Probing the Locality of Excited States with Linear Algebra

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.

Origins of the photoinitiation capacity of aromatic thiols as photoinitiatiors: a computational study

In this work, we report the photophysical properties of three thiol derivatives, commonly used as photoinitiators in thiol-ene free radical polymerization, the ultimate goal being to rationalize the main reason behind the photoinitiation efficiency. For this aim, time dependent density functional theory is used to simulate the absorption spectra of alkyl thiol (R-SH), thiophenol (PhSH) and p-(trifluoromethyl) thiophenol (p-CF₃PhSH), describe their excited state topologies, and explore their potential energy surfaces along the S-H dissociation. Excited state calculations have shown that the S-H photolysis is achieved through the triplet excited states following intersystem crossing from the originally populated singlet manifolds. More specifically, while in aromatic thiol derivatives dissociation is mainly triplet-state mediated, the first excited singlet state and first triplet state of alkyl thiol are both dissociative and hence potentially capable of generating the photoinduced radical species. We have also justified the experimental findings concerning the photoinitiator efficiency considering both their potential energy surface topologies and the absorption intensity, in the lowest energy region.

Predicting Absorption and Emission Maxima of Polycyclic Aromatic Azaborines: Reliable Transition Energies and Character

Polycyclic aromatic azaborines have potential applications as luminophores, novel fluorescent materials, organic light-emitting diodes, and fluorescent sensors. Additionally, their relative structural simplicity should allow the use of computational techniques to design and screen novel compounds in a rapid manner. Herein, the absorption and emission maxima of twelve polycyclic aromatic BN-1,2-azaborine analogues containing the N-BOH moiety were examined to determine a methodology for reliably predicting both the energy and character (local excitation [LE] vs charge transfer [CT]) of the absorption and emission maxima for these compounds. The necessity of implicit solvation models was also investigated. The cam-QTP(01) functional with a small, double-ζ quality basis set provides reliable data compared to EOM-CCSD/cc-pVDZ single-point computations. Of note, commonly used functionals for these applications (B3LYP and ωB97xD) struggle to provide reliable results for both the energy and LE character of the transitions relative to EOM-CCSD computations.

Analysis and visualization of energy densities. II. Insights from linear-response time-dependent density functional theory calculations

Inspired by the analysis of Kohn-Sham energy densities by Nakai and coworkers, we extended the energy density analysis to linear-response time-dependent density functional theory (LR-TDDFT) calculations. Using ethylene-tetrafluoroethylene and oxyluciferin-water complexes as examples, distinctive distribution patterns were demonstrated for the excitation energy densities of local excitations (within a molecular fragment) and charge-transfer excitations (between molecular fragments). It also provided a simple way to compute the effective energy of both hot carriers (particle and hole) from charge-transfer excitations via an integration of the excitation energy density over the donor and acceptor grid points.

Investigating the character of excited states in TiO2 nanoparticles from topological descriptors: implications for photocatalysis

Excited state topological descriptors based on the attachment/detachment one-electron charge density are used to investigate the centroids of photoactive TiO₂ nanoclusters and nanoparticles.

Deep-Blue Oxadiazole-Containing Thermally Activated Delayed Fluorescence Emitters for Organic Light-Emitting Diodes

A series of four novel deep-blue to sky-blue thermally activated delayed fluorescence (TADF) emitters (2CzdOXDMe, 2CzdOXD4MeOPh, 2CzdOXDPh, and 2CzdOXD4CF₃Ph) have been synthesized and characterized. These oxadiazole-based emitters demonstrated bluer emission compared with the reference emitter 2CzPN thanks to the weaker acceptor strength of the oxadiazole moieties. The oxadiazole compounds doped in hosts (mCP and PPT) emitted from 435 to 474 nm with photoluminescence quantum yields ranging from 14-55%. The emitters possess singlet-triplet excited-state energy gaps (Δ E_ST) between 0.25 and 0.46 eV resulting in delayed components ranging from 4.8 to 25.8 ms. The OLED device with 2CzdOXD4CF₃Ph shows a maximum external quantum efficiency of 11.2% with a sky-blue emission at CIE of (0.17, 0.25), while the device with 2CzdOXD4MeOPh shows a maximum external quantum efficiency of 6.6% with a deep-blue emission at CIE of (0.15, 0.11).

The role of intramolecular charge transfer and symmetry breaking in the photophysics of pyrrolo[3,2-b]pyrrole-dione

This paper reveals structurally unique π-expanded pyrrolo[3,2-b]pyrrole and its non-typical photophysical behaviour.

The effect of solvent relaxation in the ultrafast time-resolved spectroscopy of solvated benzophenone

Modeling time-resolved spectra to unravel ultra fast solvent reorganization.

Development of a Novel Index for Analysis of Electronically Excited States

Concerning the major factors in the context of excited states analyses, namely charge centroids of the orbitals involved in the excitations, the distance between orbital centroids, and overlap integrals, a new metric-the Ω index-is proposed to assign the character and optical properties of electronically excited states. Using several molecules from different classes and also a well-studied standard database for time-dependent density functional theory (TD-DFT) studies as benchmark criteria, accountability of the developed index is numerically assessed for local, charge transfer, and Rydberg excitations. It is shown that the nature of excited states can be discriminated using the Ω index, where its superior performance for those situations in which the previous descriptors were not helpful is also unveiled. Relationships are also examined between the Ω index and optical properties of some molecules under study in the framework of the sum-over-state approach. It is observed that there are correlations between the proposed index and computed hyperpolarizabilities based on the sum-over-state scheme. These findings offer the possibility of estimating excited-state properties of large systems from simple descriptors without explicitly performing calculations of high-order response functions.

Photophysics of chlorin e6: from one- and two-photon absorption to fluorescence and phosphorescence

Linear and non-linear optical properties of a known photosensitizer producing singlet oxygen, chlorin e6, have been studied, including dynamics effects.

Fluorescent benzimidazo[1,2-a]quinolines: synthesis, spectroscopic and computational studies of protonation equilibria and metal ion sensitivity

Novel benzimidazo[1,2-a]quinolines with promising pH and chemosensing properties are experimentally and computationally characterized.

Synthesis, computational, and spectroscopic analysis of tunable highly fluorescent BN-1,2-azaborine derivatives containing the N-BOH moiety

Methods to tune the luminescence wavelength and the quantum yields by controlling the power and location of electron-donor and acceptor substituents on the ring system.

A new record excited state 3MLCT lifetime for metalorganic iron(ii) complexes

The ³MLCT lifetime of iron complexes was pushed to a record lifetime of 26 ps using a new benzimidazolylidene-based C^∧N^∧C ligand opening up new perspectives on the way of applying such complexes to photoelectrochemical processes.

Two-photon-absorption DNA sensitization via solvated electron production: unraveling photochemical pathways by molecular modeling and simulation

Infrared optical properties and photochemistry of a potential therapeutic dye interacting with DNA: a multiscale computational approach.

Transition matrices and orbitals from reduced density matrix theory

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.

Rational design of multifunctional star-shaped molecules with a 1,3,5-triazine core and different arms for application in organic light-emitting diodes and organic solar cells

A series of star-shaped 1,3,5-triazine derivatives for intended application in organic light-emitting diodes (OLEDs) and organic solar cells (OSCs) were investigated theoretically to explore their optical, electronic, and charge-transport properties. Analysis of their frontier molecular orbitals (FMOs) indicated that vertical electronic transitions associated with absorption and emission by these derivatives can be characterized as intramolecular charge-transfer (ICT) processes. The calculated results show that the optical, electronic, and charge-transport properties of the derivatives are influenced by the end groups and π-bridges present. Our results suggest that the molecules under investigation could serve as donor materials in OSCs and/or luminescent materials in OLEDs. In addition, all of the molecules are expected to be promising candidates for hole- and electron-transport materials. Based on our results, we were able to propose a rational method of designing multifunctional materials for application in OLEDs and OSCs. Graphical abstract A series of multifunctional star-shaped small molecules were investigated as charge-transport and luminescent materials for OLEDs as well as charge-transport and donor materials for OSCs.

Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge-resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.