Model for IR Study of (>I, in C6H6and cci,
Acknowledgment. Partial financial support from the National Science Foundation (Research Grant No. GP 17818) is gratefully acknowledged. We are grateful to Dr. Derek Steele (Royal Holloway College, University of London) for many helpful discussions, to the Science Research Council of the United Kingdom for the support (as Senior Visiting Fellows) that made them possible, and to the Chemistry Dlepartment of Royal Holloway College for the support and hospitality provided to us while we were there (1978). References and Notes (1) R. S. Mulliken, J . Am. Chem. Soc., 74, 811 (1952). (2) W. 8. Person, R. E. Erickson, and R. E. Buckles, J. Am. Chem. Soc., 82, 29 (1960).
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(3) H. B. Friedrich and W. B. Person, J. Chem. Phys., 44, 2161 (1966). (4) M. W. Hanna, J . Am. Chem. Soc., 90, 285 (1968). (5) M. W. Hanna and D. E. Williams, J. Am. Chsm. Soc., 90,5358 (1968). (6)W. A. Lathan and K.Morokuma, J. Am. Chem. Soc.. 97.3615 (1975). (7) T. C. Jao, N. Beebe, W. 8 . Person, and R. J. Sabin, Chem.'Phys. Lett.. 26. 474 119741. -,- , (8) T. C. Jao, Ph.D. Dissertation, University of Florida, 1974. (9) A. S.Wexler, Appl. Spectrosc. Rev., 1, 29 (1967); see also, for example, D.A. Ramsay, J. Am. Chem. Soc., 74, 72 (1952). (10) L. J. Aridrews and R. M. Keefer, J. Am. Chem. Soc., 73,462 (1951). (11) W. B. Person, J . Am. Chem. Soc., 87, 167 (1965). (12) L. E. Orgel and R. S.Muliiken, J. Am. Chem. Soc., 79, 4839 (1957). (13) R. S. Mulliken and W. B. Person, "Molecular Complexes", Wiley, New York, 1969. (14) W. B. Person in "The Spectroscopy and Structure of Molecular Complexes", J. Yarwood, Ed., Plenum Press, London, 1973, Chapter 1. (15) T. C.Jao and W. B. Person, J. Phys. Chem., following article in this issue. I
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Spectroscopic Studies of Chlorine in Benzene and Carbon Tetrachloride Solutions. 2. A Model Calculation of Electrostatic Effects on the CI-CI Stretching Vibration T.-C:. Jaot Department of Chemistry and Center for Energy and Environment Research, University of Puerto Rico, Mayaguez, Puerto Rico 00708
and Willis B. Person*+ Department of Chemistry, University of Florida, Gainesville, Norida 326 I 1 (Received September 26, 1978) Publication costs asslsted by the University of Puerto Rico, Mayaguez Campus, and the NIH
A niodel for electrostatic collision-induced infrared absorption by the C1-C1 stretching vibration of Clz in benzene and in CC14 solutions is presented. This model is based upon the treatment by Fahrenfort and by van Krankendonk of collision-induced absorption in the gas phase, modified for solutions, with an approximate averaging over all orientations for the colliding molecules. Parameters for evaluating the collision-induced intensities are all evaluated from other kinds of experimental data, except for the derivative of the quadrupole moment of C12with respect to the C1-C1 stretching normal coordinate, which is taken from a quantum mechanical calculation. The predicted integrated molar absorption coefficient A for C12in CCll is 0.55 km mol-', compared to an experimental value of 0.78 km mol-'; and for Clz in benzene the calculated value is A = 1.4 km mol-', compared to 3.3 km mol-' from experiment. These results are discussed and some variations on the model calculation are presented. We believe that most of the intensity increase for the C1-C1 stretching vibration of Cl2 that occurs from CC4to benzene solution is due to the different electrostatic collision-inducedintensity, but that some of the increase may also be due to one-to-one complex formation between benzene and Clz.
Introduction In the preceding paper' we have presented some results from a new study of the infrared absorption spectrum of the C1-C1 stretching vibration for Clz in benzene, in CC14, and in solutions of benzene in CC4. The results are summarized there in Figures 11 and 12. The significant result from that study is that the C1-C1 stretching vibration, which is forbidden in the infrared spectrum for the isolated molecule, appears with measurable intensity for Clz dissolved both in pure benzene and in pure CC14 (the apparent integrated molar absorption coefficient, based on the total C12 concentration in each solution, is 3.3 km mol-l for Clz in benzene and 0.78 km mol-1 for C12 in CC14, varying more or less linearly with benzene concentration in the rnixed solvents). While it is true that these intensities are rather low (the intensity for the infrared-active C-C1 stretching fundamental in CC14, for Senior Visiting Fellow and Visting Professor, Department of Chemistry, Royal Holloway College, University of London, 1978. 0022-3654/79/2083-1185$01 .OO/O
example, is 390 km they differ significantly from zero, and the intensity must be due to the interaction between the Clz molecule and the solvent. This infrared activity for C12 in benzene has been explained previously in various ways. The activity for this vibration for C12dissolved in CC14has not previously been reported, and it requires some modification of some of the previous explanations for the infrared activity. One of the previous explanations has been that the benzene molecules form a weak one-to-one complex with Clz molecule^.^ The lower symmetry of the C12molecule in the complex allows the C1-C1 stretch to become active and quite strong; the weakness of the apparent molar absorption coefficient is because only a small fraction of the total C12 is complexed. Carbon tetrachloride is not expected to form a complex with C12, so the appearance of the C1-C1 stretching vibration in CC14 solution must be attributed to some other cause. Hanna and c0-workers~9~ have suggested that the infrared activity of the C1-C1 stretching vibration for C12in 0 1979 American Chemical
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The Journal of Physical Chemistry, Vol. 83, No. 9, 1979
benzene is due entirely to electrostatic interactions between Clz and benzene. Here the idea is that activity is induced in Clz when it collides with the benzene molecule due to a transitory quadrupole-induced dipole generated in the Clz molecule by the collision with benzene. Physically and qualitatively this explanation has considerable appeal. However, the model used p r e v i ~ u s l ywas ~ ~ rather ~ limited (considering only the axial orientation of the Cl,-benzene pair) and estimated some of the electrostatic parameters required for the calculation. The general problem of the infrared activity induced for a molecular vibration by collisions has been considered previously, for example, by Fahrenfort6 and van Kran e n d ~ n k . ~These - ~ models assumed binary collisions in the gas phase, but we have chosen to adopt their model for the collision-induced activity of the C1-C1 stretching vibration in solution. We are still assuming only binary collisions are important, but we have made other modifications that adapt the theory to provide a useful model for collisioninduced (by electrostatic interaction) infrared absorption in solution.
Derivation Following the treatments by FahrenforP and van K r a n e n d ~ n k , I -we ~ define
T . 4 . Jao and W. B. Person X
P
molecule 2
molecule 1
Figure 1. Coordinate system used in defining the orientation of symmetric molecules.
TABLE I: Parameters Used for the Calculations of the Pair-Correlation Functions of Chlorine-Benzene and Chlorine-Carbon Tetrachloride Pairs
c1,
Darameter 0 ,A Elk, K
Q(X CL(X a
loz6esu c m 2 )
4.40a 25Ta 6.14a
C,H, 5. 2 I a 440a -1E1.6~
10%esu)
From ref 12.
CCl, 4.93b 226b 26.1b
From ref 18.
From ref 4 ,
termolecular potential. For the Cl2-C6H, interaction (which is a quadrupole-quadrupole interaction) U, was given by Buckingham" and reproduced as follows:
A = ( l / l O O n c ~ , l ) ~ l(nI o / I )du
(1/4n€o)(8n3Nlzv/(300hc)I J*12'~*12
d71' (1)
Here A is the integrated molar absorption coefficient in units of km mol-l, nclz is the molar concentration of chlorine in the solution, 1 is the pathlength in cm, In (Io/I) is the absorbance, u the wavenumber in cm-l, Nlz is the number of collision pairs per mole of C12 per cubic centimeter, \k12 and \k12' are the wave functions associated with the ground and excited states of the collision pair, and y is the induced dipole moment operator for the collision pair so that .f\kl~p\klzd7 is the induced transition moment from the collision pair. The factor of lo2 is introduced to convert units to A in km mol-l, and the universal constants are evaluated in cgs units. Estimation of N12.The first step in using eq 1to predict the intensity of the electrostatic collision-induced absorption by C1, is to evaluate N12/,the number of collision pairs per mole of Clz per cm3 that occur for C12 molecules that are oriented with respect to the solvent molecule in one particular orientation. This step is needed because the value of the transition moment will be found to depend on the relative orientation of the two molecules, so that the total induced absorption will be found (in principle) from eq 1 by averaging the induced absorption over all orientations. We have obtained values of N12'for several different orientations of C12with respest to the solvent by using 2.40 because of the (1/R8) factor so that we have little interest in collisions at larger radii. Calculated values of N1ifor some different orientations of C12-C6H6are given in Table IV and for C12-CC14 in Table V. Evaluation of the Transition Moment. In order to evaluate the transition moment integral IJ\klip\k12 d71, we must first write the wave function \k12. To a very good approximation the wave function for collision pairs of molecules whose only interaction is electrostatic may be written as the product of the vibrational wave functions (\kl and \kz) for the individual molecules: *12 = ~ 1 ( ~ 1 1 ) ~ 2 ( ~ 2 1 , ~ 2 2 , ~ 2 3 , ~ ~ ~ ~ ~ Z 1(11) ~ ~ ~ Here tll is the normal coordinate describing the C1-C1 stretching mode, Ezl is the first normal coordinate for the benzene molecule, etc.; and \k12(R12,w1,wZ) is a vibrational wave function associated with the changes in the distances between, and relative orientations of, the two molecules. We are considering the induced absorption for the C1-C1 stretching vibration, so the only change in eq 11required to write \k12/ is to replace \kl(tll)by the first excited C12 vibrational wave function \kl'(Ell). We have assumed here that the collisions are not so strong that they perturb the vibrations of the constituent molecules very much. Substituting the product functions of eq 11for \k12 and *12/
PIZ
=
s * 1 2 / ~ * d1 r2 = s*
