Reclassifying exciton-phonon coupling in molecular aggregates: evidence of strong nonadiabatic coupling in oligothiophene crystals

Exciton-phonon (EP) coupling in molecular aggregates is reexamined in cases where extended intermolecular interactions result in low-energy excitons with high effective masses. The analysis is based on a single intramolecular vibrational mode with frequency omega0 and Huang-Rhys factor lambda2. When the curvature Jc at the exciton band bottom is much smaller than the free-exciton Davydov splitting W, the strength of the EP coupling is determined by comparing the nuclear relaxation energy lambda2omega0 with the curvature. In this way, weak (lambda2omega0<4piJc), intermediate I (lambda2omega0 approximately 4piJc), and strong I (lambda2omega0>4piJc) coupling regimes are introduced. The conventional intermediate (lambda2omega0 approximately W) and strong (lambda2omega0>W) EP coupling regimes originally defined by Simpson and Peterson [J. Chem. Phys. 26, 588 (1957)] are based solely on the Davydov splitting and are referred to here as intermediate II and strong II regimes, respectively. Within the intermediate I and strong I regimes the near degeneracy of the low-energy excitons allows efficient nonadiabatic coupling, resulting in a spectral splitting between the b- and ac-polarized first replicas in the vibronic progression characterizing optical absorption. Such spectral signatures are clearly observed in OT4 thin films and crystals, where splittings for the lowest energy mode with omega0=161 cm(-1) are as large as 30 cm(-1) with a small variation due to sample disorder. Numerical calculations using a multiphonon BO basis set and a Hamiltonian including linear EP coupling yield excellent agreement with experiment.     

Electronic transitions and vibronic coupling in neptunyl compounds

The low-lying electronic transitions of the neptunyl (NpO(2)(2+)) ion are characterized as either charge transfer (CT) or intra- 5f. Comparison of these classes of electronic transitions reveals significantly different photophysical properties, especially in vibronic coupling. An empirical model developed for analyses of uranyl CT vibronic transitions is used here to simulate the absorption (excitation) spectra of neptunyl in two compounds of different chemical compositions and structural symmetries. Analyses reveal that CT vibronic coupling in neptunyl has the same characteristics as that in typical uranyl analogues. The primary profile of the CT spectra is similar for neptunyl respectively with respect to chloride- and oxide-neptunium bonding interactions. On the other hand, vibronic coupling to the CT transitions is significantly different from that of f-f transitions, even within a given neptunyl compound. Electronic energy levels, vibronic coupling strength, and frequencies of various vibration modes were evaluated for transitions to the excited states of different origins in the region from 8000 cm(-1) to 21000 cm(-1) for two neptunyl compounds.     

The Excitation Spectra of Naphthalene Dimers: Frenkel and Charge‐transfer Excitons

Vertical electronic excitation energies have been calculated at the second‐order approximate coupled‐cluster (CC2) level for a series of dimeric naphthalene systems. The calculated excitation energies are compared with values obtained for a single naphthalene molecule and provide information about the coupling between the naphthalene moieties in the dimers. The calculations show that the coupling between the naphthalenes depends on the distance and the energy of the exciton. At long distances and high energies the excitons on the two naphthalenes are strongly coupled, whereas the excitation energies of the few lowest states are almost unaffected by the presence of the neighboring molecules. We have also analyzed the composition of the dimeric states that consist of the individual monomer states, to investigate the charge‐transfer (CT) and the Frenkel character of the excitons. Our results indicate that the CT exciton exists at short distances, and that its population drops as the distance between the two naphthalene increases.     

Calculations of the exciton coupling elements between the DNA bases using the transition density cube method

Excited states of the double-stranded DNA model (A)12.(T)12 were calculated in the framework of the Frenkel exciton theory. The off-diagonal elements of the exciton matrix were calculated using the transition densities and ideal dipole approximation associated with the lowest energy pipi* excitations of the individual nucleobases as obtained from time-dependent density functional theory calculations. The values of the coupling calculated with the transition density cubes (TDC) and ideal dipole approximation (IDA) methods were found to be significantly different for the small interchromophore distances. It was shown that the IDA overestimates the coupling significantly. The effects of structural fluctuations of the DNA chain on the magnitude of dipolar coupling were also found to be very significant. The difference between the maximum and minimum values was as large as 1000 and 300 cm(-1) for the IDA and TDC methods, respectively. To account for these effects, the properties of the excited states were averaged over a large number of conformations obtained from the molecular dynamics simulations. Our calculations using the TDC method indicate that the absorption of the UV light creates exciton states carrying the majority of the oscillator strength that are delocalized over at least six DNA bases. Upon relaxation, the excitation states localize over at least four contiguous bases.     

Molecular vibrations of [n]oligoacenes (n=2-5 and 10) and phonon dispersion relations of polyacene

As model compounds for nanosize carbon clusters, the phonon dispersion curves of polyacene are constructed based on density functional theory calculations for [n]oligoacenes (n=2-5, 10, and 15). Complete vibrational assignments are given for the observed Fourier-transform infrared and Raman spectra of [n]oligoacenes (n=2-5). Raman intensity distributions by the 1064-nm excitation are well reproduced by the polarizability-approximation calculations for naphthalene and anthracene, whereas several bands of naphthacene and pentacene at 1700-1100 cm(-1) are calculated to be enhanced by the resonance Raman effect. It is found from vibronic calculations that the coupled a(g) modes between the Kekulé deformation and joint CC stretching give rise to the Raman enhancements of the Franck-Condon type, and that the b(3g) mode corresponding to the graphite G mode is enhanced by vibronic coupling between the (1)L(a)((1)B(1u)) and (1)B(b)((1)B(2u)) states. The phonon dispersion curves of polyacene provide a uniform foundation for understanding molecular vibrations of the oligoacenes in terms of the phase difference. The mode correlated with the defect-sensitive D mode of the bulk carbon networks is also found for the present one-dimensional system.     

Observation of ultraviolet rotational band contours of the DNA base adenine: Determination of the transition moment

We report the first observation and analysis of rotational band contours of the jet-cooled DNA base adenine for three vibronic bands at 36,062, 36,105, and 36,248 cm(-1). The lowest npi* and pipi* states have been labeled with their excited-state vibronic symmetry, and a strong pipi*-npi* vibronic coupling via an out-of-plane vibrational mode has been revealed. The rotational band contours have been recorded by resonant two-photon ionization (R2PI) and analyzed by a genetic algorithm (GA) based fit to obtain the optimum band parameters. The vibronic band at 36,062 cm(-1) shows dominant c-type character with transition dipole moment (TDM) components mu(a)2:mu(b)2:mu(c)2 = 0.09:0.17:0.74 and those at 36 105 and 36 248 cm(-1) show abc-hybrid character with predominantly in-plane TDM components. The band at 36,062 cm(-1) has been assigned as the n --> pi* transition, and the 36,105 cm(-1) band as the pi --> pi* transition by the symmetry analysis. The band at 36,248 cm(-1) provides evidence of the strong pipi*-npi* vibronic coupling via an out-of-plane vibrational mode.     

Vibronic spectra of charge transfer excitons and of mixed charge transfer and Frenkel excitons

The linear absorption spectra in the excitonic and vibronic regions in the case of mixing of Frenkel excitons (FEs) and charge-transfer excitons (CTEs) have been theoretically studied for the exciton parameters of the crystals of MePTCDI and PTCDA. Two coupling parameters for the exciton–phonon coupling are introduced: the FE–phonon coupling and the CTE–phonon coupling. The main features of the vibronics in the absorption spectra are the following: (a) the existence of a doublet structure in the vibronic spectra of CTEs; (b) the vibronic levels of the FE at intermediate values of both coupling parameters are located in the continuum of the many-particle exciton–phonon states which makes its absorption line wide and flat; (c) in the case of strong coupling (coupling constants larger than 1) a doublet of bound states appears above this continuum; (d) in the case of vanishing CTE–phonon coupling the vibronics of the charge transfer excitons practically disappear in the absorption spectra.     

Vibronic coupling in quantum wires: applications to polydiacetylene

A theory describing vibronic coupling in direct band gap, one-dimensional semiconductors is developed to account for the photophysical properties of isolated, defect-free conjugated polymers. A Holstein-like Hamiltonian represented in a multi-particle basis set is used to evaluate absorption and emission due to Wannier-Mott excitons. The photophysical properties of such quantum wires are shown to strongly resemble those of Frenkel exciton J-aggregates. The 1(1)B(u) exciton coherence length and effective mass are readily determined from the ratio of the 0-0 and 0-1 line strengths, I(0 - 0)/I(0 - 1), in the photoluminescence spectrum. I(0 - 0)/I(0 - 1) is shown to follow a T(-1/2) dependence, in an excellent agreement with experiments on the red-phase of polydiacteylene.     

Piezomodulated reflection spectra of anthracene single crystals

The first piezomodulation spectra of Frenkel exciton states of a molecular crystal are reported for the (001) face of anthracene from 25 000 cm^?1 to 45 000 cm^?1. The piezoreflection spectra show structure at 300 K which may be correlated with that observed in the specular reflection spectra at 2 K. Davydov splittings at 300 K of 165 cm^?1 for 0–0 and 50 cm^?1 for 0–1 are observed.     

DNA scaffold supports long-lived vibronic coherence in an indodicarbocyanine (Cy5) dimer

Vibronic coupling between pigment molecules is believed to prolong coherences in photosynthetic pigment–protein complexes. Reproducing long-lived coherences using vibronically coupled chromophores in synthetic DNA constructs presents a biomimetic route to efficient artificial light harvesting. Here, we present two-dimensional (2D) electronic spectra of one monomeric Cy5 construct and two dimeric Cy5 constructs (0 bp and 1 bp between dyes) on a DNA scaffold and perform beating frequency analysis to interpret observed coherences. Power spectra of quantum beating signals of the dimers reveal high frequency oscillations that correspond to coherences between vibronic exciton states. Beating frequency maps confirm that these oscillations, 1270 cm⁻¹ and 1545 cm⁻¹ for the 0-bp dimer and 1100 cm⁻¹ for the 1-bp dimer, are coherences between vibronic exciton states and that these coherences persist for ∼300 fs. Our observations are well described by a vibronic exciton model, which predicts the excitonic coupling strength in the dimers and the resulting molecular exciton states. The energy spacing between those states closely corresponds to the observed beat frequencies. MD simulations indicate that the dyes in our constructs lie largely internal to the DNA base stacking region, similar to the native design of biological light harvesting complexes. Observed coherences persist on the timescale of photosynthetic energy transfer yielding further parallels to observed biological coherences, establishing DNA as an attractive scaffold for synthetic light harvesting applications.

Dyes coupled to DNA display distance-dependent vibronic couplings that prolongs quantum coherences detected with 2D spectroscopy.     

A computational study of the excited states of bilirubin IX

We have determined the lowest excited states of bilirubin IX by TD-DFT calculations. The lowest pair of excited states, S(1) and S(2), turn out to be of charge-transfer (CT) nature. Although DFT based methods tend to underestimate the energy of CT states, the small oscillator strengths we have computed indicate that such states may actually exist in this spectral region, but would have escaped spectroscopic detection. The next pair of excited states, S(3) and S(4), account for the most prominent spectral feature of bilirubin. They can be accurately described by the exciton coupling model, as we show by a thorough analysis of wavefunctions and properties. This finding therefore supports the interpretation of bilirubin photoisomerization behaviour, based on the exciton coupling model.     

The bending vibrational levels of the acetylene cation: a case study of the Renner-Teller effect in a molecule with two degenerate bending vibrations

Forty three vibronic levels of C2H2+, X 2Pi u, with upsilon4 = 0-6, upsilon5 = 0-3, and K = 0-4, lying at energies of 0-3520 cm(-1) above the zero-point level, have been recorded at rotational resolution. These levels were observed by double resonance, using 1+1' two-color pulsed-field ionization zero-kinetic-energy photoelectron spectroscopy. The intermediate states were single rovibrational levels chosen from the A1Au, 4nu3 (K = 1-2), 5nu3 (K = 1), nu2+4nu3 (K = 0), and 47,206 cm(-1) (K = 1) levels of C2H2. Seven of the trans-bending levels of C2H2+ (upsilon4 = 0-3, K = 0-2) had been reported previously by Pratt et al. [J. Chem. Phys. 99, 6233 (1993)]; our results for these levels agree well with theirs. A full analysis has been carried out, including the Renner-Teller effect and the vibrational anharmonicity for both the trans- and cis-bending vibrations. The rotational structure of the lowest 16 vibronic levels (consisting of the complete set of levels with upsilon4 + upsilon5 < or = 2, except for the unobserved upper (2Pi u component of the 2nu4 overtone) could be fitted by least squares using 16 parameters to give an rms deviation of 0.21 cm(-1). The vibronic coupling parameter epsilon5 (about whose magnitude there has been controversy) was determined to be -0.0273(7). For the higher vibronic levels, an additional parameter, r45, was needed to allow for the Darling-Dennison resonance between the two bending manifolds. Almost all the observed levels of the upsilon4 + upsilon5 = 3 and 4 polyads (about half of the predicted number) could then be assigned. In a final fit to 39 vibronic levels with upsilon4 + upsilon5 < or = 5, an rms deviation of 0.34 cm(-1) was obtained using 20 parameters. An interesting finding is that Hund's spin-coupling cases (a) and (b) both occur in the Sigmau components of the nu4 + 2nu5 combination level. The ionization potential of C2H2 (from the lowest rotational level of the ground state to the lowest rotational level of the cation) is found to be 91,953.77 +/- 0.09 cm(-1) (3sigma).     

Charge-transfer excitons in DNA

There have been a number of theoretical treatments of excitons in DNA, most neglecting both the intrachain and interchain wavefunction overlaps of the electron and hole, treating them as Frenkel excitons. Recently, the importance of the intrachain and interchain coupling has been highlighted. Experiments have shown that in (dA)n oligomers and in duplex (dA)n.(dT)n, to be abbreviated (A/T), where A is adenine and T is thymine, the exciton wavefunction is delocalized over several bases. In duplexes it is possible to have charge-transfer (CT) excitons. Theoretical calculations have suggested that CT excitons in DNA may have lower energy than single chain excitons. In all the calculations of excitons in DNA, the polarization of the surrounding water has been neglected. Calculations have shown, however, that polarization of the water by an excess electron or a hole in DNA lowers its energy by approximately 1/2 eV, causing it to become a polaron. It is therefore to be expected that polarization charge induced in the surrounding water has a significant effect on the properties of the exciton. In what follows, we present calculations of some properties CT excitons would have in an A/T duplex taking into account the wavefunction overlaps, the effect of the surrounding water, which results in the electron and hole becoming polarons, and the ions in the water. As expected, the CT exciton has lowest energy when the electron and hole polarons are directly opposite each other. By appropriate choice of the dielectric constant, we can obtain a CT exciton delocalized over the number of sites found in photoinduced absorption experiments. The absorption threshold that we then calculate for CT exciton creation in A/T is in reasonable agreement with the lowest singlet absorption deduced from available data.     

Fluorescence and ultraviolet absorption spectra, and the structure and vibrations of 1,2,3,4-tetrahydronaphthalene in its S1(pi,pi*) state

The ultraviolet absorption spectra in the static vapor phase and the laser induced fluorescence spectra (both fluorescence excitation and single vibronic level fluorescence spectra) of jet-cooled 1,2,3,4-tetrahydronaphthalene have been used along with theoretical calculations to assign many of the vibronic levels in the S1(pi,pi*) state. These have been compared to the corresponding vibrational levels for the S0 ground state. Analysis of the upper states of the ring-twisting vibration nu(31) and three other low-frequency modes has allowed us to construct an energy map of the lowest vibrational quantum states for both S0 and S1. The molecule is highly twisted in both electronic states with high barriers to planarity, which are calculated to be 4811 cm(-1) for S0 and 5100 cm(-1) for S1. However, the experimental data show that the barrier should be lower in the S1 state.     

Vibrational quenching of excitonic splittings in H-bonded molecular dimers: the electronic Davydov splittings cannot match experiment

The S(1)/S(2) state exciton splittings of symmetric doubly hydrogen-bonded gas-phase dimers provide spectroscopic benchmarks for the excited-state electronic couplings between UV chromophores. These have important implications for electronic energy transfer in multichromophoric systems ranging from photosynthetic light-harvesting antennae to photosynthetic reaction centers, conjugated polymers, molecular crystals, and nucleic acids. We provide laser spectroscopic data on the S(1)/S(2) excitonic splitting Δ(exp) of the doubly H-bonded o-cyanophenol (oCP) dimer and compare to the splittings of the dimers of (2-aminopyridine)(2), [(2AP)(2)], (2-pyridone)(2), [(2PY)(2)], (benzoic acid)(2), [(BZA)(2)], and (benzonitrile)(2), [(BN)(2)]. The experimental S(1)/S(2) excitonic splittings are Δ(exp) = 16.4 cm(-1) for (oCP)(2), 11.5 cm(-1) for (2AP)(2), 43.5 cm(-1) for (2PY)(2), and <1 cm(-1) for (BZA)(2). In contrast, the vertical S(1)/S(2) energy gaps Δ(calc) calculated by the approximate second-order coupled cluster (CC2) method for the same dimers are 10-40 times larger than the Δ(exp) values. The qualitative failure of this and other ab initio methods to reproduce the exciton splitting Δ(exp) arises from the Born-Oppenheimer (BO) approximation, which implicitly assumes the strong-coupling case and cannot be employed to evaluate excitonic splittings of systems that are in the weak-coupling limit. Given typical H-bond distances and oscillator strengths, the majority of H-bonded dimers lie in the weak-coupling limit. In this case, the monomer electronic-vibrational coupling upon electronic excitation must be accounted for; the excitonic splittings arise between the vibronic (and not the electronic) transitions. The discrepancy between the BO-based splittings Δ(calc) and the much smaller experimental Δ(exp) values is resolved by taking into account the quenching of the BO splitting by the intramolecular vibronic coupling in the monomer S(1) ← S(0) excitation. The vibrational quenching factors Γ for the five dimers (oCP)(2), (2AP)(2), (2AP)(2), (BN)(2), and (BZA)(2) lie in the range Γ = 0.03-0.2. The quenched excitonic splittings Γ[middle dot]Δ(calc) are found to be in very good agreement with the observed splittings Δ(exp). The vibrational quenching approach predicts reliable Δ(exp) values for the investigated dimers, confirms the importance of vibrational quenching of the electronic Davydov splittings, and provides a sound basis for predicting realistic exciton splittings in multichromophoric systems.     

C6H and C6D: electronic spectra and Renner-Teller analysis

Rotationally resolved spectra of the B(2)Π - X(2)Π 0(0)(0) electronic origin bands and 11(1)(1) μ(2)Σ-μ(2)Σ vibronic hot band transitions of both C(6)H and C(6)D have been recorded in direct absorption by cavity ring-down spectroscopy through a supersonically expanding planar plasma. For both origin and hot bands accurate spectroscopic parameters are derived from a precise rotational analysis. The origin band measurements extend earlier work and the 11(1)(1) μ(2)Σ-μ(2)Σ vibronic hot bands are discussed here for the first time. The Renner-Teller effect for the lowest bending mode ν(11) is analyzed, yielding the Renner parameters ε(11), vibrational frequencies ω(11), and the true spin-orbit coupling constants A(SO) for both (2)Π electronic states. From the Renner-Teller analysis and spectral intensity measurements as a function of plasma jet temperature, the excitation energy of the lowest-lying 11(1) μ(2)Σ vibronic state of C(6)H is determined to be (11.0 ± 0.8) cm(-1).     

Beyond exciton theory: a time-dependent DFT and Franck-Condon study of perylene diimide and its chromophoric dimer

The diimide perylene motif exhibits a dramatic intensity reversal between the 0 --> 0 and 0 --> 1 vibronic bands upon pi-pi stacking; this distinct spectral property has previously been used to measure folding dynamics in covalently bound oligomers and synthetic biological hybrid foldamers. It is also used as a tool to assess organization of the pi-stacking, indicating the presence of H- or J-aggregation. The zeroth-order exciton model, often used to describe the optical properties of chromophoric aggregates, is solely a transition dipole coupling scheme, which ignores the explicit electronic structure of the system as well as vibrational coupling to the electronic transition. We have therefore examined the optical properties of gas-phase perylene tetracarboxylic diimide (PTCDI) and its chromophoric dimer as a function of conformation to relate the excited-state distributions predicted by exciton theory with that of time-dependent density functional theory (TDDFT). Using ground- and excited-state geometries, the Franck-Condon (FC) factors for the lowest energy molecular nature electronic transition have been calculated and the origin of the intensity reversal of 0 --> 0 and 0 --> 1 vibronic bands has been proposed.     

Potential-energy surface, dynamics of van der Waals motions, and vibronic transitions in p-difluorobenzene-argon complex

The dynamics of van der Waals vibrational motions and vibronic spectrum of the complex of argon with p-difluorobenzene (ArDFB) are investigated using the ab initio method. The electronic ground-state potential-energy surface of the complex is calculated at the second-order M?ller-Plesset level of theory using a well-balanced basis set aug-cc-pVDZ and its reduced version without tight polarization functions. The dissociation energy of 351 cm(-1) and the binding energy of 402 cm(-1) determined at the Ar distance of 3.521 Angstroms from the DFB ring well agree with the experimental data available. The character of calculated vibrational levels is analyzed and the effect of a strong coupling between the stretching and bending motions is investigated. A new class of hybrid states created by this coupling is found. To investigate the vibronic S(1)-S(0) spectrum, the surfaces of the electronic transition dipole moment are calculated using the ab initio method. From these surfaces, the vibronic transition intensities are determined and employed to assign the Franck-Condon- and Herzberg-Teller-induced transitions.     

Potential-energy surface, van der Waals energy spectrum, and vibronic transitions in s-tetrazine-argon complex

The van der Waals vibrational states and the structure of the vibronic spectrum of s-tetrazine-argon complex have been studied by the ab initio methods. The potential-energy surface of the ground S(0) electronic state of the complex has been constructed by fitting the analytical many-body expansion to a large set of the interaction energy values computed using the second-order M?ller-Plesset perturbation theory combined with the standard aug-cc-pVDZ basis set. The equilibrium structure of the complex found is that with argon located above the tetrazine ring at a distance of 3.394 A. The calculated dissociation energy of 354 cm(-1) is compatible with the experiment. The van der Waals energy spectrum calculated from the potential-energy surface is explained analyzing a correlation with a simpler energy spectrum of benzene-argon. A new assignment of the S(0)-S(1) vibronic spectrum is proposed on the basis of the rigorous selection rules, vibrational energy levels in S(0) and S(1) states and vibronic transition intensities calculated from the electronic transition dipole moment surfaces.     

Analysis of the vibronic fine structure in circularly polarized emission spectra from chiral molecular aggregates

Using a Frenkel-exciton model, the degree of circular polarization of the luminescence (g(lum)) from one-dimensional, helical aggregates of chromophoric molecules is investigated theoretically. The coupling between the electronic excitation and a local, intramolecular vibrational mode is taken into account. Analytical expressions for the fluorescence band shape and g(lum) are presented for the case of strong and weak electronic coupling between the chromophoric units. Results are compared to those from numerical calculations obtained using the three particle approximation. g(lum) for the 0-0 vibronic band is found to be independent of the relative strength of electronic coupling between chromophores and excitation-vibration coupling. It depends solely on the number of coherently coupled molecules. In contrast, for the higher vibronic transitions[g(lum)] decreases with decreasing strength of the electronic coupling. In the limit of strong electronic coupling, [g(lum)] is almost constant throughout the series of vibronic transitions but for weak coupling [g(lum)] becomes vanishingly small for all vibronic transitions except for the 0-0 transition. The results are interpreted in terms of dynamic localization of the excitation during the zero point vibrational motion in the excited state of the aggregate. It is concluded that circular polarization measurements provide an independent way to determine the coherence size and bandwidth of the lowest exciton state for chiral aggregates.