Environ. Sci. Technol. 2000, 34, 3368-3371
Dechlorination Rate Constants on Iron and the Correlation with Electron Attachment Energies PAUL D. BURROW,* KAYVAN AFLATOONI, AND GORDON A. GALLUP Department of Physics and Astronomy, University of NebraskasLincoln, Lincoln, Nebraska 68588-0111
The correlation between rate constants for dehalogenation of contaminants on iron surfaces and vertical attachment energies (VAEs), a gas phase measure of the ease of reduction, is examined in a series of chlorinated alkanes and alkenes. A recent analysis has shown a good correlation of such rate constants, independent of chemical family, with the computed energies of the lowest unoccupied molecular orbitals (LUMOs) of these molecules. Noting that VAEs are the physical quantities that LUMO energies approximate, we test this result experimentally. We find that the rate constants appear to be satisfactorily correlated with VAE but only within each family. We show that this difference arises because LUMO energies are not relatively consistent in saturated and unsaturated compounds. By shifting and scaling LUMO energies to fit a few measured VAEs in each family, this useful quantum-chemical descriptor can have improved predictive value.
Introduction Dehalogenation of chlorine-bearing compounds by reduction on the surface of Fe particles is a promising means of contaminant remediation (1). Although there are general chemical guidelines for the relative magnitudes of such rates among various families of compounds, models with significant predictive power have been lacking. Recently, Scherer et al. (2) have carried out an extensive study of correlations between measured rate coefficients for disappearance of chlorinated compounds on Feo and a number of parameters characterizing the reductive properties of the molecules, such as their one- and two-electron reduction potentials and computed energies of the lowest unoccupied molecular orbitals (LUMOs). Over a series of 12 chlorinated methanes, ethanes and ethenes, the strongest correlation was found with the calculated LUMOs of the compounds. The addition of model solvation effects on these energies did not appreciably alter the quality of the correlation. Scherer et al. (2) point out that the use of quantum-chemical descriptors computed from commercial software is advantageous in that “large consistent sets of calculations” can be carried out, and these authors utilized their results to make predicted rate constants available for a much broader set of related compounds. In view of the complexity of the processes incompassed in the dechlorination rate constants, experimental validation of the surprisingly good correlation with LUMO energies would certainly seem worthwhile. The correlation, for example, has some rather nonintuitive * Corresponding author phone: (402)472-2419; fax: (402)472-2879; e-mail:
[email protected]. 3368
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implications, namely, that the orbital energy is the key player independent of its symmetry or other molecular properties such as saturation or unsaturation, except inasmuch as these affect the orbital energy. The purpose of the present contribution is to note that the actual physical quantity for which the LUMO energy is a surrogate is measurable in the gas phase for most of the molecules discussed by Scherer et al. (2), and therefore it is possible to make an entirely experimental test of the correlation they observed. This exercise sheds light on systematic effects in the calculation of LUMO energies as well; in particular, it permits a check on the consistency of the calculations in going from one family of molecules to another.
Vertical Attachment Energies The energy at which an electron can be added to a molecule is a measure of its ease of reduction. If the electron attaches to the molecule in the equilibrium geometry of its electronic ground state, then the vertical electron affinity (VEA) is the relevant measure. This quantity is simply the difference in anion and neutral energies evaluated at the equilibrium geometry of the neutral. If the anion is stable with respect to auto-detachment of the electron, that is, the energy of the anion lies below that of the neutral, then the VEA is conventionally taken to be positive and corresponds to the energy required to remove the extra electron. On the other hand, if the anion is unstable and lies above the neutral, as is the case for most of the compounds considered by Scherer et al. (2), this would imply a negative VEA. Such anions can be formed in the gas phase by temporary attachment of a free electron of the proper energy (3), and because the attachment is a very rapid process relative to nuclear motion, the positive electron impact energy at which it occurs is properly called a vertical attachment energy (VAE). Note that VAE ) -VEA. VAEs are readily determined by low-energy electron scattering measurements, in which the existence of a temporary anion state is signaled by sharp structure appearing in the total electron scattering cross section (3). Electron transmission spectroscopy (ETS) (4) is a convenient way to determine VAEs, and the reader is referred elsewhere (5, 6) for the details of the experiments and the applications of this technique to problems of chemical interest. A bibliography of ETS measurements is also available up to 1986 in the appendix of ref 6. Of course, those molecules with positive vertical electron affinities, that is, negative VAEs, are not accessible with this method since the anion states lie below zero electron impact energy. Briefly, in ETS an energy-selected beam of electrons is passed through a cell containing the target molecules at a vapor density sufficient to partially attenuate the beam. Electrons that scatter are rejected, and the unscattered, or transmitted, portion of the incident beam is collected. A sharp peak in the scattering cross section at the energy of formation of a temporary anion state causes a corresponding dip in the transmitted current. In practice the energy of the electrons in the cell is modulated with a small ac voltage and the ac component of the transmitted current is detected with a lockin amplifier (4), thus accentuating the component of the cross section that varies rapidly with energy. In a molecular orbital picture, the anion state arises by addition of an electron into the normally empty LUMO of the neutral molecule. If the energy of this orbital is computed at the equilibrium geometry of the neutral ground state, then it can serve as an approximation to the vertical difference in 10.1021/es9911519 CCC: $19.00
2000 American Chemical Society Published on Web 07/06/2000
TABLE 1. Rate Constants, LUMO Energies, and VAEs
a
compound
abbrev
kh (L m-2 h-1)
ELUMO (eV)e
VAE (eV)
trichloromethane 1,1,1,2-tetrachloroethane 1,1,2,2-tetrachloroethane 1,1,1-trichloroethane tetrachloroethene trichloroethene cis-1,2-dichloroethene trans-1,2-dichloroethene 1,1-dichloroethene vinyl chloride 1,1-dichloroethane 1,1,1-trichloroethane tetrachloromethane hexachloroethane
TCM 1112TeCA 1122TeCA 111TCA PCE TCE c12DCE t12DCE 11DCE VC 11DCA 111TCA PCM HCA
(9.2 ( 7.3) × 10-4 1.4 × 10-2 1.3 × 10-2 1.1 × 10-2 (2.1 ( 2.7) × 10-3 (3.9 ( 3.6) × 10-4 (4.1 ( 1.7) × 10-5 (1.2 ( 0.4) × 10-4 (6.4 ( 5.5) × 10-5 (5.0 ( 1.5) × 10-5 1.5 × 10-3 2.2 × 10-3 (1.2 ( 1.5) × 10-1 (3.1 ( 3.3) × 10-2
-2.277 -2.390 -1.982 -2.160 -1.689 -1.435 -1.200 -1.200 -1.140 -0.761 -1.267 -2.160 -3.054 -2.555
0.35a 0.63b 0.51b 0.64b 0.3c 0.59c 1.11c 0.80c 0.76c 1.28c 1.36b 0.64b -0.34d(est.) 0.054d(est.)
From reference 8.
b
From reference 9. c From reference 7.
d
See text. e From reference 2.
energy between the anion and the neutral. Such energies are not correct absolutely, but they have considerable use in a relative sense and we return to this later. It is worth stressing again that since attachment takes place rapidly, it is the vertical value of the electron affinity that is of importance and not the adiabatic affinity, which is the energy difference between the anion and neutral, each evaluated at its respective equilibrium geometry. Of the twelve compounds listed in the training set given by Scherer et al. (2), their Table 1, ETS data are available for ten, the six chloro-substituted ethenes (7), trichloromethane (8), 1,1,1-trichloroethane, 1,1,1,2-tetrachloroethane, and 1,1,2,2-tetrachloroethane (9). The tetrachloromethane anion in the geometry of the ground state of the neutral is known to be stable (8), and to our knowledge hexachloroethane has not been examined by ETS. Scherer et al. (2) also provide new measurements for the rate constants of 1,1-dichloroethane and 1,1,1-trichloroethane. ETS measurements on the former compound are also available (9). The lowest lying anion states of the chloroalkanes correspond to temporary occupation of the C-Cl σ* orbitals, and in the chloroethenes to the π* orbitals of the CdC double bond. Excited anion states associated with the normally empty C-Cl σ* orbitals are found at higher electron energies in the latter compounds (7).
Rate Constants and VAEs We turn now to the surface area-normalized rate constants reported by Johnson et al. (10) used in the study of Scherer et al. (2). In Figure 1 we present a semilog plot of the averaged rate constants as a function of the measured VAEs. Table 1 summarizes the compounds, the LUMO energies calculated by Scherer et al. and the measured VAEs. The absolute accuracy of the latter is generally given as ( 0.05 eV. The relative values are likely to be better. The open circles represent the chloroalkenes, the filled circles the alkanes, and the compound labels are given in Table 1. We include also the error limits specified in Scherer et al., if given. In several cases the lower error bar does not appear because the magnitude of the quoted error was larger than the average rate constant. Note that there are two rate constants for 1,1,1trichloroethane (111TCA); the lower one is a new result presented by Scherer et al. We include as well the data for 1,1-dichloroethane. The latter two points were not used in the “training set” of Scherer et al. The filled triangles indicate results for tetrachloromethane (PCM) and hexachloroethane (HCA) for which the VAEs are negative or very close to zero. We provide here estimated VAEs which are discussed later. Several features are worth noting in making a comparison with the rate constant variation with LUMO energies given
FIGURE 1. Averaged rate constants for dehalogenation on Feo as a function of vertical attachment energies. Open circles indicate the chloroalkenes and filled circles the chloroalkanes. Rates and error bars are taken from ref 2. The lower rate constant for 111TCA was new data provided in ref 2. VAEs for PCM and HCM, shown as triangles, were estimated by scaling LUMO energies to measured VAEs in other chloroalkanes. Compound abbreviations are given in Table 1. by Scherer et al. (2), in which both the alkenes and alkanes fell on the same trend line. In contrast, Figure 1 shows that when plotted versus VAE all the alkanes lie well above the trend in the alkenes, with the exception of trichloromethane. We note in this regard that the trichloromethane rate also lies well below the correlation line given by Scherer et al., as it does in the present data with respect to the rest of the alkanes. Unfortunately, there are not error limits given for some of these compounds. The two values for 1,1,1trichloroethane indicate the possibility of considerable scatter. The chloroethenes, as a family, display a good correlation with both LUMO energy and VAE, to the extent allowed by the large error limits on the rate constants. The quantumchemical approximation used by Scherer et al. (2) produced equal LUMO energies for cis- and trans-dichloroethene. ETS shows rather different VAEs for these two compounds, and Figure 1 shows that the trend in rate constants is consistent with these measured values, that is, the VAE for the ciscompound is larger and the rate constant is smaller. The results in Figure 1 suggest to us that the alkanes as a family have a different rate constant dependence lying above that of the alkenes and thus at variance with the common dependence on LUMO energy presented by Scherer et al. VOL. 34, NO. 16, 2000 / ENVIRONMENTAL SCIENCE & TECHNOLOGY
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similar the compounds are to each other, the better this agreement is, and the more reliable the predictive power in other related molecules. A recent example illustrating this approach for ETS measurements in the DNA bases has been published elsewhere (16). Similar studies for σ* orbitals have not been as extensively carried out (13, 17), although shifts in LUMO energies to match experiment have been previously employed in the chloromethanes (8). The shifting and scaling parameters for σ* LUMO energies are clearly not the same as those for the π* orbitals, as evidenced in Figure 2. We note here that the discrepancies between LUMO energies and measured VAEs are understood theoretically, but their ab initio calculation is difficult and is the subject of current research. Nevertheless, theory provides a plausible argument that these quantities are correlated. Chen and Gallup (15) give a discussion of this and provide other useful references.
Discussion FIGURE 2. LUMO energies computed in ref 2 as a function of measured vertical attachment energies. The chloroalkenes are shown with open circles and the chloroalkanes by filled circles and squares. The linear regression applies only to the chloroalkenes. (2). We return to discuss below results from other gas-phase measurements which may provide insight into the differences in the reductive mechanism.
Comparison of VAEs and LUMO Energies In Figure 2 we plot the LUMO energies calculated by Scherer et al. (2) against the measured VAEs derived from electron scattering measurements. Again, the open circles correspond to the six chloroalkenes and the filled circles to the chloroalkanes. Two other alkanes having VAEs (9) below 1.4 eV are also presented in the figure and are shown by filled squares. The LUMO energies for dichloromethane (DCM) and 1,1,2-trichloroethane (112TCA) were taken from the Supporting Information calculated by Scherer et al. (2). A linear regression to the alkene data shows a good correlation between the computed LUMO energies and the VAEs. The alkanes, however, fall entirely below the alkene line. In other data not shown, we have plotted the calculated LUMO energies of 15 chloroalkanes available as Supporting Information for the Scherer et al. paper against our measured VAEs, using data in several monochloroalkanes (11) and a much larger but unpublished set of results in dichloro- and trichloroalkanes (9, 12). The trend in these compounds also supports the separation between the two families of molecules observed in Figure 2. Relative to the alkenes, the LUMO energies of the alkanes are more stable by about 0.5 eV. This is the reason that the alkanes, having generally higher rate constants than the alkenes, appear to lie on the same trend line presented by Scherer et al. We want to stress that the heart of this problem does not lie in the LUMO calculations of Scherer et al. (2). Aside from a constant shift of -5.557 eV and a slight departure from unit slope, a plot of their LUMO energies for the saturated compounds against those calculated in our group using ab initio methods with the same basis set (6-31G*) shows good agreement. The problem is that LUMO energies computed for substantially different families of molecules, such as those for the σ* and π* orbitals of the chloro-alkanes and alkenes, respectively, are consistent within but not between groups. In unsaturated compounds, a number of comparisons (1315) have been carried out between LUMO energies and π* temporary anion states measured by ETS, the first two references being concerned primarily with finding an optimum basis set for such calculations. For a given basis it is clear that the LUMO energies can be shifted and scaled to give closer agreement with the experimental results. The more 3370
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One substantial drawback of electron scattering methods is that VAEs < 0 are not accessible. Nevertheless, as described above by shifting and scaling LUMO energies to give agreement with measured VAEs within each family, predictions of VAEs in other related compounds can be undertaken more reliably. We have employed this approach to estimate the VAEs of tetrachloromethane (PCM), for which VAE < 0, and hexachloroethane (HCA) in which VAE ∼ 0 eV. By fitting our LUMO energies to measured VAEs of 15 alkanes ranging from mono- to tetrachloroalkanes (9), we predict VAEs of -0.34 eV for PCM and 0.054 eV for HCA. These data and the associated rate constants given by Scherer et al. are shown as the filled triangles in Figure 1, thus including the higher rate constant region associated with the lower lying anion states. These two points continue the trend observed in the other alkanes. Except for trichloromethane, which remains problematical, our overall results reinforce the view that the alkanes and alkenes are characterized by different rate constant dependences. Some insight into the differences in the reductive behavior of the chloro-alkanes and alkenes is available from other gas-phase electron scattering experiments. In the dissociative attachment (DA) process, e + AB f AB-* f A + B-, a fraction of the temporary anions that are formed by electron attachment survive long enough to dissociate, producing in our case primarily Cl-. In the ethenes, this process takes place by electron attachment first into the empty π* orbital followed by molecular distortions that couple the antibonding C-Cl σ* orbital to the CdC π* orbital and allow the eventual release of Cl- (7, 18-20). This interpretation was stimulated by noting that the yield of Cl- is peaked at the energy of the π* anion state rather than near the higher lying σ* state. Furthermore, the high yields are consistent with the longer lifetimes of π* anion states relative to σ* anions, a difference that arises from the larger angular momentum barrier through which the autodetaching electron must tunnel (3). In contrast, attachment in the chloroalkanes occurs directly into the σ* orbital producing a relatively short-lived anion state. We mention these points only to suggest that if one-electron reduction of these compounds on a surface is the rate-limiting step, there are several reasons to believe that the rates might differ in these families even if the lowest anion states have identical energies. We would also like to call attention to a striking parallel between the exponential rate constant dependence on VAE shown for the alkanes in Figure 1 and the behavior of the DA cross section for production of Cl- in the gas phase. In a series of monochloro- and dichloroalkanes, the peak DA cross sections have also been shown to decline exponentially over several orders of magnitude with increasing VAE (11, 12). The latter behavior was attributed to effects related to the change in anion lifetime with VAE. While it is unclear how
this process will be affected with solvated anions, the similarity of the dependence on VAE lends credibility to remediation proceeding through electron transfer followed by DA. In summary, the use of measured VAEs will lead to a closer examination of the linkage between molecular structure and the surface reactivity of the chlorinated compounds. In particular, we find different rate constant dependences for the chloro-alkanes and alkenes. By scaling LUMO energies to VAEs within each family of molecules, quantum-chemical methods generating these descriptors will be more accurate. In conclusion, we note that the rates used by Scherer et al. (2) are averages over measurements in the literature that were carried out under many different conditions, i.e., different iron samples, surface treatments and methodologies. If such correlations are to be adequately tested, the importance of generating a standardized set of rate constants with smaller error brackets for representative members of several chemical families cannot be overemphasized.
Acknowledgments This work was supported by NSF grant CHE-9710076. We are grateful to Profs. Steve Comfort and Pat Shea of the School of Natural Resource Sciences at UN-L for bringing ref 2 to our attention and for their comments on the manuscript.
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Received for review October 7, 1999. Revised manuscript received March 22, 2000. Accepted May 25, 2000. ES9911519
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