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The Reason Why HAlCl4 Acid Does Not Exist Celina Sikorska, Sylwia Freza, and Piotr Skurski* Department of Chemistry, UniVersity of Gdan´sk, Sobieskiego 18, 80-952 Gdan´sk, Poland ReceiVed: NoVember 6, 2009; ReVised Manuscript ReceiVed: December 7, 2009
The explanation of the hypothetical HAlCl4 acid instability is provided on the basis of theoretical considerations supported by ab initio calculations. The equilibrium structures of LiAlCl4, NaAlCl4, and KAlCl4 salts were examined and compared to that of their corresponding parent acid. The process of formation of the representative NaAlCl4 salt was analyzed, and the interaction energy between NaCl and AlCl3 was estimated to be ca. 55 kcal/mol while that between HCl and AlCl3 (when the HAlCl4 species is formed) was calculated to be smaller by an order of magnitude (ca. 8 kcal/mol). The hypothetical HAlCl4 acid was identified as an HCl · · · AlCl3 adduct (with the hydrogen chloride tethered weakly to the quasi-planar aluminum chloride molecule). The electron affinity of the neutral AlCl4 superhalogen molecule was found to be the factor determining the ability to form a stable compound of MAlCl4 type. 1. Introduction The issue of the potential existence and stability of HAlCl4 acid has been raised and addressed in the literature since 1927 when Schwartz and Meyer concluded that hydrogen chloride and aluminum chloride do not combine to form a stable HAlCl4 species.1 This finding was later confirmed by Malquori,2 Boswell and McLaughlin,3 and Ipatieff.4 In addition, the observations reported in 1948 by Fontana and Herold pointed to the nonexistence of the corresponding bromo compound (i.e., HAlBr4) at room temperature.5 Despite this evidence, the substance HAlCl4 was consequently mentioned in the literature as the active catalytic species in mixtures of AlCl3 and HCl.6 Moreover, in some instances it was postulated that the HAlCl4 acid was so stable that elevated temperatures (ca. 120 °C) were required to bring about appreciable dissociation into its components.7 The confusion considering the hypothetical existence of HAlCl4 species seemed to be resolved and clarified by Brown and Pearsall who performed careful examination of the hydrogen chloride-aluminum chloride mixture under a variety of conditions including temperatures as low as -120 °C. Their experimental studies yielded no evidence indicating any combination of the two species. Therefore, it was concluded that the substance HAlCl4 must be considered as a hypothetical acid which does not exist (in detectable concentrations).8 However, in more recent literature there were references to the HAlCl4 molecule and it was postulated by Chandler and Johnson (on the basis of the ab initio calculations) that HAlCl4 could exist in acidic solutions containing HCl.9 In addition, Otto and coworkers calculated the gas phase deprotonation energy for HAlCl4 as equal to 264 kcal/mol and concluded that this acid should be even stronger than another well-recognized superacid, HTaF6.10 Since there is no experimental evidence for the existence of the HAlCl4 acid, we consider this species as either nonexisting or highly unstable. On the other hand, its salts, such as LiAlCl4,11 NaAlCl4,12 and KAlCl413 are well-known compounds with crystallographic structures determined and available. The structure of molten mixtures of alkali metal halides and aluminum * Corresponding author,
[email protected].
halides continues to be of current interest due to the potential applications of these ionic liquids as solvents for high density batteries.14 The alkali metal atom bonding in these salts was determined as primarily ionic and the lowest energy structures of these compounds seem to be the consequence of the combined attractive Coulombic interactions between the Na+ ion and the negatively charged Cl atoms as well as the repulsive interaction between Na+ and the positively charged aluminum atom.15 The main goal of this work is to provide the explanation why the HAlCl4 acid is not a detectable species. We provide and discuss the gas phase equilibrium structures of the LiAlCl4, NaAlCl4, and KAlCl4 salts as well as the lowest energy structure of their parent hypothetical HAlCl4 acid. The process of formation of the MAlCl4 salts (M ) Li, Na, K) is also analyzed and the interaction energies between MCl and AlCl3 are estimated and compared to that between HCl and AlCl3. The electron affinity of the neutral AlCl4 molecule exhibiting superhalogen nature is then discussed as the factor determining the ability to form a stable compound of MAlCl4 type. 2. Methods The geometrical structures of the MAlCl4 species (where M ) H, Li, Na, K) and the corresponding nonscaled harmonic vibrational frequencies were calculated by applying the secondorder Møller-Plesset (MP2) perturbational method with the 6-311++G(d,p) basis set.16,17 The coupled-cluster method with single, double, and noniterative triple excitations (CCSD(T))18 was used to calculate the final energies of the species at their geometries obtained with the MP2 method. The relative energies of the isomers were estimated at the CCSD(T)/6-311++G(d,p)// MP2/6-311++G(d,p) level and corrected using the zero-point vibrational energies (ZPE) obtained with the MP2 method. All calculations were performed with the GAUSSIAN03 program.19 In order to avoid erroneous results from the default direct SCF calculations, the keyword SCF ) NoVarAcc was used and the two-electron integrals were evaluated (without prescreening) to a tolerance of 10-20 a.u. The optimizations of the geometries were performed using relatively tight convergence thresholds (i.e., 10-5 hartree/bohr (or radian) for the root mean square first derivative).
10.1021/jp910589m 2010 American Chemical Society Published on Web 01/20/2010
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Sikorska et al.
TABLE 1: Geometrical Parameters and Corresponding Harmonic Vibrational Frequencies for the HCl · · · AlCl3 and MAlCl4 (M ) Li, Na, K) Speciesa species (relative energy)
geometrical parameters
vibrational frequencies
HCl · · · AlCl3 Cs (0.0 kcal/mol) global minimum
R(H-Cl1) ) 1.281 R(Al-Cl1) ) 2.523 R(Al-Cl2) ) 2.084 R(Al-Cl3,4) ) 2.088
R(HCl1Al) ) 98.55 R(Cl1AlCl2) ) 96.12 R(Cl1AlCl3) ) 98.71 ω(Cl2AlCl3Cl4) ) 153.46
ν1 ν2 ν3 ν4 ν5 ν6
(a′′) ) 19 (a′) ) 96 (a′′) ) 128 (a′) ) 149 (a′) ) 155 (a′′) ) 160
LiAlCl4 C2V (0.0 kcal/mol) global minimum
R(Li-Cl1,2) ) 2.203 R(Al-Cl1,2) ) 2.221 R(Al-Cl3,4) ) 2.093
R(LiCl1Al) ) 82.59 R(LiAlCl3) ) 120.64 R(Cl1AlCl2) ) 96.88 R(Cl1AlCl3) ) 109.76 R(Cl3AlCl4) ) 118.71 ω(LiCl1AlCl3) ) 113.91
ν1 ν2 ν3 ν4 ν5 ν6
(b2) ) 65 (a2) ) 105 (a1) ) 125 (b1) ) 166 (b2) ) 174 (a1) ) 225
LiAlCl4 C3V (+1.0 kcal/mol)
R(Li-Cl1,2,3) ) 2.391 R(Al-Cl1,2,3) ) 2.179 R(Al-Cl4) ) 2.073
R(LiCl1Al) ) 66.91 R(Cl1AlCl2) ) 97.92 R(Cl1AlCl4) ) 119.43
ν1,2 (e) ) 117 ν3,4 (e) ) 189 ν5,6 (e) ) 226 ν7 (a1) ) 230
NaAlCl4 C3V (0.0 kcal/mol) global minimum
R(Na-Cl1,2,3) ) 2.738 R(Al-Cl1,2,3) ) 2.173 R(Al-Cl4) ) 2.083
R(NaCl1Al) ) 71.80 R(Cl1AlCl2) ) 101.17 R(Cl1AlCl4) ) 116.86
υ1,2 (e) ) 98 υ3,4 (e) ) 47 υ5,6 (e) ) 184 υ7 (a1) ) 211
NaAlCl4 C2V (+1.9 kcal/mol)
R(Na-Cl1,2) ) 2.576 R(Al-Cl1,2) ) 2.207 R(Al-Cl3,4) ) 2.101
R(NaCl1Al) ) 88.39 R(NaAlCl3) ) 119.39 R(Cl1AlCl2) ) 100.60 R(Cl1AlCl3) ) 109.22 R(Cl3AlCl4) ) 117.54 ω(NaCl1AlCl3) ) 112.75
υ1 υ2 υ3 υ4 υ5 υ6
KAlCl4 C3V (0.0 kcal/mol) global minimum
R(K-Cl1,2,3) ) 3.106 R(Al-Cl1,2,3) ) 2.167 R(Al-Cl4) ) 2.090
R(KCl1Al) ) 76.41 R(Cl1AlCl2) ) 102.87 R(Cl1AlCl4) ) 115.46
ν1,2 (e) ) 76 ν3,4 (e) ) 130 ν5 (a1) ) 152 ν6,7 (e) ) 180
(b1) ) 17 (a2) ) 108 (a1) ) 115 (b2) ) 160 (b1) ) 174 (a1) ) 195
ν7 (a′) ) 221 ν8 (a′) ) 397 ν9 (a′) ) 497 ν10 (a′′) ) 613 ν11 (a′) ) 625 ν12 (a′) ) 3020 ZPE ) 8.70 ν7 (a1) ) 348 ν8 (b1) ) 384 ν9 (a1) ) 442 ν10 (b1) ) 505 ν11 (a1) ) 531 ν12 (b2) ) 610 ZPE ) 5.26 ν8 (a1) ) 368 ν9 (a1) ) 421 ν10,11 (e) ) 476 ν12 (a1) ) 645 ZPE ) 5.26 υ8 (a1) ) 227 υ9 (a1) ) 363 υ10,11 (e) ) 477 υ12 (a1) ) 614 ZPE ) 4.62 υ7 (b2) ) 234 υ8 (a1) ) 268 υ9 (a1) ) 349 υ10 (b2) ) 442 υ11 (a1) ) 522 υ12 (b1) ) 597 ZPE ) 1.92 ν8 (a1) ) 207 ν9 (a1) ) 360 ν10,11 (e) ) 485 ν12 (a1) ) 600 ZPE ) 4.381
a Bond lengths (R) in Å, valence (R) and dihedral (ω) angles in degrees, frequencies (ν) in cm-1, relative energies (in parentheses) in kcal/ mol, zero-point vibrational energies (ZPE) in kcal/mol. All the results were obtained at the MP2/6-311++G(d,p) level except the relative energies obtained with the CCSD(T) method.
3. Results 3.1. The MP2 Structures of LiAlCl4, NaAlCl4, and KAlCl4. The MP2/6-311++G(d,p) ab initio calculations revealed only one minimum energy structure for the potassium tetrachloroaluminate and two minima in the case of both LiAlCl4 and NaAlCl4. The geometrical parameters together with the corresponding harmonic vibrational frequencies obtained for these species are gathered in Table 1. The lowest energy structure for lithium tetrachloroaluminate molecule possesses C2V symmetry with the Li atom located between two Cl atoms (bidentate form); see Figure 1. The higher energy LiAlCl4 conformer is of C3V symmetry with the lithium localized on the C3 axis and bound to three chlorine atoms (tridentate form). This latter structure is only 1.0 kcal/mol higher in energy than the former (at the CCSD(T) level) while the energy of the transition state connecting these two minima was found to be only 2.6 kcal/mol above the energy of the bidentate C2V symmetry global minimum. Such a small kinetic barrier leading from the bidentate to tridentate structure and the comparable energy of the two geometrically stable isomers (i.e., not exceeding 1 kcal/mol) indicate that the interchange between the structures is probably rapid at the temperatures used experimentally. Similar conclusions could be formulated on the basis of our results considering the NaAlCl4 species. Namely, we found two
minimum energy structures: the bidentate conformer of C2V symmetry and the tridentate form possessing C3V symmetry (see Figure 1). The latter (C3V) structure is the most stable species while the bidentate NaAlCl4 conformer is 1.9 kcal/mol higher in energy. The kinetic barrier leading from the C3V symmetry species to the C2V conformer was calculated to be only 2.2 kcal/ mol which means that one should expect both isomers to be present at the elevated temperatures. In the case of the potassium tetrachloroaluminate, however, we found only one minimum energy structure; see Figure 2. The KAlCl4 molecule possesses C3V symmetry with the K atom localized on the C3 axis and bound to three Cl atoms. The geometrical parameters of the structures obtained in this work agree well with the crystallographic bond lengths and angles reported in the literature. Indeed, the Al-Cl distances in LiAlCl4 predicted by our calculations are in the 2.07-2.22 Å range (see Table 1) while the separations observed in crystals11 are in the 2.12-2.15 Å range. A similar situation can be noticed for the Al-Cl separations in the NaAlCl4 and KAlCl4 salts. Namely, the calculated Al-Cl distances for NaAlCl4 (2.08-2.21 Å) are in a good agreement with the crystallographic12 2.12-2.14 Å separations while for the potassium tetrachloroaluminate these ranges are 2.09-2.17 and 2.12-2.14 Å, respectively, for the distances calculated theoretically and obtained experimentally.13 As far as the separations between
Why HAlCl4 Acid Does Not Exist
Figure 1. The MP2 equilibrium structures of the LiAlCl4 and NaAlCl4 species. See Table 1 for the precise values of all geometrical parameters.
Figure 2. The MP2 equilibrium structures of the KAlCl4 and HCl · · · AlCl3 species. See Table 1 for the precise values of all geometrical parameters.
the chlorine atoms and alkali metal atoms are concerned, the agreement seems also satisfactory. Crystallographic data lead to the following separations:11-13 r(Li-Cl) ) 2.48-2.51 Å; r(Na-Cl) ) 2.79-2.88 Å; r(K-Cl) ) 3.10-3.31 Å while the corresponding distances predicted by our calculations are 2.20-2.39 Å, 2.58-2.74 Å, and 3.11 Å, respectively (Table 1). The MAlCl4 salts (M ) Li, Na, K) might be considered as the complexes between AlCl3 molecule and the corresponding MCl system. However, such a treatment would not be justified because of the structure of the overall MAlCl4 system in which the alkali metal atom M forms two or three (depending on the structure) equivalent bonds with the chlorine atoms (see Figures 1 and 2). The lengths of these M-Cl bonds are only slightly larger (by ca. 0.2-0.3 Å) than those calculated for the isolated MCl molecules (at the same level of theory), and those elongations are clearly the result of the fact that the alkali metal atom is involved in two or three bonding interactions in the
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2237 MAlCl4 salt instead of one in MCl species. Moreover, it needs to be pointed out that the isolated AlCl3 molecule is planar15 while the AlCl4- anion possesses a tetrahedral structure.20-23 The analysis of the LiAlCl4, NaAlCl4, and KAlCl4 geometrical structures clearly reveals the quasi-tetrahedral configuration of the four chlorine atoms around the Al center. In addition, all four Al-Cl distances are very similar (the differences among them are within 0.1 Å) which indicates that the MAlCl4 salt mimics the M+ cation bound to the AlCl4- anion. Therefore, we conclude that each of the MAlCl4 salts studied (M ) Li, Na, K) should be treated as a strongly bound system with M-Cl bonds exhibiting primarily ionic character rather than MCl · · · AlCl3 adduct (because such an adduct would possess one significantly elongated Al-Cl bond and would allow for easy distinguishing of a quasi-planar AlCl3 fragment). 3.2. The MP2 Structure of the Hypothetical HAlCl4 Acid. The geometrical structure of the HAlCl4 hypothetical system is shown in Figure 2 (as it was found at the MP2/6-311++G(d,p) level of theory). The bond lengths, valence and dihedral angles, and the corresponding nonscaled MP2 harmonic vibrational frequencies are collected in Table 1. We found only one minimum energy structure for HAlCl4 which corresponds to the Cs-symmetry staggered conformer (the corresponding Cssymmetry eclipsed rotamer possesses one imaginary frequency and connects the staggered minima as a saddle point). Our results are in a very good agreement with those reported earlier by Chandler and Johnson9 who employed the MP2 method with the similar 6-311+G(d,p) basis set to obtain the minimum energy structure of HAlCl4. In particular, the bond lengths in ref 9 differ by less than 0.001 Å and the valence angle by less than 0.003° than those collected in Table 1. At first glance the HAlCl4 structure resembles the adduct of two species, i.e., planar aluminum chloride (AlCl3) and the hydrogen chloride (HCl) molecule. Indeed, the three Al-Cl bonds are in the 2.084-2.088 Å range while the fourth Al-Cl separation is larger by 0.435 Å (20%); see Figure 2. This indicates that one of the chlorine atoms is much more weakly bound to the aluminum than the remaining Cl atoms. The corresponding stretching Al-Cl1 vibration ν7(a′) ) 221 cm-1 confirms such an observation since it is much softer than other vibrations related to the stretching Al-Cl2,3,4 modes (i.e., ν8(a′) ) 397 cm-1; ν10(a′′) ) 613 cm-1; ν11(a′) ) 625 cm-1); see Table 1. Hence, the Al-Cl1 vibration (ν7) resembles the intermolecular mode while the Al-Cl2,3,4 vibrations (ν8,10,11) seem to correspond to the stiffer intramolecular stretching modes. Moreover, this chlorine atom (labeled “1” in Figure 2) forms a polarized covalent bond with the hydrogen atom and the length of this bond (1.281 Å) is close to the H-Cl separation in the isolated hydrogen chloride (1.273 Å, as calculated at the same theory level). In addition, the three chlorine atoms in HAlCl4 (labeled “2”, “3”, “4” in Figure 2) are localized in a quasi-planar configuration around the central aluminum atom (the deviation from planarity is 27°, as indicated by the Cl2-Al-Cl3-Cl4 dihedral angle, see Table 1). This indicates that the AlCl3 fragment, albeit deformed, resembles a quasiplanar structure which is distinctive about the neutral isolated AlCl3 molecule rather than a tetrahedral-like configuration of the chlorine atoms (which would be typical if the character of the fragment were mostly ionic, resembling the AlCl4-). Therefore, we conclude that the hydrogen chloride combines with the aluminum chloride to form a weakly bound HCl · · · AlCl3 complex, not a HAlCl4 molecule. Such an adduct is expected to be susceptible to fragmentation leading to the isolated hydrogen chloride and aluminum chloride molecules.
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Figure 3. The MP2 relative energy profiles for the fragmentation channels: HCl · · · AlCl3 f AlCl3 + HCl (top) and NaAlCl4 f AlCl3 + NaCl (bottom). The asymptotes correspond to the sum of the energies of the isolated fragments and read 8.4 and 54.9 kcal/mol for [AlCl3;HCl] and [AlCl3;NaCl], respectively.
Thus the existence of the hypothetical acid described by the HAlCl4 formula needs to be excluded since such a species should rather be treated as the HCl molecule tethered to the AlCl3 system. However, the reason why this species forms the HCl · · · AlCl3 adduct rather than the covalently bound HAlCl4 molecule is yet to be discussed in the following section. 3.3. The Comparison between the Hypothetical HAlCl4 Acid and Its Salts. The geometrical structures of the HAlCl4 species and the corresponding salts were discussed in the two preceding sections. As it was concluded, each of these salts contains four chlorine atoms located in a quasi-tetrahedral configuration around the Al center with the alkali metal atom linked via two or three M-Cl interactions which indicates the ionic character of the molecule. Namely, each of the MAlCl4 (M ) Li, Na, K) molecules could be considered as the slightly deformed AlCl4- anion interacting with the M+ cation. By contrast, the structure of the HAlCl4 resembles the two much more weakly bound fragmentssthe deformed quasi-planar AlCl3 interacting with the HCl molecule. Therefore, we suggest use of the HCl · · · AlCl3 formula, rather than HAlCl4, for describing this species since it seems more proper (taking into account that this system is actually an adduct). This conclusion is confirmed by the analysis of the other geometrical parameters, such as the lengths of the Al-Cl bonds in MAlCl4 salts and in the HCl · · · AlCl3 adduct. Indeed, in each of the MAlCl4 salts considered, the Al-Cl bonds are of similar length (see Table 1) while one significantly elongated Al-Cl bond is present in the HCl · · · AlCl3 species (see Table 1, Figures 1 and 2). In order to provide a better insight into the nature of bonding for the HCl · · · AlCl3 and its salts, we decided to calculate the energy profiles for the MAlCl4 f MCl + AlCl3 fragmentation channel (where M ) H, Na). We have arbitrarily chosen the system containing sodium (NaAlCl4) as the representative salt whose energy profile we compared with that for the HCl · · · AlCl3 adduct. The plots shown in Figure 3 represent the energy changes while the MAlCl4 species is being formed by bringing
Sikorska et al. together two fragments, i.e., MCl and AlCl3. As it can be seen, the final MAlCl4 structure should be spontaneously formed in both cases but the interaction energies differ significantly. The energy change calculated for the formation of the NaAlCl4 salt is 54.9 kcal/mol (see Figure 3, bottom) while the analogous value for the HCl · · · AlCl3 species is only 8.4 kcal/mol (see Figure 3, top). This indicates much weaker interaction between the MCl and AlCl3 fragments in HCl · · · AlCl3 than in NaAlCl4 which confirms our conclusion on the type of bonding in the structure of that hypothetical acid and its salts. Finally, we would like to address the issue of the HAlCl4 acid instability. As it has been already discussed, this acid should rather be considered as an HCl · · · AlCl3 complex. Albeit only weakly stable, we believe this adduct might exist at very low temperatures in the gas phase (assuming the lack of any perturbing factors). Its “instability” in comparison to the corresponding alkali metal salts seems to be the consequence of the presence of such weak bonding (between the hydrogen chloride and aluminum chloride). However, the following issue still needs to be explained: why the MAlCl4 salts (M ) Li, Na, K) are strongly bound and stable molecules while their parent acid is not. To provide the explanation, one should recall that the AlCl4 neutral species possesses a superhalogen nature which means that it binds an extra electron and forms a very strongly bound molecular anion AlCl4- (see refs 20-23). The corresponding vertical electron detachment energy (VDE) for the AlCl4- was estimated to be 7.02 eV.23 Thus the neutral AlCl4 molecule should be capable of ionizing any approaching atomic species whose ionization potential (IP) does not exceed 7 eV. The ionization potentials of the H, Li, Na, and K atoms are well-known and read 13.60, 5.39, 5.14, and 4.34 eV, respectively.24 Hence all the IPs for the alkali metal atoms are smaller than 7 eV, but the IP for the hydrogen atom is not. The observation that IP(H) > VDE(AlCl4) while IP(Li,Na,K) < VDE(AlCl4) explains both: (i) the AlCl4 system inability to ionize the hydrogen atom, and (ii) the AlCl4 system ability to ionize any of the Li, Na, K atoms. This leads to the conclusion that the species described by the hypothetical HAlCl4 formula cannot exist as a strongly covalently bound stable molecule. Instead, the adduct-like structure is formed (with the HCl molecule tethered to the aluminum chloride) and such a situation is primarily caused by the AlCl4 molecule inability to ionize the hydrogen atom. 4. Conclusions The hypothetical acid HAlCl4 and its salts (LiAlCl4, NaAlCl4, and KAlCl4) have been studied theoretically at the CCSD(T)/ 6-311++G(d,p)//MP2/6-311++G(d,p) level. On the basis of these calculations the following conclusions have been formulated: (i) The hypothetical HAlCl4 acid should be considered as an adduct given by the HCl · · · AlCl3 formula since it consists of HCl molecule tethered weakly to the deformed quasi-planar AlCl3 system. (ii) The salts of this hypothetical acid involving alkali metal atoms (Li, Na, K) are stable molecules (LiAlCl4, NaAlCl4, and KAlCl4) exhibiting primarily ionic character of the metal-chlorine bonds. (iii) The HCl · · · AlCl3 adduct is expected to exist at low temperatures in gas phase (i.e., as an isolated species in the absence of any perturbations). (iv) The electron affinity of the neutral AlCl4 superhalogen molecule is predicted to be the primary factor determining the ability of forming a stable compound of MAlCl4 type (M ) H, Li, Na, K).
Why HAlCl4 Acid Does Not Exist Acknowledgment. This paper is dedicated to the memory of Dr. Jerzy Kruszewski. This work was supported by the Polish State Committee for Scientific Research (KBN) Grant No. DS/ 8371-4-0137-9. The computer time provided by the Academic Computer Center in Gdan´sk (TASK) is also gratefully acknowledged. References and Notes (1) Schwartz, R.; Meyer, G. Z. Anorg. Chem. 1927, 166, 190. (2) Malquori, G. Atti accad. Lincei 1928, 7, 740. (3) Boswell, M. C.; McLaughlin, R. R. Can. J. Res. 1929, 1, 400. (4) Ipatieff, V In Catalytic Reactions at High Pressures and High Temperatures; The Macmillan Company: New York, 1936; p 564. (5) Fontana, C. M.; Herold, R. J. J. Am. Chem. Soc. 1948, 70, 2881. (6) Leighton, P. A.; Heldman, J. D. J. Am. Chem. Soc. 1943, 65, 2276. (7) Powell, T. M.; Reid, E. J. Am. Chem. Soc. 1945, 67, 1020. (8) Brown, H.; Pearsall, H. J. Am. Chem. Soc. 1951, 73, 4681. (9) Chandler, W. D.; Johnson, K. E. Inorg. Chem. 1999, 38, 2050. (10) Otto, A. H.; Steiger, T.; Schrader, S. Chem. Commun. 1998, 391. (11) Perenthaler, E.; Schulz, H.; Rabenau, A. Z. Anorg. Allg. Chem. 1982, 491, 259. (12) Krebs, B.; Greiwing, H.; Brendel, C.; Taulelle, F.; Gaune-Escard, M.; Berg, R. W. Inorg. Chem. 1991, 30, 981. (13) Mairesse, G.; Barbier, P.; Wignacourt, J.-P. Acta Crystallogr. 1978, B34, 1328. (14) Blander, M.; Bierwagen, E.; Calkins, K. G.; Curtiss, L. A.; Price, D. L.; Saboungi, M.-L. J. Chem. Phys. 1992, 97, 2733.
J. Phys. Chem. A, Vol. 114, No. 5, 2010 2239 (15) Bock, C. W.; Trachtman, M.; Mains, G. J. J. Phys. Chem. 1994, 98, 478. (16) McLean, A. D.; Chandler, G. S. J. Chem. Phys. 1980, 72, 5639. (17) Krishnan, R.; Binkley, J. S.; Seeger, R.; Pople, J. A. J. Chem. Phys. 1980, 72, 650. (18) Purvis III, G. D.; Bartlett, R. J. J. Chem. Phys. 1982, 76, 1910. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A.; Gaussian 03, reVision E.01; Gaussian, Inc: Wallingford, CT, 2004. (20) Gutsev, G. L.; Boldyrev, A. I. Chem. Phys. Lett. 1981, 84, 352. (21) Gutsev, G. L.; Boldyrev, A. I. Russ. Chem. ReV. 1987, 56, 519. (22) Rytter, E.; Øye, H. A. J. Inorg. Nucl. Chem. 1973, 35, 4311. (23) Sikorska, C.; Smuczyn˜ska, S.; Skurski, P.; Anusiewicz, I. Inorg. Chem. 2008, 47, 7348. (24) Foster, P. J.; Leckenby, R. E.; Robbins, E. J. J. Phys. B: At. Mol. Phys. 1969, 2, 478.
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