B3LYP-MM A Posteriori-Corrected Functional

Recently, a number of functionals augmented with the so-called a posteriori corrections have been developed. These functionals respond to the need for a greater accuracy in computing non-covalent interactions with DFT (the popular functional B3LYP, as it is well-known, largely neglects van der Waals interactions). In contrast to the functionals in which non-covalent interactions are accounted for in the functional through a modified dependence on electronic density (such as M06-2X), the a posteriori-corrected functionals add empirical corrections to the energy (and possibly other properties) after it has been computed with regular DFT. These empirical corrections typically depend on the Cartesian coordinates of atoms, and the types of atoms, rather than the electronic density of the system, and are therefore reminiscent of corrections used in molecular mechanics methods. The simplicity of the implementation, a negligible computational cost associated with these corrections, and a much higher resultant accuracy compensate for the burden of having to parametrize these corrections for different atom and non-covalent interaction types.

Jaguar includes B3LYP-MM, an a posteriori-corrected functional parametrized on a gigantic data set of complexes that involve non-covalent interactions [82]. This functional has been shown to be more accurate for describing the energetics of van-der-Waals, hydrogen-bonded, and cation-pi interactions than B3LYP-D3 and M06-2X which also account for these types of interactions. The energy predicted by B3LYP-MM is made up of two components: the regular B3LYP energy and the MM-like correction. The latter comprises three parts:

  • Lennard-Jones-like correction to account for dispersion and induction effects (eq. (2) in [82])

  • Hydrogen bond correction to account for explicit hydrogen bonds energetics (eq. (5) in [82])

  • Cation-pi correction to account for cation-pi interactions (eq. (6) in [82])

Use of B3LYP-MM has the following limitations in the current implementation:

  • It is parametrized for two basis sets only, LACVP* and cc-pVDZ++. The latter basis set gives slightly more accurate interaction energies, according to the benchmarks.

  • The Lennard-Jones-like correction is available only for the elements H, C, N, O, F, S, Cl, and Br. The job will fail if the structure contains other elements. Positively-charged metal atoms, for which the Lennard-Jones-like correction is not computed, are not subject to this limitation. You can, however, set fall_through=1 in the gen section to compute the corrections for only the parametrized elements and set them to zero for any other elements, rather than having the job fail.

  • The cation-pi correction is computed for transition-metal ions, but was not parametrized with these ions. B3LYP-MM should be used with caution in such cases.

The B3LYP-MM functional corrections have been optimized in such a way that they already include the counterpoise (CP) correction which is needed to compensate for the basis set superposition error (BSSE). To compute the interaction energy of a complex X-Y with B3LYP-MM and correct for the BSSE, simply compute the energy of the individual fragments X and Y, and the energy of the complex X-Y, and take the difference.

If you would still like to apply the CP correction (as described in Counterpoise Calculations), B3LYP-MM has parameters that do not absorb the CP correction, and therefore, do not account for BSSE. To enable these parameters, set cpoise=1 in the input file. The explicit CP corrections (when cpoise=1) give slightly better interaction energies than the default implicit CP corrections (cpoise=0).

To use the B3LYP-MM functional, select B3LYP-MM from the Theory selector in the Input tab, or set dftname=b3lyp-mm in the gen section.

B3LYP-MM cannot be used for transition state searches.