledged. (16) (a) Sigbahn, P.; Liu, B. J. Chem. Phys. 1978,68,2457. (b) Truhlar,
D.G.;Horowitz, C. J. J . Chem. Phys. 1978,68,2466; 1979, 71, 1514(E). (17) Varandas, A.J. C.; Brown, F. B.; Mead, C. A.; Truhlar, D. G.; Blais,
N. C. J. Chem. Phys. 1987,86,6258. (18) Strictly speaking, for equality of these rate coefficients it is not sufficient to note that rotational states with n = 0 correlate with the ground bend state. That is because variational effects could bccome important for large values of j with Q = 0, and these could result in bamers that are greater than the adiabatic barrier at the saddle point. This effect does not apply for j = 0 and 1.
Department of Chemistry Emory University Atlanta, Georgia 30322
Joel M.Bowman
Received: February I , 1991; In Final Form: May 3, 1991
ADDITIONS AND CORRECTIONS 1990, Volume 94
1991, Volume 95
A. WaNqvist,* P.Ahlstrbm, and C. Karlstrbm: A New Intermolecular Energy Calculation Scheme: Applications to Potential Surface and Liquid Properties of Water..
~ MN a w * : Direct Observation of Electron-Cation Geminate Pair Produced by Picosecond Laser Pulse Excitation in Nonpolar Solvent: Excitation Wavelength Dependence of the Electron Thermalization Length. Page 1644. In the second paragraph above the Acknowledgment, delete the following sentences. "They assumed the broad Gaussian distribution and obtained the value of ...assumed distribution of the electron thermalization length." Instead, insert the following sentences. "By assuming that the yield of SIstate of TMPD via the geminate recombination is 1.0, they estimated the yield of geminate pairs from S, state to be 0.29. They also obtained the value of 0.30 by analyzing the data of Choi et a1.* for the same system. Results of our direct measurements on the yield of SI state of TMPD via geminate recombination will be published shortly elsewhere."
Page 1649. The graph of the gOH(r)function for our NEMO potential included in Figure 6 is actually the virtual charge-hydrogen distribution function. The correct Figure 6 is redrawn here and displays a better agreement with the experimental results and a correct positioning at 1.85 A of the first maximum. 201
1
3
5
7 rt AI
Flgw 6. Oxygen-hydrogen radial distribution function of NEMO, SPC, and the experimental data of Soper and P h i l l i p ~ . ' ~
Y o s b r i Hirata* and N
