Benchmark Database of Barrier Heights for Heavy Atom Transfer, Nucleophilic Substitution, Association, and Unimolecular Reactions and its Use to Test Theoretical Methods

Abstract

A benchmark database of forward and reverse barrier heights for 19 non-hydrogen-transfer reactions has been developed by using Weizmann 1 calculations, and 29 DFT methods and 6 ab initio wave-function theory (WFT) methods have been tested against the new database as well as against an older database for hydrogen atom transfer reactions. Among the tested hybrid DFT methods without kinetic energy density, MPW1K is the most accurate model for calculations of barrier heights. Among the tested hybrid meta DFT methods, BB1K and MPWB1K are the two most accurate models for the calculations of barrier heights. Overall, the results show that BB1K and MPWB1K are the two best DFT methods for calculating barrier heights, followed in order by MPW1K, MPWKCIS1K, B1B95, MPW1B95, BHandHLYP, B97-2, mPW1PW91, and B98. The popular B3LYP method has a mean unsigned error four times larger than that of BB1K. Of the methods tested, QCISD(T) is the best ab initio WFT method for barrier height calculations, and QCISD is second best, but QCISD is outperformed by the BB1K, MPWB1K, MPWKCIS1K, and MPW1K methods. 1. Introduction Density-functional theory (DFT) methods 1-59 have been shown to be more efficient than wave-function theory (WFT) methods for computational thermochemistry and thermochemical kinetics due to their excellent cost-to-performance ratio. However pure DFT methods overestimate bond energies and underestimate barrier heights (BHs) for chemical reactions. One of the practical ways to tackle this problem is to use hybrid DFT 11 (mixing Hartree-Fock (HF) theory with Kohn-Sham DFT at the level of the Fock-Kohn-Sham operator). Hybrid DFT methods can be justified theoretically by the adiabatic connection theorem (ACT). 56 Nevertheless the most popular hybrid DFT method, B3LYP, 6,11,12 is only parametrized against a data set for thermochemistry, and it significantly underestimates BHs. The first successful hybrid DFT model for thermochemical kinetics was MPW1K. 30 It was parametrized against a database of 44 BHs of 22 reactions, 21 of which are hydrogentransfer (HT) reactions. This database of BHs was updated later as BH44/3 (one part of Database/3), 42,57 BH42/04, 50,53,58 and HTBH38/04 59 by taking into account some new experimental and theoretical results in the literature and by leaving out data that are not reliable or that are not for HT reactions. This database was successfully employed in conjunction with other databases to parametrize or test some new methods such as multicoefficient correlation methods (MCCM/3), 57 hybrid meta DFT methods (BB1K, 50 MPWB1K, 53 and TPSS1KCIS, 59 where "meta" means that the hybrid density functional also depends on the Kohn-Sham orbitals in the form of a kinetic energy density), and multi-coefficient extrapolated DFT methods (MC3BB, 58 MC3MPW, 58 and a suite of methods in a previous paper 59). Since this database mainly consists of BHs for HT reactions, and in its current form, HTBH38/04, it contains only HT BHs, one of the goals of the present paper is to develop a database of BHs for non-HT ...

SCAN-based hybrid and double-hybrid density functionals from models without fitted parameters

“…Work in this direction is in progress. and double-hybrid density functionals for the 223 atomization energies (AEs) of the G3/99 set [56][57][58], the 40 ionization potentials (IPs), 25 electron affinities (EAs), and 8 proton affinities (PAs) of the G2-1 set [59], the 76 barrier heights of the NHTBH38/04 and HTBH38/04 sets [60,61], the 22 noncovalent interactions of the S22 set [62,63], and the 66 noncovalent interactions of the S66 set [64]. …”

Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections

“…[18], that contains 412 accurate experimental and accurate theoretical results, including the 18 atomic energies from the H atom to the Ar atom [44], the atomization energies (AEs) of the G3/99 set [45][46][47] (223 molecules), the ionization potentials (IPs) of the G2-1 set [48] (40 molecules, excluding SH 2 ( 2 A 1 ) and N 2 ( 2 Π) cations due to the known convergence problems for semilocal density functionals [46]), the electron affinities (EAs) of the G2-1 set (25 molecules), the proton affinities (PAs) of the G2-1 set (8 molecules), the 76 barrier heights (BHs) of the NHTBH38/04 and HTBH38/04 sets [49,50], and the 22 non-covalent interactions of the S22 set [51]. To prevent the double-counting of total energy from the KS-DFT and the dispersion corrections, all the parameters in ωB97X-D, are determined self-consistently by a leastsquares fitting procedure described in Ref.…”

“…To test the performance of ωB97X-D outside its training set, we also evaluate its performance on various test sets involving the additional 48 atomization energies in the G3/05 test set [56] (other than the 223 atomization energies in the G3/99 test set [45][46][47]), 30 chemical reaction energies taken from the NHTBH38/04 and HTBH38/04 databases [49,50], 29 non-covalent interactions [51,57], 166 optimized geometry properties of covalent systems [58], 12 intermolecular bond lengths [51] and one long-range charge transfer excitation curve of two well-separated molecules. There are a total of 286 pieces of data in the test sets.…”

Assessment of a Middle-Range Hybrid Functional

“…33 Geometries of all species as well as the best estimates for the experimental barrier heights are taken from ref 33.…”