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High-accuracy extrapolated ab initio thermochemistry. II. Minor improvements to the protocol and a vital simplification
2.J. M. L. Martin, (private communication).
5.A. Tajti, P. G. Szalay, A. G. Császár, M. Kállay, J. Gauss, E. F. Valeev, B. A. Flowers, J. Vázquez, and J. F. Stanton, J. Chem. Phys. 121, 11599 (2004).
6.As is well appreciated, “experimental” enthalpies of formation for most molecules do not come from a single experiment. Instead, the best values usually come from taking several experimental results into consideration in a critical data evaluation.
7.G. von Laszewski, B. Ruscic, P. Wagstrom et al., in Lecture Notes in Computer Science, edited by M. Parashar (Springer, Berlin, 2002), Vol. 2536, pp. 25–38;
7.B. Ruscic, R. E. Pinzon, M. L. Morton, G. von Laszevski, S. J. Bittner, S. G. Nijsure, K. A. Amin, M. Minkoff, and A. F. Wagner, J. Phys. Chem. A 108, 9979 (2004).
8.The term theoretical model chemistry was coined by People and is given to an approach in which all molecules are treated at a specific and consistent level of theory.
10.L. V. Gurvich, I. V. Veyts, and C. B. Alcock, Thermodynamic Properties of Individual Substances, 4th ed. (Hemisphere, New York, 1989).
11.Well-known tabulations of molecular enthalpies of formation include M. W. Chase, Jr., J. Phys. Chem. Ref. Data 6, 27 (1998).
12.B. Ruscic, M. Kállay, A. G. Császár, and J. F. Stanton (unpublished)
13.G. Tasi, R. Izsák, G. Matisz, A. G. Császár, M. Kállay, B. Ruscic, and J. F. Stanton, Angew. Chem., Int. Ed. Ed. (submitted).
14.W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Molecular Orbital Theory (Wiley, New York, 1986), p. 298.
21.R. D. Cowan and M. Griffin, J. Opt. Soc. Am. 66, 1010 (1976);
24.I. M. Mills, in Modern Spectroscopy: Modern Research, edited by K. N. Rao and C. W. Matthews (Academic, New York, 1972), pp. 115–140.
25.An error appears in note 62 of the original paper, in which it is stated that ROHF calculations were also used for the CN molecule. The numbers in the tables, however, are based on the ZPE calculated from UHF for CN. In this paper, the ROHF results are used.
30.Numerical results from all three implementations appear to agree with each other, and a sum-over-states direct summation program [J. Vázquez and J. F. Stanton, Mol. Phys. 104, 377 (2006)]. The correct equation isSee Ref. 5 for a definition of the symbols in this equation. In Ref. 5, the fifth and sixth terms were in error. Furthermore, the kinetic energy elements in Ref. 28 were in error, which was addressed to some degree in Ref. 27.
31.This is true, of course, for full configuration interaction wave functions and tends to be an excellent approximation for coupled-cluster methods of all types that include single excitations. Nevertheless, this assumption remains as an undesirable approximation of our original work and is rectified here.
33.J. Vázquez, J. F. Stanton, and J. M. L. Martin (unpublished)..
36.S. E. Wheeler, K. A. Robertson, W. D. Allen, H. F. Schaefer, Y. J. Bomble, and J. F. Stanton (unpublished).
37.A strong Fermi resonance exists in CO2 between and , which results in a large value of when calculated according to the formula in Ref. 30. However, one may alternatively skip the corresponding resonance denominator, which affects the ZPE calculated from the term level expression without as well as itself (the total ZPE, of course, is not affected by resonances between excited vibrational levels). In either case, the total zero-point energies are the same. The contribution for CO2 in Table I is calculated with the corresponding resonance denominator omitted, as was the ZPE given in Ref. 5.
38.Alternatives to CCSDT(Q) for the approximate treatment of quadruple excitations include the CCSDT[Q], , CCSDTQ-1a, CCSDTQ-1b, CC4, and CCSDTQ-3 schemes (see Ref. 35), of which the first two are, in fact, slightly cheaper to apply than the others. Numerical tests indicate that for total energies, the , CCSDTQ-1b, and CC4 approaches perform better than CCSDT(Q), while performance of the CCSDTQ-3 method is perhaps comparable (see Ref. 35). The CCSDT[Q] and the CCSDTQ-1a methods, on the other hand, are less accurate than any of these approaches. rms errors of the calculated heats of formation for the dataset were also evaluated using all of these methods and found to be (in ) 1.17 (CCSDT[Q]), 0.31 , 1.12 (CCSDTQ-1a), 0.32 ( CCSDTQ-1b), 0.33 (CC4), and 0.69 (CCSDTQ-3). The conclusions concerning the performance of the approximate quadruples methods for heats of formation are similar to those for total energies; however, the difference between CCSDT(Q) and the more expensive methods is, ultimately, negligible (their use is consequently not justified). We note in passing that heats of formation were also computed using CCSDTQ as well as the aforementioned approximate methods with the cc-pVTZ basis set. However, no significant improvement has been achieved with respect to the experimental values, meaning that again the extra computational cost is not justified.
39.It is interesting to note that both the HF-SCF and CCSD(T) energies extrapolated with the 345 sequence are more negative than their 456 counterparts, although the former extrapolation tends to give smaller atomization energies in one case (HF-SCF) and larger in the other (CCSD(T)). The latter is rather obvious and sensible: correlation energy always tends to increase atomization energies, and a method that tends to overestimate correlation energies would tend to overestimate binding energies, if the extrapolation error were somewhat systematic. However, for the HF-SCF cases, the extrapolation error (as measured by the difference between 345- and 456-based extrapolations) is larger for free atoms than those in molecules in the cases we have investigated, which is in turn responsible for the underestimated atomization energies. Differences between 345- and 456-based extrapolations(in ) are 269 (oxygen atom), 111 (nitrogen atom), 35 (carbon atom), 22 (hydrogen atom) [atoms], 239 (OH), 109 (CN), and 190 (CO). It is interesting, indeed a bit odd, that the error for the oxygen atom is the largest.
40.Experimental ZPE was calculated using Eq. (5) and experimental values for , , the equilibrium rotational constant, and the rotation-vibration interaction constant, [M. W. Chase, Jr., J. Phys. Chem. Ref. Data 6, 27 (1998)]..
42.In many cases, vibrational frequencies are slightly overestimated in cc-pVQZ calculations, with a consequent overestimation of the zero-point energy.
43.B. Ruscic (private communication); unpublished results from Active Thermochemical Tables ver. 1.25 using the Core (Argonne) Thermochemical Network ver. 1.048..
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