The Good, the Bad, and the Ugly: Pseudopotential Inconsistency Errors in Molecular Applications of Density Functional Theory

The Use of Effective Core Potentials with Multiconfiguration Pair-Density Functional Theory

The reliable and accurate prediction of chemical properties is a key goal in quantum chemistry. Transition-metal-containing complexes can often pose difficulties to quantum mechanical methods for multiple reasons, including many electron configurations contributing to the overall electronic description of the system and the large number of electrons significantly increasing the amount of computational resources required. Often, multiconfigurational electronic structure methods are employed for such systems, and the cost of these calculations can be reduced by the use of an effective core potential (ECP). In this work, we explore both theoretical considerations and performances of ECPs applied in the context of multiconfiguration pair-density functional theory (MC-PDFT). A mixed-basis set approach is used, using ECP basis sets for transition metals and all-electron basis sets for nonmetal atoms. We illustrate the effects that an ECP has on the key parameters used in the computation of MC-PDFT energies, and we explore how ECPs affect the prediction of physical observables for chemical systems. The dissociation curve for a metal dimer was explored, and ionization energies for transition metal-containing diatomic systems were computed and compared to experimental values. In general, we find that ECP approaches employed with MC-PDFT are able to predict ionization energies with improved accuracy compared to traditional Kohn-Sham density functional theory approaches.

A remarkably simple dispersion damping scheme and the DH24 double hybrid density functional

In recent papers, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] and then Becke [J. Chem. Phys. 159, 241101 (2023)] have developed a novel double hybrid density functional, "DH23," whose terms are based on good local physics. Its 12 coefficients are trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.73 kcal/mol for the revDH23 variant). Here, we simplify DH23 by introducing a dispersion damping scheme involving atomic numbers only and one global parameter. The resulting new functional, "DH24," performs as well as its predecessors.

Doubling down on density-functional theory

In a recent paper, Becke et al. [J. Chem. Phys. 158, 151103 (2023)] presented a novel double hybrid density functional, "DH23," whose terms are based on good physics. Its 12 coefficients were trained on the GMTKN55 (general main-group thermochemistry, kinetics, and noncovalent interactions) chemical database of Goerigk et al. [Phys. Chem. Chem. Phys. 19, 32184 (2017)]. The lowest GMTKN55 "WTMAD2" error to date for any hybrid or double hybrid density functional was obtained (1.76 kcal/mol). Here, we make some revisions to DH23 and test its efficacy on reference data beyond GMTKN55, namely, organometallic reaction energies and barrier heights. The results confirm that DH23 is robust outside its training set. In the process, a slightly smaller GMTKN55 WTMAD2 of 1.73 kcal/mol is achieved.

Error of relativistic effective core potentials for closed-shell diatomic molecules of p-block heavy and superheavy elements in DFT and TDDFT calculations

Pseudopotentials (PP) are extensively used in electronic structure calculations, particularly for molecules containing heavy elements. Parameters in PPs are mainly determined from ab initio results, and errors of such PPs in density functional theory (DFT) calculations have been studied previously. However, PP errors on results with spin-orbit coupling and those in time-dependent DFT (TDDFT) calculations have not been reported previously. In this work, we investigate the error of the small-core energy-consistent Stuttgart/Koln pseudopotentials in DFT and TDDFT calculations with and without spin-orbit coupling. Ground state bond lengths, harmonic frequencies, dissociation energies, and vertical excitation energies for a series of closed-shell diatomic heavy and superheavy p-block molecules are calculated using several popular exchange-correlation functionals. PP errors are estimated by comparing with results using the all-electron Dirac-Coulomb (-Gaunt) Hamiltonian. Our results show that the difference between ground state properties and most excitation energies in scalar-relativistic calculations with the PP and those of all-electron calculations is quite small. This difference becomes somewhat larger when spin-orbit coupling (SOC) is present, especially for properties that are affected by SOC to some extent. In addition, the errors of the PPs are insensitive to the employed exchange-correlation functionals in most cases. Our results indicate that reasonable DFT and TDDFT results can be obtained using the small-core energy-consistent Stuttgart/Koln pseudopotentials for heavy and super-heavy p-block molecules.

Greater transferability and accuracy of norm-conserving pseudopotentials using nonlinear core corrections

We present an investigation into the transferability of pseudopotentials (PPs) with a nonlinear core correction (NLCC) using the Goedecker, Teter, and Hutter (GTH) protocol across a range of pure GGA, meta-GGA and hybrid functionals, and their impact on thermochemical and non-thermochemical properties. The GTH-NLCC PP for the PBE density functional demonstrates remarkable transferability to the PBE0 and ωB97X-V exchange-correlation functionals, and relative to no NLCC, improves agreement significantly for thermochemical benchmarks compared to all-electron calculations. On the other hand, the B97M-rV meta-GGA functional performs poorly with the PBE-derived GTH-NLCC PP, which is mitigated by reoptimizing the NLCC parameters for this specific functional. The findings reveal that atomization energies exhibit the greatest improvements from use of the NLCC, which thus provides an important correction needed for covalent interactions relevant to applications involving chemical reactivity. Finally we test the NLCC-GTH PPs when combined with medium-size TZV2P molecularly optimized (MOLOPT) basis sets which are typically utilized in condensed phase simulations, and show that they lead to consistently good results when compared to all-electron calculations for atomization energies, ionization potentials, barrier heights, and non-covalent interactions, but lead to somewhat larger errors for electron affinities.