J. Phys. Chem. 1988,92, 1739-1742
1739
Correlated ab Inltio Harmonic Frequencies and Infrared Intensities for Furan, Pyrrole, and Thiophene Emmanuel D. Simandiras, Nicholas C. Handy,* and Roger D. Amos University Chemical Laboratory, Lensfeld Road, Cambridge CB2 1 E W, U.K. (Received: May 27, 1987)
Equilibrium geometries, harmonic vibrational frequencies,and infrared intensities are calculated analytically at the second-order Mdler-Plesset level (MP2) with a DZP basis for the five-membered heterocyclic aromatics furan, pyrrole, and thiophene. The results are of an accuracy to show up misassignments in the original experimental interpretation of the spectra. They also give confidence that ab initio calculations including electron correlation and using flexible basis sets can describe accurately the quadratic part of the potential energy surface. For such systems, these ab initio studies will aid the spectroscopic determination of force constants.
Introduction
(possibly transferred from similar molecules) has been successfully
The accurate determination of harmonic force fields for molecules with more than six atoms is a topic of great interest to both experimentalists and theoreticians. To our knowledge, the best up to date experimental determination of a harmonic force field reported in the literature for a molecule of this size is that for benzene,' although even in this case the result is not definitive. The availability of spectra for isotopically substituted molecules and the exploitation of high molecular symmetry are the main tools used in the experimental solution of the problem. However, the former are not always easily obtainable and the latter is very rarely present. It is therefore easy to understand why good quality a b initio force constants are absolutely necessary in these cases. With only a few exceptions,2 the a b initio calculation of harmonic force constants for molecules with more than four heavy atoms has been practicable up to now only at the S C F level with relatively small basis sets. The lack of electron correlation and basis set deficiency in these calculations have made scaling of force constants necessary in order to get reasonable agreement with experiment. It is undeniable that scaling techniques have been very useful in predicting fundamental frequencies for organic molecules. The technique of using a small set of scaling factorsI6
(1) Thakur, S. N.; Goodman, L.; Ozkabak, A. G. J. Chem. Phys. 1986, 84, 6642. Ozkabak, A. G.; Goodman, L. J. Chem. Phys. 1987, 87, 3564. (2) For a review, see for example: Binkley, J. S.; Frisch, M. J.; Schaefer, H. F. Chem. Phys. Lett. 1986, 126, 1. Hess, B. A.; Schaad, L. J.; Carsky, P.; Zahradnik, R. Chem. Rev. 1986, 86,709. (3)Simandiras, E.D.; Handy, N. C.; Amos, R. D. Chem. Phys. Lett. 1987, 133,324.Simandiras, E. D.; Amos, R. D.; Handy, N. C. Chem. Phys. 1987, 114, 9.
(4)Scott, D.W.J. Mol. Spectrosc. 1969, 31,451. 1971, 37,77. ( 5 ) Orza, J. M.; Escribano, R.; Navano, R. J. Chem. Soc., Faraday Trans. 2 1985, 81, 653. (6)Gonzalez, C. A. A.; Vallette, M. C.; Campos, R. E. C. Spectrochim. Acta, Part A 1986, 42A, 919. (7)Xie. Y.: Fan. K.: Boees. J. E. Mol. Phvs. 1986. 58. 401. (8)Huzinaga, S.'J. Chei>hys. 1%5,42, li93. Dunning, T.H. J. Chem. Phys. 1970, 53, 2823. (9)Harmony, M. D.:Lawrie. V. W.; Kuczkowski. R. L.:Schwendeman. R. Hl; Ramsey; D. A.; Lovas, F. J.; Lafferty, W. J.; Maki, A. G. J . Phys. Chem. Ref.Data 1979, 8,619. (10) Ab Initio Molecular Orbital Theory; Hehre, W. J., Radom, L., Schleyer, P. v. R., Pople, J. A. Wiley-Interscience: New York, 1986. ( 1 1) R i a , M.;Barranchina, M.; Orza, J. M . J. Mol. Spectrosc. 1967, 24, 133. (12) Navano, R.; Orza, J. M. An. Quim., Ser. A 1983, 79,557. 1983, 79, 571. 1984, 80,59. 1985, 81,5. (13)Rim, M.; Orza, J. M.; Morcillo, J. Spectrochim. Acta. 1965, 21, 689. (14)Simandiras, E. D.; Amos, R. D.; Handy, N. C.; Lee, T. J.; Rice, Schaefer, H. F. J. Am. Chem. Soc., in press. (15)Lee, T.J.; Allen, W. D.; Schaefer, H. F. J. Chem. Phys. 1987, 87, 7062. (16)Pulay, P.; Fogarasi, G.; Pongor, G.; Boggs, J. E.; Vargha, A. J . Am. Chem. Soc. 1983, 105,7037.
0022-3654/88/2092- 1739$0 1.50/0
used for molecules up to the size of na~hthalene'~ with small mean
deviations between theoretical and experimental data. However, there are several disadvantages with this approach; firstly, it relies on experimental data (that could be misassigned or simply not available) or on the transferability of scale factors. Although scale factors for very similar modes are transferable, this is not true for modes of the same type but involving different atoms. Thus, Xie et aL7 found that they could not use the C-H wagging scale factor from benzene for the N-H wagging of pyrrole. Similarly, it would be almost impossibIe to find scale factors for our other two molecules, since they are the smallest examples of aromatic molecules containing oxygen or sulfur as heteroatoms. Furthermore, the procedure of correcting a harmonic force field by comparison to observed frequencies is fundamentally incorrect, as it treats the completely different effects of lack of electron correlation, basis set incompleteness, and anharmonicity on a certain mode as a single scaling factor. Once this has been done, all information regarding anharmonic effects (which of course should never be expected to be present in a harmonic frequency computation) is lost, and the resulting force field does not have a well-defined physical meaning (Le., it is neither harmonic, nor of course anharmonic). We believe that in the long run it is preferable to determine accurate harmonic force fields, which can then assist toward a complete understanding of the potential energy surface. This can only be achieved with an overall improvement of the a b initio methods, which includes large correlated calculations of the quadratic terms and rigorous treatment of anharmonicity via higher derivatives which can now be calculated analytically at the S C F level.'* Clearly, MP2 is only the simplest method for including electron correlation, but because of this fact it has been possible to design our analytic second derivative programs3 in such a way that large numbers of atoms and basis functions can be handled. Thus, the main sources of error in a b initio calculations of harmonic vibrational frequencies, namely lack of electron correlation and basis set incompleteness, can be removed to a certain extent, without at the same time making the cost of the calculation prohibitive. Our previous applications of this method3 show that MP2 combined with medium and large basis sets can give a very significant improvement upon S C F results. In this study the MP2 programs have been used to calculate harmonic frequencies and IR intensities for furan, pyrrole, and thiophene (Figure 1). Although these are molecules well-known to all chemists, it is surprising how little accurate information on their potential energy surfaces is available from experiment. There (17)Sellers, H.; Pulay, P.; Boggs, J. E . J . Am. Chem. Sor. 1985, 107, 6487. See also ref 7 and references therein. (18) Gaw, J. F.; Yamaguchi, Y.; Schaefer, H. F. J . Chem. Phys. 1984,81, 6395. Gaw, J. F.;Yamaguchi, Y.; Schaefer, H. F.; Handy, N. C. J . Chem. Phys. 1986, 85, 5132.
0 1988 American Chemical Society
1740 The Journal of Physical Chemistry, Vol. 92, No. 7, 1988
Simandiras et al.
TABLE I: Calculated and Experimental"Structures of Furan, Pyrrole, and Thiophene
x-c , CrC2 c2-cz C,-H C2-H
MP2
furan expt
1.364 1.374 1.433 1.078 1.079
1.362 1.361 1.431 1.075 1.077
106.9 110.5 106.0 115.7 127.9
106.5 110.7 106.0 115.9 127.9
Ab
0.002 0.013 0.002 0.003 0.002
X-H
c,-x-c , x-c,-c,
Cl-Cz-C2 X-C,-H C,-C,-H
0.4 -0.2 0.0 -0.2 0.0
MP2
pyrrole expt
Ab
MP2
thiophene expt
Ab
1.375 1.391 1.424 1.078 1.079 1.007
1.370 1.382 1.417 1.076 1.077 0.996
0.005 0.009 0.007 0.002 0.002 0.01 1
1.713 1.385 1.423 1.081 1.083
1.714 1.369 1.423 1.078 1.080
-0.001 0.016 0.000 0.003 0.003
110.3 107.4 107.4 121.2 127.2
109.8 107.7 107.4 121.6 127.1
92.3 111.6 112.2 120.5 124.6
92.1 111.5 112.5 119.8 124.3
0.2 0.1 -0.3 0.7 0.3
0.5 -0.3 0.0 -0.4 0.1
Experimental substitution structures from ref 9. Bond lengths are in angstroms and angles in degrees. A is the difference between MP2 and experimental ( r s , Os).
( r e , 0,)
TABLE 11: Harmonic Vibrational Frequencies and IR Intensities Calculated at the MP2 Level for Furan" no. w I exptl vb % diff
Furan
Pyrrole
Triiophene
Figure 1. Atom numbering corresponding to the geometrical parameters
of Table I. have only been a few attempts reported in the literature to obtain a force field by a least-squares fit to experimental fundamental frequencies. These are by Scott4 for all three molecules and by Orza et aL5 and Gonzalez et aL6 for pyrrole. Xie et al.' have used a combination of experimental and small basis ab initio data to obtain a harmonic force field for pyrrole. The purpose of this study is to examine the experimental assignments for the spectra of these molecules and at the same time assess the accuracy of ab initio calculations of vibrational spectra for molecules of this size performed with the simplest correlated method.
Calculation Details For this calculation a double { Huzinaga-Dunning8 basis set was used, augmented with one set of polarization functions (DZP) on each atom. The polarization exponents were dc, 0.8; dN,0.8; do, 0.9; d,, 0.65, and p,, 1.0. The geometries were fully optimized at the MP2 level by using our analytic MP2 gradient p r ~ g r a m .The ~ geometrical parameters obtained are given in Table I, where they are compared with the experimental substitution structure^.^ It must be noted that our data correspond to the equilibrium structure (re,Oe)which is not known experimentally, and that it is safe to assume that the uncertainty of the experimental data for this size of molecule is f0.01 A for bond lengths and * O S 0 for angles. The DZP MP2 calculated bond lengths are expected from our previous studies on small molecules3 to be a few thousandths of an angstrom longer than experimental re for single bonds and up to 0.03 A longer for multiple bonds. Thus, the extremely good agreement for some bond lengths (10.002 A) is fortuitous, since the experimental rs will be generally longer than re, and at the same time DZP MP2 re are longer than the experimental ones. The increase of the basis set to a triple 5 plus two sets of polarization functions (TZ2P) will make the MP2 re shorter. However, the excellent agreement of the bond lengths and the prediction of the bond angles to within less than l o shows that MP2 DZP structures are a tremendous improvement upon S C F 3-21G (or similar) ones. (For a discussion of S C F 3-21G errors see ref 10.) The next step was to calculate the MP2 dipole moment derivatives and second derivatives analytically at the corresponding minimum. The time required for the force constant calculation was between four and five times that for the gradient on a CRAY XMP. The harmonic frequencies were then obtained by diagonalizing the mass-weighted Cartesian second derivative matrix for the most common isotopomer of each molecule. (The full
1 2 3 4 5 6 7 8
3369 3341 1527 1448 1168 1120 1033 876
0.1 0.01 22.2 3.6 0.02 10.0 45.2 11.4
3167' 3140 1491 1384 1140d 1066 99s 871
12 13 14 15 16 17 18
bl b, b, bl b, bl bl
3362 3328 1595 1301 1264 1072 883
0.8 1.5 0.2 5.4 26.4 3.4 0.1
3161 3129 1556 1267 1180 1040d 873e
9 10 11
a2 a, a2
806 668 605
0 0 0
863' 728' 613e
19 20 21
b, b2 b,
183 732 625
0.4 132.1 24.1
838 745 603
sh vs
m s vs s
m
m w vw vs
6.4 6.4 2.4 4.6 2.5 5.1 3.8 0.6 6.4 6.4 2.5 2.7 7. I 3.1 1.1 -6.6 -8.2 -1.3
vw vs
s
-6.6 -1.7 3.6
"Frequencies are in cm-' and itensities in km mol-I. bReference 11. cCorrected liquid value. dLiquid IR value. e Liquid Raman value. "onobserved band. Cartesian force constant matrices and atomic polar tensors are available from the authors.) The integrated intensities were also obtained by transforming the Cartesian dipole moment derivatives to derivatives with respect to normal coordinates and then using
where N A is Avogadro's number and di the degeneracy of the mode, to calculate the integrated intensities A,.
Results and Discussion The calculated MP2 harmonic vibrational frequencies and infrared intensities for furan, pyrrole, and thiophene are reported in Tables 11, I11 and IV, respectively. They are compared with the best available fundamental frequencies from gas- and liquid-phase IR spectra and liquid Raman spectra.' 1-13 Firstly, we note that there does not appear to be any large discrepancy between ab initio and experimental frequencies. This confirms that the experimental assignment is correct, although not all the fundamentals of furan and thiophene have been determined to the desired accuracy. The most recent experiments of Navarro and Orza'* on pyrrole guarantee that at least the gas-phase a,, b,, and b2 fundamentals are more accurate, although the IR-inactive a2 frequencies are still from a liquid-phase Raman spectrum. There is also a different assignment for v I 8 and q9
Harmonic Force Fields for Heterocyclic Aromatics
The Journal of Physical Chemistry, Vol. 92, No. 7, 1988 1741
TABLE 111: Harmonic Vibrational Frequencies and IR Intensities Calculated at the MP2 Level for Pyrrole" no. svm w I exotI vb % diff 1 3754 82.8 vs 3527 6.4 ~~~
2 3 4 5 6 7 8 9
3351 3330 1529 1462 1179 1117 1053 890
0.1 1.7 10.1 2.7 2.5 5.4 31.3 0.2
3148 3125 1470 1391 1148 1074 1018 880
13 14 15 16 17 18 19 20
3345 3316 1582 1516 1324 1188 1073 870
1.9 2.1 1.5 14.0 1.9 2.6 28.4 1.2
3140 3116 1521 1424 1287 1134 1049 863
10 11 12
793 619 604
0 0 0
21 22 23 24
763 692 638 498
8.2 214.0 0.4 53.3
vw
m S
m m m
m S
vw W S
86gC 712' 618' 826 7 20 626 474
6.4 6.6 4.0 5.1 2.7 4.0 3.4 1.1 6.5 6.4 4.0 6.5 2.9 4.8 2.3 0.8 -8.6 -1 3.1 -2.3
m vs W
vs
'Frequencies are in cm-' and intensities in km mol-'
-7.6 -3.9 1.9 5.1
Reference
12. CLiquidRaman values.
TABLE IV: Harmonic Vibrational Frequencies and IR Intensities Calculated at the MP2 Level for Tbiophene" no. svm w I exotl vb % diff 1 1.8 3328 3126 m 6.5 2 3 4 5 6 7 8
3302 1471 1420 1111 1079 885 628
1.5 8. I 1.2 5.2 3.8 25.4 0.03
3098 1409 1360 1083 1036 839 608
12 13 14 15 16 17 18
3325 3287 1542 1296 1114 909 780
0.2 3.2 0.2 10.4 7.1 1.o 0.3
3 125' 3086 1504 1256 1085' 872 763
9 10 11
822 596 516
0 0 0
89gd 683d 565d
19 20 21
768 680 447
4.0 152.2 4.4
867 712 452
S S
vw S S
vs W
S
vw S
m
6.6 4.4 4.4 2.6 4.2 5.5 3.3 6.4 6.5 2.6 3.2 2.7 4.2 2.2 -8.5 -12.7 -8.7
vs W
-1 1.4 -4.5 -1.1
"Frequencies are in cm-I and intensities in km mol-'. *Reference 13. CNonobserved'band. dCorrected values from liquid Raman spec-
tra. reported in the literature;6 however, our results support the one by Navarro and Orza. The average percent difference for our harmonic frequencies from the experiment'al fundamentals (with standard deviations in parentheses) are 6.5 (0.1) for in-plane CH and NH stretches, 3.4 (1.5) for all other in plane modes and -5.1 (5.3) for all out-of-plane vibrations. We note that the largest difference occurs for the high-frequency in-plane stretches, as would be expected because of the greater anharmonicity of these modes. A smaller part of this difference is due to basis set incompleteness and lack of higher excitations in the correlated wave function. However, as can be shown from our calculations on small molecules3 and e t h ~ l e n i m i n e , a' ~ basis set of TZ2P quality will significantly
decrease the basis set error in the high-frequency stretches, leaving only a much smaller discrepancy due to higher excitations. There is no reason why in the near future we should not be able to perform MP2 analytic second derivative calculations on these molecules with basis sets of genuine TZ2P quality. The very small standard deviation of the differences for these modes is also remarkable. This feature suggests that, as the errors due to lack of electron correlation and basis set incompleteness are gradually removed, it might be possible to treat the anharmonic correction for very similar types of vibrations as a scaling factor, although it is preferable to try to account for anharmonicity in a more rigorous manner. The anharmonic corrections for the in-plane bending and ring modes are generally much smaller than for the A-H stretching modes, and therefore the calculated harmonic frequencies provide a much more accurate description of the vibrational spectrum in this region. For example, in the case of pyrrole, a problem arising from two different assignments of the b, modes vi8 and v19 can be resolved. Gonzalez et aL6 assigned the bands at 1049 and 960 cm to v I 8 and vI9, respectively. This assignment is not in agreement with our calculations, since the frequency differences would then be 13% and 12%, respectively, and the strong observed band at 1049 cm-I would be assigned to v l g for which the predicted intensity is small. The assignment of Navarro and Orzal* is in much better agreement with our results for the bl modes when both frequencies and intensities are compared. For the other two molecules there are no similar problems on the assignments, but from the calculated intensities it is easy to understand why the v 5 and v I 8 bands of furan have not been observed in a rather low resolution gas-phase experiment. For the out-of-plane vibrations we note that the majority of the MP2 harmonic frequencies are lower than the experimental v and that the differences are quite scattered. It should firstly be noted that the differences may not be as large as they appear, as the accuracy of the experimental frequencies is much smaller in this region. This is especially true for all the a2 frequencies that haw been measured in the liquid phase. Thus, a difference of a few cm-I (which is typically the difference between liquidand gas-phase frequencies) can change significantly the percent difference for small frequencies. It is also possible that the prediction of harmonic frequencies for bending modes that are lower than the experimental fundamentals for multiply bonded and aromatic systems is a common feature of all single reference based correlated calculations. Our unpublished results with various basis sets and also Lee's"'C1 calculations show that this is the case for some small systems that include T bonding, namely C,H, and C2H4. It appears that flexible basis sets, including extended sets of polarization functions, are more important than hitherto realised. We are currently investigating this problem. The above arguments however, do not alter the value of the ab initio prediction, which provides an accurate estimate of the harmonic force field for cases where the experimental determination is extremely difficult. From the MP2 IR intensities reported in Tables 11-IV, we note that there is a good correlation with the available experimental data, Le., strong and weak bands are correctly predicted. The agreement is best for the strong and very strong bands, and this can be easily understood since the accurate experimental determination of the intensities of weak overlapping bands is certainly not easy.
Conclusion In this paper we have reported the harmonic vibrational frequencies and IR intensities of furan, pyrrole, and thiophene calculated at the correlated MP2 level with a DZP basis set. The calculated equilibrium geometries are in very good agreement with the experimental substitution structures. The currently state of the art, for this size of molecule, MP2/DZP harmonic frequencies are sufficiently accurate to support or challenge the proposed experimental assignments of the spectra, and at the same time show that the calculated harmonic force fields are close to reality
J. Phys. Chem. 1988, 92, 1742-1746
1742
TABLE V: Calculated and Experimental Rotational and Centrifugal Distortion Constants
calcd"
exptlb
pyrrole calcdo exptlb
A', MHz E' C'
9453.6 9143.8 4648.1
9447.1 9246.7 4670.8
9102.3 8935.6 4509.1
9130.6 9001.4 4532 I
8052.6 5374.0 3223 1
AJ, kHz AJK
1.653 -0.186 1.657 0.661 1.297
1.749 -0.264 1.880 0.698 1.31 I
1.464 -0.310 1.625 0.589 1.076
1.532 -0.341 1.810 0.615 1.109
0.767 -0.286 2.214 0.286 0846
furan
AK 65
6,
"This work.
thiophene calcd'
Wlodarczak et al.
and therefore a very useful tool in the accurate experimental determination of harmonic and anharmonic force constants. An interesting feature of the calculated out-of-plane vibrational frequencies is also noted, namely, that these are lower than the
experimental fundamentals. Finally, as a further help to the deconvolution of the experimental spectra, the IR intensities of the absorption bands are calculated and found to be in agreement with the qualitative experimental results. Note Added in Proof. In a recent paper, Wlodarczak, Martinache, and Demaison ( J . Mol. Spectrosc. 1988, 127, 200) investigated the rotational spectra of furan and pyrrole and published experimental values for the rotational and centrifugal distortion constants of these molecules. They regretted that ab initio values are not often available. We have used the program SPECTRO (J. F. Gaw, University of Cambridge) to generate these quantities from our harmonic force fields; these are given in Table V in the A reduction, representation 1'.
Acknowledgment. E.D.S. is grateful to the EEC for financial support. Registry No. Furan, 110-00-9; pyrrole, 109-97-7; thiophene, 110-02-1.
Excited-State Propertles of Arylmethyl Radicals Containing Naphthyl, Phenanthryl, and Blphenyl Moieties' D. Weir: L. J. Johnston, and J. C. Scaiano* Division of Chemistry, National Research Council of Canada, Ottawa, Ontario K l A OR6, Canada (Received: July 7 , 1987; In Final Form: October 6 , 1987)
The excited-stateproperties of radicals I-V have been examined in solution by using two-photon, two-laser excitation techniques. The radicals were normally generated by photolysis (308 nm) of the corresponding halomethyl precursor. The radicals were then excited by laser irradiation at 337 nm, and the fluorescence spectra, lifetimes, and, whenever possible, transient spectra (Le., I and IV) for the excited radicals were recorded. For example, for the 2-phenanthrylmethyl radical (I), the excited-state = 593 nm and its absorption spectrum shows lifetime is 79 ns in toluene at room temperature, where it fluoresces with A,, = 400 nm. The lifetime of excited I shows only a very minor temperature dependence ( E , = 0.6 kcal/mol in the 183-340 K range).
Introduction Recent reports by Meisel et al.334on the detection of emission and transient absorption from diphenylmethyl and related radicals in solution at room temperature have stimulated a number of studies of the excited-state properties of benzylic radicals. The excited state of the parent radical, benzyl, proved to be a rather elusive species at room temperature. In a recent study Meisel et alS5 have examined the temperature dependence of the fluorescence from this radical and have demonstrated that the expected fluorescence lifetime at room temperature would be around 800 ps. The short lifetime is due to the close proximity of the 12A2 and 22B2 levels, the latter providing an efficient deactivation pathway in solution at room temperature. Structural modifications (such as in diphenylmethy13,4,6.7or 1-naphthylcan lead to an increased separation between these two (1) Issued as NRCC No. 281 10. (2) Present address: Radiation Laboratory, University of Notre Dame, Notre Dame, IN 46556. (3) Bromberg, A.; Schmidt, K. H.; Meisel, D. J . Am. Chem. SOC.1984, 106, 3056. (4) Bromberg, A.; Schmidt, K. H.; Meisel, D. J . Am. Chem. SOC.1985,
levels and, as a result, a longer lifetime and more efficient fluorescence. In our earlier study of 1-naphthylmethyl radical6 we made the intriguing observation that the absorption spectrum of the excited radical was very similar to that of triplet naphthalene. It would be interesting to establish if this characteristic is shared by other systems; however, our current knowledge of the properties of excited radicals is too limited to decide whether this is the case. In this paper we report the results of a series of studies undertaken to broaden our knowledge on free-radical kxcited states and to address the question raised above. Our experiments have led to the characterization of several radicals which had not been observed before. Our studies deal with the fluorescence spectra and lifetimes of all the systems examined and the transient absorption properties of those where such measurements proved feasible.
Experimental Section Materials and General Techniques. 2-(Bromomethy1)phenanthrene and 4-(bromomethy1)biphenyl were prepared by bromination (N-bromosuccinimide) of 2-methylphenanthrene and 4-methylbiphenyl, respectively.' I 2-(Bromomethyl)naphthalene
107, 83.
(5) Meisel, D.; Das, P. K.; Hug, G. L.; Bhattacharyya, K.; Fessenden, R. W. J . A m . Chem. SOC.1986, 108, 4706. (6) Scaiano, J. C.; Tanner, M.; Weir, D. J . Am. Chem. SOC.1985, 107, 4396. (7) Weir, D.; Scaiano, J. C. Chem. Phys. Let!. 1986, 128, 156.
0022-3654/88/2092-1742$01.50/0
(8) Johnston, L. J.; Scaiano, J. C. J . Am. Chem. SOC.1985, 107, 6368. (9) Scaiano, J. C.; Johnston, L. J. Pure Appl. Chem. 1986, 58, 1273. (10) Hilinski, E. F.; Huppert, D.; Kelly, D. F.; Milton, S.V.; Rentzepis, P. M. J . Am. Chem. SOC.1984, 106, 1951.
Published 1988 by the American Chemical Society
