Nuclear Coordinate dependence of electronic transition moments in orbitally forbidden transitions: A new interpretation of deuterium isotope effects

The nuclear coordinate dependence of electronic transtion moments has been investigated for the purpose of finding new interpretations of deuterium isotope effects on spectral intensities and radiative decay rates in orbitally forbidden electronic transitions. By using “AO following nuclei” wavefunctions as the building block for the electronic wavefunction in the adiabatic BO vibronic wavefunction, the spin-free hamiltonian is diagonalized to generate eigenfunctions and eigen-energies. It is found that the electronic transtion moments based on these eigenfunctions show dependences upon the vibrational modes which are not directly involved in vibronic coupling. This leads to interpretations of the deuterium isotope effects in T₁ → S₀ radiative transitions of aromatic hydrocarbons and S₀ → S₁ absorption in pyrazine which are not based on the conventional Herzberg—Teller or non-BO coupling.     

Jahn-Teller effect in the cyclopentadienyl radical: an example of three mode coupling

The cyclopentadienyl radical C₅H₅· vibronic wavefunctions and energy levels are calculated and used to discuss the vibrational structure of the allowed ²A″₂ ←²E″₁ electronic transition in C₅H₅ and allowed A←E transitions in similar systems in which Jahn-Teller coupling occurs through two or three vibrational modes. As has been pointed out by Alpert and Silbey, the vibrational pattern predicted for single mode coupling is markedly distorted. With larger coupling parameters than those used by Alpert and Silbey, in an E ← A transition (e.g., the benzene Rydberg states) progressions in the individual coupling vibrations cannot be distinguished. In an A ← E transition (e.g., C₅H₅·), the higher progression members lose intensity and combination levels in the coupling vibrations appear. In both cases, a complex pattern of 1-1 hot band splittings results. Comparison is made with the experimental C₅H₅· spectrum, and assignments are suggested for three of the observed A″₂ state frequencies.     

Strong vibronic coupling effects in ionization spectra: The “mystery band” of butatriene

A theory of vibronic coupling in molecules is presented and applied to butatriene. The energies and coupling constants which enter the calculation are computed using ab initio Hartree—Fock and many-body methods. The influence of the energy splitting and the coupling constants on the calculated spectrum is discussed. It is definitely shown that the “mystery band” in the photoelectron spectrum of butatriene arises from the vibronic coupling between the electronic states ²B_3g and ²B_3u. To reproduce the experimental observations it is essential to include in the calculation both totally and non-totally symmetric vibrational modes.     

The Optical Spectrum of Au2+

The electronic structure of the Au₂⁺ cation is essential for understanding its catalytic activity. We present the optical spectrum of mass-selected Au₂⁺ measured via photodissociation spectroscopy. Two vibrationally resolved band systems are observed in the 290–450 nm range (at ca. 440 and ca. 325 nm), which both exhibit rather irregular structure indicative of strong vibronic and spin-orbit coupling. The experimental spectra are compared to high-level quantum-chemical calculations at the CASSCF-MRCI level including spin-orbit coupling. The results demonstrate that the understanding of the electronic structure of this simple, seemingly H₂⁺-like diatomic molecular ion strictly requires multireference and relativistic treatment including spin-orbit effects. The calculations reveal that multiple electronic states contribute to each respective band system. It is shown that popular DFT methods completely fail to describe the complex vibronic pattern of this fundamental diatomic cation.     

Polarization and assignment of the two-photon excitation spectrum of benzene vapor

The two-photon excitation (TPE) of benzene fluorescence in the vapor phase at 60 torr is reported for the total-energy region from 38 086 cm^?1 to 42 441 cm^?1 using both circular and linear polarized light from a nitrogen-pumped dye-laser. The theory of the polarization dependence of the vibronic transitions in benzene is briefly reviewed, and it is seen how transitions involving vibrations of b_1u symmetry are expressly forbidden for this type of TPE experiment in which the two photons are identical. Five vibronic origins with distinctive rotational contours and polarization dependence are identified in the TPE spectrum. The υ₁₄(b_2u) vibronic origin at 1570 cm^?1 (above the electronic origin of the ^IB_2u state) stands out very prominently in the linear polarized spectrum, but nearly disappears in the circular polarized spectrum. This striking polarization dependence indicates a significant contribution of A_2u electronic states to the intermediate states of this TPE vibronic transition. The relatively great strength of the υ₁₄ band may be due to vibronic borrowing by the b_2u mode from the ground electronic state (A_1g).     

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.     

Low temperature luminescence spectra of the d10s2 complexes Cs2MX6 (M = Se,Te and X = Cl,Br). The Jahn—Teller effect in the Γ−4(3T1u) excited state

The emission spectra of the title compounds in microcrystalline form have been measured at 10 K. The extensive vibrational progression in the e_g mode is indicative of a tetragonal Jahn—Teller distortion in the Γ^?₄(³T_1u) excited state. The vibronic coupling of a threefold electronic state with a doubly degenerate e_g mode (T—e coupling), linear in the nuclear coordinates, has been reinvestigated considering spin—orbit coupling up to second order perturbation on energy levels which result from an a¹_1gt¹_1u electron configuration. For an estimation of Jahn—Teller coupling constants, the intensity distributions in the progressions were compared with the theoretical line shape functions which were obtained from a model which also permits the determination of potential energy minima and vibrational fundamentals of the excited state. The unusually large increase in the e_g vibrational frequency compared to the ground state is due to Jahn-Teller forces which distort the potential surface, yielding steeper excited state energy curves.     

Subduced selection rules for vibronic transitions ind 3 octahedral complexes

Forbidden electronic transitions are often weakly allowed through vibronic coupling to normal modes of the molecule. In transition metal complexes, the first order strong coupling appears in many cases to select specifically one of the available asymmetric modes. In this work the Intermediate Ligand Field model has been extended to vibronic coupling. The basis functions and tensor operators are described as species subduced from the vibronic generative group SU(3) which results from the diagonal restriction of the direct product of the electronic generative group SU(2) with the three dimensional harmonic oscillator group SU(3). This model implies that transitions between strongly coupled bases are permitted only through an overall octupole operator. All lower multipoles are forbidden and in particular the dipole is eliminated by the requirement for a translationally invariant centre of mass. The model permits any combination of multipole operators for separate electronic and vibrational transitions which result in the overall octupole. This theory is applied to two cases ofd ³ complex spectra. It provides an unambiguous assignment of the⁴ A _2g -⁴ T _2g transition in the absorption spectrum of solid [MnF₆]^4– and of the MCD spectrum of the⁴ A _2g -(² T _1g ,⁴ T _2g ) region in [Cr(H₂O)₆]³⁺. In the latter complex, the observed exclusive coupling of the² T _1g state tot _1u (stretch) and the⁴ T _2g state tot _1u (twist) is predicted by the model.     

Tris (methylidene)-cyclopropane (“[3]Radialene”). Part 2. Electronic states of the molecular cation and revised UV.-absorption spectrum of the parent neutral

The photoelectron spectrum of tris (methylidene)-cyclopropane 1 (“[3]radialene”) is reported and the electronic states of 1 ⁺ assigned. Jahn-teller activity in the degenerate states of 1 ⁺is discussed. Differences in the Franck-Condon profile of the first PE band and the Rydberg series in the Vacuum-UV./UV. absorption spectrum indicate for the Rydberg series (n=3) a ¹A″₂-species, which supports earlier tentative proposals. The high intensity absorption in the 5.5 eV-6 eV energy range of the latter spectrum recorded earlier are definitely due to impurities. The vibrational fine structure of a weak band system around 5.5 eV in our spectrum suggests for this transition S₀→S₂(¹A′₁), which is dipole forbidden but borrows intensity from S₁(¹E′) trough vibronic coupling via an e′-mode. From vapor pressure measurements ε(λ_max=289 nm) = 9390± 1170 for gaseous 1 was found.     

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.     

Hydrogen bonding between solvation shells around gd3+ from cooperative vibronic spectra

Cooperative vibronic spectra involving Gd³⁺ electronic transitions and the vibrational transitions of nearby water molecules are used to determine the stretching spectrum for isotopically dilute OH in a solution of GdCl₃ in D₂O. The OH stretching spectrum of water molecules in the first hydration sphere is shifted to lower energy than that of the bulk liquid.     

The two-photon fluorescence excitation spectrum of dibenzothiophene

The two-photon fluorescence excitation spectra of dibenzothiophene crystal (≈77 K) and solution have been investigated in the spectral region 30000–38000 cm^?1 (≈3350-2600 Å). Two electronic transitions have been found. Both the oriented gas model results applied to the crystal and the circular/linear polarization ratio to the solution claim for an ¹A₁ ← ¹A₁ assignment of the transitions. Not completely resolved vibronic structures in the crystal spectrum were observed for both transitions for which a tentative assignment to A₁ total symmetry is discussed. It has been found that the intensity of the first electronic band system arises not only from a purely electronic (i.e., Franck-Condon) mechanism, but also from its interaction with a higher state through totally symmetric vibrations.     

Optische Absorptions-Spektroskopie an ionischen Ozoniden

Optical Absorption Spectroscopy on Ionic Ozonides Electronic transitions of ionic ozonides of alkali-metal and tetraorganylonium cations have been investigated in the range from 200 to 2000 nm. Optical absorption measurements of diffuse reflexion on powder and transmission on single crystals displayed a broad absorption at ∼480 nm and 490 nm, respectively. Optical spectra of the O₃^–-radical in solution gave a well resolved vibronic finestructure with spacings of ∼790 cm^–1, symmetrically to the maximum of the absorption band at 460 nm, and uneffected of the counter ion and solvent used. The finestructure allows a correlation to the ν_s-vibration of the ozonide ion in the excited state. The observed electronic transition is assigned to ²B₁ → ²A₂, based on MO-observations and ab initio calculations. Earlier reports of a strong absorption band at low energy for O₃^– cannot be reconfirmed.     

S1←S0 Vibronic spectrum and structure of 2,2-difluoroethanal in the S1 state

The vibronic spectrum of the 2,2-difluoroethanal vapor was recorded using a multipass optical cell with an optical length of at least 140 m. The spectrum in the region of 300—364 nm was assigned to the S₁S₀ electronic transition (from the ground S₀ to the first excited singlet S₁ electronic state); the vibrational structure of the spectrum was analyzed. The spectrum bands were assigned to two systems of vibronic transitions, namely, transitions between the levels of the cis-conformer (S₀) and of the S₁ conformers, with the origins (0₀ ⁰ transitions between the zero vibrational levels of conformers) at 29192 and 29087 cm^–1, respectively. Analysis of the spectrum showed that the S₁S₀ electronic excitation of the cis-conformer was followed by rotation of the CHF₂ top and pyramidal distortion of the carbonyl fragment. A number of fundamental frequencies were found for S₁ conformers, in particular, torsion and inversion energy levels. The experimental data are in satisfactory agreement with the results of quantum-chemical calculations for the 2,2-difluoroethanal molecule in the S₀ and S₁ states.     

Line shapes in electronic absorption spectra. Phenanthrene

The 3000 Å, (¹B₂ ← ¹A₁), absorption system of phenanthrene in durene crystals at 4°K illustrates an electronic transition, which is subject to near-resonance vibronic perturbations whose effect is intermediate to both the small (sparse intermediate) and large molecule (statistical) limits. Both broad (300 cm^?1) and narrow (10 cm^?1) lines are evident. A model is proposed which incorporates both these features by fast allowing for a consideration of the interaction between a small number of discrete levels, those associated with the largest coupling, followed by a treatment of the broadening of these levels through interaction with the remaining near continuum of states of the lower electronic state. Thus, one and the same electronic state provides both a sparse and dense manifold of levels. An important result of the model is that in terms of absorption intensities all the lines emerge with the same heights but differ in widths. When the intensities are summed with respect to energies this aspect is obscured. This approach has been shown to satisfactorily reproduce many of the features of the ¹B₂ absorption spectra of phenanthrene and phenanthrene-d₁₀. The ¹B₂ absorption systems have also been measured in the vapour phase and fine structure attributable to vibronic coupling and sequence band development are discussed.     

A theoretical study of the chiroptical properties of molecules with isotopically engendered chirality

There has been a considerable interest in the chiroptical properties of molecules whose chirality is exclusively due to an isotopic substitution and numerous examples for the electronic circular dichroism (CD) spectra of isotopically chiral systems have been reported in literature. Four different explanations have been proposed for the mechanism as to how the isotopic substitution induces a chiral perturbation of the otherwise achiral electronic wave function; however, up to now no conclusive answer has been given about the dominating effect responsible for the experimental observations. In this study we will present, for the first time, fully quantum-mechanical calculations of the CD spectra of three different molecular systems with isotopically engendered chirality. As examples, we consider the spectra of organic molecules with ketone and alpha-diketone carbonyl and diene chromophores. The effect of vibronic couplings for the reorientation of the electric and magnetic transition dipole moments is taken into account within the Herzberg-Teller approximation. The ground and excited state geometries and vibrational normal modes are obtained with (time-dependent) density functional theory [(TD)DFT], while the vibronic coupling effects are calculated at the TDDFT and density functional theory/multireference configuration interaction (DFT/MRCI) levels of theory. Generally, the band shapes of the experimental CD spectra are reproduced very well, and also the absolute CD intensities from the simulations are of the right order of magnitude. The sign and the intensity of the CD band are determined by a delicate balance of the contributions of a large number of individual vibronic transitions, and it is found that the vibrational normal modes with a large displacement are dominant. The separation of the calculated CD spectrum into the different contributions due to the overlap of the in-plane and out-of-plane components (regarding the symmetry plane of the unsubstituted molecule) of the electric and magnetic transition dipole moments yields information about the influence of the vibronic coupling effects for the reorientation of the corresponding transition dipole moments. In conclusion, the calculations clearly show that vibronic effects are responsible or at least dominant for the chiroptical properties of isotopically chiral organic molecules.     

Intensity distribution in the vibronic side bands of the Γ7(2 T 2g ) → Γ8(4 A 2g ) origin of ReX 6 2- doped K2PtCl6-type crystals

Intensities of vibronic transitions are calculated using an electronic vibrational coupling scheme of symmetrized and localized interactions. The model consists of an active central ion subject to a valence force field originating from nearest-neighbor displacements. The intensities of vibronic fundamentals are obtained from a generalized Lorentzian line shape function which is applied to the ₇(² T _2g ) ₈(⁴ A _2g ) transition of ReCl ₆ ^2- and ReBr ₆ ^2- in various cubic host crystals A₂MX₆ (A = Rb, Cs; M = Te, Sn, Pb; X = Cl, Br). Relative intensities of the odd vibronic side bands are calculated without knowing actual values for ligand field and spin-orbit coupling parameters, and considering only octahedral vibrational frequencies. The sidebands acquire intensity by a coupling which is cubic in the electron coordinates and linear in the nuclear normal coordinates. With some necessary approximations the present model is able to reproduce the experimental intensity distribution satisfactorily.Dedicated to Professor Dr. H. Hartmann on the occasion of his 65th birthday     

Stark shifts of the visible absorption systems of the NO−2 ion in NaNO2

Stark effect measurements on the lowest triplet and singlet transitions of the nitrite ion show that the change of dipole moment on excitation is very small (ca. 0.30 D) and of opposite sign for the two states. The dipole moment change in the triplet manifold is also found to distinctly depend on vibrational (ν₂) excitation. This is explained as a result of vibronic coupling among B₁ triplet states.     

Analysis of the chemiluminescence from electronically excited lead oxide generated in a flow tube reactor

The chemiluminescence from electronically excited lead oxide formed during the reaction between lead vapor and either ³Σ O₂ or ¹Δ O₂ has been studied. The reactions were accomplished in a flow tube reactor. A microwave discharge was used to generate ¹Δ O₂. The vibronic spectrum was analyzed and the band head assignments were used in a linear least-squares calculation to obtain the vibronic molecular constants for the X, a, b, A, B, C, C′, D, and E electronic states of lead oxide. Based on these and other molecular constants, Franck-Condon factors were calculated for the transitions to the ground state and also for the A-a and D-a transitions. Evidence was presented to support a kinetic analysis of the mechanism leading to chemiluminescence under the experimental conditions encountered in the flow tube reactor. Mechanisms presented earlier were verified by the present data.     

Polarized IR and Raman spectra of kdy(moo4)2 single crystals,and the 92MO-100MO isotope effect

Polarized IR and Raman spectra below 4000 cm^?1 for single crystals of KDy(MoO₄)₂ are presented and discussed in relation to molecular and crystal structures. The spectroscopic data indicate additional intermolecular interactions due to pair coupling of the molybdate tetrahedra. This effect, combined with the multilayer crystal structure, is found to restrict the vibrational degrees of freedom, disturbing the selection rules for vibrational transitions. The spectra of first and higher-order transitions are described on the basis of ⁹²Mo/¹⁰⁰Mo isotopic-exchange effects and Y/Dy and K/Na substitutions.