Vibronic Intensity Distribution Research Articles

Intensity of cooperative vibronic transitions in the Eu(III), Gd(III) and Tb(III) formates spectra.

The luminescence and absorption spectra of the lanthanide ions in solids and coordination compounds are characterized by sharp pure electronic lines, which are accompanied by much weaker lines of vibronic transitions. The vibronic spectroscopy is a good probing tool for investigations of the properties of surrounding ion ligands. The lanthanides formates are efficient luminescent crystals and can be viewed as the elementary type in the whole class of the oxygen-containing lanthanide coordination compounds. The intensity of vibronic transitions in spectra of luminescence and excitation europium (5 D0 →7 F2 , 7 F0 →5 D2 ), terbium (7 F6 →5 D4 ), gadolinium (6 P7/2 →8 S7/2 ) in anhydrous formates of the type Ln(HCOO)3 (Ln = Eu, Tb, Gd) and Y(HCOO)3 .2H2 O doped with Eu3+ and Tb3+ (C ~1 mol%) are reported. Also, the infrared and Raman spectra were obtained for the same compounds. Related integral intensity vibronic sidebands depend on the type of electronic transition of the same ion and varies for the same electronic transitions in different crystals. The obtained experimental data referring to the rate constants of vibronic transitions and intensity distribution in vibronic spectra on normal vibrations of the formate groups are in agreement with the predictions based on the Stavola-Dexter theory of cooperative vibronic transitions.

Observation of the missing mode effect in a poly-phenylenevinylene derivative: Effect of solvent, chain packing, and composition

Optical emission spectra of poly[2-methoxy-5-[3('),7(')-dimethyloctyloxy)-1,4-phenylenevinylene] (MDMO-PPV) in dilute solutions exhibit a vibronic progression interval (∼1225 cm(-1)) that does not correspond to any ground state vibrational mode frequency. This phenomenon is assigned as the missing mode effect (MIME) in which five key displaced polymer backbone vibrational modes in the range of 800-1600 cm(-1) contribute to the MIME interval. Emission spectra are calculated by analytically solving the time-dependent Schrödinger equation using estimates of mode-specific vibrational displacements determined independently from preresonance Raman intensities. Emission spectra of MDMO-PPV thin films and nanoparticles are measured and lineshapes show an increase of the MIME frequency to ∼1340 cm(-1) in addition to changes in vibronic intensity distributions and energies. Composite blend thin films consisting of MDMO-PPV and a fullerene derivative (1:1 w/w) exhibit a substantially larger MIME interval (∼1450 cm(-1)) that arises from an increase in polymer chain planarity. This structural change is most apparent from large decreases of the excited state displacement of an out-of-plane C-H bending mode (961 cm(-1)) that becomes forbidden in the planar structure.

Vibronic intensities in diatomic molecules

AbstractThe object of this work is to use vibronic intensity distributions to determine the bond lengths of diatomic molecules in excited electronic states without having to evaluate Franck–Condon (FC) integrals. More specifically, the intent is to derive simple linear or quadratic expressions that provide good correspondence of bond lengths obtained from experimental vibronic intensity ratios with the experimental bond lengths. To that end, we will construct power‐series expressions for the FC integral in the harmonic approximation in terms of a parameter that approaches zero as the vibrational frequencies of the two combining electronic states approach equality, show how these expressions may be truncated, and evaluate the range of bond length changes over which the various approximate equations are valid. The study covered 60 different electronic transitions in 40 different diatomics. Of these, 40 electronic transition data sets were considered good enough to merit analysis. It will be shown that both approximations perform well within the limit of their applicability. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2004

Electronic relaxation of aniline in argon matrix: A site selective laser spectroscopy

Absorption (S1←S0), fluorescence (S1→S0) and phosphorescence (T1→S0) spectra of aniline isolated in argon matrices are presented and analyzed. Upon selective laser excitation, two families of sites are characterized by electronic spectroscopy and excited state dynamics. A strong electron/phonon coupling is observed in the S1↔S0 transition due to a geometry change of the molecule. Phosphorescence spectra exhibit different vibronic intensity distribution for both sites; a1 in plane and b1 out-of-plane modes are observed. A direct estimation of the inversion splitting in the ground state (46 cm−1) is obtained from the presence of an intense doublet assigned to A13(0+)→1A1(0+,0−) vibronic transitions.

Vibronic intensity distribution and isotope shifts in the A 1Π—X 1Σ + transition of germanium monosulfide: investigations using 70Ge and 74Ge enriched isotopes

The electronic spectrum of germanium monosulfide (GeS) was produced in a microwave discharge using 70Ge and 74Ge enriched isotopes. New bands were observed in the 380–430 nm region and were shown to belong to the main transition A 1Π–X 1Σ +. Based on the vibrational isotope shifts, a comprehensive vibrational analysis of the A 1Π–X 1Σ + bands was carried out. The observation of isotopically pure spectra enabled a quantitative study of the A→X vibronic intensity distribution. The Franck–Condon factors and r-centroids were computed. By correlating the measured intensities to theory, the (relative) variation of the A→X transition moment with internuclear separation was examined.

Breakdown of the Born-Oppenheimer approximation in ZEKE states of Ag 2

Recently we reported on vibrationally resolved spectra of the ionic ground state of Ag 2 + via ZEKE spectroscopy. The vibronic intensity distributions could not be interpreted within the Franck-Condon scheme. Here, we show that it is possible to overcome this discrepancy by invoking the breakdown of the Born-Oppenheimer approximation in the ZEKE states of silver dimer. A comparison of the spectral structure of the direct ion signal with simultaneously recorded ZEKE band profiles further illustrates this non-Franck-Condon behavior.

Correlation of vibrational and electronic spectra. 1. Vibronic intensity distributions and ligand-field strengths in d-d spectra of five planar CuCl2X2 chromophores

Correlation of vibrational and electronic spectra. 1. Vibronic intensity distributions and ligand-field strengths in d-d spectra of five planar CuCl2X2 chromophores

Ab initio study of the vibrational structure of the X 2A 1 and A 2B 1 electronic states of CH +2

Results of an ab initio study of the vibronic structure of the X 2A 1, A 2B 1 system of the CH + 2 molecular ion and its isotopomers are presented. The potential energy surfaces are calculated by application of the MRD-CI method. Vibronic term values, intensity distributions and spin-orbit splittings of vibronic levels are compared. The results should guide experimental studies and enable a reliable assignment of measured lines.

Vibronic intensities in the electronic spectra of transition metal complex ions VIII: Vibrational coordinates for octahedral ions and their application to the4 A 2g ?2 E g transition of the MnF 6 2? ion

A reexamination of the vibrational coordinates appropriate in vibronic intensity calculations in octahedral coordination compounds is presented. We derive a complete set of symmetry coordinates that is orthonormal and transforms correctly under the group generators. The vibronic hamiltonian for the crystal field and ligand polarization contributions to the intensity are calculated in the basis of these coordinates. The crystal field term is evaluated both using a truncated basis set for the intermediate electronic states and using the closure approximation. These methods have been applied to the calculation of the vibronic intensity distribution for the4A2g ↔2Eg transition of the MnF62− ion and close agreement wtih experiment achieved.

Vibronic intensities in the electronic spectra of transition-metal complex ions

The vibronic intensities of the vibronic origins due to the three odd-parity vibrational modes of the Γ8(2T2g) → Γ8(4A2g) electronic transition of the ReBr2- 6 ion are calculated using both crystal-field and ligand-polarization vibronic models. The crystal-field calculations is carried out using the closure approximation, and both models employ the double-group formalism. The vibronic intensity distribution is different for the two models, but by using reasonable values of the radial integrals and atomic charges, satisfactory agreement with experiment is achieved.

Nonadiabatic representations of the 1Σ+u and 1Πu states of the N2 molecule

The vibronic bands in the dipole-allowed absorption spectrum of N2 associated with the lowest three electronic 1Σ+u and the lowest three electronic 1Πu states are represented in a basis of electronically coupled diabatic states as well as in the basis of nuclear-momentum coupled adiabatic states. Parameters defining the diabatic states and their electronic coupling energies are first evaluated by fitting the eigenvalues of a vibronic interaction matrix to the observations. The coupled-oscillator equations are then solved directly by Johnson’s numerical integration method and the diabatic representation is redetermined via the matrix method and coupled equations iteratively. The fit of the experimental vibronic terms, B values, and absorption intensities achieved with R-independent electronic coupling energies in a diabatic basis of valence and Rydberg-type states (b′+c′+e′)1Σ+u and (b+c+o)1Πu is satisfactory. Comparison with the corresponding adiabatic representation shows that the nonadiabatic perturbations are larger in that basis than in the diabatic one. The vibronic intensity distributions observed in the absorption spectrum show numerous interesting examples of intensity envelopes over discrete vibronic progressions with Fano-type resonance profiles as well as with distinctly non-Fano-type profiles which can be attributed to variations of the relevant coupling terms over the widths of the vibronic resonances.

Optical emission spectra and crystal field analysis of Pr3+ in the cubic Cs2NaYCl6 host

Unpolarized and magnetic-field-induced circularly polarized luminescence spectra are reported for Pr3+ doped into the cubic Cs2NaYCl6 host. These spectra were obtained at high resolution under variable temperature conditions, and they span the 3P0→3H4, 3H5, 3H6, 3F2, 3F3, 3F4, and 1D2→3H4 transition regions of Pr3+. The crystal field levels split out of the 3H4, 3H5, 3H6, 3F2, 3F3, and 3F4 terms are located and assigned, and an existing controversy regarding the relative locations of the 3P0 and 3P1 term levels is resolved. The spectra obtained on the Cs2NaYCl6:Pr3+ (25 mol %) system are dominated by magnetic dipole origin transitions and electric dipole (one phonon) vibronic transitions which obey octahedral (0h) selection rules. However, these spectra also include weak but persistent features which can only be accounted for in terms of Pr3+ sites with lower than 0h symmetry. A number of weak origin lines are assigned to crystal field transitions which are forbidden in 0h symmetry, and the vibronic intensity distributions observed within certain term-to-term transitions reflect the presence of some lowered site symmetries. The vibronic structure observed in the luminescence spectra is dominated by contributions from transitions involving the ν3(t1u), ν4(t1u), and ν6(t2u) PrCl3−6 cluster (moiety) modes, with lesser contributions being made by two nonmoiety modes with frequencies of ∼40 and ∼60 cm−1.

Franck–Condon analysis of the 1 1A g→1 1B u absorption in linear polyenes with two through six double bonds

The vibronic intensity distribution at room temperature and 77 °K of the 1 1Ag→1 1Bu transition for the series of linear polyenes with two through six conjugated double bonds has been measured and analyzed. These inhomogeneously broadened solution spectra can be described reasonably using only two harmonic normal modes of vibration: single and double bond stretches at ∼1200 and ∼1600 cm−1, respectively. Excited state normal coordinate displacements were determined by a least-squares fitting procedure. For both the double and single bond modes the estimated change in bond length upon excitation decreases as the length of the polyene chain increases. The bandwidth of these spectra decreases with increasing polyene length. This is well described by assuming that in solution a range of conformations differing by very small torsions about the terminal single bonds has been frozen in. The Franck–Condon analysis indicates that under these conditions all of the polyenes are approximately planar in the 1Bu state, ruling out the argument that the lack of fluorescence in butadiene and hexatriene is due to the polyene framework being significantly twisted in the lowest energy 1Bu state.

Theoretical evaluation of the vibronic intensity distribution in the phosphorescence of benzene

The relative intensity of the vibronic components of the phosphorescence spectrum of benzene has been evaluated theoretically. All mechanisms that may be responsible for the intensity of the most prominent bands have been taken into account and the relevant spin—orbit and vibronic coupling matrix elements have been evaluated. In agreement with experimental findings, it is found that vibronic coupling in the triplet manifold plays the dominant role in inducing the e 2g bands and that the ν 8 bands is the most intense. The b 2g bands appear to be weak because of substantial cancella occurring between large separate contributions. Our results indicate that consideration of all terms and of several intermediate excited states is nece to obtain a correct picture of phosphorescence of benzene.

Two-photon excitation of the [formula omitted] state of sulfur dioxide

The two-photon excitation (TPE) spectrum of sulfur dioxide is reported in the region of the C ̃ 1B 2 ← X ̃ 1A 1 [2b 1(π ∗) ← 1a 2(π)] transition. The spectrum shows considerable rovibronic structure; the band contours are identified as arising from Δ K −1 = ± 1 transitions and rotational features are assigned by comparison with synthetic spectra generated from known rotational constants. The vibronic structure observed in TPE is quite similar to that observed in the one-photon spectrum: no zero-rank tensor transitions to levels with odd v 3 are identified, though they are allowed in the presence of vibronic coupling. The vibronic intensity distribution in the TPE spectrum below the dissociation limit is similar to that in one-photon absorption. However, near the dissociation threshold (5.63–5.67 eV), marked intensity redistribution occurs, from which it is concluded that the lowest energy photo-dissociation process proceeds through asymmetric stretching of the SO bonds.

Vibronic activity and the change in geometrical structure accompanying the 580 nm electronic transition of CrO2Cl2

An analysis is presented for the vibronic intensity distribution in absorption and emission spectra of the 580 nm band system of CrO2Cl2. The marked variability of the activities of ν 2 and ν 3 in the various spectra is shown to arise from a strong rotation of the form of the normal coordinates on excitation (Duschinsky effect). It is confirmed that the 217 cm-1 interval between the d and a absorption bands corresponds to an a 1 normal mode which is assigned to ν′3, mainly symmetric CrCl2 stretching. The Franck-Condon analysis is combined with the rotational constants of Blazy and Levy to yield values for the changes in geometrical structure in the excited state. These are discussed in terms of the electronic structure of CrO2Cl2.

The franck—condon principle and sum rules for vibronic transitions in polyatomic molecules

Simple formulas for the mean number of quanta and its standard deviation, as well as limiting forms of the vibronic intensity distribution are obtained. Such relations are found to agree well with experimental data and may be useful for interpreting spectra.

Geometrical Structures of Excited States of Conjugated Molecules. II. The Calculated Vibronic Intensity Distributions in the Absorption Spectra of Naphthalene

Abstract The normal coordinates and the vibrational frequencies in the first excited singlet (1B2u), the second excited singlet (3B1u), and the first excited triplet (3B1u) states of naphthalene, whose geometries were calculated by a semiempirical method, are evaluated by assuming a simplified valence force field. The relation between the normal coordinates of two different electronic states is expressed on the basis of the Franck-Condon principle. The mixing among the excited-state normal coordinates, expressed in terms of the ground-state normal coordinates, is neglected in the present treatment. By using the simple relation between the normal coordinates of two different electronic states, the vibronic intensity distributions in the absorption spectra (1B2u←1Ag, 1Lb, 1B1u←1Ag, 3La, and 3B1u←1Ag,3La) have been calculated. The vibronic intensity distribution of the 1B2u←1Ag transition has been calculated, taking into consideration the intensity of the interpenetrating sets of the vibronic band groups on the basis of the Herzberg-Teller perturbation theory.

Moment analyses of intensity distributions in molecular electronic spectra

The use of moments in the analysis of vibronic intensity distributions in molecular electronic spectra is explored. Theoretical relations are derived for first moments. No attention need be paid to the form of individual vibrational overlap integrals. It is shown how these relations give information on the change of geometry accompanying the transition and on the dependence of the electronic transition moment on the appropriate normal coordinate. The theory is successfully applied to the 3500 AA emission spectrum of formaldehyde and to the 3400 AA spectrum of phenanthrene. An outline is given of the extension of the theory to higher moments.

Vibronic Intensity Distribution in the Phosphorescence of Benzene and Its Deuterated Isomers

The gound-state vibrational frequencies and the relative vibronic intensities of the phosphorescence are calculated for all and measured for one carbon-13 and ten of the possible twelve deuterium-substituted benzenes. The intensities are calculated within the framework of the Herzberg–Teller model. It is shown that the relative intensities for different vibronic transitions of isotopically related molecules can be expressed in terms of two factors; a normal coordinate eigenvector matrix element which is isotope dependent, and an electronic term which is isotope independent. The observed C6H6 intensities are used to evaluate the electronic parameters. Excellent agreement is found among the calculated and observed intensities and frequencies. The relative importance of the different coordinates for vibronic coupling in benzene is indicated.