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.     

Nonadiabatic coupling and diabatic electronic population dynamics on 11A2 and 11B1 states of ozone molecule

In this work, we examine nonadiabatic population dynamics for 1¹B₁ and 1¹A₂ states of ozone molecule (O₃). In O₃, two lowest singlet excited states, ¹A₂ and ¹B₁, can be coupled. Thus, population transfer between them occurs through the seam involving these two states. At any point of the seam (conical intersection), the Born-Oppenheimer approximation breaks down, and it is necessary to investigate nonadiabatic dynamics. We consider a linear vibronic coupling Hamiltonian model and evaluate vibronic coupling constant, diabatic frequencies for three modes of O₃, bilinear and quadratic coupling constants for diabatic potentials, displacements, and Huang-Rhys coupling constants using ab initio calculations. The electronic structure calculations have been performed at the multireference configuration interaction and complete active space with second-order perturbation theory with a full-valence complete active space self-consistent field methods and augmented Dunning's standard correlation-consistent-polarized quadruple zeta basis set to determine ab initio potential energy surfaces for the ground state and first two excited states of O₃, respectively. We have chosen active space comprising 18 electrons distributed over 12 active orbitals. Our calculations predict the linear vibronic coupling constant 0.123 eV. We have obtained the population on the 1¹B₁ and 1¹A₂ excited electronic states for the first 500 fs after photoexcitation.     

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.     

“Proximity effects” in radiative transitions: a model study of the role of vibronic coupling and static crystal field interactions

We report the results of a model study of the influence of vibronic coupling involving non-totally symmetric vibrations and static crystal field interactions on the spectral properties of molecules with close-lying excited electronic states. The presented results suggests that “proximity effects” brought about by solvent perturbation arise from two sources: (i) alterations in the energy separation between vibronically coupled electronic states and (ii) crystal field mixing of the isolated molecular electronic states. It is shown that crystal field mixing leads to the breakdown of the vibronic coupling scheme for non-totally symmetric vibrations in isolated molecules. This breakdown is shown to have a very pronounced effect on the spectral properties of molecules with close-lying excited electronic states. The effect of environmental perturbations on excited state frequencies, the breakdown of symmetry and polarization selection rules, and vibrational intensity distributions is discussed.     

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.     

Vibronic induced one- and two-photon absorption in a charge-transfer stilbene derivate

Both the electronic and the vibronic contributions to one- and two-photon absorption of a D-pi-D charge-transfer molecule (4-dimethylamino-4'-methyl-trans stilbene) are studied by means of density functional response theory combined with a linear coupling model. Vibronic profiles of the first four excited states are fully explored. The dominating vibrational modes for both Franck-Condon and Herzberg-Teller contributions are identified. The Franck-Condon contribution dominates the spectra of first, second, and fourth excited states. The Herzberg-Teller contribution is on the other hand of comparable size for the third excited state, where its inclusion leads to a blueshift with respect to the vertical transition. A similar vibronic coupling behavior is found for both one- and two-photon absorptions.     

Le Couplage Vibronique dans une Chaine Linéaire de Molecules Etudié par une Méthode Auto-Cohérente

We describe the correlation diagram of a linear crystal, in the traditional framework of the vibronic coupling. All lattice normal modes, except the symmetrical mode, are coupled to the excitation transfer. We therefore propose an iterative method, where every mode “sees” an effective coupling arising from the interaction of the other modes with the electronic excitation. This method is applied to a simple case (the pentamer) and the results are compared with the exact solution. In the weak coupling case this procedure gives the vibronic band structure and in the strong coupling case, the electronic band accompanied by vibrational excitations. These results show that the method employed represents an interpolation approach.     

Weak and strong vibronic coupling limits in molecules and their correlation

An exactly solvable vibronic coupling model is used to improve existing definitions of strong and weak vibronic coupling limits in molecules and to derive a unique correlation between the corresponding energy levels.     

Ab initio study of dynamical E × e Jahn-Teller and spin-orbit coupling effects in the transition-metal trifluorides TiF3, CrF3, and NiF3

Multiconfiguration ab initio methods have been employed to study the effects of Jahn-Teller (JT) and spin-orbit (SO) coupling in the transition-metal trifluorides TiF(3), CrF(3), and NiF(3), which possess spatially doubly degenerate excited states ((M)E) of even spin multiplicities (M = 2 or 4). The ground states of TiF(3), CrF(3), and NiF(3) are nondegenerate and exhibit minima of D(3h) symmetry. Potential-energy surfaces of spatially degenerate excited states have been calculated using the state-averaged complete-active-space self-consistent-field method. SO coupling is described by the matrix elements of the Breit-Pauli operator. Linear and higher order JT coupling constants for the JT-active bending and stretching modes as well as SO-coupling constants have been determined. Vibronic spectra of JT-active excited electronic states have been calculated, using JT Hamiltonians for trigonal systems with inclusion of SO coupling. The effect of higher order (up to sixth order) JT couplings on the vibronic spectra has been investigated for selected electronic states and vibrational modes with particularly strong JT couplings. While the weak SO couplings in TiF(3) and CrF(3) are almost completely quenched by the strong JT couplings, the stronger SO coupling in NiF(3) is only partially quenched by JT coupling.     

Synthesis, molecular structure, and EPR analysis of the three-coordinate Ni(I) complex [Ni(PPh3)3][BF4

The compound [Ni(PPh(3))(3)][BF(4)] x BF(3) x OEt(2) was isolated in crystalline form from the olefin oligomerization catalyst system Ni(PPh(3))(4)/BF(3) x OEt(2) and structurally characterized by X-ray diffraction. The influence of vibronic coupling on the EPR parameters of three-coordinate metal complexes with a 3d(9) electronic configuration was investigated within the framework of ligand field theory. Analytical expressions for g-tensor components and isotropic hyperfine coupling constants with ligand nuclei were obtained using first-order perturbation theory. It has been shown that the account of the vibronic interaction in the excited state predicts the existence of three-axial anisotropy of the g-tensor even at the level of first-order perturbation theory; two axes of the g-tensor located in a plane of three-coordinate structure can rotate about the main z axis when a compound is distorted by motion of ligands. It has been shown that in three points of the potential energy surface minimum, for which linear and quadric constants of the vibronic interactions have an identical signs, the HFS isotropic constant from one ligand is larger than HFS constants from the other two; for different vibronic constant signs the ratio between HFS constants varies on opposite. This theoretical researches are in the quality consent with experimental data for a three-coordinate Ni(I) and Cu(II) flat complexes.     

Vibronic intensities in centrosymmetric coordination compounds of the rare earths Part II. A vibronic crystal field-closure-ligand polarisation model and applications to the PrCl6 and UBr6 complex ions in octahedral symmetry

A symmetry adapted formalism to evaluate the vibronic intensities induced by the ungerade vibrational modes in centrosymmetric coordination compounds of the rare earths is put forward and applied to several selected electronic transitions of the PrCl³⁻₆ and UCl²⁻₆ complex ions in octahedral symmetry. This current model is based upon a modified symmetry adapted version of the combined vibronic crystal field-closure-ligand polarisation approach. This model differs from that developed in Part I of this series, in that for the vibronic crystal field contribution to the total transition dipole moment, the closure procedure is employed rather than the utilisation of a truncated basis set for the central metal intermediate electronic states. A criterion is introduced to choose an appropriate set of phases for both the electronic and the vibrational coordinates so that to ensure the right sign for the interference term (which couples together both the vibronic crystal field and the vibronic ligand polarisation contributions to the total transition dipole moment). We have focused our attention on the modulation of the intermolecular force field and a version of a modified general valence force field has been adopted. The reasons for using this formalism rather than the superposition model (SM) are fully discussed in the text. Finally, it is shown that the agreement with experiment is satisfactory for most of the components of the transitions studied, despite the apparent simplicity of our model calculation. General master equations applicable to any f^N electronic configurations are derived to show the utility and flexibility of this current formalism.     

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.     

Solid-state optical properties of linear polyconjugated molecules: pi-stack contra herringbone

The intermolecular arrangement in the solid state and the consequences on the optical and photophysical properties are studied on different derivatives of oligophenylenevinylenes by UV/VIS absorption and angular-resolved polarized fluorescence spectroscopy. Unsubstituted distyrylbenzene (DSB) organizes in a herringbone manner, with the long axes of the molecules oriented in parallel, but the short axes almost perpendicular to each other. Fluorinated distyrylbenzene (F(12)DSB) as well as the DSB:F(12)DSB cocrystals prefer cofacial pi-stacking in the solid state. For all structures, the consequence of the parallel alignment of the transition moments is a strongly blueshifted H-type absorption spectrum and a low radiative rate constant k(F). Significant differences are observed for the emission spectra: the perpendicular arrangement of the short axes in DSB crystals leads to only very weak intermolecular vibronic coupling. Hence the emission spectrum is well structured, very similar to the one in solution. For F(12)DSB and DSB:F(12)DSB, the cofacial arrangement of the adjacent molecules enables strong intermolecular vibronic coupling of adjacent molecules. Thus, an unstructured and strongly redshifted excimerlike emission spectrum is observed. The differences in the electronic nature of the excited states are highlighted by quantum-chemical calculations, revealing the contribution of interchain excitations to the electronic transitions.     

Diradicals, antiaromaticity, and the pseudo-Jahn-Teller effect: electronic and rovibronic structures of the cyclopentadienyl cation

The electronic and rovibronic structures of the cyclopentadienyl cation (C(5)H(5) (+)) and its fully deuterated isotopomer (C(5)D(5) (+)) have been investigated by pulsed-field-ionization zero-kinetic-energy (PFI-ZEKE) photoelectron spectroscopy and ab initio calculations. The vibronic structure in the two lowest electronic states of the cation has been determined using single-photon ionization from the X (2)E(1) (") ground neutral state and 1+1(') resonant two-photon ionization via several vibrational levels of the A (2)A(2) (") excited state. The cyclopentadienyl cation possesses a triplet ground electronic state (X(+) (3)A(2) (')) of D(5h) equilibrium geometry and a first excited singlet state (a(+) (1)E(2) (')) distorted by a pseudo-Jahn-Teller effect. A complete analysis of the Emultiply sign in circlee Jahn-Teller effect and of the (A+E)multiply sign in circlee pseudo-Jahn-Teller effect in the a(+) (1)E(2) (') state has been performed. This state is subject to a very weak linear Jahn-Teller effect and to an unusually strong pseudo-Jahn-Teller effect. Vibronic calculations have enabled us to partially assign the vibronic structure and determine the adiabatic singlet-triplet interval (1534+/-6 cm(-1)). The experimental spectra, a group-theoretical analysis of the vibronic coupling mechanisms, and ab initio calculations were used to establish the topology of the singlet potential energy surfaces and to characterize the pseudorotational motion of the cation on the lowest singlet potential energy surface. The analysis of the rovibronic photoionization dynamics in rotationally resolved spectra and the study of the variation of the intensity distribution with the intermediate vibrational level show that a Herzberg-Teller mechanism is responsible for the observation of the forbidden a(+) (1)E(2) (')<--A (2)A(2) (") photoionizing transition.     

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.     

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.     

Emission band shape probes of the mixed-valence excited state properties of polypyridyl-bridged bis-ruthenium(II) complexes

The absorption spectra and emission spectral band shapes of several polypyridine-ligand (PP) bridged bis-ruthenium(II) complexes imply that the Ru(II)/Ru(III) electronic coupling is weak in their lowest energy metal to ligand charge transfer (MLCT) excited states. Many of these PP-bridging ligands contain pyrazine moieties and the weak electronic coupling of the excited states contrasts to the strong electronic coupling inferred for the correlated mixed-valence ground states. Although the bimetallic complexes emit at significantly lower energy than their monometallic analogs, the vibronic contributions to their 77 K emission spectra are much stronger than expected based on comparison to the monometallic analogs (around twofold in some complexes) and this feature is characteristic of bimetallic complexes in which the mixed-valence excited states are electronically localized. The weaker excited state than ground state donor/acceptor electronic coupling in this class of complexes is attributed to PP-mediated super-exchange coupling in which the mediating orbital of the bridging ligand (PP-LUMO) is partly occupied in the MLCT excited states, but is unoccupied in the ground states; therefore, the vertical Ru(III)-PP⁻ (MLCT) energy is larger and the mixing coefficient smaller in these excited states than is found for Ru(II)-PP in the corresponding ground states.     

A dispersed fluorescence and ab initio investigation of the X2B1 and A2A1 electronic states of the PH2 molecule

In this work, the X2B1 and A2A1 electronic states of the phosphino (PH2) free radical have been studied by dispersed fluorescence and ab initio methods. PH2 molecules were produced in a molecular free-jet apparatus by laser vaporizing a silicon rod in the presence of phosphine (PH3) gas diluted in helium. The laser-induced fluorescence, from the excited A2A1 electronic state down to the ground electronic state, was dispersed and analyzed. Ten (upsilon1upsilon2upsilon3) vibrationally excited levels of the ground electronic state, with upsilon1 < or = 2, upsilon2 < or = 6, and upsilon3 = 0, have been observed. Ab initio potential-energy surfaces for the X2B1 and A2A1 electronic states have been calculated at 210 points. These two states correlate with a 2Pi(u) state at linearity and they interact by the Renner-Teller coupling and spin-orbit coupling. Using the ab initio potential-energy surfaces with our RENNER computer program system, the vibronic structure and relative intensities of the A2A1 --> X2B1 emission band system have been calculated in order to corroborate the experimental assignments.     

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.