Erratum: “On asymptotic behavior of density functional theory” [J. Chem. Phys. 139, 024104 (2013)]

Assessment of SAPT(DFT) with meta-GGA functionals

This work examines the suitability of meta-GGA functionals for symmetry-adapted perturbation theory (SAPT) calculations. The assessment is based on the term-by-term comparison with the benchmark SAPT variant based on coupled-cluster singles and doubles description of monomers, SAPT(CCSD). Testing systems include molecular complexes ranging from strong to weak and the He dimer. The following nonempirical meta-GGAs are examined: TPSS, revTPSS, MVS, SCAN, and SCAN0 with and without the asymptotic correction (AC) of the exchange-correlation potential. One range-separated meta-GGA functional, LC-PBETPSS, is also included. The AC-corrected pure meta-GGAs (with the exception of MVS) represent a definite progress in SAPT(DFT) compared to pure GGA, such as PBEAC, with their more consistent predictions of energy components. However, none of the meta-GGAs is better than the hybrid GGA approach SAPT(PBE0AC). The SAPT(DFT) electrostatic energy offers the most sensitive probe of the quality of the underlying DFT density. Both SCAN- and TPSS-based electrostatic energies agree with reference to within 5% or better which is an excellent result. We find that SCAN0 can be used in SAPT without the AC correction. The long-range corrected LC-PBETPSS is a reliable performer both for the components and total interaction energies.

Do Semilocal Density-Functional Approximations Recover Dispersion Energies at Small Intermonomer Separations?

The methods that add dispersion energies to interaction energies computed using density-functional theory (DFT), known as DFT+D methods, taper off the dispersion energies at distances near van der Waals minima and smaller based on an assumption that DFT starts to reproduce the dispersion energies there. We show that this assumption is not correct as the alleged contribution behaves unphysically and originates to a large extent from nonexchange-correlation terms. Thus, dispersion functions correct DFT in this region for deficiencies unrelated to dispersion interactions.

Evaluation of the Factors Impacting the Accuracy of 13C NMR Chemical Shift Predictions using Density Functional Theory-The Advantage of Long-Range Corrected Functionals

The various factors influencing the accuracy of ¹³C NMR calculations using density functional theory (DFT), including the basis set, exchange-correlation (XC) functional, and isotropic shielding calculation method, are evaluated. A wide selection of XC functionals (over 70) were considered, and it was found that long-range corrected functionals offer a significant improvement over the other classes of functionals. Based on a thorough study, it is recommended that for calculating NMR chemical shifts (δ) one should use the CSGT method, the COSMO solvation model, and the LC-TPSSTPSS exchange-correlation functional in conjunction with the cc-pVTZ basis set. A selection of problems in natural product identification are considered in light of the newly recommended level of theory.

Determination of structure and properties of molecular crystals from first principles

CONSPECTUS: Until recently, it had been impossible to predict structures of molecular crystals just from the knowledge of the chemical formula for the constituent molecule(s). A solution of this problem has been achieved using intermolecular force fields computed from first principles. These fields were developed by calculating interaction energies of molecular dimers and trimers using an ab initio method called symmetry-adapted perturbation theory (SAPT) based on density-functional theory (DFT) description of monomers [SAPT(DFT)]. For clusters containing up to a dozen or so atoms, interaction energies computed using SAPT(DFT) are comparable in accuracy to the results of the best wave function-based methods, whereas the former approach can be applied to systems an order of magnitude larger than the latter. In fact, for monomers with a couple dozen atoms, SAPT(DFT) is about equally time-consuming as the supermolecular DFT approach. To develop a force field, SAPT(DFT) calculations are performed for a large number of dimer and possibly also trimer configurations (grid points in intermolecular coordinates), and the interaction energies are then fitted by analytic functions. The resulting force fields can be used to determine crystal structures and properties by applying them in molecular packing, lattice energy minimization, and molecular dynamics calculations. In this way, some of the first successful determinations of crystal structures were achieved from first principles, with crystal densities and lattice parameters agreeing with experimental values to within about 1%. Crystal properties obtained using similar procedures but empirical force fields fitted to crystal data have typical errors of several percent due to low sensitivity of empirical fits to interactions beyond those of the nearest neighbors. The first-principles approach has additional advantages over the empirical approach for notional crystals and cocrystals since empirical force fields can only be extrapolated to such cases. As an alternative to applying SAPT(DFT) in crystal structure calculations, one can use supermolecular DFT interaction energies combined with scaled dispersion energies computed from simple atom-atom functions, that is, use the so-called DFT+D approach. Whereas the standard DFT methods fail for intermolecular interactions, DFT+D performs reasonably well since the dispersion correction is used not only to provide the missing dispersion contribution but also to fix other deficiencies of DFT. The latter cancellation of errors is unphysical and can be avoided by applying the so-called dispersionless density functional, dlDF. In this case, the dispersion energies are added without any scaling. The dlDF+D method is also one of the best performing DFT+D methods. The SAPT(DFT)-based approach has been applied so far only to crystals with rigid monomers. It can be extended to partly flexible monomers, that is, to monomers with only a few internal coordinates allowed to vary. However, the costs will increase relative to rigid monomer cases since the number of grid points increases exponentially with the number of dimensions. One way around this problem is to construct force fields with approximate couplings between inter- and intramonomer degrees of freedom. Another way is to calculate interaction energies (and possibly forces) "on the fly", i.e., in each step of lattice energy minimization procedure. Such an approach would be prohibitively expensive if it replaced analytic force fields at all stages of the crystal predictions procedure, but it can be used to optimize a few dozen candidate structures determined by other methods.