Strong Vibronic Coupling Research Articles

Resonant Raman studies of pyrazine with tunable uv lasers: An analysis based on the generalized vibronic theory of Raman intensity

The resonant Raman effect of pyrazine is studied with tunable uv lasers. Polycrystalline samples of pure pyrazine and pyrazine in benzene were studied at low temperature to eliminate fluorescence. Genuine Raman spectra were obtained with this cryogenic technique as close as 40 cm−1 below the 0–0 of the 1B3u transition. Using the benzene 992 cm−1 band as the reference, absolute Raman cross sections were obtained from the known absolute Raman cross section of the benzene line. It was found that ν6a and ν10a have an enhancement factor of 106, corresponding to the strong vibronic coupling case. The data were analyzed by using the strong vibronic coupling theory of Raman intensity recently developed by Hong [J. Chem. Phys. 67, 801 (1977)]. In this generalized vibronic theory both the Franck–Condon effect (for ν6a) and the nonadiabatic Herzberg–Teller coupling (for ν10a) are treated in similar fashion through the use of the Green’s function. Vibronic coupling strengths were derived from analyses of the absorption spectra and used to calculate the absolute Raman cross sections. Agreement between theory and experiments is generally good. Comparison between the Green’s function approach and the traditional weak coupling theory is also made. It is emphasized that Raman spectroscopy and electronic spectroscopy are intimately related as is evident from the success of the theory to predict consistently not only the spectral features of absorption but also the absolute Raman cross sections.

Jahn-Teller effect in EPR spectra: Multistate theory forE2orbital states in cubic symmetry

The Jahn-Teller effect for an orbitally doubly degenerate state is considered for the case of cubic symmetry. Reduction factors are defined which describe the matrix elements of the orbital operators for $E$ doublets between the various vibronic states. For the lowest six vibronic states $E$, ${A}_{1}$, ${A}_{2}$, and $E$, the reduction factors are calculated for the cases of no or weak linear vibronic coupling and strong linear vibronic coupling. In the latter case the effects of anharmonic potential energy and nonlinear vibronic coupling are also included in the reduction factor calculations. Using the reduction factors to determine the matrix elements of the orbital operators within the vibronic states, an effective Hamiltonian is formulated which describes the mixing of the vibronic levels. This defines the multistate theory in which several vibronic levels are included in the manifold of states used to describe electronic interactions. Electron-paramagnetic-resonance spectra from $^{2}E$ orbital states are predicted for a six-state vibronic manifold by calculating the strain dependence of the $g$ factor. Particular attention is given to those spectral fectures appearing in the ground state which are the result of the second excited singlet. The relationship between $p$-type and $q$-type reduction factors is discussed.

Vibronic structure in the ’’metallic’’ reflection band of the TCNQ crystal

Polarized reflection spectra off the (010) face of the first singlet transition of crystalline tetracyanoquinodimethane (TCNQ) have been measured at room and liquid helium temperatures. The spectrum consists of a massive block of high reflectivity, corresponding to a stop band 1.4 eV wide, with well defined edges at 2.8 and 4.2 eV. The reflectivity of the long wavelength edge undergoes a large increase upon cooling, and vibrational structure appears between 2.8 and 3.1 eV due to freezing out of powerful polariton scatterers, the intramolecular vibrations. All structure is assoicated with volume polaritons since it is not shifted when the crystal is coated with a layer of frozen gas. The complex dielectric function, calculated by a Kramers–Kronig transformation, shows two regions where the real part ε1 is negative. The spectra provide a test of the basic notions of strong vibronic coupling in molecular crystals. Polariton scattering by lattice phonons is weak, whereas scattering by intramolecular modes is much stronger.

Theory of resonant Raman scattering. II. Overtones and hot bands

Resonant Raman scattering is discussed in the framework of the Green’s function method in both the strong and weak vibronic coupling limits. We further elaborate on the meaning of each matrix element of the Green’s function, evaluated in the convenient basis set which is commonly referred to as the Longuet–Higgins representation. Cross sections for absorption, Rayleigh, Raman fundamentals, Raman overtones, hot bands, etc., can all be related to the matrix elements of the Green’s function. It is further emphasized that only in the vibronic view elaborated here does a simple and direct correlation exist between the light scattering processes and the Green’s functions. Some typical excitation profiles for overtones and hot bands are calculated and the consequences of strong vibronic couplings are discussed in contrast to the weak vibronic coupling case.

Theory of resonant Raman scattering in the strong vibronic coupling limit–a Green’s function approach

A Green’s function approach for resonant Raman scattering is proposed here, which is suitable for both weak and strong vibronic couplings. The formalism is based on the solution of the exact Green’s function in the Longuet–Higgins representation, using the solutions to the static equations in ordinary molecular quantum mechanics as the basis set. The physical meaning of various interaction schemes becomes clear in this representation. In particular the vibronic coupling is based on the interactions between individual zero-order vibronic levels and is carried through to infinite order, whereas the traditional first order results only account for the emission of one single vibrational quantum. Nonadiabatic contributions are also contained in the formulation. The method is applied to the following cases: (1) the change in nuclear equilibrium position due to electronic excitation, (2) vibronic coupling involving two excited states, and (3) the change in nuclear potential (force constants) due to electronic excitation. Numerical results show that the convergence is excellent even for large vibronic coupling and in exact resonance region. Furthermore, all the physical quantities of interest, such as Raman cross sections of fundamentals and overtones, absorption profiles, Franck–Condon factors, quantum yields can be obtained at the same time in this unified approach.

The electronic structure of NO2. II. The ? 2B2← ? 2A1 and ? 2B1←? 2A1 absorption systems

The results of an accurate ab initio study of the electronic structure of NO2 have been applied to an analysis of the two important visible and near infrared absorption systems of this molecule. The long wavelength absorption (λ≳6000 Å) arises from an ? 2B2←? 2A1 transition. A theoretical absorption spectrum that is generated from the C2V ab initio potential surfaces of these two states qualitatively reproduces most of the features of an experimental low resolution absorption spectrum between 9000 and 6000 Å. The (0–0) band of the transition is predicted to be several times less intense than nearby hot bands even at temperatures as low as 300 K. The computed ? 2B2 spectroscopic parameters are Te=1.18 eV, Re=1.26 Å, ϑe=102°, ω1=1461 cm−1, ω2=739 cm−1, and μ=0.46 D. There is a marked difference between experimentally determined ? 2B2 rotational constants and those deduced from the ab initio equilibrium geometry; this datum adds to the rapidly increasing evidence for strong vibronic coupling of the ? 2B2 state with high vibrational levels of the ground electronic state. The theoretical spectroscopic parameters of the experimentally better understood ? 2B1 excited state are Te=1.66 eV, Re=1.20 Å, ϑe=180°, ω1=1192 cm−1, 2 ω2=960 cm−1, ω3=2040 cm−1, and μ=0.0 D. The adiabatic excitation energy, bond angle, and bending frequency are in good agreement with experiment. However, the theoretical equilibrium bond length is significantly shorter than the value deduced from the experimental spectroscopic data and possible reasons for this discrepancy are discussed.

On the strong coupling approximation in two-state molecular spectroscopy

Two different but complementary perturbation solutions to a two-state strong vibronic coupling model are presented.

ChemInform Abstract: RADIATIVE TRIPLET LIFETIMES IN BENZENE AND AZABENZENES WITH PARTICULAR REFERENCE TO PHOSPHORESCENCE MECHANISMS IN BENZENE

Calculations of radiative triplet lifetimes of benzene and azabenzenes are carried out by making use of an INDO/S method in which the parametrization of the CNDO/S method is used, retaining the semi-empirical Slater-Condon parameters determined in the INDO/2 method. The calculated excitation energies, oscillator strengths, and radiative lifetimes are in reasonable agreement with experimental values. The possible phosphorescence mechanisms for the 3B1u state of benzene are discussed rather in detail, considering the first-order vibronic as well as the first-order spin-orbit and the second-order spin-vibronic couplings. It is concluded that the strong first-order vibronic coupling between the triplet manifolds, 3B1u and 3E1u, is responsible for the almost purely out-of-plane polarized phosphorescence of benzene, borrowing an intensity from the 3E1u-1A1g intercombination, and that the effects of the first-order spin-orbit and the second-order spin-vibronic couplings are small. The conclusion is in accord wit...

Radiative Triplet Lifetimes in Benzene and Azabenzenes with Particular Reference to Phosphorescence Mechanisms in Benzene

Abstract Calculations of radiative triplet lifetimes of benzene and azabenzenes are carried out by making use of an INDO/S method in which the parametrization of the CNDO/S method is used, retaining the semi-empirical Slater-Condon parameters determined in the INDO/2 method. The calculated excitation energies, oscillator strengths, and radiative lifetimes are in reasonable agreement with experimental values. The possible phosphorescence mechanisms for the 3B1u state of benzene are discussed rather in detail, considering the first-order vibronic as well as the first-order spin-orbit and the second-order spin-vibronic couplings. It is concluded that the strong first-order vibronic coupling between the triplet manifolds, 3B1u and 3E1u, is responsible for the almost purely out-of-plane polarized phosphorescence of benzene, borrowing an intensity from the 3E1u-1A1g intercombination, and that the effects of the first-order spin-orbit and the second-order spin-vibronic couplings are small. The conclusion is in accord with the analyses of the Zeeman and MI DP spectra presented by van Egmond and van der Waals.

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.

Resonance Raman scattering in molecular dimers

A systematic study is initiated of resonance Raman scattering in molecular systems with overlapping electronic absorption bands. Resonance Raman spectra, excitation profiles, and depolarization ratios are calculated for a simple molecular dimer in which the two overlapping Franck–Condon progressions are related through the permutational symmetry of the dimer. The model used is highly idealized, but can be solved exactly for a complete range of intermolecular coupling strengths. In the weak and strong intermolecular coupling regions, the exact results are compared with the physically more transparent results obtained from a low-order perturbation treatment. The spectra and profiles show properties characteristic of both totally symmetric and nontotally symmetric modes. The profiles and polarization dispersion curves are subject to both electronic and vibronic interference effects. Anomalous extrema of the depolarization ratio are often found to coincide with minima rather than maxima in the excitation profile. A pairwise comparison of the excitation profiles of Rayleigh lines, Raman fundamentals, and Raman overtones shows characteristic resonance–antiresonance coincidences. It is shown that interference effects of this sort are a general feature of systems exhibiting strong vibronic coupling.

Electronic and vibronic spectra of Pr 3+ in LiYF 4

The polarized absorption and fluorescence spectra of Pr 3+ in single crystals of LiYF 4 having the scheelite structure have been investigated and assignments made on the basis of S 4 site symmetry. Strong vibronic coupling associated with the 3H 4→ 3H 5, 1D 2 transitions in absorption and the 3P 0→ 3H 4,6 transitions in fluorescence was observed. Using selection rules for vibronic coupling and the known k = 0 phonons, these “extra” features of the spectrum can be accounted for in polarization and frequency.

Isotopic and vibronic coupling effects in the valence electron spectra of H2 16O, H2 18O, and D2 16O

Isotopic shift data for Hei induced high resolution valence electron spectra of H2 16O, H2 18O, and D2 16O are presented. From the differences in the vibrational subspectra we were able to deduce adiabatic ionization energies and geometries of the ions and to assign the excited vibrations to normal modes. The ν2 progression in the 2A1 band was found to be affected by strong vibronic coupling.

Vibrational Electronic Coupling and a Close Look at a Severe Case

AbstractElectronic spectroscopy, at once the oldest and most intricate branch of spectroscopy, has seen intense activity over the past decade. The difference between small‐molecule and large‐molecule spectroscopy is pointed out. The emphasis here is on larger polyatomics. Certain developments of note, especially of the interpretation of unresolved rotational fine structure, are mentioned. No point of principle has remained more tantalizing than the issue of the integrity of an electronic state: to what extent are electronic and nuclear motions really separable, in the Born‐Oppenheimer sense? There is much new theory, yet quantitative applications of theory to real cases are few, especially in polyatomic molecules. A straightforward computational approach to vibronic (= vibrational‐electronic) coupling in molecules such as naphthalene has proved to be quantitatively successful. Physical insight is harder to obtain, however, but a fairly straightforward explanation (based on a polyatomic version of Walsh's rules) can be offered for the presence of exceptionally strong vibronic coupling between two excited electronic states of azulene (C10H8). The effects of this coupling are so profound that the electronic spectrum is highly sensitive to such minor influences as partial deuteration or changes of solvent. These effects can be modelled rather successfully.

Vibronic coupling in cubic complexes

This paper examines the consequences of a strong vibronic coupling on orbitally triply degenerate levels in a cubic environment for the three cases in which spin-orbit coupling is weaker than, comparable with, or stronger than the vibronic coupling. It is shown that vibronic orbital reduction factors may be strongly temperature dependent. The consequences of this temperature dependence for the interpretation of magnetic susceptibility measurements are briefly discussed. An Appendix details a method for the evaluation of overlap integrals between harmonic oscillator eigenfunctions.

Stark effects on the B 1g and A u nπ* triplet states of p-benzoquinone

The results of polarized Stark effect absorption experiments on the lower triplet states of p-benzoquinone (PBQ)- h 4 and - d 4 in single crystals at 1.8°K are reported. These measurements give strong support for the assignment of the lowest triplet state as triplet 3B 1g (nπ*). The origin of this state in PBQ- h 4 is observed as an electric field induced transition at 18602.8 cm −1 and is interpreted as the g-inversion level of a double-minimum potential well. The line observed at 18619.7 cm −1 in the PBQ- h 4 crystal is therefore assigned as the u-inversion level of this double well with A u (B 1g Θ b 1u) total symmetry. Its intensity manifests the strong vibronic coupling that occurs among the B tg and A u nπ* triplet states along b 1u-type nuclear motions.

Lattice—Ion Interactions in the Ligand Field Theory of Trigonally Distorted Octahedral V3+ Complexes

AbstractThe theoretical expressions for the magnetic susceptibility and g‐values of trigonally distorted octahedral V3+ ion have been developed on the basis of molecular orbital method of Stevens [19] and Bose et al. [20]. Results are discussed considering the less strong vibronic coupling (dynamic Jahn‐Teller effect) in which an orbital triplet interacts with the vibrational E‐modes of the ligands. Comparison is made with experimental results on magnetic susceptibility, g‐values, and optical absorption with a unique set of values of parameters in the theoretical expressions at all temperatures. The Jahn‐Teller coupling parameter appears to be appreciable in some of the complexes.

Distortion of Excited Molecules in Organic Solids

AbstractIn this paper we present some ideas concerning the role of the crystal field in stabilizing dynamically distorted electronic states of aromatics. It is shown that a crystal field term of appropriate symmetry reveals in a dramatic way the result of strong vibronic coupling in emission spectra. Conditions under which these distortions are bound to occur are discussed with an emphasis on qualitative understanding. In this context the role of predissociating modes in spectra of aromatics is touched upon and the ideas are demonstrated through discussions of the emission spectra of pyrazine, p‐dibromobenzene and m‐dichloropyrazine.

Photoluminescence of Radiation Defects in Cubic SiC: Localized Modes and Jahn-Teller Effect

Radiation defects were introduced into cubic SiC by 120-keV He-ion implantation, or by 1-MeV electron bombardment. Some of the defects persist after a 1600 \ifmmode^\circ\else\textdegree\fi{}C anneal. A low-temperature luminescence spectrum of one of the persistent defects reveals strong vibronic coupling, with localized and resonant modes. The spectrum has an unusual temperature dependence, with two abrupt changes below 13 \ifmmode^\circ\else\textdegree\fi{}K. The changes are attributed to the Jahn-Teller effect, and the distortion is accounted for by coupling with the 66.5-meV resonant mode. A possible model for the defect is the Watkins-Corbett impurity-vacancy model that was found to be appropriate for several persistent defects in Si.

Theory of Molecular Polaritons. Application to the Reflection Spectra of Anthracene, 1,5-Bis(dimethylamino)pentamethinium Perchlorate, and Some Other Cationic Dye Crystals

The reflection spectra of anthracene in the 3800 Å region and 1,5-bis(dimethylamino)pentamethinium perchlorate (BDP) in the 4090 Å region are calculated using molecular polariton theory. In the crystal the anthracene transition, oscillator strength f = 0.1, involves weak to intermediate vibronic coupling of molecular exciton states, and the model calculations easily reproduce the main features of the observed reflection spectrum. In contrast, the intense transition (f = 3.31) of the dye BDP involves strong vibronic coupling of molecular excitons, and polariton theory with phenomenological damping constants does not adequately reproduce the “vibrational” structure observed in the reflection spectra. Theory and experiment are reconciled by considering the coupling among and distribution of two-exciton states in which vibronic and vibrational excitations occupy different lattice sites.