Vibronic Coupling Parameters Research Articles

Raman dispersion spectroscopy on the highly saddled nickel(II)-octaethyltetraphenylporphyrin reveals the symmetry of nonplanar distortions and the vibronic coupling strength of normal modes

We have measured the polarized Raman cross sections and depolarization ratios of 16 fundamental modes of nickel octaethyltetraphenylporphyrin in a CS2 solution for 16 fundamental modes, i.e., the A1g-type vibrations ν1, ν2, ν3, ν4, ν5, and φ8, the B1g vibrations ν11 and ν14, the B2g vibrations ν28, ν29, and ν30 and the antisymmetric A2g modes ν19, ν20, ν22, and ν23 as function of the excitation wavelength. The data cover the entire resonant regions of the Q- and B-bands. They were analyzed by use of a theory which describes intra- and intermolecular coupling in terms of a time-independent nonadiabatic perturbation theory [E. Unger, U. Bobinger, W. Dreybrodt, and R. Schweitzer-Stenner, J. Phys. Chem. 97, 9956 (1993)]. This approach explicitly accounts in a self-consistent way for multimode mixing with all Raman modes investigated. The vibronic coupling parameters obtained from this procedure were then used to successfully fit the vibronic side bands of the absorption spectrum and to calculate the resonance excitation profiles in absolute units. Our results show that the porphyrin macrocycle is subject to B2u-(saddling) and B1u-(ruffling) distortions which lower its symmetry to S4. Thus, evidence is provided that the porphyrin molecule maintains the nonplanar structure of its crystal phase in an organic solvent. The vibronic coupling parameters indicate a breakdown of the four-orbital model. This notion is corroborated by (ZINDO/S) calculations which reveal that significant configurational interaction occurs between the electronic transitions into |Q〉- and |1B〉-states and various porphyrin→porphyrin, metal→porphyrin, and porphyrin→metal transitions. The intrastate coupling parameters are used to estimate the excited electronic states’ displacements along the normal coordinates with respect to the ground state and their contributions to the reorganization energy. It turns out that the |B〉-state is predominantly affected by symmetric A1g-displacements, whereas the |Q〉-state is subject to A2g, B1g, and B2g displacements of its equilibrium configuration. While the former is induced by the combined effect of ruffling and saddling, the latter arises from Jahn–Teller coupling within the degenerate states.

Vibronic structure of the emission spectra from single vibronic levels of the S1 manifold in naphthalene: Theoretical simulation

The vibrational structure of electronic spectra of naphthalene is simulated by means of a perturbative calculation of the intensities, based on the vibronic basis set. The formalism is implemented to include the contribution of Herzberg–Teller induced activity for totally symmetric modes and to describe the interference between the latter and the allowed Franck–Condon intensity. Geometries, vibrational normal modes, and vibronic coupling parameters required to model the spectra are obtained by means of ab initio and semiempirical calculations. The structure of absorption and single vibronic level fluorescence spectra is reproduced in detail and consistently for all the spectra examined. It is shown that the intensity of modes ν8a and ν5a is strongly affected by interference effects, and that Dushinsky mode mixing of totally symmetric modes plays a major role in redistributing the intensity among the vibronic bands of the spectra.

Analysis of the Intervalence Band in the Oxidized Photosynthetic Bacterial Reaction Center

Electronic and vibronic coupling parameters of the oxidized photosynthetic bacterial reaction center (P+) of Rhodobacter sphaeroides are estimated by analyzing its ≈2600 cm-1 intervalence band which was recently measured by Breton et al. A two-mode model is used which pictures P+ as an unsymmetrical mixed-valence dimer. One mode (q1) has even and the other mode (q2) has odd interchange symmetry with respective frequencies ν1 ≈ 154 cm-1 and ν2 ≈ 1630 cm-1. The vibronic coupling is strong in the former and weak in the latter and in sum is larger than the electronic coupling. The asymmetry parameter which appears in the model is estimated from the ESR data of Rautter et al. The energy difference between the minima of the two coupled potential surfaces is ≈850 cm-1, whereas the Franck−Condon transition energy is ≈2100 cm-1. An analysis of the potential surfaces and probability distribution in configuration space show that P+ is a strongly delocalized mixed-valence system.

5262725 Magnetic resonance imaging method and device for reducing image errors in a magnetic resonance image

The linear and quadratic Tg ⊗ εg Jahn–Teller effect in the Tg (Tg = 2T2g, 3T1g) ground states of low-spin octahedral cyano complexes of 3d-transition metals (M = TiIII, VIII, MnIII, FeIII, CrII, MnII) has been studied. Vibronic coupling parameters have been derived using density functional theory to calculate energies of Slater determinants, which result from various electron distributions within the t2gn configuration due to the metal based t2g(3d) molecular orbitals (n = 1, 2, 3, 4). Tetragonal elongations are found in the case of TiIII, MnIII and CrII, and compressions for VIII, FeIII and MnII, and these establish the metal–ligand π-back donation as the dominant effect and driving force for the geometry distortions and energy stabilizations towards non-degenerate 2B2g(t2g1,t2g5) and 3A2g(t2g2,t2g4) ground states. The strength of the Jahn–Teller coupling is very weak and found not to follow a monotonic trend across the transition metal series but is shown to be weakest for TiIII, VIII and FeIII, slightly larger for MnIII, increases further to MnII and is found to be the strongest but is still weak for CrII.

Antiresonance in hyper‐Raman excitation spectra

AbstractA scattering model of interference between the Franck–Condon and Herzberg–Teller terms was studied in the preresonance regions of hyper‐Raman spectroscopy. It is shown how profound antiresonance effects are connected with molecular properties such as potential curve displacement and vibronic coupling parameters.

Intramolecular aspects of the electron transfer in the biferrocenium mixed-valence cation, using PKS theory

The electron transfer properties of the mixed-valence biferrocenium cation are investigated using the Piepho-Krausz-Schatz (PKS) vibronic theory. Parameters of the model are deduced from both vibrational spectroscopy (stiffness constant) and MO calculations (transfer integral and vibronic coupling parameter); the computed asymmetric distortion agrees with structural data; a specific heat Schottky anomaly, recently reported, is also explained in the frame of that model. The low-temperature transfer rate is also computed. it ranges from 1.5 × 10 10 to 8.7 x 10 12 s −1, according to the nature of the HOMO, and definitely lies higher than the Mössbauer timescale (≈ 10 8 s −1).

Franck–Condon structure of the S→S1 and S→S2 transitions in norbornadiene

We report an ab initio study of the geometry and force field of the S0, S1, and S2 electronic states of norbornadiene at the Hartree–Fock/6–31G* and configuration interaction singles/6–31+G levels of theory. The calculated Franck–Condon structures of the S0→S1 and S0→S2 transitions agree well with the structures observed in the optical absorption and energy loss spectra. It is argued that the 47 000 cm−1 absorption band which undergoes changes in the vibronic structure upon going from the gas to the solid phase owes its different activity to the freezing of the angle between the two ‘‘wings’’ of the cyclohexadiene part of the molecule. The complete neglect of differential overlap/spectroscopic parametrization method is used to locate valence states of the title molecule and to calculate vibronic coupling parameters to predict vibronic activity of the nontotally symmetric modes in the spectra. It is demonstrated that the highest frequency C=C stretching mode of the b2 symmetry is the most effective in bringing intensity into the S0→S1 transition. The positions of the five lowest valence states obtained by the complete neglect of differential overlap/spectroscopic parametrization method agree very well with the peaks of bands observed in the electron energy loss spectra.

Optical–optical double resonance multiphoton ionization spectroscopy of ammonia-d3. II. Jahn–Teller effect and related Fermi resonance of the B̃ 1E″ state

By selecting a number of resonant à 21 rotational lines in the optical–optical double resonance multiphoton ionization spectroscopy (OODR-MPI) of ammonia-d3, we have obtained rotationally resolved spectra of the ND3 B̃←à 21←X̃ 00 transitions in the range of 550–730 nm, in which not only were we able to reanalyze rotationally the previously studied bands [J. Opt. Soc. Am. B 7, 1884(1990)], but also to assign rotationally and vibronically some novel spectra pertaining to the ν1, ν3, ν4, and ν3+ν4 excitations. Based on the symmetry assignment and the relationship of the vibronic coupling level energies between the single and dual mode cases, we have found that the Jahn–Teller splitting of the ND3 B̃ state invokes a novel type of the Fermi resonance, the nonadiabatic Fermi resonance. By taking account of this Fermi resonance, the modified vibronic coupling parameters of the ν3 and ν4 modes were calculated to be λ3=0.047 and λ4=0.023, which agrees well with the previous theoretical expectation that the ammonia B̃ state is subject to a mild dynamic Jahn–Teller effect. At present, four pairs of the nonadiabatic Fermi resonance have been discovered among the ND3 nonadiabatic levels, which can be separated into two types—one with the same selection rules as a conventional Fermi resonance, i.e., B̃ 31(1/2)–B̃ 42(5/2), B̃ 11–B̃ 42(1/2), and B̃ 31(3/2)–B̃ 42(3/2), the last of which was studied quantitatively with a coupling parameter K=114, and the other with novel selection rules, i.e., B̃ 31(1/2)–B̃ 11.

Resonance Raman spectroscopy of the B1u region of benzene: Analysis in terms of pseudo-Jahn–Teller distortion

Raman spectra of benzene and benzene-d6 vapor obtained with excitation in the range from 208 to 188 nm are presented and discussed in terms of vibronic coupling of the resonant B1u state and the nearby E1u electronic state. The Raman spectra show strong activity in the binary overtones and combinations of the e2g modes ν8, ν9, and ν6 with the ν8 activity being dominant. (The Wilson numbering scheme for the modes of vibration is used throughout.) These bands, plus a progression in ν1 alone or in combination transitions involving two quanta of e2g modes, constitute the major intensity bands in the spectra. A simple first-order vibronic coupling model can be constructed which accounts adequately for most of the intensity in the Raman spectra observed in resonance with the B1u state, but this model results in a calculated absorption spectrum that is qualitatively different from that observed. The nature of the discrepancy indicates a significant Duschinsky mode rotation in the B1u state relative to the ground state. An analysis of the vibronic coupling of the B1u state with the nearby E1u state is performed using semiempirical calculation methods to provide excited state geometries, vibrational frequencies, and vibronic coupling parameters. This analysis confirms that there is strong vibronic coupling between these states resulting in a pseudo-Jahn–Teller effect. This results in a highly distorted potential surface for the B1u state with three D2h symmetry antiquinoidal minima lower in energy by ∼1000 cm−1 than the D6h symmetry geometry. The three minima of the threefold symmetric potential surface are separated by local maxima corresponding to the quinoidal geometry with a height of ∼300 cm−1. Three of the four e2g modes are calculated to have significant vibronic activity with mode 8 much stronger than modes 6 or 9. A small Jahn–Teller coupling is calculated. A strong Duschinsky rotation results from the vibronic activity of more than one mode. The absorption spectrum and the resonance Raman spectra calculated from this model are in good agreement with the experimental results. This analysis provides the first evidence for the expected pseudo-Jahn–Teller instability of the isolated 1B1u state of benzene.

Multimode analysis of depolarization ratio dispersion and excitation profiles of seven Raman fundamentals from the haeme group in ferrocytochrome c

AbstractExperimental data for depolarization ratio dispersion (DPD) and resonance excitation profiles (REPs) with high spectral resolution (20 cm−1) are provided for seven Raman fundamentals in the region between 1150 and 1650 cm−1 of the haeme spectrum from ferrocytochrome c. They cover the resonant region of the Q‐band and the preresonant region of the B‐band. A self‐consistent analysis of the depolarization ratio dispersion (DPD) and resonance excitation profiles (REPs) of these Raman lines is carried out by explicit consideration of multimode mixing. This is achieved by first formulating the Raman tensor in Loudon's formulation to fifth order for each mode, thus restricting the contribution of the fifth‐order term to the vibration itself and omitting multimode contributions. By fitting this expression to the DPDs and REPs of each Raman mode, one obtains coupling parameters which in the next step are inserted into the fifth‐order term of each mode. Thus one takes account of their contributions to multimode mixing. To account for contributions of lower frequency modes, an effective ‘helping rest mode’ was added to the multimode contributions. This procedure yields satisfactory fits to all data sets. The respective fits to the DPD and REP of the oxidation marker line at 1363 cm−1 reproduce also the corresponding REP and DPD in the resonant region of the B‐band reported by Champion and Albrecht with a high degree of accuracy. The vibronic coupling parameters obtained are consistent with the weak coupling limit. Further, they confirm the validity of Gouterman's four‐orbital model for ferrocytochrome c.

Highly resolved depolarization dispersion and excitation profiles of Raman fundamentals of protoporphyrin IX in a cytochrome c matrix

AbstractNew experimental data for depolarization dispersion (DPD) and excitation profiles (EP) with high spectral resolution (20 cm−1) are provided for Raman fundamentals of protoporphyrin IX in ferrocytochrome c between 17000 and 22 500 cm−1, covering the resonant region of the Q‐bands and the pre‐resonant region of the B‐bands. Both DPD and EPs of the lines at 1312 and 1585 cm−1 (A2g), at 1363 cm−1 (A1g) and at 1621 cm−1 (B1g) exhibit sharp structures. These result from multi‐mode contributions of vibrations which give intensity to the vibronic sideband of the Q‐absorption. On the basis of these highly resolved new data we have shown that the Raman tensor can be formulated in terms of Loudon's strictly time‐dependent perturbation formulation to third order augmented by a fifth‐order term representing the multi‐mode effects. From the EPs, which were measured in absolute units, we obtained values of vibronic coupling parameters for the Raman fundamentals which are consistent with the optical absorption spectra and show that vibronic coupling is weak for this type of molecule.

Low-energy spectrum of the Jahn-Teller impurity centres. I. Light and sound scattering as a method of determination of the Jahn-Teller impurity parameters

A method is suggested for the determination of the reduction factors from the relative intensity of the Rayleigh contribution to the non-resonant Raman scattering. The possibility of determining the reduction factors from the integral intensities of magnetic circular dichroism is also considered. The expressions for the mean values of the symmetrised displacements of the number of virtual phonons coupled with the Jahn-Teller impurity centre and the ground-state energy are obtained in terms of the light scattering cross section for an arbitrary strength of vibronic coupling. It is shown that elastic sound scattering experiments give the possibility of determining the vibronic coupling constant and parameters characterising the variation of elastic constants of impurity. The general relations for the reduction factors are examined and the analytical expressions for the multimode reduction factors in limiting case of weak and strong coupling are investigated.

Vibronic structure of nonadiabatic and fluxional states: Two-photon absorption spectroscopy of jet isolated 3s 1E′ s y m-triazine

The nature of nonadiabatic effects in the Rydberg and ground ionic states of jet-cooled sym-triazine is investigated by means of ultraviolet two-photon absorption spectroscopy. A highly resolved band system is observed in the region from 55 000 to 60 000 cm−1, which can be associated with excitation from an e′ lone pair to the 3s Rydberg orbital. A complete assignment of the low-energy bands of this system, as determined by isotope effects and comparison to model calculations, reveals a clear example of the dynamical Jahn–Teller effect for the case where only one mode, the ν6 ring distortion, is significantly active. On the basis of simple limiting models we derive approximate vibronic coupling parameters and present a quantitative description of vibronic motion in terms of adiabatic molecular coordinates. We conclude that sym-triazine, in its ground state one of the most rigid of medium-sized polyatomics, becomes strikingly fluxional in its Rydberg and ground ionic states, as the dynamic Jahn–Teller effect introduces a ring-distortion vibronic pseudorotation which can be characterized adiabatically in terms of a rotor frequency no greater than 80 cm−1. This is a limit, however, which the data shows is valid only well below a vibronic energy of 1100 cm−1, at which point the conical intersection is reached and all levels become intrinsically nonadiabatic.

Resonance Raman scattering with a forbidden but vibronically allowed electronic transition: Excitation profiles of combinations and overtones of copper tetraphenylporphyrin in the Q-band resonance

Resonance Raman scattering with the Q band of CuTPP shows a peculiar intensity pattern; bands due to combinations and overtones are strong, whereas the corresponding fundamentals are very weak. By a quantitative analysis of excitation profiles, this phenomenon has been fully accounted for on the basis of the vibronic theory of Raman intensities. Vibronic coupling parameters between the Q and B states of CuTPP have been obtained.

ChemInform Abstract: VIBRONIC ANALYSIS OF CIRCULAR DICHROISM SPECTRA OF DIMERIC SYSTEMS. CHIRAL MOLECULES CONSISTING OF TWO POLYACENE CHROMOPHORES

The CD spectra of (6R,15R)‐(+)‐6,15‐dihydro‐6,15‐ethanonaphtho [2,3‐c]pentaphene (DEP) and (7R,14R)‐(+)‐7,14‐dihydro‐7,14‐ethanondibenz [a,h] anthracene (DEA) are analyzed as dimers of anthracene and naphthalene, respectively. It is shown that vibronic coupling effects are essential in understanding the vibronic structure of CD spectra in these molecules. The simple molecular dimer model is shown to explain the main vibronic features of the CD spectra, but an extension of that model is needed to achieve good quantitative agreement between experimental and theoretical CD spectra for physically reasonable exciton and vibronic coupling parameters. This extended dimer model allows for a mixing of electronic states of monomers via electronic intermonomer interaction. It is shown that the CD spectrum of DEP locates the hidden 1Lb state of the anthracene molecule about 2150 cm−1 above the origin of the 1La state, and that these two states are electronically coupled in DEP. Only these two assumptions taken togeth...

Strong non-condon effects induced by electron correlation: N 2O +

The vibronic structure of the third band in the photoelectron spectrum of N 2O is investigated. It is shown by ab initio Green's function calculations that there are two ionic states within the energy range of the band which have almost equal spectral intensities due to strong electron correlation. These electronic states interact vibronically through both totally symmetric modes. By adjusting some of the vibronic coupling parameters the experimental results can be qualitatively reproduced. The nature of the vibronic structure is discussed in terms of nonadiabatic and non-Condon effects. The importance of this type of vibronic coupling effects in the inner valence region of ionization spectra is pointed out.

Vibronic analysis of circular dichroism spectra of dimeric systems. Chiral molecules consisting of two polyacene chromophores

The CD spectra of (6R,15R)-(+)-6,15-dihydro-6,15-ethanonaphtho [2,3-c]pentaphene (DEP) and (7R,14R)-(+)-7,14-dihydro-7,14-ethanondibenz [a,h] anthracene (DEA) are analyzed as dimers of anthracene and naphthalene, respectively. It is shown that vibronic coupling effects are essential in understanding the vibronic structure of CD spectra in these molecules. The simple molecular dimer model is shown to explain the main vibronic features of the CD spectra, but an extension of that model is needed to achieve good quantitative agreement between experimental and theoretical CD spectra for physically reasonable exciton and vibronic coupling parameters. This extended dimer model allows for a mixing of electronic states of monomers via electronic intermonomer interaction. It is shown that the CD spectrum of DEP locates the hidden 1Lb state of the anthracene molecule about 2150 cm−1 above the origin of the 1La state, and that these two states are electronically coupled in DEP. Only these two assumptions taken together can well explain the CD and absorption spectra of DEP for the same set of parameters. We show that the CD spectra of DEA indicate strong mixing of the 1Lb and 1Bb and of the 1Bb and 1Cb states of naphthalene molecule via intermonomer interaction. The calculations presented here point out that the main reasons of previous failure to explain the vibronic structure of the CD spectra of DEP and DEA is the brakedown of the Born–Oppenheimer approximation in these dimers.

Lifetime lengthening through rotational coupling: Decay in the 1B1g and 1A u states of para-benzoquinone

The lower excitations in the B1g and Au singlet states of para-benzoquinone correspond to the small molecule limit. Stern–Volmer type experiments in a supersonic jet have given the collision-free lifetimes of these states. These lifetimes increase with increasing rotation, which is due to the increased (Coriolis) coupling with the background manifold. Values for the vibronic and Coriolis coupling parameters can be extracted from the data. It then becomes evident that at about 2000 cm−1 above the origin the rotational effects are masked by the singlet–triplet radiationless decay, and indeed above that energy no rotational effects are observed.

Jahn–Teller, pseudo Jahn–Teller coupling, and circular dichroism spectra of (E+A) e systemsa),b)

The vibronic coupling problem in a (E+A)e system of molecular levels is analyzed. Both Jahn–Teller and pseudo Jahn–Teller interactions are taken into account. The Jahn–Teller interaction is assumed to be linear and/or quadratic, whereas the pseudo Jahn–Teller interaction is taken linear in the doubly degenerate nuclear coordinate. Systems of vibronic levels are discussed for different sets of vibronic coupling parameters and energy gaps, and corresponding chiro−optical spectra are presented.

Vibronic Effects in Mossbauer Spectra: The 57Fe Quadrupole Splitting in FeCO3

The methods developed by Orbach and coworkers for calculating spin-lattice relaxation rates have been generalized to enable calculation of the effects of vibronic admixture between low-lying electronic states on observables, such as the Mossbauer quadrupole splitting, associated with magnetic ions in crystals. Emphasis is placed on the need to take proper account of the symmetry properties of the phonons until a late stage in the calculation. Application is made to the temperature dependence of the 57Fe quadrupole splitting in FeC03 , and it is concluded that, in general, vibronic coupling effects must be considered before static splitting parameters are extracted from experimental data relating to the temperature-dependent populations of electronic levels. The superposition model of the crystal field is employed to estimate the vibronic coupling parameters.