J. Phys. Chem. 1984,88, 4492-4494
4492
Bond Energles of the Cesium Halides Determined by Collision- Induced Dissociation E. K. Parks* and S. Wexler Chemistry Division, Argonne National Laboratory, Argonne, Nlinois 60439 (Received: April 1 , 1983)
The bond energies of the four cesium halides are determined from the threshold for collision-induceddissociation to ion pairs by rare gas atoms. The bond energies (to neutral atoms) are 5.32 A 0.08, 4.58 A 0.08, 4.00 A 0.08, and 3.47 0.15 eV for CsF, CsCl, CsBr, and CsI, respectively. Except for CsI the ion thresholds are obtained from the sharply peaked cross section vs. energy curves for CsM' + X-formation (M = rare gas atom; X- = halide ion) and for CsI the ion threshold is obtained from the onset of the channel M + Cs' + I-. Comparison is made with bond energies determined by other techniques as well as that derived from the T-Rittner model potential.
*
Introduction
The highly ionic character of the alkali halides makes them fundamentally interesting molecules to study. This interest is in large part because their internuclear potentials can be modeled successfully with interactions which are largely classical in nature.' The development of model potentials, however, hinges on the availability of accurate spectroscopic and thermochemical data for these molecules, from which one can judge the accuracy of the theoretical models. For virtually all the alkali halides spectroscopic data of great accuracy have been obtained from microwave and radio-frequency spectroscopy, yielding precise values for internuclear separations, vibrational frequencies, and other potential constants, as well as the electric dipole moments.* However, the most important parameter in the model potentials, and the least well-known, is the bond dissociation energy Do(or simply the bond energy). In some cases ostensibly accurate determinations of Dofor the same molecule, by different techniques, differ by as much as 5%. While errors of this magnitude may not seem large, model potentials of the alkali halides yield bond energies that are in general accurate to better than 5%. In this paper we present experimentally determined bond energies of the four cesium halides, with error limits of less than 2% for CsF, CsC1, and CsBr and -3% for CsI. The results are in excellent agreement with the recent photofragmentation results of Su and rile^^-^ on CsCl, CsBr, and CsI. The results for CsF represent, we believe, the most accurate determination of its bond energy to date. The Method
The basis of the method is the dissociation of the cesium halides by collision with aerodynamically accelerated rare gas atoms leading to a pair of oppositely charged ions. The specific reactions of interest are M
+ CsX
-
-
+ Cs+ + XCsM+ + XM
Cs+
+ XM-
(la) (1b) (IC)
where M is Ar, Kr, or Xe, and CsX is one of the four cesium halides. Reaction l a is referred to as three-body dissociation and reactions l b and IC are referred to as molecular ion formation. The experiments involve the crossed molecular beam method, so that the dissociation of the molecule results from a single encounter of the rare gas projectile M with the cesium halide target CsX.
The energy required for the dissociation is obtained by accelerating the M species in a seeded jet, a method pioneered by Professor John F e m 6 A beam of accelerated M atoms is then crossed with a thermal beam of CsX, and the ionic products are determined by time-of-flight mass spectrometry. Absolute cross sections for ion pair formation are determined as a function of the relative kinetic energy. In Figure 1 we give an example of reactions l a and l b for the case of Xe colliding with CsBr. The curve labeled Cs+ corresponds to reaction l a and that labeled CsXe+ corresponds to reaction lb. Reaction IC was observed only for the case of CsI. In principle, the energy corresponding to the dissociation threshold of reaction l a (E,) is the ionic dissociation energy of CsX (for CsX in the ground state). Experimentally, however, this only occurs if the mass of the projectile mMis heavier than or at least equal to the halogen atom mass mx.'-9 If m M > mx, the energy transferred into the target molecule can reach 100% even for ground-state CsX molecules, and thus the observed dissociation threshold is equal to the ionic dissociation energy. If mM < mx, either internal energy in the target molecule or a relative collision energy in excess of Eo is necessary to induce dissociation. The dissociation energy to neutrals Do can be obtained from E,, the ionization potential of Cs (Zcs), and the electron affinity of X ( A x ) :
Do = Eo - I,,
+ Ax
for m M
> mx
(2)
Both ICs and A x are known to better than 0.01 eV.l0 In order to obtain Eo from the experimental results the behavior of the dissociation cross section in the threshold region must be known. For reaction l a the cross section has the form" (3)
where E,,, is the initial M-CsX relative kinetic energy, E,, is the total energy, Le., Erelplus the initial CsX internal energy E,nt,and A is a scaling parameter. Values of Eo and n can be obtained by a trial and error procedure in which eq 3 with selected values of Eo and n is averaged over the measured velocity distribution of M and the thermal distribution of internal states of CsX. The averaging procedures are discussed in ref I . As a consequence of the velocity averaging and the relatively slow rise in the cross (6) N. Abuaf, J. B. Anderson, R. P. Andres, J. B. Fenn, and D. G. H. Marsden, Science, 155, 991 (1967). (7) S. H. Sheen, G. Dimoplon, E. K. Parks, and S. Wexler, J. Chem. Phys., 68, 4950 (1978).
( I ) B. T. Gowda and S. W. Benson, J . Phys. Chem., 86,847 (1982), and references contained therein. (2) Thomas R. Dyke, "Alkali Halide Vapors", P. Davidovits and D. L. McFadden, . _. Ed., Academic Press, New York. 1979., n -126. -(3) T-M. R. Su and S. J. Riley, J . Chem.'Phys.,71, 3194 (1979). (4) T-M. R. Su and S. J. Riley, J. Chem. Phys., 72, 1614 (1980). (5) T-M. R. Su and S. J. Riley, J . Chem. Phys., 72, 6632 (1980).
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( 8 ) E. K. Parks, M. Inoue, and S . Wexler, J . Chem. Phys., 76, 1357 (1982). (9) E. K. Parks, L. G. Pobo, and S. Wexler, J . Chem. Phys., in press. (10) H. Hotop and W. C. Lineberger, J. Phys. Chem. Ref.Data, 4, 539 (1975). (11) E. K. Parks, A. Wagner, and S . Wexler, J . Chem. Phys., 58, 5502 (1973).
0 1984 American Chemical Society
The Journal of Physical Chemistry, Vol. 88, No. 20, 1984 4493
Bond Energies of the Cesium Halides TABLE I: Bond Energies (eV) of the Cesium Halides present experiment photofragment s ectroscopy thermochemical photoionizatione calculation from T-Rittner potential
B
a
Reference 3.
Reference 4 .
E,
Reference 5.
ENERGY
CsF
CsCl
CsBr
CSI
5.32 i 0.08
4.58 f 0.08 4.53 i 0.09c 4.6 1 4.58 i 0.05 4.421
4.00 t 0.08 3.99 * 0.04b 4.19 4.17 i 0.04 3.936
3.47 + 0.15 3.46 i 0.02a 3.57 3.57 * 0.04 3.340
5.19 5.27 i 0.06 5.243
Reference 16. e Reference 1 7 .
(ev)
Figure 1. Absolute cross sections for formation of Cs+ and CsXe' in collisions of Xe atoms with CsBr molecules as functions of the relative kinetic energy. The dashed curves are the assumed cross sections corresponding to CsBr initially in the ground state. The solid curves result from averaging with respect to the internal energy distribution of CsBr and the relative kinetic energy distribution of Xe on CsBr. Eoindicates the experimentally determined threshold for three-body dissociation. section as given by eq 3, E, can be determined in this manner only to within -0.15 eV. The bond energy of CsI was obtained in this way.8 For the other three cesium halides an alternate procedure can be used to determine a more precise value of Eo. This method makes use of reaction lb. In contrast to the rather slow rise of three-body dissociation from threshold, reaction l b has an extremely sharp onset at threshold. In fact, the state-to-state cross section, Le., the cross section corresponding to a particular internal state of the reactant CsX with internal energy Ei,,(CsX), and a particular internal state of the product CsM+ with internal energy Eint(CsM+), begins with a finite value at the threshold. The state-to-state threshold energy E t h is given by At energies above the step the cross section may rise or fall depending on the propensity for CsM' formation as the relative energy increases. Experiments have shown9 that if mM> mX the cross section falls after the step while if mM N mx it is relatively flat for energies up to at least several electronvolts above threshold. (For mM < mx,molecular ion formation is generally not observed.) Experimentally, it is not the state-to-state cross section that is measured but the total cross section for CsM+ formation. The dashed line associated with the CsXe+ curve in Figure 1 gives the unaveraged total cross section for CsM+ formation corresponding to Ei,,(CsX) = 0. The construction of this curve is discussed in ref 7. The rapidly rising portion of the curve will be referred to as the step, although strictly speaking only the state-to-state cross section has a threshold step. The base of the step occurs at the threshold energy for the ground state of CsXe+, Le., Eth= Eo D,(CsM+), while the top of the step occurs at an energy corresponding to formation of CsXe+ at its dissociation limit, i.e., Eth = Eo. The shape of the curve in the rapidly rising step region depends on the number of internal states of CsM+ that are energetically allowed at a given Ere,and their relative contribution to the cross section, Le., their relative step heights. The shape of the curve above the step has been adjusted to give the best fit to the experimental data subsequent to the averaging procedures.
It is, however, the occurrence of the sharp edge at E t h = Eo that permits a more precise determination of Eo, irrespective of the details of the cross section near the base of the step or in the region above the step. The experimental value of Eo was obtained in each case by adjusting Eo to give the best fit of the energy averaged cross section to the experimental data in the sharply peaked region of the experimental curve. The determination of E, by the above procedure is subject to a number of approximations, each of which will be discussed below. Since the relative step heights for the internal states of the CsM' product molecule are unknown, the statistical model is employed, which assumes that each rovibrational state has the same step height. In addition, it is assumed that only levels up to the dissociation limit are bound, Le., metastable rotationally bound molecular ions are not included. The statistical assumption itself should not significantly affect the determination of Eo. Since the vibrational spacing decreases significantly near the CsM+ dissociation limit, the rovibrational level density is correspondingly higher there than near the base of the step in Figure 1. As a result, the threshold step is almost vertical at energies just below E,,, A very nonstatistical distribution of the vibrational levels of CsM' would be necessary to alter significantly the vertical rise of the cross section just below Eo. Owing to the relatively weak bonding in CsM' (0.12 eV for CsXe+, 0.10 eV for CsKr', and 0.063 eV for CsAr+),12we believe that such an effect is unlikely. The existence of metastable rotationally bound CsM' molecules is, in principle, a more severe problem, because these introduce contributions to the step at energies above Eo. In practice, however, the CsM' potential supports rotationally bound levels only for a small energy E* above the dissociation limit. For the CsXe+, CsKr', and CsAr' potentials given by Rajan and Gislason,12E* is 0.052, 0.043, and 0.027 eV, respectively. In addition, the level density which is largest near the dissociation limit rapidly decreases to zero as E E*, thus decreasing the importance of the metastable levels. Tunneling through the rotational barrier will tend to further reduce their contribution. It is therefore unlikely that the existence of rotationally bound CsM' influences the determination of the true ionic dissociation limit Eo by more than a few hundredths of an electronvolt. The final approximation that is made in the threshold analysis relates to the initial internal energy E,,, of the CsX molecule. In the thermal averaging E,,, is treated statistically, i.e., its effect is simply to reduce the relative kinetic energy threshold (E,,,,under the experimental conditions is -0.20 eV). No other explicit dependence of the cross section on Ehtis assumed. However, when mM Im x (except for Ar colliding with CsCl), and for CsI in particular, this assumption is not valid. In these cases there often exists an CsX internal energy threshold below which CsM+ does not form at all at any relative energy. This generally leads to a strong dependence of the cross section for CsM' formation on the CsX temperature, reflecting the strong effect of internal energy. In all cases for which the above step behavior was used to determine E,, we believe that the statistical assumption is valid. For Xe colliding with CsF, the dependence of the CsXe+ cross section on the CsF temperature was experimentally measured and found to be completely flat, Le., there was no change in the cross section with CsF t e m p e r a t ~ r e .This ~ demonstrates the validity of the statistical assumption in this case. Owing to the light mass
-
(12) M. S . Rajan and E. A. Gislason, J . Chern. Phys., 78, 2428 (1983).
4494
J . Phys. Chem. 1984,88,4494-4497
of both F and C1 compared to Xe, we believe the same result would be obtained for CsCl as well. Planar three-dimensional trajectory calculations9 of Xe colliding with CsF, CsC1, and CsBr demonstrate the formation of CsXe’ at Erel= Eo with zero initial internal energy in the cesium halide. Collisions of Xe with CsBr, in particular, showed a high propensity for CsXe+ formation over a wide range of collision parameters, which correlates well with the particularly large cross section for CsXe+ formation obtained experimentally for this system. This suggests that the statistical assumption is most likely valid in this case as well. Trajectory calculation on CsI yielded no CsXe+ formation under the same initial conditions in agreement with the experimental results.’ Results
The bond dissociation energies of the cesium halides derived from the above analysis are given in Table I, along with values obtained from several other techniques. The parameters in eq 2 required to convert Eo into Do are Zc8= 3.893 eV and the electron affinities of the four halogens which are 3.399, 3.615, 3.364, and 3.061 eV for F, C1, Br, and I atoms, respectively.1° For CsF three values of Eo were obtained from Ar, Kr, and Xe collisions; they are 5.83, 5.79, and 5.81 eV, re~pectively.~ The average was used to determine Do in Table I. For CsCl the three values of Eo were 4.87, 4.85, and 4.85 eV for Ar, Kr, and Xe, respe~tively.~For CsBr the step behavior at threshold was only observed for Xe collisions, and thus only a single value of Eoequal to 4.53 eV was ~ b t a i n e d . As ~ mentioned earlier, the bond energy of CsI was obtained from reaction la, since the step behavior of the CsXe’ cross section in this case was strongly distorted due to threshold effects involving the CsI internal energy! An analysis of reaction l a for the other three halides would give Eo values which are entirely consistent with those derived from reaction 2a, but with larger error limits. The error limits given in Table I reflect a combination of curve-fitting errors coupled with an -0.5% error limit in the measurement of the velocity of the projectile. The assigned error
limit of 0.08 eV is an absolute error limit. The relative errors between the different cesium halides are likely to be somewhat smaller. The present experiments are in excellent agreement with the photofragmentation measurements of Su and rile^.^-^ The photofragmentation method is analogous to the collisional dissociation method, with a photon providing the energy input rather than the rare gas atom collision. The bond energy is obtained in the former not by measuring the threshold for dissociation (to neutrals in this case) but by measuring the relative translational energy of the dissociated Cs and X atoms coupled with the photon energy. Also included in Table I is a calculation of the bond energies from the T-Rittner model of Brummer and Karp1~s.l~(The T-Rittner model yields Eo,from which one calculates Do via eq 2 . ) The input to the model includes the CsX equilibrium internuclear separations and vibrational frequencies given by Huber and Herzberg,14the ion polarizabilities given by Coker,15and the halogen electron affinities given above. The coefficient of the R6 term in the T-Rittner model was obtained with the London approximation (see ref 13). The average difference between the measured and calculated values for Eo is 2.2%. Acknowledgment. This work was performed under the auspices of the Office of Basic Energy Sciences, Division of Chemical Science, US. Department of Energy, under Contract W-31109-Eng-38. Registry No. CsF, 13400-13-0; CsC1, 7647-17-8; CsBr, 7787-69-1; CSI, 7789-17-5. (13) P. Brummer and M. Karplus, J. Chem. Phys., 58, 3903 (1973). (14) K. P. Huber and G. Herzberg, “Molecular Spectra and Molecular Structure”, Van Nostrand-Reinhold, New York, 1978. (15) H. Coker, J . Phys. Chem., 80, 2078 (1976). (16) L. Brewer and E. Brackett, Chem. Reu., 61,425 (1961). (17) J. Berkowitz, J . Chem. Phys., 50, 3503 (1969); Adu. High Temp. Chem., 3, 158 (1971).
Dynamics of the Chemlionization Reaction of Antimony Pentafluoride J. A. Russell, J. F. Hershberger, J. J. McAndrew, R. J. Cross,* and M. Saunders* Department of Chemistry, Yale University, New Haven, Connecticut 0651I (Received: July 1 I , 1983)
-
-
Using crossed molecular beams we have measured the product angular and energy distributions for SbFs + C6H5COC1 SbF5CI- + C6H5COtand for SbzFlo+ C6H5CHzC1 SbF6- + C7H7++ SbF,Cl. In both cases the product distributions are symmetric about the center of mass which indicates that the reaction proceeds by way of a long-lived collision complex. However, in the first reaction, this symmetry appears to be broken at the highest energy studied so that the reaction becomes direct at higher energies. The first reaction has a threshold at roughly 2.9 eV.
Introduction
In the past 20 years much has been learned about how a chemically reactive collision occurs in detail,’ how bonds are made and broken, and how energy is transferred from one part of the system to another during the reaction. Most of these studies have necesarily focused on the simple systems of three or four atoms or atomlike groups. However, most chemical reactions are more complicated than this. The potential-energy surfaces have a higher dimensionality and may exhibit complicated features not seen in simpler systems. Therefore, we must examine more complicated systems to see how these basic ideas need to be extended. Fur(1) D. R. Herschbach, Faraday Discuss. Chem. Soc., 55,233 (1973). R. B. Bernstein, “Chemical Dynamics via Molecular Beam and Laser Techniques”, Oxford University Press, Oxford, 1982.
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thermore, the organic and inorganic chemists will not seriously think in terms of chemical dynamics until chemical reactions of interest to them are successfully studied by modern techniques in the field of dynamics. With these goals in mind, we have been using crossed molecular beams to study organic reactions.24 We have recently investigated the halide abstraction reactions of antimony pentafluoride and its polymers3r4 SbF5
+ RX
-
SbF5X- + R+
(1)
~~~
(2) K. T. Alben, A. Auerbach, W. M. Ollison, J. Weiner, and R. J. Cross, 1.Am. Chem. SOC.,100, 3274 (1978). (3) A. Auerbach, R. J. Cross, and M. Saunders, J . Am. Chem. Soc., 100, 4908 (1978). (4) L. Lee, J. A. Russell, R. T. M. Su, R. J. Cross, and M. Saunders, J. Am. Chem. Soc., 103, 5031 (1981).
0 1984 American Chemical Society
