Optimal Tuning Perspective of Range-Separated Double Hybrid Functionals

Spin Currents via the Gauge Principle for Meta-Generalized Gradient Exchange-Correlation Functionals

The prominence of density functional theory in the field of electronic structure computation stems from its ability to usefully balance accuracy and computational effort. At the base of this ability is a functional of the electron density: the exchange-correlation energy. This functional satisfies known exact conditions that guide the derivation of approximations. The strongly constrained and appropriately normed (SCAN) approximation stands out as a successful, modern, example. In this Letter, we demonstrate how the SU(2) gauge invariance of the exchange-correlation functional in spin current density functional theory allows us to add an explicit dependence on spin currents in the SCAN functional (here called JSCAN)-and similar meta-generalized-gradient functional approximations-solely invoking first principles. In passing, a spin-current dependent generalization of the electron localization function (here called JELF) is also derived. The extended forms are implemented in a developer's version of the crystal23 program. Applications on molecules and materials confirm the practical relevance of the extensions.

Ensemble Ground State of a Many-Electron System with Fractional Electron Number and Spin: Piecewise-Linearity and Flat-Plane Condition Generalized

Description of many-electron systems with a fractional electron number (Ntot) and fractional spin (Mtot) is of great importance in physical chemistry, solid-state physics, and materials science. In this Letter, we provide an exact description of the zero-temperature ensemble ground state of a general, finite, many-electron system and characterize the dependence of the energy and the spin-densities on both Ntot and Mtot, when the total spin is at its equilibrium value. We generalize the piecewise-linearity principle and the flat-plane condition and determine which pure states contribute to the ground-state ensemble. We find a new derivative discontinuity, which manifests for spin variation at a constant Ntot, as a jump in the Kohn-Sham potential. We identify a previously unknown degeneracy of the ground state, such that the total energy and density are unique, but the spin-densities are not. Our findings serve as a basis for development of advanced approximations in density functional theory and other many-electron methods.

Theoretical Study of Structure and Photophysics of Homologous Series of Bis(arylydene)cycloalkanones

Photophysical properties of a series of bis(arylydene)cycloalkanone dyes with various donor substituents are studied using quantum chemistry. Their capacity for luminescence and nonradiative relaxation through trans-cis isomerization is related to their structure, in particular, to the donor capacity of the substituents and the degree of conjugation due to the central cycloalkanone moiety. It is shown that cyclohexanone central moiety introduces distortions and disrupts the conjugation, thus leading to a nonmonotonic change in their properties. The increasing donor capacity of the substituents causes increase in the HOMO energy (rise in the oxidation potential) and decrease in the HOMO-LUMO gap, which results in the red shift of the absorption spectra. The ability of the excited dye to relax through fluorescence or through trans-cis isomerization is governed by the height of the barrier between the Franck-Condon and S1-S0 conical intersection regions on the potential energy surface of the lowest π-π* excited state. This barrier also correlates with the donor capacity of the substituents and the degree of conjugation between the central and donor moieties. The calculated fluorescence and trans-cis isomerization rates are in good agreement with the observed fluorescence quantum yields.

Embedding vertex corrections in GW self-energy: Theory, implementation, and outlook

The vertex function (Γ) within the Green's function formalism encapsulates information about all higher-order electron-electron interaction beyond those mediated by density fluctuations. Herein, we present an efficient approach that embeds vertex corrections in the one-shot GW correlation self-energy for isolated and periodic systems. The vertex-corrected self-energy is constructed through the proposed separation-propagation-recombination procedure: the electronic Hilbert space is separated into an active space and its orthogonal complement denoted as the "rest;" the active component is propagated by a space-specific effective Hamiltonian different from the rest. The vertex corrections are introduced by a rescaled time-dependent nonlocal exchange interaction. The direct Γ correction to the self-energy is further updated by adjusting the rescaling factor in a self-consistent post-processing cycle. Our embedding method is tested mainly on donor-acceptor charge-transfer systems. The embedded vertex effects consistently and significantly correct the quasiparticle energies of the gap-edge states. The fundamental gap is generally improved by 1-3 eV upon the one-shot GW approximation. Furthermore, we provide an outlook for applications of (embedded) vertex corrections in calculations of extended solids.

Benefits of Range-Separated Hybrid and Double-Hybrid Functionals for a Large and Diverse Data Set of Reaction Energies and Barrier Heights

To better understand the thermochemical kinetics and mechanism of a specific chemical reaction, an accurate estimation of barrier heights (forward and reverse) and reaction energies is vital. Because of the large size of reactants and transition state structures involved in real-life mechanistic studies (e.g., enzymatically catalyzed reactions), density functional theory remains the workhorse for such calculations. In this paper, we have assessed the performance of 91 density functionals for modeling the reaction energies and barrier heights on a large and chemically diverse data set (BH9) composed of 449 organic chemistry reactions. We have shown that range-separated hybrid functionals perform better than the global hybrids for BH9 barrier heights and reaction energies. Except for the PBE-based range-separated nonempirical double hybrids, range separation of the exchange term helps improve the performance for barrier heights and reaction energies. The 16-parameter Berkeley double hybrid, ωB97M(2), performs remarkably well for both properties. However, our minimally empirical range-separated double hybrid functionals offer marginally better accuracy than ωB97M(2) for BH9 barrier heights and reaction energies.