Self-Consistent Heats of Formation for the Ethyl ... - ACS Publications

Apr 30, 2010 - With the technique of threshold photoelectron photoion coincidence (TPEPICO) spectrometry, the 0 K appearance energy of an ion can be ...
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J. Phys. Chem. A 2010, 114, 6117–6123

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Self-Consistent Heats of Formation for the Ethyl Cation, Ethyl Bromide, and Ethyl Iodide from Threshold Photoelectron Photoion Coincidence Spectroscopy Sampada Borkar and Ba´lint Szta´ray* Department of Chemistry, UniVersity of the Pacific, Stockton, California 95211 ReceiVed: March 10, 2010; ReVised Manuscript ReceiVed: April 8, 2010

The dissociative photoionization onsets of Br and I loss reactions were measured for C2H5Br and C2H5I, respectively, by threshold photoelectron photoion coincidence (TPEPICO) spectroscopy to establish the heats of formation of these two basic ethyl halides. The appearance energy of ethyl cation from ethyl bromide was found to be 1074.2 ( 0.8 kJ mol-1, and that from ethyl iodide was found to be 1016.4 ( 0.8 kJ mol-1. The heats of formation of ethyl bromide and ethyl iodide are interconnected through the ethyl cation. In establishing the thermochemistry of the ethyl halides, the ethyl cation heat of formation was concluded to be 915.5 ( 1.3 kJ mol-1 on the basis of a recent value for ethyl radical heat of formation and the well-established ionization energy and on the basis of ab initio isodesmic calculations using recent PEPICO data. Using this anchor, we obtained the following heats of formation: ∆fH°0K[EtBr] ) -40.8 ( 1.5 kJ mol-1 and ∆fH°0K[EtI] ) 6.3 ( 1.5 kJ mol-1. These results are more consistent with the higher EtBr heats of formation values in the literature, contrary to recent findings. For ethyl iodide, the latest calorimetric value does not agree within the claimed accuracy. Introduction Quantum chemical calculations are now capable of achieving (1 kJ mol-1 accuracy in determining the thermochemistry of small molecules.1-5 Another recent development in modern thermochemistry is the emergence of active thermochemical tables.6,7 These tables are an invaluable source of the latest thermochemical values determined either by experiment or by theory. The biggest advantage of these active tables is their ability of automatically updating all values in a self-consistent manner when newer values connecting two or more species are entered. These two major factors have generated a clear pressure on experimentalists to establish more accurate thermochemical data that lead to more reliable heats of formation for a wide variety of neutrals and ions. Furthermore, it is important for high-quality experimental results to keep pace with the new quantum chemical methods to test their reliability on larger and larger systems. A large number of disparities are observed in the heats of formation of the smaller alkyl radicals, especially those derived from studies of different kinds of chemical equilibria.8-11 The large uncertainties in these heats of formation created by these disparities increase the uncertainties in calculating primary, secondary, and tertiary C-H bond energies. Quantum chemical calculations may be used for calculating the thermochemistry of some of the alkyl halides.12-16 However, each of the halogens present a certain kind of challenge to theoreticians; bromides and especially iodides are difficult to calculate, because of the large number of electrons in these atoms, the lack of high-end basis sets and the fact that relativistic effects become very important for these high-z atoms.17,18 On the other hand, thermochemical data on bromides and iodides can even be easier to measure experimentally; for example, the dissociative photoionization of alkyl bromides and iodides are simpler than that of chlorides.19 * Author to whom correspondence should be addressed. E-mail: bsztaray@ pacific.edu.

The value of the C2H5Br heat of formation is not well established, with 298 K literature values ranging from -67.8 to -61.9 kJ mol-1.20,21 Current thermochemical compilations list a value by Wagman et al.22 of -64.52 kJ mol-1 (most likely a typo based on the work by Lane et al.23) and a higher value -61.9 ( 1.7 kJ mol-1 by Pedley et al.21 A heat of formation of -63.6 ( 2.1 kJ mol-1 used by Kudchadker et al.24 in a critical evaluation of the thermodynamic properties of bromo- and iodoethanes comes from Cox and Pilcher25 and falls between the extremes of the numbers above. On the basis of arguments that consider the heat of formation of the ethyl radical and cation, it has been concluded recently that the lower (Wagman) value is more likely. The state of the 298 K heat of formation of C2H5I seems more reassuring, with historical data ranging between -10.0 and -7.7 kJ mol-1;26,27 while the two more recent literature values seem to agree with each other within experimental error: -7.2 ( 0.8 kJ mol-1 by Carson et al.,28 and -8.4 ( 1.7 kJ mol-1 by Kudchadker et al.24 referring to Cox and Pilcher,25 while this value in fact originates from the same group as the -7.2 kJ mol-1. The fact that these two numbers agree within the claimed uncertainty and the rather enviable error bar of this latter value suggests that the thermochemistry of ethyl iodide is well established. The importance of the heats of formation of these alkyl halides comes from the fact that one of the most fundamental alkyl cation’s heat of formation is based on these values. For the longest time, the ethyl cation’s heat of formation was based on a TPEPICO measurement of ethyl iodide,29 while a PFIPEPICO study (see later) of ethyl bromide suggests a slightly different value,30 but within the uncertainty of this number. This heat of formation value is especially crucial, as the gas-phase proton affinity scale is based on the “well established” heat of formation of the ethyl cation and of the ethene molecule.31 The thermochemistry of the ethyl cation will be discussed later on the basis of the new experimental results.

10.1021/jp102162f  2010 American Chemical Society Published on Web 04/30/2010

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With the technique of threshold photoelectron photoion coincidence (TPEPICO) spectrometry, the 0 K appearance energy of an ion can be measured to a kJ mol-1 accuracy or better.32 In this technique, the dissociation of energy selected photoions is measured with time-of-flight mass spectrometry, and from the disappearance of the precursor ion signal very accurate 0 K appearance energy can be determined for the following fragmentation reaction:33

AB + hν f AB•+ + e- f A+ + B• + eRecent advances in the TPEPICO and, recently the iPEPICO (imaging PEPICO) techniques allow sub-kJ mol-1 accuracy for small molecules.33-36 In the past decade, TPEPICO spectroscopy has been used to investigate the dissociation of various ions to derive accurate thermochemical and kinetic data on a number of organic and organometallic species.32,37-39 Studies that are most relevant from this work’s point of view include dihalides, H2CXY, where X, Y ) Cl, Br, and I to establish their heats of formation using H2CCl2 as an anchor;40 vinyl bromide and 1,1,2-tribromoethane,41 vinyl chloride and vinyl iodide,42 chloroform, and 1,1,2,2tetrachloroethane.43 Recently, we have determined the heats of formation of mixed chloro-bromo haloform compounds using both CHCl3, and CHBr3 as anchors.39 As mentioned above, there are earlier coincidence measurements published on the appearance energy of the ethyl cation from both ethyl bromide30,44 and ethyl iodide.29 For ethyl bromide, an early TPEPICO study by Baer et al. published a value of 11.21 ( 0.05 eV,44 while a more recent PFI-PEPICO study by Baer and Ng reports a value of 11.130 ( 0.005 eV.30 While this latter technique is most elegant, and the energy resolution of the experiment is superior to the 1 Å resolution of our monochromator, the signal-to-noise ratio of the photoion signal is rather poor. Furthermore, due to the considerable efforts associated with the measurements, the data points are more than 10 meV apart, close to the disappearance of the precursor ion signal. Therefore, the reported uncertainty of the 0 K appearance energy may be overly optimistic. For ethyl iodide, an early PEPICO experiment by Baer lists an E0 value of 10.49 ( 0.04 eV.29 In deriving this number, the assumed 200 K thermal energy distribution is used to convert the crossover energy of 10.43 eV to the 0 K onset. The effect of the hot-electron contamination was not taken into account and the signal-tonoise is quite unfortunate at the dissociation threshold. In this study, from the EtI heat of formation by Rosenstock et al.27 an ethyl cation 0 K heat of formation of 913 ( 4 kJ mol-1 was determined, in considerable disagreement with previous data, but in good agreement with the value determined from the EtBr PFI-PEPICO study two decades later. Our approach in the present study was to use both ethyl bromide and ethyl iodide together to determine the heat of formation of the two neutral precursor molecules and of the ethyl cation as the common anchor, since these two compounds are interconnected through the C2H5+ cation as shown below:

Borkar and Szta´ray Therefore, combining the two TPEPICO 0 K appearance energies directly yield the difference of the heat of formation of ethyl bromide and ethyl iodide. Experimental Details The samples of C2H5I and C2H5Br were purchased from Sigma Aldrich and were used without further purification. The details of the TPEPICO spectrometer have been described previously.32-34 Briefly, the vapor of the sample was introduced into the ionization chamber through a temperature controlled inlet system consisting of a large copper block in which cooled methanol was circulating, and the sample vapor traveled approximately 10 cm, thermalizing with the walls. The ionization region is enclosed in copper plates attached to the cooled copper block to minimize the amount of background room-temperature molecules. The molecules were ionized with vacuum ultraviolet (VUV) light generated from a hydrogen discharge lamp and dispersed by a 1 m normal incidence monochromator. The entrance and exit slits of the monochromator were set to 100 µm, which resulted in a resolution of 1 Å (about 8 meV at 10 eV photon energy). The photon energy scale was calibrated using the hydrogen Lyman-R resonance line. The electrons and ions were extracted in opposite directions in a constant electric field of 20 V cm-1. Threshold electrons were velocity focused by extraction with gridless apertures in a 13 cm long drift tube set to 77 V through a 1.4 mm aperture onto a center Channeltron detector.34 Hot electrons are focused into concentric rings with diameters determined by their initial velocity perpendicular to the extraction axis. A fraction of these hot electrons are collected by a second Channeltron located next to the central Channeltron. The effect of the hot electrons (i.e., energetic electrons with a zero perpendicular velocity component) can now be eliminated by subtracting a fraction of the pure hot-electron signal from the central signal as described by Szta´ray and Baer.33 Ions were directed into a linear time-offlight (LinTOF) mass spectrometer with a Wiley-McLaren space-focusing geometry. In the linear TOF, ions were first accelerated by a 20 Vcm-1 field in the 5 cm first acceleration region, then they were rapidly accelerated to 260 eV in a 5 mm long second acceleration region. After exiting the acceleration regions, they finally drifted across a 34 cm field-free region and were detected with tandem microchannel plates (MCPs). The two electron and the ion signals served as the start and stop signals respectively for two time-to-pulse-height-converters, the output of which is fed into multichannel analyzer cards generating the two TOF spectra that correspond to the center electron detector and the hot-electron detector, respectively. Since the ethyl bromide and ethyl iodide ions dissociate rapidly on the time scale of ion extraction, their TOF peaks are symmetric and sharp, and the only information we obtain from these data is the relative abundance of the parent and fragment ions. Because only the peak areas are of interest, to correct for hot electron contamination, the precursor and fragment ion counts are simply multiplied by a constant factor (0.153 in this case) and subtracted from the center coincidence counts. (In the case of metastable fragment ion peaks, the actual TOF distributions would have to be subtracted.) The subtraction factor is obtained by taking the ratio of the precursor ion intensities in the center and hot-electron TOF spectra at photon energies well in excess of the 0 K dissociation limit, where no parent ion should be present. This factor remains constant for all wavelengths and, in general, remains constant from one molecule to the next if the collection efficiencies of the detectors do not change. Since the dissociation of the ethyl bromide and especially the ethyl iodide ions results in a very large mass-loss compared

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to the mass of the precursor ions, the collection efficiency of the ion detector has to be taken into account. Although in the present setup, the Chevron stack of MCPs is floated at 4 kV or higher, there can be significant differences between the detection efficiency of the ethyl cation (m/z 29) and of the ethyl bromide molecular ion (m/z 108) or the ethyl iodide molecular ion (m/z 156). Interestingly, the coincidence experiment is ideally suited to compensate for this effect, as absolute collection efficiencies can be determined for both the photoelectrons and the photoions. Briefly, the coincidence frequency can be calculated as

fc ) ηe · ηi · f where f is the frequency of the ionization events and ηe and ηi are the electron and ion collection efficiencies, respectively. The electron and the ion detection frequencies are simply

fe ) ηe · f and fi ) ηi · f

Figure 1. Breakdown diagram of EtBr+. Points are experimentally measured ion abundances, and lines are the best-fit modeling of the data. The downward arrow indicates the 0 K dissociation onset.

Therefore, when all ions and electrons come from the threshold ionization events, the absolute electron and ion collection efficiencies can be calculated as

ηe )

fc fc and ηi ) fi fe

The absolute electron collection efficiency, however, can only be calculated very close to the adiabatic IE because, at higher photon energies, most of the ion signal comes from nonthreshold ionization events. The ion collection efficiency, on the other hand, can still be calculated at any photon energies, provided that the coincidence counts and the total electron counts both correspond to (subtracted) threshold electrons. By determining the ion collection efficiency at photon energies resulting only in precursor ions vs only in fragment ions, we can obtain the correction factor for the ion detection efficiencies. In the case of EtBr+, the correction factor was found to be 1.55, while for EtI+ the factor was 1.57. Note, however, that this latter measurement was done at a later time with an improved setup of the ion detector, floated at a higher ion impact voltage. Another correction concerning the absolute coincidence counts has to be taken into account, and that is of the paralysis effect due to high count rates in a single-start single-stop coincidence setup. We have recently published a detailed analysis of the TPHC-based single-start single-stop vs triggered TDC-based single-start multistop vs trigger-less multistart multistop coincidence data acquisition modes.45 At very high count rates, the peak shapes, detected coincidence count rates, and signal-to-noise can be distorted in the first two data acquisition modes, while the trigger-less setup provides better signal-to-noise and no artifacts. Currently, this measurement mode is utilized at the new iPEPICO instrument on the VUV beamline of the Swiss Light Source.36 In our TPHCbased experiments, the signal paralysis due to the exponential false coincidence background has to be compensated for in the case of very high count rates (with respect to typical flight times). This, of course, is most important with the reflectron TOF setup, where the flight times are much longer, but all of our TOF spectra were corrected for false coincidences as described earlier.45 Quantum Chemical Calculations For the TPEPICO data analysis of fast dissociations, it is necessary to use the vibrational frequencies and the rotational

Figure 2. Breakdown diagram of EtI+. Points are experimentally measured ion abundances, and lines are the best-fit modeling of the data. The downward arrow indicates the 0 K dissociation onset.

constants of the neutral precursors. For this purpose, density functional calculations were performed on ethyl bromide and ethyl iodide using the hybrid B3LYP functional46 with the 6-311G(d,p) basis sets.47-49 Harmonic vibrational frequencies were calculated on fully optimized geometries at the above level, the minima were confirmed on the basis of the absence of imaginary frequencies, and the calculated harmonic frequencies were used without scaling in the density of states calculations. To establish the theoretical thermochemistry of the ethyl cation, the high level infinite basis set extrapolation methods CBS-APNO50 and W1U1 were used for two quasi-isodesmic reactions, as detailed in the thermochemistry section (see later). Briefly, CBS-APNO and W1U 0 K energies were calculated for methane, ethane, propane neutrals, and the methyl, ethyl, and isopropyl cations. All calculations were done using the Gaussian 03 Revision E.01 quantum chemical code.51 Results and Discussion Experimental Data and Data Analysis. TPEPICO TOF spectra were collected in the photon energy ranges 10.8-11.4 and 10.25-10.7 eV for ethyl bromide and ethyl iodide, respectively. Sample temperatures were -60, -30, 0, and +20 °C for EtBr and -50, -30, and -12 °C for EtI. The breakdown curves, which show the relative ion abundances as a function of the photon energy, are shown in Figures 1 and 2 for EtBr and EtI, respectively. In the case of both experiments, only a

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Figure 3. Summary of the 0 K thermochemistry of EtBr and EtI. Vertical solid lines indicate literature heats of formation; dotted lines are the heats of formation from the present study with shaded areas showing the uncertainty. The large arrow shows the difference of the EtBr and EtI heats of formation that comes directly from the two TPEPICO experiments.

single dissociation channel was observed within the photon energy range, that is, the dissociation of the halogen atom from the molecular ion. This is in contrast to ethyl chloride where the first dissociation channel is a HCl-loss, and the Cl-loss happens in competition with this at slightly higher photon energies.19 To obtain the 0 K dissociation energy, the experimental data have to be modeled in terms of the thermal energy distribution of the neutral precursors molecules.32 For large molecules (larger than a few atoms), it is a good approximation that the neutral internal energy distribution is transposed onto the ion manifold, and those species that have more internal energy than the dissociation energy will dissociate. The fractional parent ion abundance, plotted as a function of the photon energy (the breakdown curve), therefore, corresponds to the cumulative distribution function (cdf) of the ion internal energy with the dissociation energy as the integration limit, and, thus, to the cdf of the neutral internal energy at the experimental temperature:

BD(hν) )

∫0E -IE Pi(E,hν) dE = ∫0E -hν Pn(E) dE 0

0

where Pi is the ion’s internal energy distribution, as a function of the photon energy. Pn, the neutral molecule’s internal energy distribution function can be calculated by the simple Boltzmann formula: Pn(E) ) Fn(E) · e-E/kT. Fn(E) is the neutral molecule’s density of states function calculated using the molecule’s vibrational frequencies and rotational constants determined by density functional theory. It is easy to see that at hν ) E0 - IE the above integral becomes 0; therefore, the disappearance of the parent ion signal directly gives the 0 K dissociation energy. This quantity, however, can be obtained to a better precision by modeling the whole of the breakdown curve and varying the assumed E0 for the best fit of the calculated and measured breakdown curves. Since E0 is independent of the sample temperature (the width of the energy distribution), but the shape of breakdown curve varies with the temperature, redundant sets of data can be measured that all have to result in the same E0. In our case, there are four quasi-independent experimental data sets for ethyl bromide and three for ethyl iodide that could each be used to extract the ionic bond-energy; this redundancy allows us to cut down on the estimated uncertainty of the derived onsets. In Figure 1, one can see that below 10.9 eV, the only ion is the ethyl bromide molecular ion, and as it dissociates at higher photon energies, the fragment ion (C2H5+) starts to appear. At approximately 11.15 eV, the precursor ion signal has completely vanished, indicating the E0. The molecular ion’s breakdown curves at various temperatures all vanish at this point, even though the curves themselves are broader at higher temperatures. By fitting the modeled breakdown curves to the experimental data, we found the best 0 K appearance energy E0(EtBrfEt+) to be 11.133 ( 0.008 eV.

In the modeling calculations, we have experimented with both the sample temperature, by relaxing it to the best fit to the experimental data or fixing it to the nominal temperatures, and the description of the internal rotation or torsional vibration of the methyl group. In the case of the ethyl bromide experiment, the relaxed model temperatures were consistently 10-15 °C higher than the nominal temperatures. The average of the bond energies derived at either nominal or relaxed temperatures agreed within 4 meV, while the standard deviation of the E0 values corresponding to different temperatures was 4.5 meV. We have shown earlier that, in some cases the large amplitude internal rotations of the methyl group have to be treated separately.37 Whether this internal mode is a vibration, a hindered rotation, or a free rotation depends on the barrier, which differs for the neutral molecule, ion, or the TS. For methyl amines, Boedi et al.37 found that for the correct modeling of the internal energy distributions, the internal rotations of the methyl group needed to be treated as hindered rotors in monomethylamine, but in the larger trimethylamine they had to be treated as vibrations. In the present study, we have carried out the modeling calculations by assuming that every mode in the molecule can be treated as a vibration, and also assuming that the methyl group is a hindered rotor. The extracted appearance energies only changed well within the experimental accuracy (the largest difference was below 4 meV) whether the methyl torsional mode was treated as an internal rotor or an oscillator. Taking the uncertainty of the photon energy, the good agreement between the temperature dependent data sets, and the consistency of the numbers between the two models, an error of (8 meV is likely a conservative estimate. For ethyl iodide, as shown in Figure 2, the overall shape of the breakdown curves is very similar to that of EtBr, with little or no fragment ion signal below 10.35 eV, and no precursor ion signal above 10.55 eV. The temperature-dependent breakdown curves are also consistent with wider curves at higher temperatures. To determine the 0 K appearance energy of the Et+, the same modeling was performed as detailed for EtBr, resulting in an E0(EtIfEt+) of 10.534 ( 0.008 eV. Thermochemistry. As mentioned in the Introduction, combining the 0 K appearance energy of the ethyl cation from EtBr and from EtI directly results in the heat-of-formation difference of the two neutral molecules. Using the values of ∆fH°0K[Br] ) 117.92 ( 0.06 kJ mol-1 and ∆fH°0K[I] ) 107.16 ( 0.04 kJ mol-1 from the NIST-JANAF Thermochemical Tables,52 we obtain a ∆[∆fH°0K] value of 47.0 ( 1.1 kJ mol-1. The recommended value of the ethyl bromide heat of formation of -42.63 kJ mol-1 from the PFI-PEPICO paper30 yields a heat of formation for ethyl iodide of ∆fH°0K[EtI] ) 4.4 kJ mol-1 or ∆fH°298K[EtI] ) -11.6 kJ mol-1. This value is 4.4 kJ mol-1 lower than the latest calorimetry value,28 and 3.2 kJ mol-1 lower than an older literature number,24,25 clearly outside of their confidence inter-

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TABLE 1: Summary of the Thermochemistry the Ethyl Halides, the Ethyl Radical, and Cationa molecule

∆fH°298K/kJ mol-1

∆fH°0K/kJ mol-1

AE0K(C2H5+)/kJ mol-1

C2H5Br

-62.9 ( 1.5 -63.6 ( 2.1c,d -64.0e -61.9 ( 1.7g -64.52h

-40.8 ( 1.5 -41.8 ( 2.1c,d -41.9f -39.8 ( 1.7f -42.63h

1074.2 ( 0.8

C 2H 5I

-9.8 ( 1.5b -8.4 ( 1.7c,d -7.2 ( 0.8j

6.3 ( 1.5b 7.5 ( 1.7c,d 8.9 ( 0.8k

C2H5•

120.7 ( 1m

C2H5+

b

900.5 + 2.0i

b

IE/eV

b

1073.8 ( 0.5i 1016.4 ( 0.8b 1012.1 ( 3.9l

132.3 ( 1m

8.117 ( 0.008n 8.119o

915.5 ( 1.3b 913.2 + 2.0i 915.4 + 2.1p 912.9 + 4.2l 916.6 + 2q

a In all thermochemical derivations, the stationary electron convention was used. b This work. c Kudchadker et al.24 d Cox et al.25 e Lane et al.23 f Converted from the corresponding 298 K value using H°298K - H°0K ) 13.44 kJ mol-1. g Pedley et al.21 h Wagman et al.22 i Baer et al.30 j Carson et al.28 k Converted from the 298 K value of Carson et al. using H°298K - H°0K ) 13.72 kJ mol-1. l Baer.29 m Bodi et al.37 n Ruscic et al.55 o Lau et al.57 p Rosenstock et al.62 q Traeger et al.54

vals. If we chose the Pedley et al.21 value for the ethyl bromide heat of formation of ∆fH°0K[EtBr] ) -39.8 ( 1.7 kJ mol-1, the EtI 0 K heat of formation is 7.2 ( 2.0 kJ mol-1, which agrees nicely with both literature values. This seems to suggest that for ethyl bromide it is not the lower Wagman value that is correct but rather the higher Pedley number. However, it is not unreasonable to assume that the heat of formation of the ethyl cation is a more suitable anchor than either of the alkyl halides. The lower EtBr heat of formation, combined with our E0 yields a ∆fH°0K[Et+] ) 913.6 kJ mol-1, while the higher value results in ∆fH°0K[Et+] ) 916.5 kJ mol-1. The relationship between the measured ∆[∆fH°0K] value between EtBr and EtI in relation to the literature heats of formation is depicted in Figure 3. The heat of formation of the ethyl cation is one of the most fundamental values in thermochemistry: (a) in itself it is important for a number of combustion processes; (b) the gasphase proton affinity ladder is based on this anchor.31 The “accepted” value for the 0 K heat of formation is 912.8 ( 2.0 kJ mol-1 based on the adiabatic IE of the ethyl radical of 913.2 ( 2.0 kJ mol-1 based on the ethyl bromide PFI-PEPICO.30 The former value is based on the heat of formation of the ethyl radical by Brouard et al.53 while the latter uses the Wagman value for ethyl bromide. Traeger et al.54 lists a ∆fH°0K[Et+] of 916.6 ( 2.0 kJ mol-1, which is nicely in line with our ethyl cation appearance energy from ethyl iodide, or the Pedley heat of formation of the ethyl bromide. To determine a reliable heat of formation of the ethyl cation, we chose two approaches based on (a) the ethyl radical and its ionization energy and (b) isodesmic reactions involving alkyl ions of well-known heats of formation. Recently, we published a study on primary amines, in which an isodesmic reaction network was calculated at the W1U and CBS-APNO levels of theory to minimize the errors in the heats of formation of the title compounds, and the radicals that result in their TPEPICO ionic dissociations.37 In this work, a new value of ∆fH°298K[Et•] ) 120.7 ( 1.0 kJ mol-1 or ∆fH°0K[Et•] ) 132.3 ( 1.0 kJ mol-1 was obtained. This is slightly higher than the experimental value on which the Ruscic et al.55 ethyl cation heat of formation is based but it is nicely in line with a more recent theoretical value of 131.5 ( 1.0 kJ mol-1 by Marshall.56 For the adiabatic ionization energy of the ethyl radical, the experimental value of Ruscic et al.55 and a recent high-level

calculation by Ng et al.57 agree very well, the two values are 8.117 ( 0.008 and 8.119 eV, respectively. Using the experimental IE and the Bodi et al.37 value of the ethyl radical, we get ∆fH°0K[Et+] ) 915.5 ( 1.3 kJ mol-1. Another approach for obtaining a reliable heat of formation of the ethyl cation can be based on other alkyl cations, for which the heat of formation is well established. Reaction heats were calculated for the following “isodesmic” reactions at the CBSAPNO and the W1U levels of theory: ∆rH°0K reaction +

+

CH3 + C2H6 f CH4 + C2H5 i-C3H7+ + C2H6 f C3H8 + C2H5+

CBS-APNO

W1U

-183.2 75.7

-181.2 76.9

Note that the bridged structure of the ethyl cation is different from the structure of the other two alkyl cations; therefore, the reaction is only quasi-isodesmic, and it is assumed that the high level of theory does a good job on describing this bridging hydrogen. In deriving the heat of formation of the ethyl cation, we use the ∆rH°0K[CH3+] ) 1099.37 ( 0.1 kJ mol-1 from a recent methyl iodide paper by Bodi et al.58 that is based on the very accurate heat of formation of methane6 of ∆fH°0K[CH4] ) -66.58 ( 0.06 kJ mol-1 and the CH3+ + H onset from methane (14.323 ( 0.001 eV) reported by Weitzel et al.59 For the iPr+, a very recent accurate number is available from the iPEPICO work of Stevens et al.;60 they determined a ∆fH°0K[iPr+] ) 824.6 ( 0.5 kJ mol-1 based on ∆fH°0K[C3H8] ) -82.4 ( 0.5 kJ mol-1.61 Combining these accurate literature values with our CBS-APNO calculations, the 0 K heat of formation of the ethyl cation is 914.8 kJ mol-1 based on CH3+ and 914.7 kJ mol-1 based on i-Pr+. At the W1U levels, the two values are 916.8 and 916.0 kJ mol-1, respectively. These numbers agree well with each other, and the average value of 915.6 kJ mol-1 agrees remarkably well with the ethyl cation’s heat of formation based on the ethyl radical. Therefore, we decided to determine the heats of formation of ethyl bromide and ethyl iodide based on the ethyl cation’s heat of formation of ∆fH°0K[Et+] ) 915.5 ( 1.3 kJ mol-1. Using our TPEPICO appearance energies, the fol-

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lowing values were obtained: ∆fH°0K[EtBr] ) -40.8 ( 1.5 kJ mol-1 and ∆fH°0K[EtI] ) 6.3 ( 1.5 kJ mol-1. Within error bars, these numbers agree with the Pedley value for ethyl bromide and suggest that the newer value on ethyl iodide is off by approximately 2 kJ mol-1. The most important thermochemical values of the ethyl halides, the ethyl cation, and radical are listed in Table 1. Conclusions Recent advances in threshold photoelectron photoion coincidence spectrometry allow the determination of appearance energies to an accuracy of 1 kJ mol-1 or less. Since the interconnected heats of formation of ethyl bromide, ethyl iodide, and the ethyl cation are still under debate, the dissociative photoionization onsets of Br and I loss reactions were measured for C2H5Br and C2H5I by temperature-dependent TPEPICO to establish the heats of formation of these three species. The appearance energy of ethyl cation from ethyl bromide was found to be 1074.2 ( 0.8 kJ mol-1 and that from ethyl iodide was found to be 1016.4 ( 0.8 kJ mol-1. The heats of formation of ethyl bromide and ethyl iodide are interconnected through the ethyl cation, the thermochemistry of which is very important on its own and through its role in the proton affinity ladder. In establishing the thermochemistry of the ethyl halides, the ethyl cation heat of formation was concluded to be 915.5 ( 1.3 kJ mol-1 based on a recent value for the ethyl radical heat of formation and the well-established ionization energy and on ab initio isodesmic calculations using recent PEPICO data. These calculations, although the reaction heats differ by as much as kJ mol-1, agree well with each other and with the value coming from the ethyl radical. Using this species as the anchor, the following heats of formations were obtained: ∆fH°0K[EtBr] ) -40.8 ( 1.5 kJ mol-1 and ∆fH°0K[EtI] ) 6.3 ( 1.5 kJ mol-1. These results are more consistent with the higher EtBr heats of formation values in the literature, contrary to recent findings. For ethyl iodide, the latest calorimetric value does not agree within the claimed confidence interval, and needs to be revised. Acknowledgment. The measurements were carried out on the TPEPICO apparatus built in the laboratory of Professor Tomas Baer at the University of North Carolina at Chapel Hill, supported by the grants from the U.S. National Science Foundation, the U.S. Department of Energy, and the Hungarian Science Fund (OTKA #71644). This experiment was donated to the University of the Pacific in 2009, for which we are eternally grateful. B.Sz. gratefully acknowledges the support of the ACS Petroleum Research Fund. References and Notes (1) Martin, J. M. L.; de Oliveira, G. Towards standard methods for benchmark quality ab initio thermochemistry - W1 and W2 theory. J. Chem. Phys. 1999, 111 (5), 1843–1856. (2) Tajti, A.; Szalay, P. G.; Csaszar, A. G.; Kallay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vazquez, J.; Stanton, J. F. HEAT: High accuracy extrapolated ab initio thermochemistry. J. Chem. Phys. 2004, 121 (23), 11599–11613. (3) Bomble, Y. J.; Vazquez, J.; Kallay, M.; Michauk, C.; Szalay, P. G.; Csaszar, A. G.; Gauss, J.; Stanton, J. F. High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification. J. Chem. Phys. 2006, 125 (6), 064108-1-064108-8. (4) Karton, A.; Rabinovich, E.; Martin, J. M. L.; Ruscic, B. W4 theory for computational thermochemistry: In pursuit of confident sub-kJ/mol predictions. J. Chem. Phys. 2006, 125 (14), 144108-1-144108-17. (5) Harding, M. E.; Vazquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. High-accuracy extrapolated ab initio thermochemistry. III. Additional improvements and overview. J. Chem. Phys. 2008, 128 (11), 114111-1-114111-15.

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