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«Jan M.L. Martin∗ Department of Organic Chemistry, Kimmelman Building, Room 262, Weizmann Institute of Science, 76100 Rehovot, Israel. Email: ...»

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In the present case, the A+B/l3 formula predicts a CCSD limit contribution to TAE[SiF4 ] of 119.28 kcal/mol from the (A)VQZ+2d1f and (A)V5Z+2d1f results, with the extrapolation accounting for 2.27 kcal/mol of the final result. For comparison, extrapolation from two smaller basis sets, (A)VTZ+2d1f and (A)VQZ+2d1f, yields 119.62 kcal/mol, while the A + B/(l + 1/2)α formula applied to all three values yields a much smaller value of 118.87 kcal/mol.

The (T) contribution is computed as 9.11 and 9.61 kcal/mol, respectively, in the (A)VTZ+2d1f and (A)VQZ+2d1f basis sets: assuming A + B/l3 behavior, this extrapolates to a limit of 9.98 kcal/mol. We thus finally find a basis set limit valence correlation contribution of 129.26 kcal/mol.

As expected, the Si(2s,2p) and F(1s) inner-shell correlation energy is quite substantial in absolute terms, accounting for some 28% of the overall correlation energy excluding the very deep Si(1s) core. As we have seen in the past for second-row molecules, however, the differential contribution to TAE nearly cancels, in this case being only +0.08 kcal/mol. This contribution is definitely dwarfed by that of scalar relativistic effects, which as we noted we compute to be −1.88 kcal/mol.

Combining all of the above with the atomic spin-orbit correction noted in the Methods section, we finally obtain a “bottom-of-the-well” TAEe of 573.92 kcal/mol; combined with the experimentally derived ZPE, we obtain TAE0 =565.89 kcal/mol.

Combining this with the CODATA heats of formation of F(g) and SiF4 (g), we finally ◦ ◦ obtain ∆Hf,0 [Si(g)]=107.34 kcal/mol. Using the more recent ∆Hf,0 [SiF4 (g)] instead, this value is reduced to 107.15 kcal/mol.

In order to make an assessment of the probable error in these values, we should consider both the uncertainty in the calculated TAE0 and the propagated experimental uncertain ◦ ties in ∆Hf,0 [SiF4 (g)] and ∆Hf,0 [F(g)]. Using exactly the same method as we have employed, MdO obtained a mean absolute error of 0.22 kcal/mol for a wide variety of first-and second-row molecules, which dropped as low as 0.16 kcal/mol when some molecules with significant nondynamical correlation effects were eliminated. Erring on the side of caution, we assign 0.22 kcal/mol as a standard deviation rather than an upper limit to the error.

Given uncertainties of 0.07 and 0.20 kcal/mol in the CODATA heats of formation for F(g) ◦ and SiF4 (g), respectively, we obtain 107.34±0.41 kcal/mol for ∆Hf,0 [Si(g)]. Employing the ◦ more recent Johnson [12] ∆Hf [SiF4 (g)] instead, which has a smaller uncertainty, we propose ◦ ∆Hf,0 [Si(g)]=107.15±0.38 kcal/mol as our final estimate. (At 298.15 K, using the CODATA H298 − H0 functions, this corresponds to 108.19±0.38 kcal/mol.) Our final estimate is in fact within the reduced error limits of Desai [5], ◦ ∆Hf,0 [Si(g)]=106.5±1.0 kcal/mol. It agrees to within combined uncertainties with the GS value after applying CG’s relativistic correction, 107.4±0.5 kcal/mol, which suggests that the ‘spurious’ Si(cr)→Si(amorph) transition enthalpy discussed in the introduction may indeed have been a fair estimate. In previous calculations [44,45] on SiF4 and SiCl4, respectively, Bauschlicher and coworkers derived values of 107.5±2 and 107.8±2 kcal/mol, respectively, in which the error bars are very conservative. In the context of a review article [38] on highaccuracy theoretical thermochemistry, Martin recently repeated the GS calculation on SiH4 using techniques similar to those employed here, and obtained a TAE0 [SiH4 (g)] consistent ◦ with ∆Hf,0 [Si(g)]=107.55±0.5 kcal/mol if the Si(cr)→Si(amorph) phase transition enthalpy ◦ was indeed included. We conclude that all data support a slight increase in ∆Hf,0 [Si(g)] to the 107.15±0.38 kcal/mol value proposed in the present work.

As a final note, we consider the performance of some ‘standard’ theoretical thermochemistry methods for this molecule, compared to our benchmark TAEe =573.92±0.22 kcal/mol.

As noted previously [46], G2 theory [47] fails dismally, underestimating TAE0 by 8.2 kcal/mol even as both spin-orbit splitting and scalar relativistics were neglected, which would together have increased the gap by a further 3.85 kcal/mol. G3 theory [48] represents a substantial improvement, being 2.2 kcal/mol below our value including spin-orbit corrections: applying the scalar relativistic correction to their value (or, equivalently, deleting it from our own calculation) would however increase that gap to a still substantial 4.1 kcal/mol. Interestingly, both CBS-Q and CBS-QB3 [49] predict much higher values, 576.0 and 577.0 kcal/mol, respectively. Neither value includes spin-orbit or relativistic corrections: upon applying them, we find that they underestimate our best result by only −1.8 and −0.8 kcal/mol, respectively. Finally, the W1 theory very recently proposed by Martin and de Oliveira [30] yields a value of 573.85 kcal/mol, only 0.07 kcal/mol below the present calibration result. (W1 theory includes both scalar relativistic and spin-orbit corrections as standard parts of the method.)

IV. CONCLUSIONS

From an exhaustive ab initio calibration study on the SiF4 molecule, we obtain a total atomization energy at 0 K of 565.89±0.22 kcal/mol. This value includes rather substantial scalar relativistic (−1.88 kcal/mol) and atomic spin-orbit (−1.97 kcal/mol) effects, as well as more minor effects of inner-shell correlation (−0.08 kcal/mol) and anharmonicity in the zero-point energy (+0.04 kcal/mol). In combination with experimentally very precisely ◦ known heats of formation of F(g) and SiF4 (g), we obtain ∆Hf,0 [Si(g)]=107.15±0.38 kcal/mol ◦ (∆Hf,298 [Si(g)]=108.19±0.38 kcal/mol). This confirms the suggestion of Grev and Schaefer [6] that the rather uncertain JANAF/CODATA value of 106.5±1.9 kcal/mol should be revised upward, albeit to about 1 kcal/mol lower than their suggested 108.1±0.5 kcal/mol.





The revision will be relevant for future computational studies on heats of formation of silicon compounds. Among standard computational thermochemistry methods, G2 and G3 theory exhibit large errors, while CBS-Q performs relatively well and the very recent W1 theory reproduces the present calibration result to 0.1 kcal/mol.

–  –  –

JM is a Yigal Allon Fellow, the incumbent of the Helen and Milton A. Kimmelman Career Development Chair (Weizmann Institute), and an Honorary Research Associate (“Onderzoeksleider in eremandaat”) of the National Science Foundation of Belgium (NFWO/FNRS).

This research was supported by the Minerva Foundation, Munich, Germany (JM), by the National Science Foundation (USA) through Cooperative Agreement DACI-9619020 and Grant No. CHE-9700627 (PRT), and by a grant of computer time from SDSC. The authors thank Drs. C. W. Bauschlicher Jr. and T. J. Lee (NASA Ames Research Center) as well as Drs. R.D. Johnson III, P.A.G. O’Hare, and particularly K. K. Irikura (NIST) for helpful discussions, and Victor Hazlewood for assistance with running the largest CCSD calculation reported here.

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[1] Martin, J. M. L.; Taylor, P. R.; J. Phys. Chem. A 1998, 102, 2995 [2] Cox, J.D.; Wagman, D.D.; Medvedev, V.A.; CODATA key values for thermodynamics;

Hemisphere: New York, 1989 [3] Storms, E.; Mueller, B.; J. Phys. Chem. 1977, 81, 318 [4] NIST-JANAF Thermochemical Tables, 4th Edition, Ed. M. W. Chase Jr., J. Phys.

Chem. Ref. Data Monograph 9 (1998).

[5] Desai, P. D.; J. Phys. Chem. Ref. Data 1986, 15, 967 [6] Grev, R. S.; Schaefer III, H. F.; J. Chem. Phys. 1992, 97, 8389 [7] Ochterski, J.A.; Petersson, G.A.; Wiberg, K.B.; J. Am. Chem. Soc. 1995, 117, 11299 [8] Collins, C. L.; Grev, R. S.; J. Chem. Phys. 1998, 108, 5465 [9] Samzow, R.; Heß, B. A.; Jansen, G.; J. Chem. Phys. 1992, 96, 1227 and references therein.

[10] Gunn, S. R.; Green, L. G.; J. Phys. Chem. 1961, 65, 779 [11] Rossini, F. D., et al., Circular of the National Bureau of Standards Nr. 500 (1952), quoted in Ref. [10].

[12] Johnson, G. K.; J. Chem. Thermodyn. 1986, 18, 801-802 [13] Wise, S. W.; Margrave, J. L.; Feder, H. M.; Hubbard, W. N.; J. Phys. Chem. 1963, 67, [14] Werner, H.-J.; Knowles, P. J.; MOLPRO 97.3, a package of ab initio programs, with contributions from Alml¨f, J.; Amos, R. D.; Berning, A.; Cooper, D. L.; Deegan, M.

o J. O.; Dobbyn, A. J.; Eckert, F.; Elbert, S. T.; Hampel, C.; Lindh, R.; Lloyd, A. W.;

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[15] Purvis III, G. D.; Bartlett, R. J.; J. Chem. Phys. 1982, 76, 1910 [16] Raghavachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gordon, M.; Chem. Phys. Lett.

157, 479 (1989) [17] Watts, J. D.; Gauss, J.; Bartlett, R. J.; J. Chem. Phys. 1993, 98, 8718 [18] Lee, T. J.; Taylor, P. R.; Int. J. Quantum Chem. Symp. 1989, 23, 199 [19] Lee, T. J.; Scuseria, G. E.; In Quantum mechanical electronic structure calculations with chemical accuracy; Langhoff, S. R., Ed.; Kluwer: Dordrecht, The Netherlands, 1995, pp.

47–108.

[20] Dunning Jr., T. H.; J. Chem. Phys. 1989, 90, 1007 [21] Woon, D. E.; Dunning Jr., T. H.; J. Chem. Phys. 1993, 98, 1358.

[22] Martin, J. M. L.; J. Chem. Phys. 1998, 108, 2791 [23] Bauschlicher Jr., C. W.; Partridge, H.; Chem. Phys. Lett. 1995, 240, 533 [24] Martin, J. M. L.; Uzan, O.; Chem. Phys. Lett. 1998, 282, 16 [25] Martin, J. M. L.; J. Phys. Chem. A 1998, 102, 1394 [26] In fact, it has been argued that SiF4 is best viewed as Si4+ (F− )4 : Gillespie, R. J.; J.

Chem. Educ. 1998, 75, 923-925 [27] Kendall, R. A.; Dunning, T. H.; Harrison, R. J.; J. Chem. Phys. 1992, 96, 6796 [28] Martin, J. M. L.; Chem. Phys. Lett. 1996, 259, 669 [29] McDowell, R. S.; Reisfeld, M. J.; Patterson, C. W.; Krohn, B. J.; Vasquez, M. C.;

Laguna, G. A.; J. Chem. Phys. 1982, 77, 4337–4343 [30] Martin, J. M. L.; de Oliveira, G.;, J. Chem. Phys., submitted.

[31] Martin, J. M. L.; Taylor, P. R.; Chem. Phys. Lett. 1994, 225, 473 [32] Martin, J. M. L.; Chem. Phys. Lett. 1995, 242, 343 [33] Cowan, R. D.; Griffin, M.; J. Opt. Soc. Am. 1976, 66, 1010 [34] Martin, R. L.; J. Phys. Chem. 1983, 87, 750 [35] Gdanitz, R. J.; Ahlrichs, R.; Chem. Phys. Lett. 1988, 143, 413 [36] Moore, C. E.;, Atomic energy levels, Natl. Bur. Stand. (US) Circ. 1949, 467.

[37] Heß, B. A.; Marian, C. M.; Peyerimhoff, S. D.; in Modern Electronic Structure Theory, Vol. 1, (Yarkony, D. R., Ed.); World Scientific, Singapore, 1995, p. 152–278.

[38] Martin, J. M. L.; in NATO ASI Symposium Volume Energetics of stable molecules and reactive intermediates (ed. M. E. Minas da Piedade), Kluwer, to appear in 1999.

[39] Feller, D.; J. Chem. Phys. 1992, 96, 6104 [40] Klopper, W.; Noga, J.; Koch, H.; Helgaker, T.; Theor. Chem. Acc. 1997, 97, 164-176 [41] Schwartz, C.; In Methods in Computational Physics 2; Alder, B. J., Ed.; Academic Press:

New York, 1963.

[42] W. Kutzelnigg and J. D. Morgan III, J. Chem. Phys. 1992, 96, 4484; erratum 1992, 97, 8821 [43] Halkier, A.; Helgaker, T.; Jørgensen, P.; Klopper, W.; Koch, H.; Olsen, J.; Wilson, A.

K.; Chem. Phys. Lett. 1998, 286, 243 [44] Ricca, A.; Bauschlicher Jr., C. W.; J. Phys. Chem. A 1998, 102, 876–880 [45] Bauschlicher Jr., C. W.; Partridge, H.; Chem. Phys. Lett. 1997, 276, 47–54 [46] Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Pople, J. A.; J. Chem. Phys. 1997, 106, 1063–1079 [47] Curtiss, L. A.; Raghavachari, K.; Trucks, G. W.; Pople, J. A.; J. Chem. Phys. 1991, 94, 7221 [48] Curtiss, L. A.; Raghavachari, K.; Redfern, P. C.; Rassolov, V.; Pople, J. A.; J. Chem.

Phys. 1998, 109, 7764–7776 [49] Ochterski, J. W.; Petersson, G. A.; Montgomery Jr., J. A.; J. Chem. Phys. 1996, 104, 2598 and references therein.

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