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.     

Charge transfer vibronic transitions in uranyl tetrachloride compounds

The electronic and vibronic interactions of uranyl (UO(2))(2+) in three tetrachloride crystals have been investigated with spectroscopic experiments and theoretical modeling. Analysis and simulation of the absorption and photoluminescence spectra have resulted in a quantitative understanding of the charge transfer vibronic transitions of uranyl in the crystals. The spectra obtained at liquid helium temperature consist of extremely narrow zero-phonon lines (ZPL) and vibronic bands. The observed ZPLs are assigned to the first group of the excited states formed by electronic excitation from the 3σ ground state into the f(δ,?) orbitals of uranyl. The Huang-Rhys theory of vibronic coupling is modified successfully for simulating both the absorption and luminescence spectra. It is shown that only vibronic coupling to the axially symmetric stretching mode is Franck-Condon allowed, whereas other modes are involved through coupling with the symmetric stretching mode. The energies of electronic transitions, vibration frequencies of various local modes, and changes in the O═U═O bond length of uranyl in different electronic states and in different coordination geometries are evaluated in empirical simulations of the optical spectra. Multiple uranyl sites derived from the resolution of a superlattice at low temperature are resolved by crystallographic characterization and time- and energy-resolved spectroscopic studies. The present empirical simulation provides insights into fundamental understanding of uranyl electronic interactions and is useful for quantitative characterization of uranyl coordination.     

Spectroscopic studies of the electronic and vibrational spectra of tetramethylammonium fluorochromate(VI)

The electronic and vibrational spectra of tetramethylammonium fluorochromate(VI) have been measured. The observed electronic transitions correlated simply and directly with those of CrO ₄ ²⁻ . The electronic spectrum shows a weak band at about 450 nm and the edge of a very strong, broad band which extends beyond 344 nm. The intervening band has been identified with o oxygen-to-chromium charge transfer. This band exhibits a partially resolved vibrational progression or vibronic coupling due to excitation of a symmetric stretching mode in the CrO₃ group. This vibronic coupling is analyzed completely due to spectral correlation and symmetry of transitions, the Duschinsky effect, vibronic-spin-orbit coupling, environmental effect, anharmonicity order, vibrational intervals, and electronic rearrangement. The text was submitted by the authors in English.     

Identification of the optically active vibrational modes in the photoluminescence of MEH-PPV films

The temperature dependence of the photoluminescence properties of a thin film of poly[2-methoxy-5-(2(')-ethylhexyloxy)-p-phenylene-vinylene], MEH-PPV, fabricated by spin coating, is analyzed. The evolution with temperature of the peak energy of the purely electronic transition, of the first vibronic band, of the effective conjugation length, and of the Huang-Rhys factors are discussed. The asymmetric character of the pure electronic transition peak and the contribution of the individual vibrational modes to the first vibronic band line shape are considered by a model developed by Cury et al. [J. Chem. Phys. 121, 3836 (2004)]. The temperature dependence of the Huang-Rhys factors of the main vibrational modes pertaining to the first vibronic band allows us to identify two competing vibrational modes. These results show that the electron coupling to different vibrational modes depends on temperature via reduction of thermal disorder.     

Laser-induced fluorescence spectroscopy of NC3S

In a discharged supersonic jet of acetonitrile and carbon disulfide, we have for the first time observed an electronic transition of the NC(3)S radical using laser-induced fluorescence (LIF) spectroscopy. A progression originating from the C-S stretching mode of the upper electronic state appears in the excitation spectrum. Each band of the progression has a polyad structure due to anharmonic resonances with even overtones of bending modes. Rotationally resolved spectra have been observed by high-resolution laser scans, and the electronic transition is assigned to A 2Pii-X 2Pii. For the vibronic origin band, the position and the effective rotational constant of the upper level have been determined to be 21 553.874(1) and 0.046 689(4) cm(-1), respectively. The dispersed fluorescence spectrum from the zero vibrational level of A 2Pi3/2 has also been observed; its vibrational structure is similar to that of the LIF excitation spectrum, showing a prominent C-S stretching progression with polyad structures. The vibrational frequencies of the C-S stretching mode in the ground and excited electronic states are determined to be 550 and 520 cm(-1), respectively. Fluorescence decay profiles have been measured for several vibronic levels of the A state.     

Heme charge-transfer band III is vibronically coupled to the Soret band

A complete resonance Raman excitation profile of the heme charge-transfer band known as band III is presented. The data obtained throughout the near-infrared region show preresonance with the Q-band, but the data also clearly show the enhancement of a number of modes in the spectral region of band III. Only nontotally symmetric modes are observed to have resonance enhancement in the band III region. The observed resonance enhancements in modes of B(1g) symmetry are compared with the enhancements of those same modes in the excitation profiles of the Q-band of deoxy myoglobin, also presented here for this first time. The Q-band data agree well with the theory of vibronic coupling in metalloporphyrins (Shelnutt, J. A. J. Chem. Phys. 1981, 74, 6644-6657). The strong vibronic coupling of the Q-band of the deoxy form of hemes is discussed in terms of the enhancement of modes with both B(1g) and A(2g) symmetry. The comparison between the Q-band and band III reveals that, consistent with the theory, only modes of B(1g) symmetry are enhanced in the vicinity of band III. These results show that band III is vibronically coupled to the Soret band. The coupling of band III to modes with strong rhombic distortion of the heme macrocycle calls into question the hypothesis that the axial iron out-of-plane displacement is primarily responsible for the structure-dynamics correlations observed in myoglobin.     

Laser induced fluorescence spectroscopy of a mixed dimer between 2-pyridone and 7-azaindole

We report here the laser induced fluorescence excitation (FE) and dispersed fluorescence (DF) spectra of a 1:1 mixed dimer between 7-azaindole (7AI) and 2-pyridone (2PY) measured in a supersonic free jet expansion of helium. Density functional theoretical calculation at the B3LYP/6-311++G** level has been performed for predictions of the dimer geometry and normal mode vibrational frequencies in the ground electronic state. A planar doubly hydrogen-bonded structure has been predicted to be the most preferred geometry of the dimer. In the FE spectrum, sharp vibronic bands are observed only for excitation of the 2PY moiety. A large number of low-frequency vibronic bands show up in both the FE and DF spectra, and those bands have been assigned to in-plane hydrogen bond vibrations of the dimer. Spectral analyses reveal Duschinsky-type mixing among those modes in the excited state. No distinct vibronic band structure in the FE spectrum was observed corresponding to excitations of the 7AI moiety, and the observation has been explained in terms of nonradiative electronic relaxation routes involving the 2PY moiety.     

Vibronic coupling in benzene cation and anion: vibronic coupling and frontier electron density in Jahn-Teller molecules

Vibronic coupling constants of Jahn-Teller molecules, benzene radical cation and anion, are computed as matrix elements of the electronic part of the vibronic coupling operator using the electronic wave functions calculated by generalized restricted Hartree-Fock and state-averaged complete active space self-consistent-field methods. The calculated vibronic coupling constants for benzene cation agree well with the experimental and theoretical values. Vibronic coupling density analysis, which illustrates the local properties of the coupling, is performed in order to explain the order of magnitude of the coupling constant from view of the electronic and vibrational structures. This analysis reveals that the couplings of the e2g2 and e2g3 modes in which the large displacements locate on C-C bonds are strong in the cation. On the other hand, they are greatly weakened in the anion because of the decrease of electron density in the region of the C-C bonds, which originates from the antibonding nature of the singly occupied molecular orbital of the anion. However, the difference of the electronic structure has a little influence on the vibronic coupling of the e2g4 mode. These results indicate that the vibronic coupling depends not only on the direction of the nuclear displacement but also on the frontier electron density.     

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.     

Solute-solvent intermolecular vibronic coupling as manifested by the molecular near-field effect in resonance hyper-Raman scattering

Vibronic coupling within the excited electronic manifold of the solute all-trans-β-carotene through the vibrational motions of the solvent cyclohexane is shown to manifest as the "molecular near-field effect," in which the solvent hyper-Raman bands are subject to marked intensity enhancements under the presence of all-trans-β-carotene. The resonance hyper-Raman excitation profiles of the enhanced solvent bands exhibit similar peaks to those of the solute bands in the wavenumber region of 21,700-25,000 cm(-1) (10,850-12,500 cm(-1) in the hyper-Raman exciting wavenumber), where the solute all-trans-β-carotene shows a strong absorption assigned to the 1A(g) → 1B(u) transition. This fact indicates that the solvent hyper-Raman bands gain their intensities through resonances with the electronic states of the solute. The observed excitation profiles are quantitatively analyzed and are successfully accounted for by an extended vibronic theory of resonance hyper-Raman scattering that incorporates the vibronic coupling within the excited electronic manifold of all-trans-β-carotene through the vibrational motions of cyclohexane. It is shown that the major resonance arises from the B-term (vibronic) coupling between the first excited vibrational level (v = 1) of the 1B(u) state and the ground vibrational level (v = 0) of a nearby A(g) state through ungerade vibrational modes of both the solute and the solvent molecules. The inversion symmetry of the solute all-trans-β-carotene is preserved, suggesting the weak perturbative nature of the solute-solvent interaction in the molecular near-field effect. The present study introduces a new concept, "intermolecular vibronic coupling," which may provide an experimentally accessible∕theoretically tractable model for understanding weak solute-solvent interactions in liquid.     

Vibronic contributions to DICD in achiral molecules

The theory of dispersion-induced circular dichroism (the CD induced in a transition of an achiral species through long-range dispersive coupling with a chiral species) is extended to include vibronic terms. Symmetry rules are deduced for DICD-active vibronic states. It is shown that the intensity distribution over DICD-active vibrations within a given electronic band of the achiral species gives both insight into the mechanism through which the DICD appears, and vibronic spectral data not accessible through direct absorption studies. Applications to the carbonyl chromophore and comparison with recent experimental studies suggest that vibronic terms may predominate in certain cases over those expected from the purely electronic case.     

Spin—orbit and vibronic perturbations on the chiroptical spectra of dissymmetric pseudo-tetragonal metal complexes

The influence of spin—orbit and vibronic interactions upon the chiroptical properties of nearly degenerate dd transitions in metal complexes of pseudo-tetragonal symmetry is investigated. A model system is considered in which three nearly degenerate dd excited states are coupled via both spinorbit and vibronic interactions. Vibronic interactions among the three nearly degenerate dd electronic states are assumed to arise from a pseudo-Jahn—Teller (PJT) mechanism involving three different vibrational modes (each nontotally symmetric in the point group of the undistorted model system).A vibronic hamiltonian is constructed (for the excited states of the model system) which includes linear coupling terms in each of the three PJT-active vibrational modes as well as a linear coupling term in one totally symmetric mode of the system and a spin—orbit interaction term. Wavefunctions and eigenvalues for the spin—orbit/vibronic perturbed excited states. of the model system are obtained by diagonalizing this hamiltonian in a basis constructed of uncoupled vibrational and electronic (orbital and spin) wavefunctions.Rotatory strengths associated with transitions to vibronic levels of the perturbed system are calculated and “rotatory strength spectra” are computed assuming gaussian shaped vibronic spectral components. Calculations are carried out for a number of vibronic and spin—orbit coupling parameters and for various splitting energies between the interacting electronic states. The calculated results suggest that chiroptical spectra associated with transitions to a set of nearly degenerate dd excited states of a chiral transition metal complex cannot be interpreted directly without some consideration of the effects introduced by spin—orbit and vibronic perturbations. These perturbations can lead to substantial alterations in the sign patterns and intensity distributions of rotatory strength among vibronic levels derived from the interacting electronic states and it is generally not valid to assign specific features in the observed circular dichroism spectra to transitions between states with well-defined electronic (orbital and spin) identities.Our theoretical model is conservative with respect to the total (or net) rotatory strength associated with transitions to levels derived from the three interacting electronic states; the vibronic and spin—orbit coupling operators are operative only within this set of states. That is, the total (or net) rotatory strength associated with these transitions remains invariant to the vibronic and spin—orbit coupling parameters of the model.     

Resonantly enhanced multiphoton ionization and zero kinetic energy photoelectron spectroscopy of chrysene: a comparison with tetracene

We report the electronic and vibrational spectroscopy of chrysene using resonantly enhanced multiphoton ionization (REMPI) and zero kinetic energy (ZEKE) photoelectron spectroscopy. As an isomer of tetracene, chrysene contains a kink in the middle of the four fused hexagonal rings, which complicates not just the symmetry but, more importantly, the molecular orbitals and hence vibronic transitions. Incidentally, the two nearby electronically excited states of chrysene have the same symmetry, and vibronic coupling introduces no out-of-plane vibrational modes. As a result, the REMPI spectrum of chrysene contains essentially only in-plane ring deformation modes, similar to that of tetracene. However, density functional calculations using gaussian even after the inclusion of vibronic coupling can only duplicate the observed REMPI spectrum in a qualitative sense, and the agreement is considerably worse than our recent work on a few pericondensed polycyclic aromatic hydrocarbons and on tetracene. The ZEKE spectrum of chrysene via the origin band of the intermediate electronic state S(1), however, can be qualitatively reproduced by a straightforward Franck-Condon calculation. The ZEKE spectra from vibrationally excited states of the S(1), on the other hand, demonstrate some degree of mode selectivity: the overall intensity of the ZEKE spectrum can vary by an order of magnitude depending on the vibrational mode of the intermediate state. A scaling factor in the theoretical vibrational frequency for the cation is also needed to compare with the experimental result, unlike tetracene and pentacene.     

Zero-point fluctuations in naphthalene and their effect on charge transport parameters

We calculate the effect of vibronic coupling on the charge transport parameters in crystalline naphthalene, between 0 and 400 K. We find that nuclear fluctuations can cause large changes in both the energy of a charge on a molecule and on the electronic coupling between molecules. As a result, nuclear fluctuations cause wide distributions of both energies and couplings. We show that these distributions have a small temperature dependence and that, even at high temperatures, vibronic coupling is dominated by the effect of zero-point fluctuations. Because of the importance of zero-point fluctuations, we find that the distributions of energies and couplings have substantial width, even at 0 K. Furthermore, vibronic coupling with high energy modes may be significant, even though these modes are never thermally activated. Our results have implications for the temperature dependence of charge mobilities in organic semiconductors.     

Asymmetric band profile of the Soret band of deoxymyoglobin is caused by electronic and vibronic perturbations of the heme group rather than by a doming deformation

We measured the Soret band of deoxymyoglobin (deoxyMb), myoglobin cyanide (MbCN), and aquo-metmyoglobin (all from horse heart) with absorption and circular dichroism (CD) spectroscopies. A clear non-coincidence was observed between the absorption and CD profiles of deoxyMb and MbCN, with the CD profiles red- and blueshifted with respect to the absorption band position, respectively. On the contrary, the CD and absorption profiles of aquametMb were nearly identical. The observed noncoincidence indicates a splitting of the excited B state due to heme-protein interactions. CD and absorption profiles of deoxyMb and MbCN were self-consistently analyzed by employing a perturbation approach for weak vibronic coupling as well as the relative intensities and depolarization ratios of seven bands in the respective resonance Raman spectra measured with B-band excitation. The respective B(y) component was found to dominate the observed Cotton effect of both myoglobin derivatives. The different signs of the noncoincidences between CD and absorption bands observed for deoxyMb and MbCN are due to different signs of the respective matrix elements of A(1g) electronic interstate coupling, which reflects an imbalance of Gouterman's 50:50 states. The splitting of the B band reflects contributions from electronic and vibronic perturbations of B(1g) symmetry. The results of our analysis suggest that the broad and asymmetric absorption band of deoxyMb results from this band splitting rather than from its dependence on heme doming. Thus, we are able to explain recent findings that the temperature dependences of CO rebinding to myoglobin and the Soret band profile are uncorrelated[Ormos et al., Proc. Natl. Acad. Sci U.S.A. 95, 6762 (1998)].     

Nuclear coordinate dependence of electronic matrix elements for radiationless transitions

The nuclear coordinate dependence of the electronic matrix elements for radiationless transitions (in the weak coupling limit) is investigated by the use of a Q-centroid approximation. This approach bears a similarity to the familiar r-centroid method in diatomic spectroscopy, but has a wholy different physical character. Because the Q-centroid for electronic relaxation is obtained as an average with density of states weighted Franck—Condon factors, it is not restricted to geometries near the equilibrium position of the initial electronic state as it is in the case of radiative transitions (in the weak coupling limit). For totally symmetric vibrations, it is shown that the Q-centroids for poor accepting modes are in the vicinity of the equilibrium positions for this vibration, while those for good accepting modes tend towards the surface crossing along those vibrational modes. Thus, in the case of dominant accepting modes, the electronic matrix element reflects a Teller surface crossing mechanism for electronic relaxation, even though the density of states weighted Franck—Condon factors reflect a tunnelling mechanism. For non-totally symmetric vibrations, Q-centroids may be large or small independent of their accepting mode capabilities. Thus, coupling mechanisms, which are “forbidden” at the equilibrium geometry in aromatic hydrocarbons, may become allowed and even dominant because of very distorted Q-centroid configurations. This leads to another possible reason for the absence of observation of a vibration that is clearly assignable as a promoting mode in the single vibronic level fluorescence studies of benzene-like molecules. The results underscore previous warnings as to the enormous errors incurred by using the Condon approximation for the nuclear coordinate dependent energy denominators that appear in the electronic matrix elements.     

Contributions of symmetric and asymmetric normal coordinates to the intervalence electronic absorption and resonance Raman spectra of a strongly coupled p-phenylenediamine radical cation

Resonance Raman spectroscopy, electronic absorption spectroscopy, and the time-dependent theory of spectroscopy are used to analyze the intervalence electron transfer properties of a strongly delocalized class III molecule, the tetraalkyl-p-phenylene diamine radical cation bis(3-oxo-9-azabicyclo[3.3.1]non-9-yl)benzene ((k33)(2)PD(+)). This molecule is a prototypical system for strongly coupled organic intervalence electron transfer spectroscopy. Resonance Raman excitation profiles in resonance with the lowest energy absorption band are measured. The normal modes of vibration that are most strongly coupled to the intervalence transition are identified and assigned by using UB3LYP/6-31G(d) calculations. Excited state distortions are obtained, and the resonance Raman intensities and excitation profiles are calculated by using the time-dependent theory of Raman spectroscopy. The most highly distorted normal modes are all totally symmetric, but intervalence electron transfer absorption spectra are usually interpreted in terms of a model based on coupling between potential surfaces that are displaced along an asymmetric normal coordinate. This model provides a convenient physical picture for the intervalence compound, but it is inadequate for explaining the spectra. The absorption spectrum arising from only the strongly coupled surfaces consists of a single narrow band, in contrast to the broad, vibronically structured experimental spectrum. The electronic absorption spectrum of (k33)(2)PD(+) is calculated by using exactly the same potential surfaces as those used for the Raman calculations. The importance of symmetric normal coordinates, in addition to the asymmetric coordinate, is discussed. The observed vibronic structure is an example of the missing mode effect; the spacing is interpreted in terms of the time-dependent overlaps in the time domain.     

Quasibound continuum states in SiF4 (D2A1) photoionization: photoelectron-vibrational coupling

The authors report a fully vibrationally resolved photoelectron spectroscopy investigation of a nonplanar molecule studied over a range of excitation energies. Experimental results for all four fundamental vibrational modes are presented. In each case significant non-Franck-Condon effects are seen. The vibrational branching ratio for the totally symmetric mode nu1+ is found to be strongly affected by resonant excitation in the SiF4+ (D2A1) photoionization channel. This is shown to be the result of two distinct shape resonances, which for the first time have been both confirmed by theoretical calculations. Vibrationally resolved Schwinger photoionization calculations are used to understand the vibronic coupling for the photoelectrons, both using ab initio and harmonic vibrational wave functions.     

Theoretical study of the electronic nonadiabatic transitions in the photoelectron spectroscopy of F2O

The photoelectron spectrum of F2O pertaining to ionizations to the ground (X2B1) and low-lying excited electronic states (A2B2, B2A1, and C2A2) of F2O+ is investigated theoretically. The near equilibrium potential energy surfaces of the ground electronic state (X2B1) of F2O and the mentioned ground and excited electronic states of F2O+ reported by Wang et al. ( J. Chem. Phys. 2001, 114, 10682) for the C2v configuration are extended for the Cs geometry assuming a harmonic vibration along the asymmetric stretching mode. The vibronic interactions between the A2B2 and B2A1 electronic states of F2O+ are treated within a linear coupling approach, and the strength of the vibronic coupling parameter is calculated by an ab initio method. The nuclear dynamics is simulated by both time-independent quantum mechanical and time-dependent wave packet approaches. Although the first photoelectron band exhibits resolved vibrational progression along the symmetric stretching mode, the second one is highly overlapping. The latter is attributed to the nonadiabatic interactions among the energetically close A2B2, B2A1, and C2A2 electronic states of F2O+. The theoretical findings are in good accord with the available experimental results.     

The influence of vibronic interactions on the chiroptical spectra of dissymmetric pseudo tetragonal metal complexes

The influence of vibronic interactions on the chiroptical spectra associated with a threesome of nearly degenerate electronic excited states in a dissymmetric molecular system is examined on a formal theoretical model. The model considers two vibrational modes to be effective in promoting pseudo Jahn-Teller (PJT) type interactions between the three closely spaced electronic excited states. Formal expressions are developed for the rotatory strengths of individual vibronic levels derived from the coupled electronic states. Two mode (vibrational)-three state (electronic) vibronic Hamiltonians are constructed (basis set size, 63–108, depending upon interaction parameters used) and diagonalized for a large number of different parameter sets representative of various vibronic coupling strengths, electronic energy level spacings, oscillator (vibrational mode) frequencies, and electronic rotatory strengths. Diagonalization of these vibronic Hamiltonians yields vibronic wave functions and energies which are then used to calculate rotatory strength spectra for the model system. The calculated results demonstrate the profound influence which vibronic interactions of the PJT type may have on the sign patterns and intensity distributions within the rotatory strength spectrum associated with a set of nearly degenerate electronic states. The implication of these results for the interpretation of circular dichroism spectra of chiral transition metal complexes with pseudo tetragonal symmetry are discussed.