J. Phys. Chem. 1982,86,3789-3793
transition for pyrene on silica gel may also reflect the importance of an asymmetric interaction on the molecule, part of which is in an environment approaching the vapor or inert solvent. This aspect of the photophysics of adsorbed species invites theoretical attention.
Conclusion The picture that emerges from these results can be summarized as follows. The distribution of pyrene molecules on the surfaces in question is not random: there appear to be preferred sites. The result is an inhomogeneous distribution which yields a multicomponent decay. Strong evidence exists for the formation of a very weakly bound ground-state bimolecular association product, particularly on silica gel, and the data suggest associating this phenomenon with particular sites at which an interaction stabilizes this bimolecular association. The data also indicate that this phenomenon may be related to some peculiarity of the hydrogen-bonding interaction with the A system of the aromatic hydrocarbon. It is suggested that
3789
the static and highly asymmetric interaction may cause pyrene to behave in a manner different from that in hydroxylic solvents where the interactions are rapidly averaged and, on the time scale of the lifetime of pyrene, the interactions are symmetric over the whole of the A system. If the silanol groups are blocked by a long-chain alcohol and polyalcohol, the pyrene molecules appear forced to be adsorbed in areas of weaker interactions where the tendency to form the bimolecular ground-state arrangement is diminished. The mobility during the lifetime also appears to be greatly enhanced, and dynamic excimer formation is then possible. Acknowledgment. Acknowledgment is made by P.deM. to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of this work, and to the National Science and Engineering Research Council of Canada for additional support. W.R.W. acknowledges support from the National Science and Engineering Research Council of Canada for support of this work.
Electron Spin Resonance of Matrix-Isolated K+***HCID. M. Lindsay,' Department of Chemistry, City University of New York, City College, New Yo&, New York 10031
M. C. R. Symons, Department of Chemistry, The Unlverslty of Leicester, Leicester LE 1 7RH, England
D. R. Herschbach, Department of Chemistry, Harvard University, C a m b r w , Massachusetts 02 138
and Alvin L. Kwiram Department of Chemistry, University of Washington, Seattle, Washington 98195 (Received:April 23, 1982)
ESR spectra assigned to the previously unobserved u* radical HCl- have been obtained by the reaction K + HC1- K+ + HC1- in an argon matrix. Experimental spin populations, pSs = 2%, p3,, = 19% on chlorine, and plS = 85% on hydrogen, show that HC1- is an authentic u* radical in which there is a significant bonding participation by both atomic moieties. The spectra show no hyperfine (hf) splitting from the alkali, but replacement of K+ by Na+ has a pronounced effect on the spin distribution in HCl-. The absence of a strong atomic hydrogen spectrum shows that there is little tendency to produce H + KC1. These results indicate formation of a stable reaction complex K+.* .HCl-, for which further reaction is hindered by an energy barrier as previously indicated by molecular-beam studies of the reaction dynamics.
Introduction In recent years it has become apparent that radicals having a u* structure are common intermediates in a variety of liquid-phase and solid-state reactions.' These species, in which the unpaired electron occupies an antibonding u orbital, can be formed either by direct electron attachment or by a dimerization mechanism. For exampie: the (RS-SR)- anion can be prepared in both ways: (1) RS-SR + e- = (RSLSR)RS. + RS- = (RSLSR)(2) (1) M. C. R. Symons, Pure Appl. Chem., 53, 223 (1981). (2)R.L.Peterson, D. J. Nelson, and M. C. R. Symons, J. Chem. Soc., Perkin Trans. 2, 2005 (1977);225 (1978). 0022-3654/82/2086-3789$01.25/0
Most u* radicals encountered in electron spin resonance (ESR) studies have been of the type ALA, although a few aspmetric A-B radicals, such as R3PLSR,3 R3PLhal,3 and H3NL-hal?' have also been reported. However, other than the group 2A6 and group 2B' diatomic hydrides, no u* radicals involving hydrogen as one component have (3) M. C. R. Symons and R. L. Petersen, J. Chem. Soc., Faraday Trans. I , 210 (1979). (4) F. W. Patten, Phys. Reu., 175, 1216 (1968). (5)M.C. R. Symons, J. Chem. Res., Synop., 160 (1981). (6)L.B. Knight, Jr., and W. Weltner, Jr., J. Chem. Phys., 54,3875 (1971);L.B. Knight, Jr., J. M. Brom, Jr., and W. Weltner Jr., ibid., 56, 1152 (1972). (7)L. B. Knight, Jr., and W. Weltner, Jr., J. Chem. Phys., 55, 2061 (1971).
0 1982 American Chemical Society
3700
The Joumal of Physical Chemistty, Vol. 86, No. 19, 1982
been authenticated. Several potential candidates for an A-H structure have been suggested. In most instances, however, the ESR spectra do not show the expected characteristics'bs of such species: a large proton hyperfine (hf) coupling constant together with Agll N 0 and Ag, > 0. Thus, ESR spectra originally attributed to H2S-,9 H2O-,loand RSH-" are better assigned to, respectively, (HSLSH)-,&l2N o t - (formed from impurities),13and In a somewhat different category is the ESR spectrum originally attributed14 to an R3PAH radical having a tetrahedral u* structure. Although the proton hf coupling (158 G) is of the right magnitude, this would also be expected15of the more usual phosphoranyl radical structure, R3HP.. In this paper we present unambiguous evidence for the u* radical (H-Cl)-. The radical was formed by codepositing atomic potassium and HC1 in an argon matrix and evidently arises from an "electron-jump" or "harpooning" reaction16 K
+ HC1-
K+
+ HC1-
(3)
At large internuclear distances the ionic (K+ + HC1-) state lies above the covalent (K HCl) ground state by an amount I - E, where I and E are respectively the ionization potential of the donor and the electron affinity of the acceptor. As the reactants approach, the ionic state becomes progressively more stable as a result of the Coulombic attraction between cation and anion. At some critical distance, given approximately by16 (energies in eV) r, = 14.4/(1- E ) A,the two curves cross and the ionic state lies lowest. For K + HC1, with I = 4.3 eV" and E -0.8 eV,1°J9 rc 3 A. The electron-jump mechanism is of considerable interest because of its probable role in many elementary reactions, including the reactive scattering of potassium with both HC120-22and HBr (the prototype molecular-beam reaction).23* In the gas phase, however, K+ + HC1- undergoes further reaction to KC1 plus atomic hydrogen. In the absence of stabilizing collisions, the reaction complex K+. .HCT cannot reduce its internal energy and so assume an independent existence. Thus, as in the condensed-state reactions noted above, the radical anion is a transient intermediate whose presence is only indirectly inferred.
+
-
-
Experimental Section K+...HCl- was formed by codepositing argon (Matheson, ~
(8) M. C. R. Symons,Adv. Chem. Ser., No. 82,1 (1968). (9)J. E. Bennett, B. Mile, and A. Thomas, J. Chem. Soc., Chem. Commun., 186 (1966). (10)A. Abou-Kais and J. C. Vedrine, Chem. Phys. Lett., 45, 117 (1977). (11)J. H.Hadley, Jr., and W. Gordy, h o c . Natl. Acad. Sci. U.S.A., 74,216 (1977). (12)M. J. Lin and J. H. Lunsford, J. Phys. Chem., SO, 2015 (1976). (13) M. C. R. Symons, D. R. Brown, and J. C. Vedrine, Chem. Phys. Lett., 52, 133 (1977). (14)M. C. R. Symons,Mol. Phys., 24,885 (1972). (15) M. C. R. Symons,Mol. Phys., 27,785 (1974). (16)D. R. Herschbach, Adu. Chem. Phys., 10,319(1966). (17)A. Hermann, E.Schumacher, and L. Woste, J.Chem. Phys., 68, 2327 (1978). (18)D. C.Frost and C. A. McDowell, J. Chem. Phys., 29,503(1958). (19)K. Lacmann and D. R. Herschbach, Chem. Phys. Lett., 6 , 106 (1970). (20)T. J. Odiorne and P. R. Brooks, J.Chem. Phys., 51,4676 (1969). (21)T. J. Odiorne, P. R. Brooks, and J. V. V. Kasper, J. Chem. Phys., 55, 1980 (1971). (22)J. G. Pruett, F. R. Grabiner, and P. R. Brooks, J. Chem. Phys., 60,3336 (1974);63,1173 (1975). (23)E.H. Taylor and S.Datz, J. Chem. Phys., 23, 1711 (1955). (24)S.Datz, D. R. Herschbach, and E. H. Taylor, J. Chem. Phys., 35, 1549 (1961).
Lindsay et al.
D
I LOW FIELD T R I N S I T I O N S
1
3000 GAUSS
I
13050
1
3100
1 3150 GAUSS
The Journal of Physical Chemistry, Vol. 86, No. 19, 1982 3791
Electron Spin Resonance of Matrix-Isolated Kt. * .HCI-
TABLE 11: Comparison o f Measured and Calculated Line Positionsa for t h e Perpendicular Transitions in HCl-
TABLE I: Comparison o f Measured and Calculated Line Positionsa for t h e Parallel Transitions in HCI-
37c1
3 5 c 1
mH
measd
mc1
+1/2 +3/2 +1/2 -112 -312 -112 + 3 / 2 t1/2 -112 -312
' Units:
calcd
diff
3014.2 3014.1 + 0 . 1 3061.8 3061.5 + 0 . 3 3108.9 3155.3 3156.3 - 1 . 0 3443.5 3490.6 3490.9 - 0 . 3 3537.6 3538.3 -0.7 3586.0 3585.7 + 0 . 3
measd
calcd
3026.3 3066.4 3105.1 3144.1 3455.4
3026.0 3065.5 3105.0 3144.5 3455.4 3494.9 3534.4 3574.8 3573.9
3
mC1
diff
mH
+0.3 +0.9 +0.1 -0.4 0.0
+1/2 +3/2 +1/2 -112 -312 -112 + 3 / 2 t1/2 -112 -312
+1.0
gauss.
5c1
37c1
measd
calcd
diff
3053.5 3071.9 3091.1 3110.2 3485.4 3503.9 3523.4 3542.5
3053.2 3072.2 3091.2 3110.2 3485.3 3504.3 3523.3 3542.3
measd
calcd
diff
+0.3 3058.0 -0.3 3073.8 -0.1 3089.6 0.0 3104.2 3105.4 -1.2 +0.1 3490.1 -0.4 3505.9 +O.l 3521.7 +0.2 3537.5
a Units: gauss.
nucleus. The parallel and perpendicular quartet features within each set correspond to an additional, but anisotropic, hf interaction with a single chlorine nucleus. Parallel transitions may be assigned to both chlorine isotopes, %C1and 37Cl,whose natural abundances are 76% and 24%, respectively. However, the perpendicular transitions from the W l isotope are largely obscured by overlap with the more abundant W 1 isotope. In Figure 1,full lines represent measured field positions whereas broken lines pertain to those calculated as described below. Other features in the spectrum correspond to unreacted potassium atoms%and a very weak atomic hydrogen ~ p e c t r u m . ~ A 1-h photolysis (450-W xenon arc) increased the atomic hydrogen intensity approximately 40-fold. Largely outside the span of Figure 1 are a series of K3 transitions which occur in the range 3195-3443 G.28 The spectra show no resolved hf splitting from potassium. However, the neighboring alkali cation exerts at least an electrostatic influence on HC1-. Preliminary ESR spectra from Na HC1 are qualitatively similar to Figure 1 but have significantly different chlorine and hydrogen hf constants. These spectra also show no hf splitting from the cation. ESR transitions were analyzed by using standard formulasm ge HI,= -[He - AII(Cl)mcl- A I I ( H ) ~ -H I g,,
+
ge g,
H, = -[He - A,(Cl)mcl - A,(H)mH] -
for the parallel and perpendicular lines, respectively. Here,
Heand g, = 2.0023 are the resonance field and the g value for a free electron, and glland g, are g-tensor elements for an axially symmetric molecule. The axially symmetric hf tensors, A(H) and A(Cl), describe the (isotropic + anisotropic) interaction of the electron spin ( S = 1 2) with the proton spin ( I H = 112) and either a 35Clor C1 nucleus, both having I = 312; mH = f 1 / 2 and mcl = *3/2, f 1 / 2 are nuclear spin projection quantum numbers. The chlorine and proton hf energies are treated to first order and second order, respectively. For I = 112, third-order correctionsm to the hf energy are identically zero. The
.c
(26) C. K.Jen, V. A. Bowers, E. L. Cochran, and S. N. Foner, Phys. Reu., 126,1749 (1962). (27) S. N.Foner, E. L. Cochran, V. A. Bowers, and C. K. Jen, J . Chem. Phys., 32,963 (1980). (281 G. A. ThomDson and D. M. Lindsav. J. Chem. Phys., 74, 959 (igiij. (29) A. Abragam and B. Bleaney, "Electron Paramagnetic bsonance of Transition-MetalIons", Oxford University Press, London, 1970.
TABLE 111: Parallel ( I )and Perpendicular (I)Parameters for HCI- in an Argon Matrix and H Atom Parameters' IAl, G HC1-( 11) HCl-(i) H atom
g
3 5 c 1
37 c 1
2.0017 ( 2 ) 2.0031 ( 2 ) 2.0017 ( 6 )
47.3 ( 4 ) 19.0 ( 4 )
39.4 ( 5 ) 15.gb
'H
427.3 ( 7 ) 430.3 ( 4 ) 504.2 ( 9 )
'
Experimental uncertainties (see text) are given in parentheses. Calculated by using A ( 3 5 C l ) / A 37C1) ( = 1.201 from ref 31. TABLE IV: Isotropic (a) and Dipolar (2') hf Constants' for HC1- in Argonb a
TI
35Cl +28.4 ( 4 ) -9.4 ( 3 ) 'H +429.3 ( 5 ) + 1 . 0 ( 4 )
TI
P ns
+18.9 ( 5 ) +0.017 -2.0 ( 3 ) t 0 . 8 4 7
P 3D
+0.185
a Units: gauss. Estimated uncertainties (see text) are given in parentheses. Spin populations, p 3 s and p J P o n chlorine, p 1s o n hydrogen, are molecular a and T constants divided by the corresponding atomic value^.^*^ 3 3
second-order correction to the chlorine hf coupling constant (51G) is small compared to the approximately 4-G powder line width. Also neglected is the chlorine nuclear quadrupole interaction. Electric field gradients arising from partial occupancy of a chlorine 3p orbital or from the adjacent alkali cation both contribute line shifts of order 0.1 G. Tables I and I1 compare the observed line positions with those calculated by using eq 4 and 5 and the best-fit parameters given in Table 111. The average discrepancy, *0.4 G, is considered satisfactory in view of the large line widths and overlap of the two isotopic species. Estimated uncertainties in the magnetic parameters (given in parentheses) represent one standard deviation uncertainty in the mean of several measurements. The errors in the atomic hydrogen parameters are derived from calibration uncertainties. The ratio of experimental hf constants, AII(35C1)/AIl(37C1) = 1.201 f 0.025, provides a good check on the spectral assignment to HC1-. This value is in excellent agreement with that predicted from the ratio of nuclear g factors, g3,/g,, = 1 . 2 0 ~ ~ ~ Table IV shows the most likely decomposition of the experimental A tensor (Table 111) into isotropic (a) and dipolar (T) componenta, A = a1 + T. Table IV also gives experimental spin populations, p3aand p3p on chlorine and pla on hydrogen. These were derived by scaling the measured hf constants to the corresponding atomic values a # C 1 ) = 1672 G,32T,(=Cl) = 50.8 G,32and ala(H)= 506.8 (30) N. M. Atherton, "Electron Spin Resonance", Wiley, New York, 1973. (31) E. R. Andrew, "NuclearMagnetic Resonance",Cambridge University Press, London, 1955, Appendix 2.
3702
The Journal of Physical Chem/stry, Voi. 86, No. 19, 1982 H
H
CI
K
4s
30
,’
-,-
;
;
4s
----,+:::, 4s 4P
,
c I
#t---
I (01
40
ca
H
,-\
HCI-
( b l KH’
3p
(clCaH
1
F@ue 2. Qualitative molecular orbital dlagrams for HCI-, NaH+, and
CaH.
G.= Since matrix interactionsa and effects arising from orbital contraction or expansion upon molecule formation35 have not been included, uncertainties in the experimental spin populations are difficult to assess. While the ESR spectra do not directly measure the signs of the hf tensor elementa, only when both All(C1)and A,(Cl) are assumed positive is the total spin population, Cp = 1.05, close to unity. The same argument gives a(H) = +429.3 G, with T,(H) = +1.0 G. The proton dipolar hf constant is of the correct magnitude but opposite in sign to that expected from spin density on the adjacent chlorine nucleus. If the bond distance in HCl- is assumed to be equal to that in the neutral diatomic, then a 20% point spin on chlorine -2.5 G. Spin density in a 2p, orbital on gives T,(H) hydrogen will also make a negative contribution to T,(H), but this must be small in order to keep Cp close to unity. One possibility is a small, but negative, spin density in the HCl- overlap region, similar to that found in other small radicals.3sJ7 This additional spin density would also serve to bring Cp closer to unity.
-
Discussion Figure 2 shows mol& orbital (MO) schemes for HC1-, NaH+, and CaH. Atomic energy levels are from refs 38 and 39, but the MO positions are drawn qualitatively. For HC1- (Figure 2a), the unpaired electron occupies an antibonding a* orbital whose composition, as deduced from the spin populations of Table IV, is 13a) = 0.9211s) - 0.4313~~) - 0.1313s) Consistent with the predictions of Figure 2a, this indicates a significant admixture of the chlorine 3pa orbital and the (32)J. A.McMillan and T. Halpem, “HyperfineInteractions: Tables of Isotropic and Anisotropic Parameters for the Atoms Hydrogen to Bismuth”, Argonne National Laboratory Report ANL-7784,1971. (33)P.Kusch and V. W. Hughes, “Handbuch der Physik”,S.Flugge, Ed.,Springer, West Berlin, 1969. (34)For example, Table I11 gives a = 504.2 G for atomic hydrogen in argon. This is approximately0.5% smaller than the g a s - p b hf constant a = 506.8 G from ref 33. (35)The use of the frw-atom hf constant can lead to errors of several percent, particularly in the case of radical ions containing hydrogen: M. C. R. Symons, Nature (London),224,686 (1969). (36) In particular, small organic radicals: H. M. McConnell, J. Chem. Phys., 28, 1188 (1968). (37)For example, the isovalent NaH+ radical: T. A. Claxton and N. A. Smith, Tram. Faraday Soc., 67,1859(1971). Natl. Bur. (38)C. E. Moore, Natl. Stand. Ref. Data Ser. (US., Stand.), 35 (1971). (39)J. C. Slater, Phys. Reu., 98, 1039 (1955).
Lindsay et
al.
1s orbital of hydrogen.@ Since A q and Ag, are small and therefore comparable in magnitude to both matrix shifts and uncertainties in the absolute field positions, a quantitative interpretation of the g-tensor data is not worthwhile. However, spin-orbit coupling between the filled chlorine 3pa orbitals and 3p, of 13a) is predicted41to give a positive Ag,, in qualitative agreement with the measured value, AgL = +0.0008 from Table 111. The approximately 20% 3pa character of HC1‘ contrasts sharply with the bonding in the isovalent radicals NaH+ and KH+ (Figure 2b).42 For potassium, the inner-shell 3p orbital is energetically remote from H(1s) and the dominant interaction is with the valence 4s orbital. Thus, both NaH+ and KH+ are best viewed as a radicals with an approximately 5% isotropic spin population on the alkali as deduced from the ESR spectra.42 As noted earlier, both the group 2A and 2B hydride& are true 6 radicals. Figure 2c illustrates the bonding in CaH. As with KH+, the dominant interaction is between H(1s) and the valence orbitals of the metal. For CaH the Is, 4s, and 4p contributions are estimated6to be 1070,a%, and 30%, respectively, although the 4s/4p ratio is only approximately determined. Thus, in contrast to HC1-, the unpaired electron is only slightly localized on hydrogen. The ESR spectra give little information on the interaction between K+ and HC1-. Electrostatic considerations would suggest a linear arrangement -H-Cl-K+ which is also consistent with (but not determined by) the axial symmetry of the ESR spectra. Neither K HCl nor Na HCl show hf splitting from the cation, and, for a “traditional” contact ion pair,43particularily in the case of Na+HCl-, this would be expected.44 For the structure envisioned above, however, chlorine might “shield” the cation from the 85% spin population on hydrogen and so make the spin density at the alkali nucleus unusually small. Since, in the gas phase, ground-state HC1- dissociate^'^^^^ to H C1-, ita stability in these experiments must result from the effect of a nearby cation and/or the surrounding matrix. The stabilization of a normally repulsive state by an alkali cation has long been invoked to explain the efficient quenching of electronic energy in gas-phase collis i o n ~ . ’ Our ~ ~ ~ESR results show that the cation (Na+ or K+) d w indeed have a noticeable influence on the bonding in HCl-. Since ESR is very sensitive to the presence of atomic hydrogen, the weak atom signal from the K + HC1 reaction indicates little tendency to form H + KC1. This observation is consistent with facile formation of K+ + HC1-, as would be expected for a harpooning mechanism,16and
+
+
+
(40)Since the ionization potentials of H and C1 are very nearly equal, a >20% chlorine 3p character might have been expected. Together with the relatively small AgL, this suggests that the chlorine orbitals should lie lower in energy than is indicated in Figure 2a. This might result from an electrostatic interaction with the nearby K+ or it could reflect the limitations of simple MO theory when applied to negative ions. (41)P.W. Atkins and M. C. R. Symons, “The Structure of Inorganic Radicals”, Elsevier, New York, 1967. (42)M. B. D.Bloom, R. S.Eachus, and M. C. R. Symons, J. Chem. SOC., Chem. Commun., 1495 (1968). (43)M. C. R. Symons, J. Phys. Chem., 71, 172 (1967). (44)For example, matrix-isolated alkali superoxide molecules. While KC02-shows no alkali hf splitting, the sodium hf splitting in Na+02-is 2-4 G. See D.M. Lindsay, D. R. Herachbach, and A. L.Kwiram, Chem. Phys. Lett., 25, 175 (1974). (45)This may not be the case for all hydrogen halide negative ions. Very recent mass-spectrometric measurements have identified HI- and possibly HBr-. See D. Spence, W. A. Chupka, and C. M. Stevens, J. Chem. Phys., 76, 2759 (1982). (46)E.Bauer, E. R. Fisher, and F. R. Gilmore, J. Chem. Phys., 51, 4173 (1969).
J. Phys. Chem. 1882,86,3793-3796
a barrier in the potential energy surface which prevents further reaction of the intermediate complex. Reactive scatteringexperiments on K HC1 show an approximately 100-fold increase in reactivity when HC1 is vibrationally excited.2l Moreover, a comparable increase in the reactant translational energy is much less effective in promoting reaction.22 This is the expected behavior for passage across a 'late barrier'', i.e., reaction on a potential energy surface which has a barrier in the exit channel 0nly.~~9~' Since K + HC1 = H KC1 is endothermic by approximately 2 kcal/mol," this need not imply an activation energy. The
+
+
(47) J. C. Polanyi and W. H. Wong, J. Chem. Phys., 51,1429 (1969).
3793
+
threshold for formation of H KC1 is also about 2 kcal/mol, and this probably corresponds22to the reaction endothermicity. Acknowledgment. Acknowledgment is made to the donors of the Petroleum Research Fund, administered by the American Chemical Society, for partial support of the research. Additional support was provided by the City University of New York PSC-BHE Research Award Program and by the National Science Foundation under grant no. CHE 79-13260. (48) Dissociation energies from K. P. Huber and G . Herzberg, "Constants of Diatomic Molecules", Van Nostrand, New York, 1979.
Estimation of the Liquid-State Transition Dipole Interaction Constant from the 2v2 Mode of Methyl Iodide F. 0. Baglln and L. M. Wllkes' h p a f l m n t of a m t s b y , Unhwshy of Nevada, Reno, Nevada 89557 (ReceIv6d: May 3, 1982)
The shape of the fundamental and overtone of the v2 Raman signal profile of CHJ in the liquid phase was studied as a neat liquid and in a solution with CD31. The dilution had a greater effect on the fwhm (full width at half-maximum)of the overtone signal profile than on the fundamental, however, both narrowed upon dilution. As Oxtoby has noted, if the anharmonicities for a molecule are small, then there is a contribution from the resonant energy transfer term of the perturbation Hamiltonian to the overtone band which can be estimated. This transfer term arises from the transition dipole interactions generated between nearby oscillators of the same energy in the liquid state.
Introduction In recent years a great deal of interest has developed in the signal contours observed from spontaneous Raman spectroscopy and the relationship of those signal shapes to molecular dynamics in gases and liquids.'" Vibrational relaxation is the most prominent mechanism of nonreorientational broadening of the spectral line shape^.^^^ Two types of vibrational relaxation processes have been identified, energy relaxation'fi and dephasingFlO with the latter being the faster process."J2 The work of Gordon' has greatly aided the ability to quantify the relationship between signal contour and molecular motion. This work involves a Fourier inversion on the signal contour which leads, by an approximation, to the autocorrelation function which, in turn, gives a statistical picture in the time domain of the relaxation processes (with the fastest process de(1) Gordon, R. G.J. Chem. Phys. 1964,40,1973; 1965,42,3658; 1966, 43,1302. (2) Bratos, S.; Rios, J.; Guieeany, Y. J. Chem. Phys. 1970, 52, 439. Bratos, S.; Marechal, E. Phys. Rev. A 1971,4, 1078. (3) Bartoli, F. J.; Litovitz, T. A. J. Chem. Phys. 1972, 56,404, 413. (4) Ndie, L. A.; Peticolas, W. L. J. Chem. Phys. 1972,57, 3145. (5) Wright, R. B.; Schwartz, M.; Wang, C. H. J. Chem. Phys. 1973,58, 5125. (6) Wang, C. H. Mol. Phys. 1977,33, 207. (7) Laubereau, k; von der Linde, D.; Kaiser, W. Phys. Rev. Lett. 1972, 28, 1162. (8) Laubereau, A.; Kirschner, L.; Kaiser, W. Opt. Commun. 1973,9, 182. Laubereau, A.; Kehl, G.; Kaiser, W. Zbid. 1974,11, 74. (9) von der Lmde, D.; Laubereau, A.; Kaiser, W. Phys. Reu. Lett. 1971, 26,964. (10) Laubereau, A. Chem. Phys. Lett. 27, 1974,600. (11) Tokuhiro, T.; Rothschild, W. G. J. Chem. Phys. 1975,62, 2150. (12) Rothschild, W. G.; Roaaaco, G. J.; Livingston, R. C. J. Chem. Phys. 1976,62, 1253. 0022-365418212086-3793$01.25/0
termining the signal contour). The vibrational autocorrelation relaxation function can be written @vt = (qui(t) qvii(0)) where qui is the vth normal mode of the molecule i. It is derived by using appropriate approximations of the time dependence of the normal coordinate qu,which describes intramolecular vibrations of the active molecules. These intramolecular vibrations should be effected by the intermolecular perturbation p o t e n t i a l ~ . ~ ,Direct ~ J ~ transfer of vibrational energy to translational and reorientational motions is a relatively slow process in the liquid state, unless there are other fundamentals, overtones, combination bands, or hot bands near the vth normal mode.13 On the other hand, vibrational dephasing is generally quite rapid and is the main contributor to signal shape. The details of the dephasing process depend, to a great extent, on the types of interactions experienced by the active molecules as well as the relative time span of the interactions. The theory of Bratos et a1.2 considers the transition frequency to be slowly varying, giving a frequency distribution function which varies with time, leading to a Gaussian vibrational relaxation function.14 With increasing times, such that the interaction time is much greater than the correlation time, the vibrational relaxation function approximates a simple exponential. The signal contour then becomes Lorentzian and the vibrational dephasing process is governed by collisions in the (13) D6ge, G.; Arndt, R.; Khuen, A. Chem. Phys. 1977,21, 53. (14) Rothschild, W. G. J . Chem. Phys. 1976, 65,455.
0 1982 American Chemical Society
