Effects of the locality of a potential derived from hybrid density functionals on Kohn-Sham orbitals and excited states

Density functional theory for doped TiO2: current research strategies and advancements

Since the inception of the density functional theory (DFT) by Hohenberg and Kohn in 1964, it rapidly became an indispensable theoretical tool across various disciplines, such as chemistry, biology, and materials science, among others. This theory has ushered in a new era of computational research, paving the way for substantial advancements in fundamental understanding. Today, DFT is routinely employed for a diverse range of applications, such as probing new material properties and providing a profound understanding of the mechanisms underlying physical, chemical, and biological processes. Even after decades of active utilization, the improvement of DFT principles has never been slowed down, meaning that more accurate theoretical results are continuously generated with time. This work highlights the latest achievements acquired by DFT in the specific research field, namely the theoretical investigations of doped TiO2systems, which have not been comprehensively reviewed and summarized yet. Successful progress in this niche is currently hard to imagine without the support by DFT. It can accurately reveal new TiO2properties after introducing the desired dopant and help to find the optimal system design for a specific application prior to proceeding to more time-consuming and expensive experimental research. Hence, by evaluating a selection of the most recent research studies, we aim to highlight the pertinent aspects of DFT as they relate to the study of doped TiO2systems. We also aim to shed light on the strengths and weaknesses of DFT and present the primary strategies employed thus far to predict the properties of various doped TiO2systems reliably.

Visualizing and characterizing excited states from time-dependent density functional theory

Time-dependent density functional theory (TD-DFT) is the most widely-used electronic structure method for excited states, due to a favorable combination of low cost and semi-quantitative accuracy in many contexts, even if there are well recognized limitations. This Perspective describes various ways in which excited states from TD-DFT calculations can be visualized and analyzed, both qualitatively and quantitatively. This includes not just orbitals and densities but also well-defined statistical measures of electron-hole separation and of Frenkel-type exciton delocalization. Emphasis is placed on mathematical connections between methods that have often been discussed separately. Particular attention is paid to charge-transfer diagnostics, which provide indicators of when TD-DFT may not be trustworthy due to its categorical failure to describe long-range electron transfer. Measures of exciton size and charge separation that are directly connected to the underlying transition density are recommended over more ad hoc metrics for quantifying charge-transfer character.

Unveiling the Physics Behind Hybrid Functionals

We show that accurate exchange-correlation hybrid functionals give very physically optimized effective-correlation potentials, capable of correctly describing the quantum oscillations of atoms and molecules. Based on this analysis and on understanding the error cancellation between semilocal exchange and correlation functionals, we propose a very simple, semilocal correlation potential model compatible with the exact exchange of density functional theory, which performs remarkably well for charge densities and orbital energies.

Building Molecular Complexity from Quinizarin: Conjoined Coumarins and Coronene Analogs

The double Knoevenagel condensation of 1,4-dibenzoyloxyanthraquinone with methyl esters of arylacetic acids affords a series of compounds based upon a previously unknown 1,8-dioxa-benzo[e]pyrene-2,7-dione heterocyclic core. The aryl groups incorporated in the 3- and 6-positions can be oxidatively coupled to the π-expanded backbone to produce a further new heterocyclic core: 1,10-dioxa-dibenzo[dj]coronene-2,9-dione. The intriguing optical properties of these π-expanded coumarin derivatives are discussed and rationalized through quantum chemical calculations. The broad absorption bands of 1,8-dioxa-benzo[e]pyrene-2,7-dione-based dyes are attributed to both HOMO-1→LUMO and HOMO→LUMO transitions, which have a similar energy. Weakly coupled electron-donating aryl substituents result in a moderate bathochromic shift of both the absorption and emission by 30-60 nm in toluene. The emissive properties of these compounds are in part determined by the oscillator strength of the main transition, lifetimes of the excited state, and by the energy match of the excited state with a triplet state of a similar energy. The 1,10-dioxa-dibenzo[dj]coronene-2,9-dione displays a much smaller Stokes shift, yet a markedly increased fluorescence quantum yield of 90 % owing to the increased rigidity compared with the 1,8-dioxa-benzo[e]pyrene-2,7-dione core.

Study of Li Adsorption on Graphdiyne Using Hybrid DFT Calculations

Promising applications of graphdiyne have often been initiated by theoretical predictions especially using DFT known as the most powerful first-principles electronic structure calculation method. However, there is no systematic study on the reliability of DFT for the prediction of the electronic properties of the graphdiyne. Here, we performed a study of Li adsorption on the graphdiyne using hybrid DFT with LC-ωPBE and compared the results with those of PBE, because accurate prediction of the Li adsorption is important for performance as a Li storage that was first theoretically suggested and then experimentally realized. Our results show that PBE overestimates the adsorption energy inside a pore and the barrier height at the transition state of in-plane diffusion compared to the those of LC-ωPBE. In particular, LC-ωPBE predicted almost barrier-less in-plane diffusion of Li on the graphdiyne because of the presence of both in-plane and out-of-plane π orbitals. Also, LC-ωPBE favors a high spin state due to the exact exchange energy when several Li atoms are adsorbed on the graphdiyne, whereas PBE favors a low spin state. Thus, the use of the hybrid DFT is critical for reliable predictions on the electronic properties of the graphdiyne.

Non-empirical atomistic dipole-interaction-model for quantum plasmon simulation of nanoparticles

Plasmonic nanoparticles in the quantum regime exhibit characteristic optical properties that cannot be described by classical theories. Time-dependent density functional theory (TDDFT) is rising as a versatile tool for study on such systems, but its application has been limited to very small clusters due to rapidly growing computational costs. We propose an atomistic dipole-interaction-model for quantum plasmon simulations as a practical alternative. Namely the atomic dipole approximation represents induced dipoles with atomic polarizabilities obtained from TDDFT without empirical parameters. It showed very good agreement with TDDFT for plasmonic spectra of small silver clusters at much lower computational cost, though it is not appropriate for molecular-like excitations. It could also reproduce the plasmonic band shift experimentally observed in sub-10 nm silver particles.