Empirical correction of nondynamical correlation energy for density functionals

Wanyi Jiang, Chris C. Jeffrey, and Angela K. Wilson J. Phys. Chem. A 2012, 116, 9969 (Paywall)
Contributed by Grant Hill.

The inability of common density functionals to correctly account for dispersion interactions has been addressed in a number of ways, but the most popular method is to add an empirical dispersion correction to the DFT energy [1]. In this paper, Wilson and co-workers propose an empirical correction for nondynamic correlation that operates in a superficially similar way.

If one defines nondynamic correlation as the significant contribution of several electronic configurations to the total energy of a system, it can be seen that this type of correlation becomes important for a number of chemically relevant situations, including the breaking of covalent bonds. Some of the methods typically used to recover nondynamic correlation include CASSCF and MRCI, with the common theme that they quickly become expensive in terms of computational cost, and that a degree of expertise is required in the choice of which orbitals and electrons to include in the active space of nondynamic correlation. The method proposed attempts to bypass these difficulties by carrying out a standard DFT calculation, then adding a correction for nondynamic correlation (with an empirical scale factor) via a CASCI calculation including a small set of orbitals in the active space. The authors suggest that this choice of orbitals can be automated, producing a computationally efficient black-box method.

The initial results indicate that the method performs well for the torsion of ethylene and automerization of cyclobutadiene, yet when investigating barrier heights it seems that the best results are produced when only the transition state is empirically corrected. The results presented suggest that the method is worthy of further investigation, and I for one would be very interested to see if how it performs for spin-state splittings of transition metal complexes [2].

References
[1] See S. Grimme, J. Antony, S. Ehrlich, and H. Krieg J. Chem. Phys. 2010, 132, 154104 and references therein.
[2] For a perspective on spin-state splittings in bio-inorganic systems see M. Swart Int. J. Quantum Chem. 2012, DOI: 10.1002/qua.24255