Performance of Gradient-Corrected and Hybrid Density Functional Theory: Role of the Underlying Local Density Approximation and the Gradient Correction

Limiting factors in the accuracy of DFT calculation for redox potentials

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Assessment of DFT Methods for Transition Metals with the TMC151 Compilation of Data Sets and Comparison with Accuracies for Main-Group Chemistry

In the present study, we have gathered a collection (that we term TMC151) of accurate reference data for transition-metal reactions for the assessment of quantum chemistry methods. It comprises diatomic dissociation energies and reaction energies and barriers for prototypical transition-metal reactions. Our assessment of a diverse range of different types of DFT methods shows that the most accurate functionals include ωB97M-V, ωB97X-V, MN15, and B97M-rV. Notably, they have also been previously validated to be highly robust for main-group chemistry. Nevertheless, even these methods show substantially worse accuracies for transition metals than for main-group chemistry. For less accurate methods, there is not a good correlation between their accuracies for main-group and transition-metal chemistries. Thus, in the development of new DFT, it is important to assess the accuracies for both types of data. In this regard, we have formulated the TMC34 model for efficient assessment of the performance for transition metals, which complements our previously developed MG8 model for main-group chemistry. Together, they provide a cost-effective means for initial assessment of new methodologies.

How to computationally calculate thermochemical properties objectively, accurately, and as economically as possible

We have developed the WnX series of quantum chemistry composite protocols for the computation of highly-accurate thermochemical quantities with advanced efficiency and applicability. The W1X-type methods have a general accuracy of ~3–4 kJ mol−1 and they can currently be applied to systems with ~20–30 atoms. Higher-level methods include W2X, W3X and W3X-L, with the most accurate of these being W3X-L. It can be applied to molecules with ~10–20 atoms and is generally accurate to ~1.5 kJ mol−1. The WnX procedures have opened up new possibilities for computational chemists in pursue of accurate thermochemical values in a highly-productive manner.