Benchmark calculations of chemical reactions in density functional theory: Comparison of the accurate Kohn–Sham solution with generalized gradient approximations for the H2+H and H2+H2 reactions

Abstract

The Kohn-Sham ͑KS͒ solution is constructed from an accurate CI density and the KS exchange and correlation energies E x and E c , as well as the corresponding exchange and exchange-correlation energy densities ⑀ x (r) and ⑀ xc (r), which are obtained for the hydrogen abstraction reaction HϩH 2 and the symmetrical four-center exchange reaction H 2 ϩH 2 . The KS quantities are compared with those of the standard GGAs. Comparison shows that the GGA exchange functional represents both exchange and molecular nondynamical left-right correlation, while the GGA correlation functional represents only the dynamical part of the correlation. This role of the GGA exchange functional is especially important for the transition states ͑TS͒ of the reactions where the left-right correlation is enhanced. Standard GGAs tend to underestimate the barrier height for the reaction HϩH 2 and to overestimate it for the reaction H 2 ϩH 2 . For H 2 ϩH 2 the Kohn-Sham orbital degeneracy in the square TS is represented with an equi-ensemble KS solution for both accurate KS/CI and GGA, while near the TS ensemble solutions with unequal occupations of the degenerate highest occupied orbitals are obtained. For the GGA ensemble solution a special ensemble formula for the GGA exchange functional is proposed. Application of this formula to the H 2 ϩH 2 reaction reduces appreciably the reaction barriers calculated with GGAs and leads to much better agreement with the accurate value. The too low GGA barriers for the HϩH 2 reaction are attributed to overestimation of the dynamical correlation in the TS by the GGA correlation functionals. In order to correct this error, it is recommended to modify the dependence of the approximate correlation functionals on the local polarization with the purpose of reducing the approximate correlation energy for intermediate values, which are expected to characterize the TS's of radical abstraction reactions.

Perspective: Fifty years of density-functional theory in chemical physics

“…204 It is not possible to represent the D 4h density of the open-shell square H 4 structure, or structures near it, without fractional occupancies. 202,204 The B13 barrier of 141.2 kcal/mol in this H 4 system (unpublished) is in fair agreement with the high-level WFT barrier 202 of 147.6 kcal/mol. A few other B13 avoided-crossing barriers can be found in the very recent Ref.…”

“…An excellent discussion of the energy surface of the prototypical H 4 system, with an avoided-crossing transition state at the square geometry, can be found in Ref. 202. Fractional occupancies 202,203 are implicated in this and other avoided-crossing problems.…”

“…202. Fractional occupancies 202,203 are implicated in this and other avoided-crossing problems. 204 It is not possible to represent the D 4h density of the open-shell square H 4 structure, or structures near it, without fractional occupancies.…”

Hartree–Fock orbitals significantly improve the reaction barrier heights predicted by semilocal density functionals

“…HCTH407 is parametrized to a data set including accurate 1e-SIE-free XC potentials of atoms and small molecules and thus presumably incorporates some sort of effective 1e-SIC. 32,33 In this context, we note that Baerends and co-workers found that semilocal DFT calculations using accurate ab initio electronic structures significantly underestimate hydrogen transfer 50 and nucleophilic substitution 51 reaction barriers, with results comparable to self-consistent semilocal DFT. Despite this, the post-X results of Table III indicate that a more general principle is at work.…”

Broken symmetry in density-functional theory: Analysis and cure

“…We believe that the presented approach shows to be useful for many applications of DFT, especially for molecules, where the calculations of chemical reactions have observed similar problems of basic DFT. 10 More details and comparisons with other ensemble DFT approaches are left for forthcoming studies.…”