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The gas phase acidity of HBF4(HF-BF3) |
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PhysChemComm,
Volume 2,
Issue 12,
1999,
Page 62-66
A. H. Otto,
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摘要:
The gas phase acidity of HBF4 (HF–BF3) A. H. Otto Institut für Anorganische und Analytische Chemie, Technical University Berlin, Sekr. C2, Strasse des 17. Juni, D-10623 Berlin, Germany Received 23rd September 1999, Accepted 6th October 1999, Published 12th October 1999 The gas phase acidity of the complex superacid HBF4 and the interaction of BF3 with HF as well as the F� detachment from BF4� have been calculated ab initio using high accuracy energy models [CBS-4, CBS-Q, CBS-QB3, G1, G2(MP2) and G2] as well as the density functional B3LYP formalism. All methods but CBS-4 and G1 provide practically equal acidity data for the gas phase and one may recommend 288–289 kcal mol–1 for the Gibbs free energy and 291–292 kcal mol–1 for the corresponding enthalpy at 298 K.The complex HF–BF3 is unstable in vacuo as the Gibbs free energy of decomposition into HF and BF3 is predicted to be between –3.6 and –4.6 kcal mol–1 depending on the method used. The conjugated base BF4� is stable with respect to fluoride ion detachment. We recommend 81–82 kcal mol–1 and 72–73 kcal mol–1 for the enthalpy and the Gibbs free energy, respectively. 1. Introduction Superacids play an important role in organic and inorganic chemistry.1–8 However, there are only few reliable experimental9,10 and theoretical10–14 studies dealing with the estimation of their acidities in the gas phase. Tetrafluoroboric acid (HBF4) is one of the smallest molecules possessing superacidic properties, i.e., it is stronger than pure sulfuric acid.Although high level ab initio results for some salts15 and the conjugated base15,16 have been reported, there is a complete lack of gas phase acidity data. However, from microwave spectroscopy is known17 that the HF–BF3 complex exhibits a Cs (cis) geometry. The aim of this work is to apply accurate quantum chemical methods in order to obtain reliable results for the gas phase acidity of HBF4 and also for the decomposition with respect to BF3 and HF as well as for the F� detachment from BF4� . 2. Computational details The following model chemistries were used for all calculations: (1) The complete basis set methods18 CBS-4, CBS-Q, CBSQB3. The starting point for this technique is the observation that the largest errors in thermochemical calculations result from basis set truncation.The CBS models take advantage of the asymptotic convergence of pair natural orbital expansions to extrapolate to the estimated complete basis set limit. While the accuracy increases from CBS-4 through CBS-Q and CBS-QB3 to CBS-APNO (not used in this study), the expense grows dramatically. An interesting alternative to the pure ab initio MO procedures has been developed very recently, using CBS-QB3. It combines the basis set expansion with the density functional theory (B3LYP) and also calculations of the correlation energies by CC (coupled cluster) theory and MP4 (Møller–Plesset perturbation theory of the fourth order). In contrast to all other CBS modifications CBS-QB3 PhysChemComm, 1999, 12 uses B3LYP/CBSB7 for both calculating frequencies and geometries.The performance in predicting acidities was tested for two less expensive methods.19 CBS-4 gave a root mean square deviation from the experimental values of 2.65 kcal mol–1 while for CBS-Q a value of 1.65 kcal mol–1 was obtained. The test set, however, contained only "pure" chemical compounds and not any complexes of the van der Waals (vdW) type. As the frequencies are calculated from the Hartree–Fock optimised minima of the split valence basis sets, thermal corrections could not be reliable due to poor geometries. As will be shown below (Table 5), for example, the (H)F–B distance is underestimated essentially. (2) Gaussian theory methods. Several methods of this kind of model chemistry20–22 have been elaborated in the last decade.The first step was the Gaussian-1 (G1) theory20 which was improved by the G2 technique21 somewhat later. G1 and G2 theories are essentially approximations to QCISD(T)/6-311+G(3df,2p) energies replacing one large calculation with four smaller (and in sum faster) ones. As the latter is very time, disk space and memory consuming the G2(MP2) model22 has been proposed as a good compromise between cost and performance. All three methods are high-accuracy energy models using reasonably good geometries [MP2(fu)/6-31G(d)]. The sole weakness is obviously the fact that frequencies are calculated at the HF/6-31G(d) level which could lead to errors by the same reasons mentioned above for the CBS methods.(3) Density functional calculations. Becke’s hybrid exchange functional23 was used in combination with the correlation functional of Lee, Yang and Parr24 (B3LYP) and the 6-311++G(3df,2p) standard basis set in order to optimise geometries and compute thermal corrections to the energies. Frequencies were used without scaling. (4) Hartree–Fock optimisation. In order to test the influence of diffuse functions on the B–F(H) distance, optimisations of the cis-structure of HBF4 were carried out at the HF/6- 31+G(d) level of theory.Table 1 Enthalpiesa (Eh) calculated at several levels of sophistication F� Method cis-HBF4 BF4� BF3 HF trans-HBF4 100.343820 100.367166 100.355756 100.356609 100.343725 100.346698 100.473251 324.237008 324.286613 324.259001 324.261704 324.222570 324.232930 324.673877 424.128861 424.195393 424.157579 424.161328 424.106097 424.121190 424.686177 424.586264 424.648304 424.620083 424.624026 424.570184 424.583945 425.150623 424.585172 424.647391 424.619317 424.623066 424.569336 424.583087 425.149877 G1 CBS-4 CBS-Q CBS-QB3 G2(MP2) G2 B3LYPb 99.757566 99.781556 99.764381 99.764908 99.753329 99.758238 99.886333 a Sums of the energies and the thermal corrections using standard formulae. b Using the 6-311++G(3df,2p) standard basis set.Frequencies have been calculated at the same level and were used without scaling. Table 2 Gibbs free energiesa (Eh) calculated at several levels of sophistication Method F� BF4� BF3 HF trans-HBF4 cis-HBF4 100.363508 100.386908 100.375430 100.376316 100.363413 100.366386 100.492961 324.265986 324.315650 324.287912 324.290649 324.251548 324.261907 324.702787 424.159582 424.225927 424.188211 424.192029 424.136817 424.151910 424.716845 424.623406 424.683096 424.656918 424.660789 424.607326 424.621087 425.188418 424.623694 424.683095 424.657676 424.661168 424.607858 424.621609 425.189336 G1 CBS-4 CBS-Q CBS-QB3 G2(MP2) G2 B3LYPb 99.774085 99.798075 99.780901 99.781427 99.769848 99.774758 99.902852 a Sums of the energies and the thermal corrections using standard formulae. b Using the 6-311++G(3df,2p) standard basis set.Frequencies have been calculated at the same level and were used without scaling. All calculations were performed using the GAUSSIAN 94W and 98W system of programs25 running on a Pentium II/333 MHz (256 MB RAM) PC. For more details about the ab initio methods used see ref. 26. s The calculated acidities by the CBS-Q, CBS-QB3, G2(MP2) and G2 techniques are very similar (Table 4). Further one may see that G1 shows a value somewhat lower while CBS-4 seems to fail. The reasons for the latter are quite clear: The 3-21G basis set used is not capable of predicting accurate interaction distances of vdW complexes. Consequently the energy for HBF4 calculated at any correlated level is too high and the resulting acidity is overestimated.In addition, the difference between the deprotonation energy and the corresponding free energy is 3.2 kcal mol–1 for the (more accurate) G2 model while CBS-4 predicts the same value to be 4.6 kcal mol–1. Inaccurate small vibrational modes are responsible for the error in the latter case. Thus, the CBS-4 method is not suitable for calculating acidities of vdW molecules. It is remarkable that B3LYP, G2, CBS-Q and CBS-QB3 predicts practically the same propensity of HBF4 to abstract the proton. G2 G2(MP2) CBS-QB3 CBS-Q CBS-4 B3LYPa –0.47 0.58 –0.54 0.33 –0.53 0.33 –0.60 0.24 –0.48 0.48 –0.57 0.00 G2 G2(MP2) CBS-QB3 CBS-Q 289.8 291.9 288.1 292.7 288.9 291.2 287.7 291.7 287.9 285.7 280.2 3.Results and discussion 3.1. Acidity The energies calculated including correction for enthalpies and Gibbs free energies are presented in the Tables 1 and 2, respectively. In agreement with the finding reported earlier17 all methods but CBS-4 found the cis-Cs geometry of HBF4 to correspond to the only minimum while for the trans-C structure one imaginary frequency was obtained. The resulting torsional barrier is very small (Table 3). The sole exception is CBS-4 which located two minimum geometries possessing equal stabilities. Table 3 The cis–trans activation energies (kcal mol–1) for HBF4 G1 –0.69 0.18 DH°298 DG°298 a Using the 6-311++G(3df,2p) standard basis set. Frequencies have been calculated at the same level and were used without scaling.Table 4 Calculated acidities (kcal mol–1) of HBF4 G1 288.5 284.5 DH°298 DG°298 a Using the 6-311++G(3df,2p) standard basis set. Frequencies have been calculated at the same level and were used without scaling.Table 5 The B–F(H) bond length (Å) of cis-HBF4 as an indicator of optimisation quality CBS-QB3 CBS-Q CBS-4 B3LYP/CBSB7 HF/6-31G(d) Method HF/3-21G(*) HF/6-31G(d') Frequencies 96 77 47 NBFa 2.379 2.360 1.839 rBF(H) –4.46 –3.50 DDG°298b –1.64 Method HF/3-21G(*) MP2/6-31G(d') B3LYP/CBSB7 MP2(fu)/6-31G(d) HF/6-31+G(d) 6-311++G(3df,2p) MWd Geometries 2.379 2.295 1.839 rBF(H) a Number of basis functions. b Correction to the Gibbs free energy (kcal mol–1). c Ref. 17. d Microwave spectroscopy.Therefore, the best calculation methods give for HBF4 a deprotonation enthalpy of 291–292 kcal mol–1 in the gas phase. This is almost 20 kcal mol–1 lower than the corresponding energies found for sulfuric acid.9,12 The deviations from the values calculated for HClO4 (299.5 kcal mol–1), FSO3H (299.7 kcal mol–1) and ClSO3H (296.5 kcal mol–1)12 at the MP2/6-311++ G(d,p)//3-21G(*) level are smaller. Nevertheless, HBF4 is predicted to be the strongest of all named acids and its strength is also higher than that of CF3SO3H (301.9 kcal mol–1 calculated14 and 305.9 2.4 kcal mol–1 measured9). At this point it is necessary to emphasise that all model chemistries generate HBF4 geometries being in poor (CBS-4) or moderate agreement with experiment.17 A suitable measure for the quality of a method in reproducing the geometry of HBF4 is the B–F(H) vdW distance (Table 5, Fig.1). Thus, thermal free energy corrections, for example, range from –1.6 to –5.4 kcal mol– 1 depending on the method. In contrast, B3LYP performs much better when large basis sets are used. Following the suggestion of one referee, HF/6-31+G(d) optimisation results were, in addition, included in Table 5. One can see that diffuse functions are necessary for describing the weak interaction bond correctly. The strong dependence of the B–F(H) distance on the level of theory was shown previously.17 Fig. 1 The B3LYP/6-311++G(3df,2p) optimised gas phase structure of cis-HBF4 (Cs) B3LYP Exp.c HF G1 G2(MP2) G2 HF/6-31+G(d) 6-311++G(3df,2p) MWd 205 97 77 2.559 2.524 2.388 2.544 (2) –5.39 –4.30 –3.34 2.559 2.524 2.255 2.544 (2) 3.2.Stability of the acid with respect to HBF4 ® HF + BF3 The vdW interaction energy has already been calculated by Phillips and co-workers.17 They found values between 3 and 4 kcal mol–1 when basis sets of triple zeta quality were used in combination with MP4. After corrections for basis set superposition error the interaction energy is reduced by 0.5 kcal mol–1. These results are confirmed by the present calculations using the CBS-Q, G2(MP2) and G2 model chemistries (Table 6), however, the predicted values in the present study are still somewhat smaller. Turning to thermochemical properties at normal conditions one may see that, although the enthalpy is calculated to be positive at these three levels the contributions from entropy become essential.The values for the free energy are negative, i.e., HBF4 is in vacuo unstable with respect to the decomposition into HF and BF3. In contrast to all other methods, the CBS-4 model even provides negative enthalpies for the decomposition process. In other words, CBS-4 overestimates the instability of HBF4 which is a consequence of the inaccurate geometry used for energy calculations, again. 4� 3.3. Stability of the conjugated base with respect to BF ® BF3 + F� The calculation of the fluoride ion detachment from BF4� is a rather routine problem as any basis set superposition errors (BSSE) are meaningless for this process.However, although the corresponding enthalpy was measured by using different experimental methods27–32 the values detected cover a considerably large range from 72 kcal mol–1 (ref. 29) via 79 kcal mol–1 (refs. 28 and 30) up to 92 kcal mol–1 (ref. 31) and 94 kcal mol–1(ref. 32). The agreement between the best theoretical methods CBS-Q, G2(MP2) and G2 is remarkable but also G1 and even CBS- 4 seem to make a good job (Table 7). Generally, the enthalpy values are in reasonable agreement with the results of ab initio data from a paper of Williams et al.16 which reported data from 80 to 85 kcal mol–1. The most reliable values from the present calculations are, obviously, 81–82 kcal mol–1 for the enthalpy and 72–73 kcal mol–1 for the free energy.Table 6 Calculated stabilities of the acid with respect to HBF4 ®HF + BF3 (kcal mol–1) CBS-Q CBS-4 G1 2.9 –3.6 –4.0 –12.2 2.7 –3.6 DH°298 DG°298 a Using the 6-311++G(3df,2p) standard basis set.Frequencies have been calculated at the same level and were used without scaling. b The value (ref. 17) is a binding energy. Table 7 Stability of the conjugated base with respect to BF4�® BF3 + F� (kcal mol–1) CBS-QB3 CBS-Q CBS-4 G1 84.5 75.3 84.2 74.9 79.8 70.4 84.3 75.0 DH°298 DG°298 a Using the 6-311++G(3df,2p) standard basis set. Frequencies have been calculated at the same level and were used without scaling. b See text. 4,3 4. Conclusions High level model chemistries give unequivocal evidence that HBF4 is a superacid, being stronger than several other very strong superacids, for example, sulfuric acid, HClO FSO3H, ClSO3H and CF3SO3H.From reliable calculations we recommend 288–289 kcal mol–1 for the Gibbs free energy of deprotonation in the gas phase and 291–292 kcal mol–1 for the corresponding enthalpy. It was shown that the entropy factor plays a significant role in the stability of HBF4. The decomposition into HF and BF3 is exothermic and the values predicted for the Gibbs free reaction energies lie between –3.6 and –4.6 kcal mol–1 depending on the method used. Thus, the complex HF–BF is unstable in vacuo. The conjugated base BF4� is stable with respect to fluoride ion detachment. The values calculated with the best methods are in good agreement with ab initio data published previously.As the techniques used in the present work are more reliable we are able to recommend 81–82 kcal mol–1 and 72–73 kcal mol–1 for the enthalpy and the Gibbs free energy, respectively. Acknowledgements I am very indebted to Dr. S. Schrader from the University of Potsdam for making Gaussian codes available to me. Furthermore, I would like to thank one referee for helpful suggestions. References 1 G. A. Olah, Angew. Chem., 1973, 85, 183. 2 G. A. Olah, G. K. S. Prakash and J. Sommer, Science, 1979, 206, 13. 3 G. A. Olah and J. Sommer, La Recherche, 1979, 10, 624. 4 G. A. Olah, My search of carbocations and their role in chemistry, Prix Nobel, 1994 (pub.1995), 117–144, Nobel lecture, Dec. 8, 1994. 5 G. A. Olah, G. K. S. Prakash and J. Sommer, Superacids, Wiley, New York, 1986. 6 R. Jost and J. Sommer, Rev. Chem. Intermed., 1988, 9,171. 7 P. v. R. Schleyer and C. Maerker, Pure Appl. Chem., 1995, 67, 755. Exp.b G2 G2(MP2) CBS-QB3 B3LYPa 3–4 1.7 –4.0 2.2 –4.2 1.9 –4.6 3.0 –3.6 G2 Pa Exp.b 72–94 79.0 69.8 81.6 72.3 81.7 72.4 8 T. A. O'Donnel, Superacids and Acidic Melts as Inorganic Chemical Reaction Media, VCH Publishers, New York, 1993. 9 A. A. Viggiano, M. J. Henchman, F. Dale, C. A. Deakyne and J. F. Paulson, J. Am. Chem. Soc., 1992, 114, 4299. 10 I. A. Koppel, R. W. Taft, F. Anvia, Sh.-Zh. Zhu, Li-Qu. Hu, K.-S. Sung, D.D. DesMarteau, L. M. Yagupolskii, Yu. L. Yagupolskii, N. V. Ignat'ev, N. V. Kondratenko, A. Yu. Volkonskii, V. M. Vlasov, R. Notario and P.- Ch. Maria, J. Am. Chem. Soc., 1994, 116, 3047. 11 P. Burk, I. A. Koppel, I. Koppel, L. Yagupolskii and R. W. Taft, J. Comput. Chem., 1996, 17, 30. 12 A. H. Otto, S. Schrader, Th. Steiger and M. Schneider, J. Chem. Soc., Faraday Trans., 1997, 93, 3927. 13 A. H. Otto, Th. Steiger and S. Schrader, J. Chem. Soc., Chem. Commun., 1998, 391. 14 A. H. Otto, Th. Steiger and S. Schrader, J. Mol. Struct., 1998, 471, 105. 15 M. Spoliti, N. Sana and V. Di Martino, Theochem., 1992, 258, 83. 16 S. D. Williams, W. Harper, G. Mamontov, L. J. Tortorelli and G. Shankle, J. Comput. Chem., 1996, 17, 1696. 17 J.A. Phillips, M. Canagaratna, H. Goodfriend, A. Grushow, J. Almlöf and K. R. Leopold, J. Am Chem. Soc., 1995, 117, 12549. 18 (a) J. W. Ochterski, G. A. Petersson and J. A. Montgomery, Jr., J. Chem. Phys., 1996, 104, 2598; (b) J. A. Montgomery, Jr, M. J. Frisch, J. W. Ochterski and 21 L. A. Curtiss, K. Raghavachari, G. W. Trucks and J. A. G. A. Petersson, J. Chem. Phys., 1999, 110, 2822.. 19 J. W. Ochterski, G. A. Petersson and K. B. Wiberg, J. Am. Chem. Soc., 1995, 117, 11299. 20 J. A. Pople, M. Head-Gordon, D.-J. Fox, K. Raghavachari and L. A. Curtiss, J. Chem. Phys., 1989, 90, 5622. Pople, J. Chem. Phys. 1991, 94, 7221. 22 L. A. Curtiss, K. Raghavachari and J. A. Pople, J. Chem. Phys., 1993, 98, 1293. 23 A. D. Becke, Chem. Phys. 1993, 98, 5648. 24 C. Lee, W. Yang and R. G. Parr, Phys. Rev. B, 1988, 37, 785. 25 Gaussian 94W, Revision E.3, M. J. Frisch et al., Gaussian, Inc., Pittsburgh PA, 1998.26 J. B. Foresman and A. E. Frisch, Exploring Chemistry with Electronic Structure Methods, 2nd edn., Gaussian, Inc., Pittsburgh, PA, 1996. 27 Ref. 29–32 are taken from J. E. Bartmess, ’Negative Ion Energetics Data’ in NIST Chemistry WebBook, NIST Standard Reference Database Number 69, ed. W. G. Mallard and P. J. Linstrom, November 1998, National Institute of Standards and Technology, Gaithersburg MD, 20899 (http://webbook.nist.gov/chemistry). 28 M. Veljkovic, O. Neskovic, K. F. Zmbov, A. Y. Borshchevsky, V. E. Vaisberg and L. N. Sidorov, Rapid Commun. Mass Spectrom., 1991, 5, 37. 29 J. W. Larson and T. B. McMahon, J. Am. Chem. Soc., 1985, 107, 766. 30 A. T. Pyatenko, A. V. Guasarov and L. N. Gorokhov, Russ. J. Phys. Chem., 1984, 58, 1. 31 T. E. Mallouk, G. L. Rosenthal, G. Muller, R. Brusasco and N. Bartlett, Inorg. Chem., 1984, 23, 3167. 32 N. V. Krivtsov, K. V. Titova and V. Ya. Rosolovskii, Russ. J. Inorg. Chem., 1977, 22, 374. Paper 9/07705G PhysChemComm © The Royal Society of Chemistry 1999
ISSN:1460-2733
DOI:10.1039/a907705g
出版商:RSC
年代:1999
数据来源: RSC
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