1Ag State Research Articles

The Solvent-Dependent Photophysics of Diphenyloctatetraene.

Despite many decades of study, the excited state photophysics of polyenes remains controversial. In diphenylpolyenes with conjugated backbones that contain between 2 and 4 double carbon-carbon bonds, the first two excited electronic states are nearly degenerate but of entirely different character, and their energy splitting is strongly dependent on solvent polarizability. To examine the interplay between these different states, steady-state and time-resolved fluorescence spectroscopies were used to undertake a comprehensive investigation of diphenylocatetraene's (DPO) excited state dynamics in 10 solvents of different polarizabilities and polarities, ranging from weakly interacting alkanes to polar hydrogen-bonding alcohols. These data revealed that photopreparation of the optically bright 1Bu state resulted in fast (<170 ps) internal conversion to the lower-lying optically dark 2Ag state. The 2Ag state is responsible for almost all the observed DPO fluorescence and gains oscillator strength via vibronic intensity stealing with the near-degenerate 1Bu state. The fluorescence lifetime associated with the 2Ag state decayed monoexponentially (4.2-7.2 ns) in contrast to prior biexponential decay kinetics reported for similar polyenes, diphenylbutadiene and diphenylhexatriene. An analysis combining the measured fluorescence lifetimes and fluorescence quantum yields (the latter varying between 7 and 21%) allowed for a 190 cm-1 Herzberg-Teller vibronic coupling constant between the 1Bu and 2Ag states to be determined. The analysis also revealed that the ordering of electronic states remains constant in all the solvents studied, with the 2Ag state minimum always lower in energy than that of the 1Bu state, thus making it a relatively simple polyene compared to structurally similar diphenylhexatriene.

Quantifying the Relaxation Dynamics of Higher Electronic Excited States in Perylene.

Gating logical operations through high-lying electronic excited states presents opportunities for developing ultrafast, subnanometer computational devices. A lack of molecular systems with sufficiently long-lived higher excited states has hindered practical realization of such devices, but recent studies have reported intriguing photophysics from high-lying excited states of perylene. In this work, we use femtosecond spectroscopy supported by quantum chemical calculations to identify and quantify the relaxation dynamics of monomeric perylene's higher electronic excited states. The 21B2u state is accessed through single-photon absorption at 250 nm, while the optically dark 21Ag state is excited via the 11B3u state. Population of either state results in subpicosecond relaxation to the 11B3u state, and we quantify 21Ag and 21B2u state lifetimes of 340 and 530 fs, respectively. These lifetimes are significantly longer than the singlet fission time constant from the perylene 21B2u state, suggesting that the higher electronic states of perylene may be useful for gating logical operations.

Theory of singlet fission in carotenoid dimers.

We develop a theory of singlet fission in carotenoid dimers. Following photoexcitation of the "bright" state (i.e., a singlet electron-hole pair) in a single carotenoid, the first step in the singlet fission process is ultrafast intramolecular conversion into the highly correlated "dark" (or 2Ag) state. This state has both entangled singlet triplet-pair and charge-transfer character. Our theory is predicated on the assumption that it is the singlet triplet-pair component of the "dark" state that undergoes bimolecular singlet fission. We use valence bond theory to develop a minimal two-chain model of the triplet-pair states. The single and double chain triplet-pair spectra are described, as this helps explain the dynamics and the equilibrated populations. We simulate the dynamics of the initial entangled pair state using the quantum Liouville equation, including both spin-conserving and spin-nonconserving dephasing processes. By computing the intrachain and interchain singlet, triplet, and quintet triplet-pair populations, we show that singlet fission critically depends on the interchain coupling and the driving potential (that determines endothermic vs exothermic fission).

Unveiling the double triplet nature of the 2Ag state in conjugated stilbenoid compounds to achieve efficient singlet fission.

In this investigation, the excited-state evolution in a series of all-trans stilbenoid compounds, displaying a low-lying dark singlet state of 2Ag-like symmetry nearly degenerate with the bright 1Bu state, was unveiled by employing advanced ultrafast spectroscopies while probing the effect of solvent polarizability. Together with the dual emission, femtosecond transient absorption and broadband fluorescence up-conversion disclosed the double nature of the 2Ag-like state showing both singlet features, a lifetime typical of a singlet and the ability to emit, and a triplet character, exhibiting a triplet-like absorption spectrum. The ultrafast formation (in hundreds of femtoseconds) from the non-relaxed upper singlet state led to the identification of 2Ag as the correlated triplet pair of singlet fission. The spectral difference obtained by comparison of transient absorption peaks of the 2Ag (1TT) and the triplet states was found to be in remarkable agreement with the observed triplet yield and the 1(TT) separation rate constant. Indeed, this spectral shift provided an experimental method to gain qualitative insight into the ease of separation of the 1(TT) and the relative SF efficiency. The highly conjugated polyene-like structures enable the ultrafast formation of the double triplet, but then the large binding energy prevents the triplet separation and thus the effective completion of singlet fission. Even though thermodynamically feasible for all the investigated stilbenoids according to TD-DFT calculations, singlet fission resulted to occur efficiently in the case of 1-(pyridyl-4-ylethenyl)-4-(p-nitrostyryl)benzene and nitro-styrylfuran with the triplet yield reaching 120% and 140%, respectively, triggered by their greatly enhanced intramolecular charge transfer character relative to the other compounds in the series.

Mechanism of Singlet Fission in Carotenoids from a Polyene Model System.

Singlet fission (SF) is the process of formation of multiple excitons (triplet) from a locally excited singlet state. The mechanism of SF in polyacenes has been shown to proceed via a charge transfer intermediate state. However, carotenoids are not understood in the context of SF. This is possibly due to the complicated multireference nature of the low-lying excited states of carotenoids and the presence of a dark 21Ag state below the optically bright 1Bu state. In this work, we show that the dark Ag state in polyenes and/or carotenoids, along with the charge transfer states, plays a pivotal role in the SF process. We notice that the relative importance of these states varies with a change in geometry and the overall presence of multiple pathways is crucial to the success of the SF process in carotenoid aggregates and disordered geometries.

Theory of the dark state of polyenes and carotenoids

A theory is developed to describe the singlet dark state (usually labeled S1 or 2Ag) of polyenes and carotenoids. The theory assumes that in principle this state is a linear combination of a singlet triplet-pair and an odd-parity charge-transfer exciton. Crucially, these components only couple when the triplet-pair occupies neighboring dimers, such that an electron transfer between the triplets creates a nearest-neighbor charge-transfer excitation. This local coupling stabilises the 2Ag state and induces a nearest neighbor attraction between the triplets. In addition, because of the electron-hole attraction in the exciton, the increased probability that the electron-hole pair occupies neighboring dimers enhances the triplet-triplet attraction: the triplet pair is `slaved' to the charge-transfer exciton. The theory also predicts that as the Coulomb interaction is increased, the 2Ag state evolves from a predominately odd-parity charge-transfer exciton state with a small component of triplet-pair character to a state predominately composed of a triplet-pair with some exciton character. Above a critical Coulomb interaction there is a decoupling of the triplet-pair and charge-transfer exciton subspaces, such that the 2Ag state becomes entirely composed of an unbound spin-correlated triplet pair. The predictions of this theory are qualitatively consistent with high-level density matrix renormalization group calculations of the Pariser-Parr-Pople (or extended Hubbard) model.

Full-frequency dynamical Bethe-Salpeter equation without frequency and a study of double excitations.

The Bethe-Salpeter equation (BSE) that results from the GW approximation to the self-energy is a frequency-dependent (nonlinear) eigenvalue problem due to the dynamically screened Coulomb interaction between electrons and holes. The computational time required for a numerically exact treatment of this frequency dependence is O(N6), where N is the system size. To avoid the common static screening approximation, we show that the full-frequency dynamical BSE can be exactly reformulated as a frequency-independent eigenvalue problem in an expanded space of single and double excitations. When combined with an iterative eigensolver and the density fitting approximation to the electron repulsion integrals, this reformulation yields a dynamical BSE algorithm whose computational time is O(N5), which we verify numerically. Furthermore, the reformulation provides direct access to excited states with dominant double excitation character, which are completely absent in the spectrum of the statically screened BSE. We study the 21Ag state of butadiene, hexatriene, and octatetraene and find that GW/BSE overestimates the excitation energy by about 1.5-2eV and significantly underestimates the double excitation character.

Vibronic interaction in trans-dichloroethene studied by vibration- and angle-resolved photoelectron spectroscopy using 19-90 eV photon energy.

Valence photoelectron spectra and photoelectron angular distributions of trans-dichloroethene have been measured with vibrational resolution at photon energies between 19 eV and 90 eV. Calculations of photoelectron anisotropy parameters, β, and harmonic vibrational modes help provide initial insight into the molecular structure. The photon energy range encompasses the expected position of the atomic Cl 3p Cooper minimum. A corresponding dip observed here in the anisotropy of certain photoelectron bands permits the identification and characterization of those molecular orbitals that retain a localized atomic Cl character. The adiabatic approximation holds for the X2Au state photoelectron band, but vibronic coupling was inferred within the A-B-C and the D-E states by noting various failures of the Franck-Condon model, including vibrationally dependent β-parameters. This is further explored using the linear vibronic coupling model with interaction parameters obtained from ab initio calculations. The A/B photoelectron band is appreciably affected by vibronic coupling, owing to the low-lying conical intersection of the A2Ag and B2Bu states. The C2Bg band is also affected, but to a lesser extent. The adiabatic minima of the D2Au and E2Ag states are almost degenerate, and the vibronic interaction between these states is considerable. The potential energy surface of the D2Au state is predicted to have a double-minimum shape with respect to the au deformations of the molecular structure. The irregular vibrational structure of the resulting single photoelectron band reflects the non-adiabatic nuclear dynamics occurring on the two coupled potential energy surfaces above the energy of their conical intersection.

Photoisomerization dynamics of trans-trans, cis-trans, and cis-cis diphenylbutadiene from broadband transient absorption spectroscopy and calculations.

The photoisomerization path and dynamics of trans-trans (ttD), cis-trans (ctD), and cis-cis (ccD) 1,4-diphenyl-1,3-butadiene (DPB) in solution are studied with broadband transient absorption (TA) spectroscopy and quantum chemical calculations. For ttD in n-hexane, 2-photon-excited TA spectra indicate that the 2Ag state is located above 1-photon allowed 1Bu (S1) by ∼1000 cm-1. Following S0 → S1 optical excitation, the isomerization occurs via torsion about a butadiene double bond to perpendicular molecular configuration P. The P-state is detected in ccD with an excited-state absorption band at 390 nm. This P-band develops during S1 → P half-torsion with time of 0.15 ps, followed further by P → S0 half-torsion and simultaneous decay with 1.6 ps in acetonitrile and 5 ps in n-hexane. In addition, two oscillation cycles between P and S1 population are observed before equilibration in n-hexane. For ctD, an indication of rising and decaying P is found in acetonitrile. The vast majority of ctD species photoisomerizes to ttD and not to ccD, in agreement a with calculated low torsional barrier about the cis double bond and high barrier about the trans double bond. Photoisomerization yield Y and time τi depend drastically on the solvent polarity. Thus, in n-hexane, the isomerization ttD → ctD has yield Ytt,ct = 0.1 and time τi = 829 ps, while in acetonitrile, Ytt,ct = 0.4 and τi = 27 ps. The 30-fold acceleration of the isomerization in acetonitrile clearly reflects a highly polar character of P, consistent with a dipole moment μP > 9.6 D. The results for DPB are discussed in comparison to stilbene.

Nature of the 11Bu and 21Ag Excited States of Butadiene and the Goldilocks Principle of Basis Set Diffuseness.

Butadiene, being the simplest conjugated organic molecule, has been studied extensively by experiments and various high-level theoretical methods. Previous studies conclude that the complete active space (CAS) self-consistent field (SCF) method was unable to obtain the correct 11Bu and 21Ag state ordering and that it introduces artificial valence-Rydberg mixing into the 11Bu state because of the lack of external correlation. Basis sets and initial guesses specifically constructed for this problem were able to improve the vertical excitation energy of the 11Bu state but did not resolve the controversy of the nature of the 11Bu state. In the present work, we demonstrate that, using standard intermediately diffuse basis sets such as jul-cc-pVTZ and ma-TZVP, CASSCF is able to obtain the 11Bu and 21Ag states of trans-butadiene with much improved vertical excitation energy and reasonable wave function characteristics, and it provides a good reference wave function (capable of yielding quantitative excitation energies for excited states) for three methods that treat electron correlation in different ways, namely, multiconfiguration pair-density functional theory (MC-PDFT), CAS second-order perturbation theory (PT2), and multistate (MS) CASPT2. We demonstrate that a combined analysis of the orbital second moments, state second moments, and MC-PDFT energy components is a very useful approach in determining excited-state characteristics and assigning states, and we show that basis sets without diffuse functions or with very diffuse basis functions are not stable or accurate in predicting the excited states of butadiene. We show that the 21Ag state is valence-like and has an atypical double/single excitation character and the 11Bu state has a certain degree of Rydberg character that is not artificial, settling the decades of controversy of the characters of these states.

Nonadiabatic Investigation of the Electronic Spectroscopy of trans-1,3-Butadiene.

Low-lying UV spectroscopy of trans-1,3-butadiene has been extensively studied by experimentalists and theorists. Though a host of techniques has been applied to understand its lowest electronic states, there are still important open questions. Among these are the positions of the two lowest valence excited states and the factors responsible for the spectral shape of the lowest allowed transitions. We present results from EOM-CC calculations in extended basis sets that are used to parametrize a three-electronic-state Koppel, Domcke, and Cederbaum (KDC) model. We test the sensitivity of the KDC model to a variety of parameters and address several outstanding questions regarding the spectrum. We find that the overall shape of the spectrum is determined primarily by the Franck-Condon envelope of the 11Bu state and that the princple impact of the doubly excited 21Ag state is to broaden the 11Bu peaks. There is only modest sensitivity to the relative position of these two states. We find that the lowest Rydberg state, the 11Bg state, has an unexpected impact on the third peak in the spectrum, and its effect is considerably more energy-dependent than that of the 21Ag state.

The characterization of electronic defect states of single and double carbon vacancies in graphene sheets using molecular density functional theory

ABSTRACTA detailed picture of the electronic states manifolds of single- and double-vacancy defects in molecular models of graphene based on polycyclic aromatic hydrocarbons (PAHs) is presented. DFT calculations using various density functionals including long-range corrected ones have been performed for pyrene, circumpyrene and 7a,7z-periacene. It has been found for pyrene defect models that DFT results reproduced well the set of closely-spaced singlet and triplet states predicted by the CCSD(T) and previous MRCI + Q calculations, indicating the applicability of DFT for accessing the excited states manifolds also for larger graphene models. For the single-carbon vacancy defect, all structures have a triplet ground state. As expected, in the largest system, 7a,7z-periacene-1C, the lowest lying states are much closer in energy. For all double-vacancy defect structures, a significant rearrangement of the electronic states with increasing size of the sheet is observed. The closed-shell 1Ag state in the smallest systems is destabilised in the extended 7a,7z-periacene system, which has the 3B2u state as the ground state. As observed for the single-vacancy defect, the lowest lying states are closer in energy for the larger systems, since there are more π orbitals close in energy available. For all states, the formation of the bridging bonds for the double vacancy leads to distances shorter than for the single vacancy defect indicating a larger rigidity of the former structure which does not allow stronger distortions.

Single, Double Electronic Excitations and Exciton Effective Conjugation Lengths in π-Conjugated Systems.

The 21Ag and 11Bu excited states of two prototypical π-conjugated compounds, polyacetylene and polydiacetylene, are investigated with the recently developed particle-particle random phase approximation (pp-RPA) method combined with the B3LYP functional. The polymer-limit transition energies are estimated as 1.38 and 1.72 eV for the 21Ag and 11Bu states, respectively, from an extrapolation of the computed excitation energies of model oligomers. These values increase to 1.95 and 2.24 eV for the same transitions when ground-state structures with ∼33% larger bond length alternation are adopted. Applying the pp-RPA to the vertical excitation energies in oligodiacetylene, the polymer-limit transition energies of the 21Ag and 11Bu states are computed to be 2.06 and 2.28 eV, respectively. These results are in good agreement with experimental values or theoretical best estimates, indicating that the pp-RPA method shows great promise for understanding many photophysical phenomena involving both single and double excitations.

Linear-Response Density Cumulant Theory for Excited Electronic States.

We present a linear-response formulation of density cumulant theory (DCT) that provides a balanced and accurate description of many electronic states simultaneously. In the original DCT formulation, only information about a single electronic state (usually, the ground state) is obtained. We discuss the derivation of linear-response DCT, present its implementation for the ODC-12 method (LR-ODC-12), and benchmark its performance for excitation energies in small molecules (N2, CO, HCN, HNC, C2H2, and H2CO), as well as challenging excited states in ethylene, butadiene, and hexatriene. For small molecules, LR-ODC-12 shows smaller mean absolute errors in excitation energies than equation-of-motion coupled cluster theory with single and double excitations (EOM-CCSD), relative to the reference data from EOM-CCSDT. In a study of butadiene and hexatriene, LR-ODC-12 correctly describes the relative energies of the singly excited 11Bu and the doubly excited 21Ag states, in excellent agreement with highly accurate semistochastic heat-bath configuration interaction results, while EOM-CCSD overestimates the energy of the 21Ag state by almost 1 eV. Our results demonstrate that linear-response DCT is a promising theoretical approach for excited states of molecules.

Photoluminescence, photoacoustic, and scintillation properties of Te4+-doped Cs2HfCl6 crystals

Photoluminescence, photoacoustic, and scintillation properties are reported for 1.0, 3.0, 5.0, and 10 mol% Te4+-doped Cs2HfCl6 crystals grown using the vertical Bridgman–Stockbarger method. The UV − VIS light excited emission spectra showed an emission band peaking at 575 nm which can be ascribed to transitions from the 3T1u and 3A1u states to the 1A1g state of Te4+ ions. Excitation spectra monitored at emission wavelength of 575 nm showed bands at 230–250 (charge transfer on a HfCl62−), 275–300 (1A1g → 3T1u), 300–340 (1A1g → 3T2u, 3Eu), and 360–460 nm (1A1g → 1T1u). The X-ray induced scintillation spectra exhibited a yellow emission band at 575 nm, which is similar to the emission band for excitation by UV–VIS light. Scintillation light yields of the crystals were estimated to be approximately 11,700 (1.0 mol%), 13,100 (3.0 mol%), 9600 (5.0 mol%), and 9000 (10 mol%) photons/MeV, respectively. Scintillation light yield was inversely correlated with the PA intensity.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. I. Time-resolved photoelectron-photoion coincidence spectroscopy.

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans' correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. II. Ab initio multiple spawning simulations.

The excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene (BD), has long been the subject of controversy due to its strong coupling, ultrafast time scales and the difficulties that theory faces in describing the relevant electronic states in a balanced fashion. Here we apply Ab Initio Multiple Spawning (AIMS) using state-averaged complete active space multistate second order perturbation theory [SA-3-CAS(4/4)-MSPT2] which describes both static and dynamic electron correlation effects, providing a balanced description of both the initially prepared bright 11Bu (ππ*) state and non-adiabatically coupled dark 21Ag state of BD. Importantly, AIMS allows for on-the-fly calculations of experimental observables. We validate our approach by directly simulating the time resolved photoelectron-photoion coincidence spectroscopy results presented in Paper I [A. E. Boguslavskiy et al., J. Chem. Phys. 148, 164302 (2018)], demonstrating excellent agreement with experiment. Our simulations reveal that the initial excitation to the 11Bu state rapidly evolves via wavepacket dynamics that follow both bright- and dark-state pathways as well as mixtures of these. In order to test the sensitivity of the AIMS results to the relative ordering of states, we considered two hypothetical scenarios biased toward either the bright 1Bu or the dark 21Ag state. In contrast with AIMS/SA-3-CAS(4/4)-MSPT2 simulations, neither of these scenarios yields favorable agreement with experiment. Thus, we conclude that the excited state non-adiabatic dynamics in BD involves both of these ultrafast pathways.

Lycopene crystalloids exhibit singlet exciton fission in tomatoes.

Transient absorption studies conducted on in vitro lycopene aggregates, as well as on lycopene crystalloids inside tomato chromoplasts, reveal the appearance of a long-lived excited state, which we unambiguously identified as lycopene triplet. These triplet states must be generated by singlet exciton fission, which occurs from the lycopene 2Ag state. This is the first time the singlet fission process has ever been shown to occur in a biological material. We propose that the formation of carotenoid assemblies in chromoplasts may constitute a photoprotective process during chromoplast maturation, in addition to their function in signaling processes.

Structure and dynamics of the radical cation of ethane arising from the Jahn-Teller and pseudo-Jahn-Teller effects.

The pulsed-field-ionization zero-kinetic-energy photoelectron spectrum of C2H6 has been recorded in the region of the adiabatic ionization threshold. The partially rotationally resolved spectrum indicates the existence of several vibronic states of C2H6+ with less than 600 cm-1 of internal excitation. The analysis of the rotational structures assisted by ab initio calculations enabled the determination of the adiabatic ionization energy of C2H6 and the investigation of the structure and dynamics of C2H6+ at low energies. The ground state of C2H6+ is found to be a 2Ag state of diborane-like structure with strongly mixed (a1g)-1 and (eg)-1 configurations. The vibrational structure reveals the importance of large-amplitude nuclear motions involving the diborane distortion modes, the C-C stretching motion, and the internal rotation at elongated C-C distances. The spectrum is analyzed in the light of the information obtained in earlier studies of C2H6+ by ab initio quantum chemistry, EPR spectroscopy and photoelectron spectroscopy.

Doubly Excited Character or Static Correlation of the Reference State in the Controversial 21Ag State of trans-Butadiene?

Butadiene is the simplest polyene and has long served as a model system for many chemical and spectroscopic properties. However, this small molecule has presented significant challenges to theoretical chemistry. The 21Ag state, which is dark but photochemically important, is a prime source of this difficulty. Previous studies attributed the notorious difficulty in treating this state to strong double excitation character of the 21Ag state, which prevents the application of linear response (LR) methods. Therefore, one would require methods with much higher computational cost, especially for the analogues of this state in longer polyenes, and consequently studies of longer polyenes are very limited. In the present work, we argue that the difficulty stems more significantly from the inherently multiconfigurational character of the ground state. In addition, we validate the possibility of employing LR time-dependent density functional theory to investigate such a state with reasonable accuracy.