An accurate description of the Bergman reaction using restricted and unrestricted DFT:: Stability test, spin density, and on-top pair density

被引:253
作者
Gräfenstein, J [1 ]
Hjerpe, AM [1 ]
Kraka, E [1 ]
Cremer, D [1 ]
机构
[1] Univ Gothenburg, Dept Theoret Chem, S-41320 Gothenburg, Sweden
关键词
D O I
10.1021/jp993122q
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
DFT calculations provide a reliable description of the Bergman reaction of(Z)-hex-3-ene-1,5-diyne 1 provided the following are considered. (a) Restricted DFT (RDFT) calculations along the reaction path have to be replaced by unrestricted DFT (UDFT) calculations at those locations where the former description becomes unstable. This is the case in the region of the p-didehydrobenzene biradical 2, which possesses significant multireference character. (b) LSD and pure GGA functionals are more stable than hybrid functionals, which can be directly related to the composition of these functionals. With increasing instability, RDFT calculations lead to increasing errors in the S-T splitting and the geometry of 2 as well as in the energetics of the Bergman reaction. (c) LSD and CCA Functionals underestimate the energy barrier of the Bergman reaction of 1. This becomes obvious when the correct experimental barrier is considered, which was not clone in previous DFT investigations. (d) The best description of the Bergman reaction is provided by a mixed RDFT/UDFT description using the B3LYP functional (average error of 2.7 kcal/mol). Although the B3LYP functional is rather unstable, its semiempirical calibration helps to compensate for the typical underestimation of barriers by GGA functionals, which demonstrates chat the performance of a hybrid functional does not necessarily have to do with its stability. (e) Application of the sum formula to the UB3LYP energy of biradical 2 improves the description of the Bergman reaction so that the most reliable data are obtained at RB3LYP-UB3LYP(sum)/G-311+G(3df,3pd). Activation enthalpies at 470 K for forward and backward reaction are 29.9 and 21.4 kcal/mol, respectively (exptl values, 28.23 +/- 0.5 and 19.75 +/- 0.7 kcal/mol), while the calculated reaction enthalpy at 298 K is 8.5 kcal/mol (exptl value, 8.5 +/- 1.0 kcal/mol) in reasonable agreement with experiment. The calculated S-T splitting is 2.6 kcal/mol (after correction, 4.9 kcal/mol; exptl value, 3.8 +/- 0.5 kcal/mol at 298 K). It is shown that the UDFT description covers static correlation effects needed for the correct treatment of 2S. Total and on-top pair density reflect this, while Kohn-Sham orbitals and spin density have to be considered as physically not meaningful intermediates in line with the interpretation given by Perdew, Savin, and Burke (Phys. Rev. A 1995, 51, 4531).
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页码:1748 / 1761
页数:14
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