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J . Phys. Chem. 1990, 94, 1844-1847
Kerr Effects, Rayleigh Depolarization Ratios, Polarizabilities, and Hyperpolarizabilities of Fluorobenzene and Pentatluorobenzene Ian R. Gentle, Mark R. Hesling, and Geoffrey L. D. Ritchie* Department of Chemistry, University of New England, New South Wales 2351, Australia (Received: July 3, 1989)
Measurements of the vapor-phase electric-field-induced birefringences and Rayleigh depolarization ratios of fluorobenzene and pentafluorobenzene are used to separate the variously temperature-dependent contributions to the zero-density Kerr constants of these molecules. The derived first Kerr hyperpolarizabilities are rather imprecise, but reliable values are obtained for all three optical-frequencyprincipal polarizabilitiesof both molecules. Results ( l@axx/Cm2 VI,etc., x direction coincident with C,axis, z direction perpendicular to molecular plane) emerge as 13.54f 0.31, 13.44 0.42,7.13 f 0.16for fluorobenzene and 13.70f 0.37,13.93f 0.47,6.86 f 0.15for pentafluorobenzeneat 632.8nm. Trends in the polarizabilitiesof the molecules benzene, fluorobenzene, 1,3,5-trifluorobenzene, pentafluorobenzene, and hexafluorobenzene are considered.
*
Introduction
Considerable effort has been devoted to the investigation of the polarizability of the several fluorobenzenes in the sequence from benzene to hexafluorobenzene, not only because of the intrinsic interest in this quantity'-2 but also because knowledge of it is required in order to evaluate other molecular properties, for example, quadrupole moments3s4and magnetic anisotropies5-' from field-induced birefringence. Although the dilute-solution Kerr constants of these molecules have been much used as a source of i n f ~ r m a t i o n , ' analysis * ~ ~ ~ of the data to yield polarizability anisotropies is attended by serious problems, as previously noted.s For example, with carbon tetrachloride or cyclohexane as solvents, the apparent polarizability anisotropies of benzene and hexafluorobenzene as solutes are only ~65435%of the free-molecule values2 Such difficulties can largely be overcome if observations are made on the species in the vapor rather than the dilute-solution state. To this end, we recently reportedEa study of the temperature dependence of the vapor-state Kerr effects of benzene, 1,3,5trifluorobenzene, and hexafluorobenzene. The investigation described here is concerned with the dipolar molecules fluorobenzene and pentafluorobenzene, for which there are additional contributions to the effects. Measurements of the vapor-state electric-field-induced birefringences and Rayleigh depolarization ratios were used to separate the variously temperature-dependent terms in the zero-density Kerr constants, and to obtain experimental values of the relevant polarizabilities and hyperpolarizabilities of these molecules. The results made it possible to examine how the polarizability is affected by progressive replacement of hydrogen by fluorine in benzene, fluorobenzene, 1,3,5-trifluorobenzene, pentafluorobenzene, and hexafluorobenzene. (1)(a) Le Fkvre, C. G.; Le F&re, R. J. W. J. Chem. SOC.1954, 1577-1588. (b) Le Fkvre, R. J. W.; Purnachandra Rao, B. J. Chem. SOC. 1958, 1465-1468. (c) Le Wvre, R. J. W.; Radford, D. V.; Ritchie, G. L. D.; Stiles, P. J. J . Chem. SOC.( E ) 1968, 148-156. (d) Aroney, M.J.; Cleaver, G.; Pierens. R. K.; Le Fsvre. R. J. W. J. Chem. Soc., Perkins Trans 2 1974, 3-5. (2)Bogaard, M. P.; Buckingham, A. D.; Pierens, R. K.; White, A. H. J. Chem. SOC.,Faraday Trans, I 1978, 74,3008-3015. (3) (a) Vrbancich, J.; Ritchie, G. L. D. J. Chem. SOC.,Faraday Trans. 2 1980, 76, 648-659. (b) Dennis, G. R.; Gentle, I. R.; Ritchie, G. L. D. J . Chem. SOC.,Faraday Trans. 2 1983, 79, 529-538. (4)Battaglia, M. R.; Buckingham, A. D.; Williams, J. H. Chem. Phys. Lett. 1981, 78,421-423. (5) (a) Cheng, C. L.; Murthy, D. S. N.; Ritchie, G. L. D. Mol. Phys. 1971,
22, 1137-1140. (b) Battaglia, M. R.; Ritchie, G. L. D. J . Chem. SOC., Faraday Trans. 2 1977, 73, 209-221. (c) Ritchie, G. L. D.; Vrbancich, J. Ausf. J . Chem. 1982, 35, 869-880. (6) Bogaard, M. P.;Buckingham, A. D.; Corfield, M. G.; Dunmur, D. A,; White, A. H. Chem. Phys. Lett. 1972, 12, 558-559. (7)(a) Lukins, P. B.; Buckingham, A. D.; Ritchie, G. L. D. J. Phys. Chem. 1984, 88, 2414-2418. (b) Lukins, P. B.; Ritchie, G. L. D. J . Phys. Chem. 1985, 89, 1312-1314. ( 8 ) Gentle, 1. R.; Ritchie, G. L. D. J . Phys. Chem. 1989, 93,774C7744.
0022-3654/90/2094-1844$02.50/0
TABLE I: Temperature Dependence of the Vapor-State Kerr Effects of Fluorobenzene and Pentafluorobenzene at 632.8 nm i03Ti/ no. of IO~B/ 1027~~/ TIK K-' Dressures o l k P a m3 mol-' m5 V2mol-'
Fluorobenzene 490.3 456.9 423.7 395.7 381.6 370.8 349.3 330.8 315.6
2.040 2.189 2.360 2.527 2.621 2.697 2.863 3.023 3.169
490.6 457.2 423.9 395.9 38 1.7 349.4 33 1 .O 315.5
2.040 2.187 2.359 2.526 2.620 2.862 3.021 3.170
7 7 8 8 8 8 8 7 4
21-85 22-75 1 1-84 11-85 10-8 1 24-73 10-6 1 10-38 10-18
-492 -586 -703 -832 -910 -993 -1 I63 -1 33 1 -1472
*
40.5 0.2 46.4f 0.2 52.9 f 0.2 60.3 f 0.2 64.3 f 0.6 68.5 f 0.4 75.7 f 0.4 80.7 f 0.9 89.0 f 1.6
Pentafluorobenzene 8 8 8 7 8 7 8 4
14-54 14-51 13-52 9.5-52 9.0-52 9.5-51 9.3-34 7.7-15
-701 -823 -981 -1158 -1262 -1600 -1927 -2260
38.1 f 0.2 43.4 f 0.3 49.0f 0.2 55.9 f 0.3 58.6 f 0.2 68.5 f 0.4 76.5 f 0.3 84.9f 1.4
Experimental Section
Samples used for measurements of the electric-field-induced birefringences (Kerr effects) and Rayleigh depolarization ratios were as follows: fluorobenzene (Merck, >99%), twice fractionally distilled from phosphorus pentoxide with a calcium chloride drying tube to maintain a dry atmosphere, purity >99.9%; pentafluorobenzene (Aldrich, 98%), similarly treated, purity >99.9%. The purities were determined by gas chromatography. Immediately prior to use each sample was subjected to several freeze-pump-thaw cycles and vacuum-distilled into the appropriate apparatus. Equipment and procedures for measurements of the temperature and pressure dependence of the vapor-phase electrooptical Kerr , ~ definition effect at 632.8 nm were as previously d e s ~ r i b e d . ~The of the molar Kerr constant, ,K, islo
K , = 6 n V , [ ( n 2+ 2)2(c,
+ 2)2]-1[(nil- n,)F2],,,
(1)
where n and cr are the refractive index and relative permittivity of the medium in the absence of the field, n,,- n, is the fieldinduced birefringence for light polarized parallel and perpendicular to the uniform electric field F , and V, is the molar volume. (9)Gentle, I. R.; Laver, D. R.; Ritchie, G. L. D. J . Phys. Chem. 1989, 93. 3035-3038. ( I O ) (a) Buckingham, A. D.; Orr, B. J. Proc. R. Sm. London, Ser. A. 1968, 305,259-269. (b) Buckingham, A. D.; Orr, B. J. Trans. Faraday SOC.1969, 65,673-68I.
0 1990 American Chemical Society
Polarizabilities of Fluorobenzenes Observations on fluorobenzene and pentafluorobenzene were made at eight or nine temperatures within the available span (~315-490 K) and, at each temperature, over a range of pressures (=7-85 kPa) up to about 70% of the equilibrium vapor pressure. Density virial coefficients, B,” were used to obtain molar volumes, V,, from the vapor temperatures and pressures. Because data for pentafluorobenzene were available for only three temperatures at the lower end of the range of interest here, the known values of B and the electric dipole moment, p,I2 were used to determine the values of c / k and u appropriate to a Stockmayer potential for this molecule. The results (elk = 1095 K, u = 0.365 nm) were tested, in conjunction with a tabulation of the reduced second virial coeffi~ient,’~ by recalculation of B for the same three temperatures. Since the recalculated and experimental data agreed to within 6%, the same parameters were used to estimate the value of B at each of the eight temperatures shown in Table I. In any case, the experimental pressures were kept as low as was consistent with acceptable precision in the birefringence measurements, so that negligibly small errors arose from uncertainties in the virial coefficients. As already explained,8-I0the observed birefringences, nil - n,, and the molar volumes, V,, were used to calculate values of ,KO = (2/27)(nl1- n,)V,F2, and the zero-density molar Kerr constant, AK, at each temperature was obtained from the intercept The results are summarized of a linear graph of ,KO against in Table I , where the errors quoted are precisions taken as the standard deviations obtained from the least-squares fitting of straight lines to the density-dependence data; the overall accuracy is estimated as f2%. Although the Kerr effects of both fluorobenzene and pentafluorobenzene as solutes in nondipolar solvents have been much studied, neither species has previously been examined in the vapor phase. A brief description of the apparatus developed in Armidale for measurements of the Rayleigh depolarization ratios, p o = G [ c , of gases and vapors has already appeared.I4 Significant improvements, most notably greatly reduced instrumental scattering, have since been achieved, and these will be detailed elsewhere. For consistency with the Kerr-effect study, a IO-mW He-Ne laser ( A = 632.8 nm) was used as the light source. Rayleigh depolarization ratios at 632.8 nm (expressed here as 102po) emerged from repeated observations as 2.03 f 0.02 and 2.36 f 0.02 for fluorobenzene and pentafluorobenzene, respectively. The result for fluorobenzene is in agreement with that reported by Bogaard and others.2
Discussion The classical statistical mechanical expression for the zerodensity molar Kerr constant, AK, of a dipolar molecule is, in S I units, iOb-i
where p is the molecular dipole moment, a and a0 are the mean optical-frequency and static polarizabilities, axxis the component of the optical-frequency polarizability in the direction of the dipole moment, K and KO are optical-frequency and static polarizability parameters such that and
( I I ) Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures; Clarendon Press: Oxford, U.K., 1980. (12) Doraiswamy, S.; Sharma, S. D. Pramana 1974, 2, 219-225. (1 3) Hirschfelder, J. 0.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids; Wiley: New York, 1964. (14) Craven, 1. E.; Hesling, M . R.; Laver, D. R.; Lukins, P. B.; Ritchie, G . L. D.; Vrbancich, J. J . Phys. Cbem. 1989, 93, 627-631. ( 1 5 ) Relevant conversion factors are (a/esu) = 0.8988 X 10l6 ( a / C m2 VI), (@/mu) = 2.6944 X 1020 (p/C m3 V 2 ) , (ylesu) = 0.8078 X lo2 (y/C m4 V-9.
The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
2.2
2.6
3.0
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3.4
1 0 3 -~1 i K-1 Figure 1. Temperature dependence of the zero-density molar Kerr constants of fluorobenzene and pentafluorobenzene.
TABLE 11: Analysis of the Temperature Dependence of the Zero-Density Kerr Effects of Fluorobenzene and Pentafluorobenzene at 632.8 nm DroDertY 1060yK/C m4 V-3 0 loz1 X slope/m5 V2K2 mol-Ib loz4 X intercept/m5 V-2 K mol-l 1030r/C m 1040a/C m2 v-l
CIHSF 0.4 7.96 f 0.24 3.5 f 0.6 5.27 f 0.07c 1 1 .37c 12.448 3.48 f 0.03 -0.9 f 0.4 2.17 f 0.09 13.54 f 0.31 13.44 f 0.42 7.13 f 0.16
m2 v-l 102K2 1oSopK/Cm3 V-2 1o4O(01, - a ) / C m2 V-” i040a,,/C m2 V-’ i040a,/C m2 V-l 1040a,,/C m2 V-’
CAHF, 0.6 6.70 f 0.21 4.8 f 0.5 4.80 f 0.17d 11.9 =11.5* 4.06 f 0.04 -0.8 f 0.4 2.20 f 0.17 13.70 f 0.37 13.93 f 0.47 6.86 f 0.15
‘Interpolated from data for C6H6, 1,3,5-C6H3F3,and C6F6 in ref 8. Slope and intercept of eq 4; see text. Reference 16. Reference 12. ‘Reference 2. /Interpolated value. ZReferences 16 and 17. *Assumed value. ‘Locations of molecular axes: x coincident with C, axis, z perpendicular to plane.
[3~,~,~(-w;w,O,O)- yqapB(-w;O,O,O)] / 10 are the first and second Kerr hyperpolarizabilities, respectively. As recently shown,* yK makes only a very small contribution ( ~ 2 % to ) the Kerr constants of C&6, C6H3F3,and C6F6 at normal temperatures and in view of the known, albeit imperfect, additivity of this property, it is entirely reasonable to interpolate values for the dipolar molecules C6H5Fand C6HF5,for which the Kerr constants are about 5 times larger. It is therefore advantageous to recast eq 2 in the form [AK - ( N ~ / 8 l t o ) Y ~ ] =T ( N A / 8 1 t 0 k )x {[(2/3)pPK (9/5)cU(u°KKo] (3/10k)p2(~,,
+
+
- a)?-’) (4)
so that a plot of the left-hand side against T I can be expected to yield a straight line with intercept and slope proportional to [(2/3)pPK + ( 9 / 5 ) a a ° K K o ] and p2(a, - a ) , respectively. Figure 1 displays the values of [ A K- ( N A / 8 1 c o ) y KT] derived from the experimental results in Table I and the interpolated estimates of -yK, together with the fitted linear plots of this quantity against T i ; and Table I1 contains the numerical values of yKthat were used, the s l o p and intercepts of the straight lines, and the analysis of these quantities in terms of molecular properties. Other necessary data for C6HSFand C6HF5 are the dipole moments, determined by the techniques of dielectric polarization16 and microwave spectroscopy,I2 respectively; the mean opticalfrequency and static polarizabilities, obtained from refractive (16) McAlpine, K. B.; Smyth, C. P. J . Cbem. Pbys. 1935, 3, 55-57.
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The Journal of Physical Chemistry, Vol. 94, No. 5, 1990
Gentle et al.
TABLE Ill: Contributions to the Zero-Density Kerr Constants of Fluorobenzene and Pentafluorobenzene at 300 K" term C6H5F ( N A 1/d~Y K 0.34 (+0.3%) (2N~/243cokT)doK -6.27 (-6.2%) (9NA/405eok7')aa K K 17.95 (+17.9%) ( N A / 2 7 0 ~ ~ k ~ r Z )-p a) ~ ( c ~88.45 ~ ~ (+88.0%) 100.47 AK r?
C6HF5
0.51 (+0.6%) -5.51 (-6.1%) 21.44 (+23.6%) 74.48 (+81.9%) 90.92
Equation 2; entries are 1O2'AK/mS V~mol-', etc.
indexes2 and dielectric p e r m i t t i ~ i t i e s ;and ~ ~ , the ~ ~ values of KK' == K~ = 5p0 (3 - 4pO)-I derived from the vapor-phase Rayleigh depolarization ratios reported above. The absolute and percentage contributions of the four terms in eq 1 to the values of AK for C6H5Fand C6HF5at 300 K are shown in Table 111. Obviously, the observed effect is dominated by the k2(axx- a ) term (=88%, 82%) and the (YCYOKKO term (=18%, 24%); the oppositely signed contributions from kLpKare small (== -6%, -6%); and the interpolated contributions from yKare negligible (0.3%, 0.6%). Once again, the first hyperpolarizabilities are rather poorly determined by the Kerr-effect method, but the results, the first for such large molecules in the vapor phase, are nevertheless of interest. In particular, the value of LpK (quoted here as 1OSopK/Cm3 V 2 ) found in this study for gaseous C6H5F (-0.9 f 0.4) can be compared with values of a closely related first hyperpolarizability, p, obtained from observations of electricfield-induced second-harmonic generation'* by the pure liquid (-0.39,19 -0.9420), and with an estimate from a modified CNDO/2-CI computational method (-0.7621). Such comparisons are, of course, complicated by the effects of dispersion and other factors,22but the level of agreement appears to be reasonable. In contrast to the intercepts, the slopes of the plots of [AK ( N A / 8Ito)rK] T against T i are well determined (=f3%) for both C6H5Fand C6HF5. Because of the uncertainties in the dipole moments, particularly that of C6HF5,the derived polarizability anisotropies, 1040(ax,- a ) / C m 2 V-', are less well determined (f4%, *8%); but the result for C6H5F (2.17 f 0.09) is in agreement with, and of considerably higher precision than, the result obtained earlier (2.1 f 0.7) from the Cotton-Mouton effect, together with the magnetizabilities, the mean polarizability, and the Rayleigh depolarization ratio of this m o l e c ~ l e . ' ~To derive the three principal polarizabilities of each molecule, the values of axx- a so deduced were combined with values of K~ from the Rayleigh depolarization ratios reported here, and the known mean polarizabilities. The quadratic nature of eq 3a results in two solutions (i.e~,two possible sets of polarizabilities) in each case, but the choice between these is unambiguous, because the magnitudes of the components must satisfy the condition aXX= cyyy >> a,,, where the x direction is coincident with the C2 axis and the z direction is perpendicular to the molecular plane. In the case of C ~ H S Fthe , polarizabilities in Table I1 are in excellent agreement with those derived in the earlier and for both C6H5Fand C6HF5the two in-plane polarizabilities are indistin( 1 7) Landolt-Bornstein. Numerical Data and Functional Relationships, 6th ed.; Springer-Verlag: Berlin, 1959; Vol. 2, Part 6, p 881. ( 1 8) Note that in our convention the positive x direction coincides with the direction (- to +) of the dipole moment, so that BK has the same sign as rBK, the measured quantity; in the ESHG studies the reference axis is directed from the center of the ring through the carbon atom to which the fluorine atom is attached, and in consequence fJK and B, so defined, have opposite signs. Also, BK= -( 12/5)8, so that values of BK (in SI units) can be derived from literature values of B (in cgs electrostatic units) as (BK/C m3 V-*) = -(0.8907 X (Blesu). (19) Levine, B. F.; Bethea, C.G . J . Chem. Phys. 1975, 63, 2666-2682. (20) Zyss, J. J . Chem. Phys. 1979, 70, 3333-3340. (21) (a) Docherty, V. J.; Pugh, D.; Morley, J. 0. J. Chem. Soc., Faraday Trans. 2 1985, 81, 1179-1192. (b) Pugh, D.; Morley, J. 0. Molecular Hyperpolarizabilities of Organic Materials. In Non-linear Optical Properties of Organic Molecules and Crystals; Chemia, D. S . , Zyss, J., Eds.; Academic Press: Orlando, FL, 1987; Vol. 1, pp 193-225. (c) Morley, J. 0.;Docherty, V . J.; Pugh, D. J . Chem. Soc., Perkin Trans. 2 1987, 1357-1360. (22) Bogaard, M. P.; Orr, B. J. Electric Dipole Polarizabilities of Atoms and Molecules. I n MTP International Review of Science; Phys. Chem. Ser. 2; Buckingham. A . D., Ed.; Butterworths: London, 1975; Vol. 2, pp 149-194.
Aa
I
-10
0
1
2
3
4
5
6
Number of fluorine atoms
Figure 2. Dependence of a , A a , a,, and a,, on the number of fluorine atoms for molecules in the sequence from benzene to hexafluorobenzene.
guishable in magnitude, as had previously been assumed3bfor the former molecule. The precision of the results further demonstrates the usefulness of the Kerr effect as a route to molecular polarizabilities. Finally, it is of interest to compare the polarizability parameters a, axx, and cyzz here considered for C6H5Fand C6HF5with the analogous quantities* for C6H6, 1,3,5-C6H3F3,and C6F6;and Figure 2 graphs all four properties against the number of fluorine atoms in these molecules. Of course, the refractivity and mean polarizability of the fluorine atom and the carbon-fluorine bond are known to be very similar to those of the hydrogen atom and the carbon-hydrogen bond, respecti~ely.~~ It is, therefore, hardly surprising that the mean molecular polarizability, a property known to be predominantly additive rather than constitutive in nature, is effectively constant through the sequence from C6H6 to c6F6. However, in view of the very different charge distributions of C6H6 and (36, as manifested in their large but oppositely signed molecular quadrupole moments,3ait is by no means obvious how the polarizability anisotropy, and the individual components of the polarizability, might vary on fluorine substitution. The answer is clear from Figure 2; progressive introduction of fluorine atoms into benzene results in a small and regular increase in cyxx, the in-plane component, and a similarly small and regular decrease in cyzz, the out-of-plane component of the polarizability, presumably because of inductive and conjugative interactions between the substituents and the ring. In consequence of these necessarily opposed effects, the magnitude of the negatively signed polarizability anisotropy increases, once again regularly, from C6H6 to C6F6. Neither the presence or absence of a molecular dipole moment nor the magnitude of the molecular quadrupole moment has any apparent effect on these trends.
Summary The present study of the electric-field-induced birefringences and Rayleigh depolarization ratios of fluorobenzene and pentafluorobenzene has provided definitive experimental values of the variously temperature dependent contributions to the zero-density Kerr constants of these molecules. Although the derived first Kerr hyperpolarizabilities, PK,are rather imprecise, the results are the first for such large molecules in the vapor phase; and that for fluorobenzene is in reasonable agreement with values of a closely related first hyperpolarizability determined from observations of electric-field-induced second-harmonic generation in the pure (23) For C,HSF and C,HFS, a,, a and A a = (Za,, - a,, - ayy)/2. (24) Le Ftvre, R. J. W. Molecular Gfractivity and Polarizability. In Advances in Physical Organic Chemistry; Gold, V.. Ed.; Academic Press: London, 1965; pp 1-90.
J . Phys. Chem. 1990, 94, 1847-1850 liquid. By contrast, the measurements, in conjunction with other data, yielded high-precision values for all three principal polarizabilities of fluorobenzene and pentafluorobenzene, and for both molecules the two in-plane components were found to be indistinguishable in magnitude. Trends in the mean polarizability, the in-plane and out-of-plane components, and the polarizability anisotropy in the molecules benzene, fluorobenzene, 1,3,5-tri-
1847
fluorobenzene, pentafluorobenzene, and hexafluorobenzene were also considered.
Acknowledgment. A Commonwealth Postgraduate Research Award (to 1.R.G.) and financial support from the Australian Research ~ o ~ n c(to i l G.L.D.R.1 are gratefully acknowledged. Registry No. C&F,
462-06-6; C6HF5, 363-72-4.
Correlation Function Diagnosis of Chaotic Vibrations in HCN Young June Cho, Paul R. Winter, Harold H. Harris,* Department of Chemistry, University of Missouri-St.
Louis, S t . Louis, Missouri 631 21
Eugene D. Fleischmann,t and John E. A d a m Department of Chemistry, University of Missouri-Columbia, (Received: July 3, 1989; In Final Form: September 2, 1989)
Columbia, Missouri 6521 1
Classical trajectory calculations on the potential energy surface of Murrell, Carter, and Halonen have been performed from semiclassical starting conditions between the zero-point energy and dissociation. Diagnosis of the onset of classical chaos has been accomplished in several ways, but especially by using as a criterion the amplitude of the four-mode instantaneous correlation function. The onset of chaos occurs first in the bending mode, at approximately 11 000 cm-I. At the dissociation limit, virtually all trajectories starting from overtones of the bend are chaotic within 41 ps of the start of the trajectory. On the other hand, the corresponding threshold when overtones of the stretching vibrations are initially excited is near 26 000 cm-’, and only a fraction of those trajectories just below dissociation become chaotic.
Introduction
There is a continuing interest in our laboratories in the nature of intramolecular energy transfer in small molecules, especially through the application of classical trajectory methods. Since one of us (J.E.A.) earlier successfully applied the spectral intensity method of Noid et al.’ to the computation of rotational-vibrational spectra of models of both an isolated HCl molecule and one adsorbed on argon,2 one of our interests was the application of the method to a polyatomic. The simplest polyatomic is, of course, a linear triatomic. We have chosen to study H C N both because there is available a potential energy surface highly accurate up to the isomerization barrier3 and because there is a wealth of experimental information concerning vibrational f r e q ~ e n c i e s , ~ dipole moments,5 and IR integrated intensities? The apparently irregular/chaotic dynamics of HCN (earlier reported by Lehmann et al.7-9and by Founargiotakis et al.lO)led us further to consider criteria more convenient and less subjective than the spectral intensity method and more easily applicable to large-dimensional problems than the examination of Poincare surfaces of section. We have modified the correlation function approach first applied to a two-mode model of H 2 0 by Muckerman et al.” and applied it to HCN and also examined other correlation-function approaches to the transition from quasiperiodic to stochastic vibration. Calculational Details
All of our computations employed the semiempirical potential energy surface (PES) devised by Murrell et aL3 which yields almost exactly the known vibrational frequencies of HCN, HNC, and their isotopic variants. Bacic and Light have computed accurate vibrational quantum levels in this potential, up to the isomerization barrier.I2 (Fleming and Hutchinson13have recently demonstrated the utility of a two-mode model for the high-energy vibrations of the molecule, if the two modes are in “optimal” Present address: Supercomputer Computations Research Institute, Florida State University, Tallahassee, FL 32306-3006. * Author to whom correspondence should be addressed.
0022-3654/90/2094-1847$02.50/0
coordinates in the potential energy surface of B0ts~hwina.l~) Lehmann, Scherer, and Klemperer had used the Murrell surface for classical trajectory calculations but had provided excitation only to the C-H bond, while the C-N bond and the bend were given zero-point vibrational energy. In their earlier ~ o r k , ~ , ~ Lehmann et al. reported that the transition to chaotic motion is rather abrupt, occurring low in the vibrational well at 12 990 cm-’ ( I ) (1) Noid, D. W.; Koszykowski, M. L.; Marcus, R. A. J . Chem. Phys. 1977, 67, 404. Koszykowski, M. J.; Noid, D. W.; Marcus, R. A. J . Phys. Chem. 1982,86,2113, and references cited therein. Some molecule systems are also described in: Koszykowski, M. L.; Pfeffer, G. A,; Noid, D. W. In Chaotic Phenomena in Astrophysics; Eichhorn, H.; Ed.; Ann. N.Y. Acad. Sci. 1987, 497, 127. (2) Adams, J. E. J . Chem. Phys. 1986, 84, 3589. (3) (a) Carter, S.; Mills, I. M.; Murrell, J. N. J . Mol. Spectrosc. 1980,81, 1 IO. (b) Murrell, J. N.; Carter, S.; Halonen, L. 0.J . Chem. Phys. 1982, 93, 307. (4) Douglas, A. E.; Sharma, D. J . Chem. Phys. 1953,21,448. Rank, D. H.; Skorinko, G.; Eastman, D. P.; Wiggins, T. A. J . Opt. SOC.Am. 1960, 50, 421. Rank, D. H.; Schearer, J. N.; Wiggins, T. A. Phys. Reu. 1954, 94, 575.
Rank, D. H.; Guenther, A. H.; Schearer, J. N.; Wiggins, T. A. J . Opt. SOC. A m . 1957,47, 148. Rank, D. H.; Skorinko, G.; Eastman, D. P.; Wiggins, T. A. J. Mol. Spectrosc. 1960, 4, 518. Dagg, I. R.; Thompson, H. W. Trans. Faraday SOC.1956, 52, 455. Checkland, P. B.; Thompson, H. W. Trans. Faraday SOC.1955, 51, 1. Allen, H. C.; Tidwell, E. D.; Plyler, E. K. J . Chem. Phys. 1956, 25, 302. Maki, A. G.; Blaine, L. R. J. Mol. Spectrosc. 1964, 12, 45. (5) Ebenstein, W. L.; Muenter, J. S. J . Chem. Phys. 1984,80, 89. DeLeon, R. L.; Muenter, J. S. J. Chem. Phys. 1984, 80, 3992. (6) Foley, H. M. Phys. Reo. 1946, 69, 628. Hyde, G. E.; Hornig, D. F. J . Chem. Phys. 1952, 20, 647. Finzi, J.; Wang, J. H. S.; Mastrup, F. N. J . A D D ~Phvs. . 1977.48,2681. Kim, K.: Kina. W. T. J. Chem. Phvs. 1979, 71. 1967. Smith, I. W. M. J. Chem. SOC.,Faraday Trans. 2 1981, 77, 2357. (7) Lehmann, K. K.; Scherer, G. J.; Klemperer, W. J . Chem. Phys. 1982, 76, 644 I . (8) Lehmann, K. K.; Scherer, G. J.; Klemperer, W. J . Chem. Phys. 1982, 77, 2853. (9) Lehmann, K. K.; Scherer, G. J.; Klemperer, W. J . Chem. Phys. 1983, 78, 608.
(IO) Founargiotakis, M.; Farantos, S. C.; Tennyson, J. J. Chem. Phys. 1988, 88, 1598. (I 1) Muckerman, J. T.; Noid, D. W.; Child, M. S. J . Chem. Phys. 1983, 78, 3981. (12) Bacic, Z.; Light, J. C. J . Chem. Phys. 1987, 86, 3065. (13) Fleming, P. R.; Hutchinson, J. S . J . Chem. Phys. 1989, 90, 1735. (14) Botschwina, P. J. Chem. SOC.,Faraday Trans. 2 1988, 84, 1263.
0 1990 American Chemical Society
