A first principles examination of phosphorescence.

This paper explores phosphorescence from a first principles standpoint, and examines the intricacies involved in calculating the spin-forbidden T 1 → S 0 transition dipole moment, to highlight that the mechanism is not as complicated to compute as it seems. Using gas phase acridine as a case study, we break down the formalism required to compute the phosphorescent spectra within both the Franck-Condon and Herzberg-Teller regimes by coupling the first triplet excited state up to the S 4 and T 4 states. Despite the first singlet excited state appearing as an L b state and not of nπ* character, the second order corrected rate constant was found to be 0.402 s-1, comparing well with experimental phosphorescent lifetimes of acridine derivatives. In showing only certain states are required to accurately describe the matrix elements as well as how to find these states, our calculations suggest that the nπ* state only weakly couples to the T 1 state. This suggest its importance hinges on its ability to quench fluorescence and exalt non-radiative mechanisms rather than its contribution to the transition dipole moment. A followup investigation into the T 1 → S 0 transition dipole moment's growth as a function of its coupling to other electronic states highlights that terms dominating the matrix element arise entirely from the inclusion of states with strong spin-orbit coupling terms. This means that while the expansion of the transition dipole moment can extend to include an infinite number of electronic states, only certain states need to be included.

Exciton Dynamics of a Diketo-Pyrrolopyrrole Core for All Low-Lying Electronic Excited States Using Density Functional Theory-Based Methods.

Ab initio treatments of interexcited state internal conversion (IC) are more often than not missing from exciton dynamic descriptions, because of their inherent complexity. Here, we define "interexcited state IC" as a same-spin nonradiative transition between states i and j, where i ≠ j ≠ 0. Competing directly with multiexciton processes such as singlet fission or triplet photoupconversion, inclusion of this mechanism in the narrative of molecular photophysics would allow for strategic synthesis of chromophores for more efficient photon-harvesting applications. Herein, we present a robust formalism which can model these rates using density functional theory (DFT)-based methods within the Franck-Condon and Herzberg-Teller regime. Using an unsubstituted diketo-pyrrolopyrrole (DPP) core as a case study, we illustrate the exciton dynamics along the first four excited states for both singlet and triplet manifolds, showing ultrafast same-spin transfer mechanisms due to all excited states, excluding the first triplet level, being in close energetic proximity (within 0.8 eV of each other). The resulting electron same-spin rates outcompete the electron spin-flipping intersystem crossing (ISC) rates, with excitons firmly obeying Kasha's rule as they cascade down from the high-lying excited states toward the lower states. Furthermore, we calculated that only the first singlet excited state displayed a reasonable probability of triplet exciton generation, of ∼40%, with a near-zero chance of the exciton reverting to the singlet manifold once the electron-hole pair are of parallel spin.

The quantum chemical solvation of indole: accounting for strong solute-solvent interactions using implicit/explicit models.

In this paper, we investigate the efficacy of different quantum chemical solvent modelling methods of indole in both water and methylcyclohexane solutions. The goal is to show that one can yield good photophysical properties in strongly coupled solute-solvent systems using standard DFT methods. We use standard and linearly-corrected Polarisable Continuum Models (PCM), as well as explicit solvation models, and compare the different model parameters, including the choice of density functional, basis set, and number of explicit solvent molecules. We demonstrate that implicit models overestimate energies and oscillator strengths. In particular, for indole-water, no level inversion is observed, suggesting a dielectric medium on its own is insufficient. In contrast, energies are seen to converge fairly rapidly with respect to cluster size towards experimentally measured properties in the explicit models. We find that the use of B3LYP with a diffuse basis set can adequately represent the photophysics of the system with a cluster size of between 9-12 explicit water molecules. Sampling of configurations from a molecular dynamics simulation suggests that the single point results are suitably representative of the solvated ensemble. For indole-water, we show that solvent reorganisation plays a significant role in stabilisation of the excited state energies. It is hoped that the findings and observations of this study will aid in the choice of solvation model parameters in future studies.

Efficient enumeration of bosonic configurations with applications to the calculation of non-radiative rates.

This work presents algorithms for the efficient enumeration of configuration spaces following Boltzmann-like statistics, with example applications to the calculation of non-radiative rates, and an open-source implementation. Configuration spaces are found in several areas of physics, particularly wherever there are energy levels that possess variable occupations. In bosonic systems, where there are no upper limits on the occupation of each level, enumeration of all possible configurations is an exceptionally hard problem. We look at the case where the levels need to be filled to satisfy an energy criterion, for example, a target excitation energy, which is a type of knapsack problem as found in combinatorics. We present analyses of the density of configuration spaces in arbitrary dimensions and how particular forms of kernel can be used to envelope the important regions. In this way, we arrive at three new algorithms for enumeration of such spaces that are several orders of magnitude more efficient than the naive brute force approach. Finally, we show how these can be applied to the particular case of internal conversion rates in a selection of molecules and discuss how a stochastic approach can, in principle, reduce the computational complexity to polynomial time.

Bilirubin analogues as model compounds for exciton coupling.

A series of phycobilin analogues have been investigated in terms of coupled excitonic systems. These compounds consist of a monomer, a tetrapyrrole structurally similar to bilirubin (bR), and two conjugated bR analogues. Spectroscopic and computational methods have been used to investigate the degree of interchromophore coupling. We find the synthesised bR analogue shows stronger excitonic coupling than bR, owing to a different molecular geometry. The excitonic coupling in the conjugated molecules can be controlled by modifying the bridge side-group. New computed energy levels for bR using the DFT/MRCI method are also presented, which improve on published values and re-assign the character of excited singlet states.

A computational exploration of aggregation-induced excitonic quenching mechanisms for perylene diimide chromophores.

Perylene diimide (PDI) derivatives are widely used materials for luminescent solar concentrator (LSC) applications due to their attractive optical and electronic properties. In this work, we study aggregation-induced exciton quenching pathways in four PDI derivatives with increasing steric bulk, which were previously synthesized. We combine molecular dynamics and quantum chemical methods to simulate the aggregation behavior of chromophores at low concentration and compute their excited state properties. We found that PDIs with small steric bulk are prone to aggregate in a solid state matrix, while those with large steric volume displayed greater tendencies to isolate themselves. We find that for the aggregation class of PDI dimers, the optically accessible excitations are in close energetic proximity to triplet charge transfer (CT) states, thus facilitating inter-system crossing and reducing overall LSC performance. While direct singlet fission pathways appear endothermic, evidence is found for the facilitation of a singlet fission pathway via intermediate CT states. Conversely, the insulation class of PDI does not suffer from aggregation-induced photoluminescence quenching at the concentrations studied here and therefore display high photon output. These findings should aid in the choice of PDI derivatives for various solar applications and suggest further avenues for functionalization and study.

The UVA response of enolic dibenzoylmethane: beyond the static approach.

Enolic dibenzoylmethane is used in cosmetic sunscreens as a UVA filter because it strongly absorbs radiation around 340 nm. Assessing the absorption properties solely on the basis of the vertical excitation spectrum at the minimum of the potential energy surface leads to the conclusion that the nπ* state is not initially photoexcited. Since this molecule exhibits large changes in structure due to nuclear thermal and quantum fluctuations, it is not sufficient to consider one molecular configuration but an ensemble of configurations. In this work, we simulate its UVA response by employing the DFT/MRCI method in conjunction with configurations sampled from density functional theory-based classical and path integral molecular dynamics as well as by computing Franck-Condon factors. Our findings indicate that thermal and nuclear quantum fluctuations symmetrically broaden the excited states' absorption within the semi-classical approximation and thus it is necessary to include vibronic effects in order to correctly reproduce the experimental spectrum. The absorption is largely dominated by the ππ* state but there is a minor contribution from the nπ* state, contrary to the static result. The crossing between these two states occurs during the intramolecular proton transfer. This knowledge is of importance for studying photorelaxation mechanisms of dibenzoylmethane and other ß-diketone compounds.

Nonadiabatic photodynamics and UV absorption spectrum of all-trans-octatetraene.

The short-time molecular quantum dynamics of all-trans-octatetraene after electronic excitation to the first bright valence state is theoretically investigated. A semiempirical approach of a multireference configuration interaction based on density functional theory, the so called hybrid DFT/MRCI, in both its original and redesigned formulations, is used for treating the electronic part of the problem. The nuclear kinetic part is defined with the help of symmetry-adapted internal coordinates also suitable for a large amplitude displacement. By incorporating ten in-plane and two out-of-plane nuclear degrees of freedom in the underlying Hamiltonian, the results of the time evolution of the excited wave packet are discussed. We show that the population transfer between the two coupled low-lying states in all-trans-octatetraene occurs in a 100-200 fs time regime. The calculated UV absorption spectra describe the main vibronic features correctly except for the band associated with the single-bond stretching motion which lacks intensity. The possible products of the photoisomerization in terms of symmetry-adapted coordinates are also discussed.

Redesign of the DFT/MRCI Hamiltonian.

The combined density functional theory and multireference configuration interaction (DFT/MRCI) method of Grimme and Waletzke [J. Chem. Phys. 111, 5645 (1999)] is a well-established semi-empirical quantum chemical method for efficiently computing excited-state properties of organic molecules. As it turns out, the method fails to treat bi-chromophores owing to the strong dependence of the parameters on the excitation class. In this work, we present an alternative form of correcting the matrix elements of a MRCI Hamiltonian which is built from a Kohn-Sham set of orbitals. It is based on the idea of constructing individual energy shifts for each of the state functions of a configuration. The new parameterization is spin-invariant and incorporates less empirism compared to the original formulation. By utilizing damping techniques together with an algorithm of selecting important configurations for treating static electron correlation, the high computational efficiency has been preserved. The robustness of the original and redesigned Hamiltonians has been tested on experimentally known vertical excitation energies of organic molecules yielding similar statistics for the two parameterizations. Besides that, our new formulation is free from artificially low-lying doubly excited states, producing qualitatively correct and consistent results for excimers. The way of modifying matrix elements of the MRCI Hamiltonian presented here shall be considered as default choice when investigating photophysical processes of bi-chromophoric systems such as singlet fission or triplet-triplet upconversion.