Electronic States of the Benzene Dimer: A Simple Case of Complexity

Revisiting the benzene excimer using [2,2] paracyclophane model system: Experiment and theory

We report high-level calculations of the excited states of [2,2]-paracyclophane (PCP), which was recently investigated experimentally by ultrafast pump-probe experiments on oriented single crystals [Haggag et al., ChemPhotoChem 6 e202200181 (2022)]. PCP, in which the orientation of the two benzene rings and their range of motion are constrained, serves as a model for studying benzene excimer formation. The character of the excimer state and the state responsible for the brightest transition are similar to those of the benzene dimer. The constrained structure of PCP allows one to focus on the most important degree of freedom, the inter-ring distance. The calculations explain the main features of the transient absorption spectral evolution. This brightest transition of the excimer is polarized along the inter-fragment axis. The absorption of the light polarized in the plane of the rings reveals the presence of other absorbing states of Rydberg character, with much weaker intensities. We also report new transient absorption data obtained by a broadband 8 fs pump, which time-resolve strong modulations of the excimer absorption. The combination of theory and experiment provides a detailed picture of the evolution of the electronic structure of the PCP excimer in the course of a single molecular vibration.

Total absorption spectrum of benzene aggregates obtained from two different approaches

CONTEXT

The study of molecular aggregation effects on the electronic spectrum is essential for the development of optoelectronic devices. However, investigating the entire valence absorption spectrum of aggregates using quantum mechanical methods is a challenging task. In this work, we perform systematic simulations of the absorption spectrum of benzene molecular clusters up to 35 eV applying two approaches based on time-dependent density functional theory. The results show that depending on the dimer packing, different energy shifts occur for the symmetry allowed [Formula: see text] transition, in comparison to the monomer. The transition intensity increases for the band around 6 eV for larger aggregates from the monomer to dimers and tetramer, indicating the occurrence of the symmetry forbidden (in [Formula: see text] point group) [Formula: see text] [Formula: see text] transition. The benzene crystal exhibits a large redshift following the experimental spectrum. Also, the continuum regions of all spectra show a good agreement with the experiments both in gas and solid phases.

METHODS

Geometry optimization of the monomer was carried out with Gaussian 09 software using the PBE0/def2-TZVP level of theory. We used dimers and tetramer molecular geometries extracted from the experimental crystal structure. The absorption spectra were directly obtained by the Liouville-Lanczos TDDFT approach with plane waves basis set or indirectly by TDDFT pseudo-spectra calculated in a [Formula: see text] basis followed by analytic continuation procedure to obtain complex polarizability. The former is available at Quantum ESPRESSO, and the latter was calculated using Gaussian 09 with the post-processing performed with a code previously developed in our group.

Intermolecular-Type Conical Intersections in Benzene Dimer

The equilibrium and conical intersection geometries of the benzene dimer were computed in the framework of the conventional, linear-response time-dependent and spin-flipped time-dependent density functional theories (known as DFT, TDDFT and SF-TDDFT) as well as using the multiconfigurational complete active space self-consistent field (CASSCF) method considering the minimally augmented def2-TZVPP and the 6-31G(d,p) basis sets. It was found that the stacking distance between the benzene monomers decreases by about 0.5 Å in the first electronic excited state, due to the stronger intermolecular interaction energy, bringing the two monomers closer together. Intermolecular-type conical intersection (CI) geometries can be formed between the two benzene molecules, when (i) both monomer rings show planar deformation and (ii) weaker (approximately 1.6-1.8 Å long) C-C bonds are formed between the two monomers, with parallel and antiparallel orientation with respect to the monomer. These intermolecular-type CIs look energetically more favorable than dimeric CIs containing only one deformed monomer. The validity of the dimer-type CI geometries obtained by SF-TDDFT was confirmed by the CASSCF method. The nudged elastic band method used for finding the optimal relaxation path has confirmed both the accessibility of these intermolecular-type CIs and the possibility of the radiationless deactivation of the electronic excited states through these CI geometries. Although not as energetically favorable as the previous two CI geometries, there are other CI geometries characterized by the relative rotation of monomers at different angles around a vertical C-C axis.

Benzene Excimer and Excited Multimers: Electronic Character, Interaction Nature, and Aromaticity

In this Letter we analyze the forces involved in the formation of the benzene excimer and its electron structure, and (anti)aromatic character. We extend our study to excited states in molecular aggregates, the triplet excimer and the benzene-tricyanobenzene exciplex. Electronic wave functions are decomposed in terms of localized excitations and ion-pair configurations through diabatization, and we show that excimer (anti)aromaticity can be described as the linear combination of ground, excited, and ionic molecular states. Our analysis concludes that the benzene excimer must be characterized as antiaromatic, with weaker antiaromaticity than the molecular excited singlet. Moreover, we define a model electronic Hamiltonian for the excimer state and we use it as a building block for the extrapolation of electronic Hamiltonians in molecular aggregates. Benzene multimers present a nonuniform (anti)aromatic character, with the center of the column being antiaromatic and the edges behaving as aromatic. The implications of this work go beyond the study of the excimer, providing a general framework for the calculation and characterization of excited states in aggregates.

Interplay of Open-Shell Spin-Coupling and Jahn-Teller Distortion in Benzene Radical Cation Probed by X-ray Spectroscopy

We report a theoretical investigation and elucidation of the X-ray absorption spectra of neutral benzene and of the benzene cation. The generation of the cation by multiphoton ultraviolet (UV) ionization and the measurement of the carbon K-edge spectra of both species using a table-top high-harmonic generation source are described in the companion experimental paper [Epshtein, M.; et al. J. Phys. Chem. A http://dx.doi.org/10.1021/acs.jpca.0c08736]. We show that the 1s_C → π transition serves as a sensitive signature of the transient cation formation, as it occurs outside of the spectral window of the parent neutral species. Moreover, the presence of the unpaired (spectator) electron in the π-subshell of the cation and the high symmetry of the system result in significant differences relative to neutral benzene in the spectral features associated with the 1s_C → π* transitions. High-level calculations using equation-of-motion coupled-cluster theory provide the interpretation of the experimental spectra and insight into the electronic structure of benzene and its cation. The prominent split structure of the 1s_C → π* band of the cation is attributed to the interplay between the coupling of the core → π* excitation with the unpaired electron in the π-subshell and the Jahn-Teller distortion. The calculations attribute most of the splitting (∼1-1.2 eV) to the spin coupling, which is visible already at the Franck-Condon structure, and we estimate the additional splitting due to structural relaxation to be around ∼0.1-0.2 eV. These results suggest that X-ray absorption with increased resolution might be able to disentangle electronic and structural aspects of the Jahn-Teller effect in the benzene cation.

Exciplex Stabilization in Asymmetric Acene Dimers

Excimers play an important role in photochemical processes ranging from singlet fission to DNA damage, and the characteristic red-shift in fluorescence spectra associated with excimer formation can provide information about aggregate formation and the orientation of chromophores. When a mixture of chromophores is present, exciplex formation may lead to spectral characteristics distinct from those of either monomer or the corresponding excimers. To predict the effects of aggregation in a system containing a mixture of small acenes, binding energies and minimum-energy geometries have been calculated for three mixed S₁ exciplexes. Benchmark CASSCF/NEVPT2 multireference binding energies of 18.2, 27.7, and 49.3 kJ/mol are reported for the benzene-naphthalene, benzene-anthracene, and naphthalene-anthracene exciplexes, respectively. TDDFT calculations have been performed using a range of exchange-correlation functionals, showing that many functionals perform inconsistently, and the error in binding energy often depends on the character of the monomer excitation from which the exciplex state is derived. Moderate exciplex stabilization observed for the benzene-naphthalene and naphthalene-anthracene exciplexes results from a mixture of charge transfer and exciton delocalization.

Predicting aromatic exciplex fluorescence emission energies

Analysis of PAH exciplex TDDFT fluorescence energies shows a linear relationship between the mean monomer HOMO–LUMO gap and complex fluorescence.

Dynamics of benzene excimer formation from the parallel-displaced dimer

Excimers play a key role in a variety of excited-state processes, such as exciton trapping, fluorescence quenching, and singlet-fission. The dynamics of benzene excimer formation in the first 2 ps after S₁ excitation from the parallel-displaced geometry of the benzene dimer is reported here. It was simulated via nonadiabatic surface-hopping dynamics using the second-order algebraic diagrammatic construction (ADC(2)). After excitation, the benzene rings take ∼0.5-1.0 ps to approach each other in a parallel-stacked structure of the S₁ minimum and stay in the excimer region for ∼0.1-0.4 ps before leaving due to excess vibrational energy. The S₁-S₂ gap widens considerably while the rings visit the excimer region in the potential energy surface. Our work provides detailed insight into correlations between nuclear and electronic structure in the excimer and shows that decreased ring distance goes along with enhanced charge transfer and that fast exciton transfer happens between the rings, leading to the equal probability of finding the exciton in each ring after around 1.0 ps.

Striking the right balance of intermolecular coupling for high-efficiency singlet fission

Singlet fission is a process that splits collective excitations, or excitons, into two with unity efficiency. This exciton splitting process, unique to molecular photophysics, has the potential to considerably improve the efficiency of optoelectronic devices through more efficient light harvesting. While the first step of singlet fission has been characterized in great detail, subsequent steps critical to achieving overall highly-efficient singlet-to-triplet conversion are only just beginning to become well understood. One of the most elementary suggestions, which has yet to be tested, is that an appropriately balanced coupling is necessary to ensure overall highly efficient singlet fission; that is, the coupling needs to be strong enough so that the first step is fast and efficient, yet weak enough to ensure the independent behavior of the resultant triplets. In this work, we show how high overall singlet-to-triplet conversion efficiencies can be achieved in singlet fission by ensuring that the triplets comprising the triplet pair behave as independently as possible. We show that side chain sterics govern local packing in amorphous pentacene derivative nanoparticles, and that this in turn controls both the rate at which triplet pairs form and the rate at which they decay. We show how compact side chains and stronger couplings promote a triplet pair that effectively couples to the ground state, whereas bulkier side chains promote a triplet pair that appears more like two independent and long-lived triplet excitations. Our results show that the triplet pair is not emissive, that its decay is best viewed as internal conversion rather than triplet-triplet annihilation, and perhaps most critically that, in contrast to a number of recent suggestions, the triplets comprising the initially formed triplet pair cannot be considered independently. This work represents a significant step toward better understanding intermediates in singlet fission, and how molecular packing and couplings govern overall triplet yields.

Excimer formation and evolution of excited state properties in discrete dimeric stacking of an anthracene derivative: a computational investigation

Herein, density functional theory (DFT) computations were performed to investigate the discrete dimer of a mono-substituted anthracene derivative (2-TA-AN), which exhibited highly efficient pure excimer fluorescence in its crystal form. As a more practical model, its geometry, potential energy curve and excited state property were systematically calculated to better understand the excimer formation process and photophysical properties. The compressed excimer geometry is responsible for the highly efficient excimer emission, arising from the enhanced rigidity that greatly suppresses its non-radiative vibrations. Potential energy curves along three directions reveal the non-uniqueness of excimer formation along the long axis of anthracene, which is in a good agreement with the experimental findings. Upon decreasing the displacement, the intermonomer charge-transfer (CT) component gradually increased towards an approximately equivalent hybridization with the locally-emissive (LE) state of the monomer during the formation of the excimer. The excimer emission wavelength versus intermonomer CT content shows a similar trend along the three directions, revealing a turning point related to the essential transition of the excited state properties from the LE of the monomer to the HLCT of the excimer. The present results will contribute to the better understanding of the structure-property relationships in excimer formation and photophysical properties.

How do London Dispersion Interactions Impact the Photochemical Processes of Molecular Switches?

In the last two decades, linear-response time-dependent density functional theory (LR-TDDFT) has become one of the most widely used approaches for the computation of the excited-state properties of atoms and molecules. Despite its success in describing the photochemistry and the photophysics of a vast majority of molecular systems, its domain of applicability has been limited by several substantial drawbacks. Commonly identified problems of LR-TDDFT include the correct description of Rydberg states, charge-transfer excited states, doubly excited states, and nearly degenerate states. In addition to these widely recognized shortcomings, the approximate functionals used in LR-TDDFT are unable to fully describe London dispersion interactions. In this work, we aim at understanding the impact of van der Waals interactions on the properties of chemical systems beyond their electronic ground state. For this purpose, we compare the results of excited-state energy profiles and dynamic trajectories for the prototypical cis-stilbene molecule with its 3-3',5-5'-tetra-tert-butyl derivative. While the explicit treatment of London dispersion interactions results in negligible changes for the cis-stilbene, we show that these attractive forces have a substantial influence on the energetics and structural evolution of the substituted derivative. In the latter case, intramolecular dispersion interactions impact the outcome of the simulation qualitatively, leading to an increased preference for the photocyclization pathway. The methodological consequences of this work are not uniquely applicable to the illustrative stilbene case. In fact, this molecule is representative of a whole class of chemical situations, where dispersion forces dominate the interactions between the unexcited substituents of a photoexcited chromophore. This is, for instance, a common situation in organic photovoltaics where donor molecules are usually functionalized with long alkyl side chains to improve solubility and assembly.

Photophysics and peripheral ring size dependent aggregate emission of cross-conjugated enediynes: applications to white light emission and vapor sensing

Photophysical understanding of organic fluorophores with π-conjugated scaffolds is crucial as such dyes are central to optoelectronic applications.

A structural study on the excimer state of an isolated benzene dimer using infrared spectroscopy in the skeletal vibration region

IR spectroscopy on an isolated benzene excimer reveals that both the electronic and vibrational excitations are in resonance.

Two's Company, Three's a Crowd: Exciton Localization in Cofacially Arrayed Polyfluorenes

Understanding the mechanisms of long-range energy transfer through polychromophoric assemblies is critically important in photovoltaics and biochemical systems. Using a set of cofacially arrayed polyfluorenes (Fn), we investigate the mechanism of (singlet) exciton delocalization in π-stacked polychromophoric assemblies. Calculations reveal that effective stabilization of an excimeric state requires an ideal sandwich-like arrangement; yet surprisingly, emission spectroscopy indicates that exciton delocalization is limited to only two fluorene units for all n. Herein, we show that delocalization is determined by the interplay between the energetic gain from delocalization, which quickly saturates beyond two units in larger Fn, and an energetic penalty associated with structural reorganization, which increases linearly with n. With these insights, we propose a hopping mechanism for exciton transfer, based upon the presence of multiple excimeric tautomers of similar energy in larger polyfluorenes (n ≥ 4) together with the anticipated low thermal barrier of their interconversion.

Identification of a new electron-transfer relaxation pathway in photoexcited pyrrole dimers

Photoinduced electron transfer is central to many biological processes and technological applications, such as the harvesting of solar energy and molecular electronics. The electron donor and acceptor units involved in electron transfer are often held in place by covalent bonds, π-π interactions or hydrogen bonds. Here, using time-resolved photoelectron spectroscopy and ab initio calculations, we reveal the existence of a new, low-energy, photoinduced electron-transfer mechanism in molecules held together by an NH⋯π bond. Specifically, we capture the electron-transfer process in a pyrrole dimer, from the excited π-system of the donor pyrrole to a Rydberg orbital localized on the N-atom of the acceptor pyrrole, mediated by an N-H stretch on the acceptor molecule. The resulting charge-transfer state is surprisingly long lived and leads to efficient electronic relaxation. We propose that this relaxation pathway plays an important role in biological and technological systems containing the pyrrole building block.

Singlet Fission in a Covalently Linked Cofacial Alkynyltetracene Dimer

Singlet fission is a process in which a singlet exciton converts into two triplet excitons. To investigate this phenomenon, we synthesized two covalently linked 5-ethynyl-tetracene (ET) dimers with differing degrees of intertetracene overlap: BET-X, with large, cofacial overlap of tetracene π-orbitals, and BET-B, with twisted arrangement between tetracenes exhibits less overlap between the tetracene π-orbitals. The two compounds were crystallographically characterized and studied by absorption and emission spectroscopy in solution, in PMMA and neat thin films. The results show that singlet fission occurs within 1 ps in an amorphous thin film of BET-B with high efficiency (triplet yield: 154%). In solution and the PMMA matrix the S1 of BET-B relaxes to a correlated triplet pair (1)(T1T1) on a time scale of 2 ps, which decays to the ground state without forming separated triplets, suggesting that triplet energy transfer from (1)(T1T1) to a nearby chromophore is essential for producing free triplets. In support of this hypothesis, selective excitation of BET-B doped into a thin film of diphenyltetracene (DPT) leads to formation of the (1)(T1T1) state of BET-B, followed by generation of both DPT and BET-B triplets. For the structurally cofacial BET-X, an intermediate forms in <180 fs and returns to the ground state more rapidly than BET-B. First-principles calculations predict a 2 orders of magnitude faster rate of singlet fission to the (1)(T1T1) state in BET-B relative to that of crystalline tetracene, attributing the rate increase to greater coupling between the S1 and (1)(T1T1) states and favorable energetics for formation of the separated triplets.

Excitonic splittings in molecular dimers: why static ab initio calculations cannot match them

After decades of research on molecular excitons, only few molecular dimers are available on which exciton and vibronic coupling theories can be rigorously tested. In centrosymmetric H-bonded dimers consisting of identical (hetero)aromatic chromophores, the monomer electronic transition dipole moment vectors subtract or add, yielding S₀ → S₁ and S₀ → S₂ transitions that are symmetry-forbidden or -allowed, respectively. Symmetry breaking by ¹²C/¹³C or H/D isotopic substitution renders the forbidden transition weakly allowed. The excitonic coupling (Davydov splitting) can then be measured between the S₀ → S₁ and S₀ → S₂ vibrationless bands. We discuss the mass-specific excitonic spectra of five H-bonded dimers that are supersonically cooled to a few K and investigated using two-color resonant two-photon ionization spectroscopy. The excitonic splittings Δ_calc predicted by ab initio methods are 5-25 times larger than the experimental excitonic splittings Δ_exp. The purely electronic ab initio splittings need to be reduced ("quenched"), reflecting the coupling of the electronic transition to the optically active vibrations of the monomers. The so-called quenching factors Γ < 1 can be determined from experiment (Γ_exp) and/or calculation (Γ_calc). The vibronically quenched splittings Γ·Δ_calc are found to nicely reproduce the experimental exciton splittings.

Real time observation of the excimer formation dynamics of a gas phase benzene dimer by picosecond pump–probe spectroscopy

Photoexcitation of a T-shaped benzene dimer provides a sandwiched excimer in 10 ps accompanying a 1000 times faster intracluster vibrational energy redistribution rate than that of the benzene monomer.