Semiempirical hybrid density functional with perturbative second-order correlation

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Abstract
A new hybrid density functional for general chemistry applications is proposed. It is based on a mixing of standard generalized gradient approximations (GGAs) for exchange by Becke (B) and for correlation by Lee, Yang, and Parr (LYP) with Hartree-Fock (HF) exchange and a perturbative second-order correlation part (PT2) that is obtained from the Kohn-Sham (GGA) orbitals and eigenvalues. This virtual orbital-dependent functional contains only two global parameters that describe the mixture of HF and GGA exchange (ax) and of the PT2 and GGA correlation (c), respectively. The parameters are obtained in a least-squares-fit procedure to the G2∕97 set of heat of formations. Opposed to conventional hybrid functionals, the optimum ax is found to be quite large (53% with c=27%) which at least in part explains the success for many problematic molecular systems compared to conventional approaches. The performance of the new functional termed B2-PLYP is assessed by the G2∕97 standard benchmark set, a second test suite of atoms, molecules, and reactions that are considered as electronically very difficult (including transition-metal compounds, weakly bonded complexes, and reaction barriers) and comparisons with other hybrid functionals of GGA and meta-GGA types. According to many realistic tests, B2-PLYP can be regarded as the best general purpose density functional for molecules (e.g., a mean absolute deviation for the two test sets of only 1.8 and 3.2kcal∕mol compared to about 3 and 5kcal∕mol, respectively, for the best other density functionals). Very importantly, also the maximum and minium errors (outliers) are strongly reduced (by about 10–20kcal∕mol). Furthermore, very good results are obtained for transition state barriers but unlike previous attempts at such a good description, this definitely comes not at the expense of equilibrium properties. Preliminary calculations of the equilibrium bond lengths and harmonic vibrational frequencies for diatomic molecules and transition-metal complexes also show very promising results. The uniformity with which B2-PLYP improves for a wide range of chemical systems emphasizes the need of (virtual) orbital-dependent terms that describe nonlocal electron correlation in accurate exchange-correlation functionals. From a practical point of view, the new functional seems to be very robust and it is thus suggested as an efficient quantum chemical method of general purpose.