Electronic couplings for photo-induced processes from subsystem time-dependent density-functional theory: The role of the diabatization

Theoretical description of photoinduced electron transfer in donor-acceptor supramolecular complexes based on carbon buckybowls

Herein, we explore, from a theoretical perspective, the nonradiative photoinduced processes (charge separation and energy transfer) within a family of donor-acceptor supramolecular complexes based on the electron-donor truxene-tetrathiafulvalene (truxTTF) derivative and a series of curved fullerene fragments (buckybowls) of different shapes and sizes (C30H12, C32H12, and C38H14) as electron acceptors that successfully combine with truxTTF via non-covalent interactions. The resulting supramolecular complexes (truxTTF·C30H12, truxTTF·C32H12, and truxTTF·C38H14) undergo charge-separation processes upon photoexcitation through charge-transfer states involving the donor and acceptor units. Despite the not so different size of the buckybowls, they present noticeable differences in the charge-separation efficiency owing to a complex decay post-photoexcitation mechanism involving several low-lying excited states of different natures (local and charge-transfer excitations), all closely spaced in energy. In this intricate scenario, we have adopted a theoretical approach combining electronic structure calculations at (time-dependent) density functional theory, a multistate multifragment diabatization method, the Marcus-Levitch-Jortner semiclassical rate expression, and a kinetic model to estimate the charge separation rate constants of the supramolecular heterodimers. Our outcomes highlight that the efficiency of the photoinduced charge-separation process increases with the extension of the buckybowl backbone. The supramolecular heterodimer with the largest buckybowl (truxTTF·C38H14) displays multiple and efficient electron-transfer pathways, providing a global photoinduced charge separation in the ultrafast time scale in line with the experimental findings. The study reported indicates that modifications in the shape and size of buckybowl systems can give rise to attractive novel acceptors for potential photovoltaic applications.

Unraveling the mechanisms of triplet state formation in a heavy-atom free photosensitizer

Triplet excited state generation plays a pivotal role in photosensitizers, however the reliance on transition metals and heavy atoms can limit the utility of these systems. In this study, we demonstrate that an interplay of competing quantum effects controls the high triplet quantum yield in a prototypical boron dipyrromethene-anthracene (BD-An) donor-acceptor dyad photosensitizer, which is only captured by an accurate treatment of both inner and outer sphere reorganization energies. Our ab initio-derived model provides excellent agreement with experimentally measured spectra, triplet yields and excited state kinetic data, including the triplet lifetime. We find that rapid triplet state formation occurs primarily via high-energy triplet states through both spin-orbit coupled charge transfer and El-Sayed's rule breaking intersystem crossing, rather than direct spin-orbit coupled charge transfer to the lowest lying triplet state. Our calculations also reveal that competing effects of nuclear tunneling, electronic state recrossing, and electronic polarizability dictate the rate of non-productive ground state recombination. This study sheds light on the quantum effects driving efficient triplet formation in the BD-An system, and offers a promising simulation methodology for diverse photochemical systems.

Triplet Excitation-Energy Transfer Couplings from Subsystem Time-Dependent Density-Functional Theory

We present an implementation of triplet excitation-energy transfer (TEET) couplings based on subsystem-based time-dependent density-functional theory (sTDDFT). TEET couplings are systematically investigated by comparing "exact" and approximate variants of sTDDFT. We demonstrate that, while sTDDFT utilizing explicit approximate non-additive kinetic energy (NAKE) density functionals is well-suited for describing singlet EET processes, it is inadequate for characterizing TEET. However, we show that projection-based embedding (PbE)-based sTDDFT addresses the challenges faced by NAKE-sTDDFT and emerges as a promising method for accurately describing electronic couplings in TEET processes. We also introduce the mixed PbE-/NAKE-embedding procedure to investigate the TEET effects in solvated pairs of chromophores. This approach offers a good balance between accuracy and efficiency, enabling comprehensive studies of TEET processes in complex environments.

Towards the description of charge transfer states in solubilised LHCII using subsystem DFT

Light harvesting complex II (LHCII) in plants and green algae have been shown to adapt their absorption properties, depending on the concentration of sunlight, switching between a light harvesting and a non-harvesting or quenched state. In a recent work, combining classical molecular dynamics (MD) simulations with quantum chemical calculations (Liguori et al. in Sci Rep 5:15661, 2015) on LHCII, it was shown that the Chl611-Chl612 cluster of the terminal emitter domain can play an important role in modifying the spectral properties of the complex. In that work the importance of charge transfer (CT) effects was highlighted, in re-shaping the absorption intensity of the chlorophyll dimer. Here in this work, we investigate the combined effect of the local excited (LE) and CT states in shaping the energy landscape of the chlorophyll dimer. Using subsystem Density Functional Theory over the classical [Formula: see text]s MD trajectory we look explicitly into the excitation energies of the LE and the CT states of the dimer and their corresponding couplings. Upon doing so, we observe a drop in the excitation energies of the CT states, accompanied by an increase in the couplings between the LE/LE and the LE/CT states facilitated by a shorter interchromophoric distance upon equilibration. Both these changes in conjunction, effectively produces a red-shift of the low-lying mixed exciton/CT states of the supramolecular chromophore pair.

Characterization of excited states in time-dependent density functional theory using localized molecular orbitals

Localized molecular orbitals are often used for the analysis of chemical bonds, but they can also serve to efficiently and comprehensibly compute linear response properties. While conventional canonical molecular orbitals provide an adequate basis for the treatment of excited states, a chemically meaningful identification of the different excited-state processes is difficult within such a delocalized orbital basis. In this work, starting from an initial set of supermolecular canonical molecular orbitals, we provide a simple one-step top-down embedding procedure for generating a set of orbitals, which are localized in terms of the supermolecule but delocalized over each subsystem composing the supermolecule. Using an orbital partitioning scheme based on such sets of localized orbitals, we further present a procedure for the construction of local excitations and charge-transfer states within the linear response framework of time-dependent density functional theory (TDDFT). This procedure provides direct access to approximate diabatic excitation energies and, under the Tamm-Dancoff approximation, also their corresponding electronic couplings-quantities that are of primary importance in modeling energy transfer processes in complex biological systems. Our approach is compared with a recently developed diabatization procedure based on subsystem TDDFT using projection operators, which leads to a similar set of working equations. Although both of these methods differ in the general localization strategies adopted and the type of basis functions (Slaters vs Gaussians) employed, an overall decent agreement is obtained.

Subsystem density-functional theory: A reliable tool for spin-density based properties

Subsystem density-functional theory compiles a set of features that allow for efficiently calculating properties of very large open-shell radical systems such as organic radical crystals, proteins, or deoxyribonucleic acid stacks. It is computationally less costly than correlated ab initio wave function approaches and can pragmatically avoid the overdelocalization problem of Kohn-Sham density-functional theory without employing hard constraints on the electron-density. Additionally, subsystem density-functional theory calculations commonly start from isolated fragment electron densities, pragmatically preserving a priori specified subsystem spin-patterns throughout the calculation. Methods based on subsystem density-functional theory have seen a rapid development over the past years and have become important tools for describing open-shell properties. In this Perspective, we address open questions and possible developments toward challenging future applications in connection with subsystem density-functional theory for spin-dependent properties.

Exciton transport in molecular organic semiconductors boosted by transient quantum delocalization

Designing molecular materials with very large exciton diffusion lengths would remove some of the intrinsic limitations of present-day organic optoelectronic devices. Yet, the nature of excitons in these materials is still not sufficiently well understood. Here we present Frenkel exciton surface hopping, an efficient method to propagate excitons through truly nano-scale materials by solving the time-dependent Schrödinger equation coupled to nuclear motion. We find a clear correlation between diffusion constant and quantum delocalization of the exciton. In materials featuring some of the highest diffusion lengths to date, e.g. the non-fullerene acceptor Y6, the exciton propagates via a transient delocalization mechanism, reminiscent to what was recently proposed for charge transport. Yet, the extent of delocalization is rather modest, even in Y6, and found to be limited by the relatively large exciton reorganization energy. On this basis we chart out a path for rationally improving exciton transport in organic optoelectronic materials.

The Seamless Connection of Local and Collective Excited States in Subsystem Time-Dependent Density Functional Theory

The theoretical understanding of photoinduced processes in multichromophoric systems requires, as an essential ingredient, the possibility of accurately describing their electronically excited states. However, the size of these systems often prohibits the usage of conventional electronic-structure methods, so that often multiscale approaches based on phenomenologically motivated models are employed. In contrast, subsystem time-dependent density functional theory (sTDDFT) allows for a subsystem-based ab initio description of multichromophoric systems and therefore allows for, in principle, an exact description of photoinduced processes. This Perspective aims to outline the theoretical foundations and commonly used practical realizations as well as to illustrate benefits of recent developments and open issues in the field of sTDDFT. Prospective, potential future applications and possible methodological developments are discussed.

Low-Scaling Excited State Calculation Using the Block Interaction Product State

We develop an automatic and efficient scheme for the accurate construction of the bases for excitonic models, which can enable "black-box" excited state structure calculations for large molecular systems. These new and optimized bases, which are named the block interaction product state (BIPS), can be expressed as the direct products of the local states for each chromophore. Each chromophore's local states are selected by diagonalization of its reduced density matrix, which is obtained by quantum chemical calculation of the small subsystem composed of the chromophore and its nearest neighbors. We implemented the BIPS framework with fragment-based calculations considering two- and three-body interactions. Test calculations for eight different molecular aggregates demonstrate that this framework provides an accurate description of not only the excitation energies but also the first-order wave function properties (dipole moment and transition dipole moment) of the low-lying excited states at a low-scaling computational cost.

Understanding the Relation between Structural and Spectral Properties of Light-Harvesting Complex II

Light-harvesting complex II (LHCII) is a pigment-protein complex present in higher plants and green algae. LHCII represents the main site of light absorption, and its role is to transfer the excitation energy toward the photosynthetic reaction centers, where primary energy conversion reactions take place. The optical properties of LHCII are known to depend on protein conformation. However, the relation between the structural and spectroscopic properties of the pigments is not fully understood yet. In this respect, previous classical molecular dynamics simulations of LHCII in a model membrane [Sci. Rep. 2015, 5, 1-10] have shown that the configuration and excitonic coupling of a chlorophyll (Chl) dimer functioning as the main terminal emitter of the complex are particularly sensitive to conformational changes. Here, we use quantum chemistry calculations to investigate in greater detail the effect of pigment-pigment interactions on the excited-state landscape. While most previous studies have used a local picture in which electrons are localized on single pigments, here we achieve a more accurate description of the Chl dimer by adopting a supramolecular picture where time-dependent density functional theory is applied to the whole system at once. Our results show that specific dimer configurations characterized by shorter inter-pigment distances can result in a sizable intensity decrease (up to 36%) of the Chl absorption bands in the visible spectral region. Such a decrease can be predicted only when accounting for Chl-Chl charge-transfer excitations, which is possible using the above-mentioned supramolecular approach. The charge-transfer character of the excitations is quantified by two types of analyses: one focusing on the composition of the excitations and the other directly on the observable total absorption intensities.