Symmetry-forbidden Transitions Research Articles

Observation of symmetery forbidden transitions in the room temperature photoreflectance spectrum of a GaAs/GaAlAs multiple quantum well

We have measured the room temperature photoreflectance spectrum from a 100A/150A GaAs/GaAlAs multiple quantum well (MQW) ( x ≈ 0.17). The entire spectrum from the MQW has been fit by a third-derivative functional form lineshape expression. In addition to all the allowed quantum transitions we have clearly observed features from several symmetry forbidden transitions. There also appears to be evidence for unconfined transitions, i.e. energies above the band gap of the GaAlAs barrier layer. There is good agreement between the experimentally determined energies of the various features and a theoretical calculation.

Effects of Coriolis interaction on the rotational line intensities of symmetry-forbidden electronic transitions

The effect of Coriolis coupling on intensities in infrared rotation–vibration bands is here extended to vibronically allowed transitions between electronic states of a nearly symmetric top. Within the framework of the Herzberg–Teller treatment of vibronic interaction, equations are developed which describe the intensity distribution in the p- and r-form branches of a vibronic transition in the cases where Coriolis interaction perturbs one or both vibrational levels associated with the transition. The à 1A2–X̃ 1A1 transition in H2CO is used as an example to illustrate the theory.

Theory of molecular symmetry in dynamic N.M.R. spectra of intramolecularly exchanging spin systems

The form of dynamic N.M.R. lineshape equation for intramolecularly exchanging spin systems is derived which contains explicitly the symmetries of the rearranging spcies. The lineshape equation is formulated in the composite Liouville space which comprises only one primitive space for each chemically distinct species. Two types of symmetry invariances, macroscopic and microscopic, are recognized, the former being inherent in all systems of symmetric species undergoing exchange. It is shown formally that, owing to the macroscopic invariance of symmetry, exchange processes do not couple symmetry-allowed with symmetry-forbidden transitions. A construction of a symmetry-adopted operator basis is described in which both the symmetry invariances effect the corresponding factorization of spectral matrices. It is demonstrated, using the example of intramolecular rearrangements in octahedral transition metal complexes, H4 ML 4, the extent to which both the macroscopic and microscopic factorizations can simplify the lineshape calculations.

Analysis of the molecular electronic absorption spectra of shock-heated aromatic compounds

Advantage has been taken of the rapid and homogeneous heating of a sample in a shock wave to record the electronic absorption spectra of the 1A1g→1B2u transition in benzene and the corresponding 1A1→1B1 transition in toluene as a function of temperature over the range 700–1300 K, prior to thermal decomposition.A model for the band-shape function of electronic absorption spectra of symmetry-allowed and symmetry-forbidden transitions in the context of the Herzberg–Teller theory is proposed based upon the assumption of harmonic oscillators. For symmetry-forbidden transitions, frequency changes in the promoting modes are ignored and only the linear Herzberg–Teller terms are considered to account for the dependence of the electronic transition moment upon nuclear coordinates. Explicit attention is paid to the temperature dependence of the band-shape function and it is shown, in conjunction with a moment analysis of the band-shape function, how important molecular parameters may be deduced in favourable instances, which are determined chiefly by the inherent molecular complexity and symmetry point group of the molecule. It is shown by a moment analysis of the shock data that the induced and allowed transition moments in toluene are of comparable magnitude.

Intensity enhancement of symmetry forbidden transitions in solid solutions of benzene and naphthalene

Intensity enhancement of symmetry forbidden transitions in solid solutions of benzene and naphthalene has been measured at various temperatures. The effect, which consists essentially in allowing electronically forbidden transitions as a result of intermolecular interactions is attributed to two factors: ‘self-borrowing’ and ‘solvent borrowing’. Their relative contribution depends on the site symmetry of the solvent, thus explaining the marked intensity change in absorption of the ‘forbidden bands’ observed in phase transitions. ‘Forbidden bands’ were detected in the 1 A 1 g → 1B 2 u transition and not in the 1 A 1 g → 1B 1 u transition and a qualitative explanation for this difference is presented.

Intensit�s des Transitions �lectroniques de [PdCl4]2? Intensities of Electronic Transitions of [PdCl4]2?

The oscillator strengths of the symmetry-forbidden transitions of the ion [PdCl4]2− were calculated by a method based on the evaluation of the MO of the distorted ion. It is not very likely that the transition to1B1g (a1g(d z 2)→b1g) state, weak, mainlyz polarized, explains the band that appears as a shoulder observed towards 30 000 cm−1 in the absorption spectrum. If this band is specific of the ion [PdCl4]2−, the assignment to the forbidden charge-transfer transition,1A1g →1B2g, is more plausible.

A study of spin and symmetry forbidden transitions in CS2 by high resolution energy-loss spectroscopy

Energy-loss spectra of CS2 are presented in the energy-loss range 6–17 eV. Measurements of the variation of the intensity of spectral features with electron energy, and scattering angle were used to identify spin and symmetry forbidden transitions and where possible assignments have been suggested. A new Rydberg series, consisting of electric quadrupole transitions and converging to the lowest ionisation potential has been analysed, and assigned as an ns series. Three Rydberg series converging to the third ionisation limit were detected for the first time, and the assignment of these together with the optically-observed series are discussed. No new series were detected converging to the fourth ionisation potential, but the change in shape of members of two previously observed series, from dips to peaks as the electron energy is reduced was noted. In addition to the forbidden Rydberg series, two new triplet valence states at 6.9–7.4 eV and 12.4–12.7 eV have been detected, and the excitation energies of a number of unassigned, forbidden transitions have been measured.

Some features of two-particle exciton-phonon excitations in molecular crystals

In this paper we present the results of a theoretical study of the optical absorption line shapes in the two-particle exciton-intramolecular phonon (IP) excitation regime in molecular crystals. The exciton-IP coupling was handled considering the exciton and the IP as a pair of interacting pseudo-particles and exploring the conditions for branching-off a two-particle bound state (TPBS) from the two-particle-continuum (TP), without invoking the exciton-IP decoupling approximation. We were able to handle both symmetry-allowed electronic transitions as well as symmetry-forbidden, vibronically-induced, electronic excitations. For symmetry-forbidden transitions we have provided a systemic derivation of Rashba's, Koster—Slater type formula where the local perturbation results from quadratic IP coupling. For the case of symmetry-allowed electronic transitions we derived a new approximate expression for the line shape, incorporating both linear and quadratic coupling terms and elucidating the conditions for a peaceful coexistence of TP and TPBS. Next, we have considered the exciton-IP system coupled to intermolecular lattice phonons (LP), taking into account the effects of bath diagonal “strong” coupling and of off-diagonal “weak” coupling. The diagonal exciton-LP coupling results in the appearance of side bands which should be viewed as three-particle resonances corresponding to an exciton + IP + LP. Off-diagonal exciton-LP coupling results in the relaxation of the exciton-IP TPBS to the TP continuum at finite temperatures. Finally, we have explored the effects of static structural disorder on the exciton-IP system, considering the effects of Anderson-type diagonal disorder. Configurational averaging was performed utilizing the coherent potential approximation, while the disorder field was represented in terms of a lorentzian distribution of the site excitation energies. Structural disorder drastically affects the TPBS, while the TP continuum is only slightly affected by disorder scattering.

Electron impact study of the energy levels of t r a n s-1,3-butadiene

The electron impact energy loss spectrum of trans-1,3-butadiene has been investigated at incident energies from 7.5 to 34 eV and scattering angles from 0 to 70°. Energy resolutions of 45 to 75 meV were used. The energy loss spectrum at 33 eV and 0° was found to correspond almost exactly to the optical absorption spectrum measured by McDiarmid. The only minor difference was a weak band which appeared in the energy loss spectrum at 7.80 eV. An investigation of the relative intensities of the three diffuse vibronic bands of the intense N→V1 transition centered near 5.92 eV showed that the relative intensities of these bands were not constant below incident energies of 15 eV and that whereas the low energy 5.74 eV vibronic band was enhanced at 0° scattering angle, the high energy 6.08 eV band was enhanced at 70°. These results are consistent with the presence of two forbidden transitions in the 5.7 to 6.2 eV energy loss region: a symmetry forbidden transition near 5.80 eV and a singlet–triplet transition near 6.10 eV—in excellent agreement with some, but not all, of the recent theoretical calculations on 1,3-butadiene. Detailed studies of the higher energy region above 6.5 eV energy loss did not reveal the presence of any underlying valence transitions although the results are not conclusive because of the intense Rydberg structure in this region. The Rydberg transitions at 7.08 and 8.0 eV were found to have differential scattering cross sections which were very different from those of the nearby transitions.

On the calculation of polyatomic Franck–Condon factors: Application to the 1A1g→1B2u absorption band of benzene

Two methods for calculating polyatomic Franck–Condon integrals are reported. The first method uses a coordinate transformation on the normal coordinates of both the ground and excited electronic states. This transformation effectively removes any Duschinsky mixing and allows the multidimensional Franck–Condon integral to be written as a sum of integrals each of which is a product of one-dimensional harmonic oscillator overlap integrals. The second method uses contact transformation perturbation theory to construct a representation of the vibrational wavefunctions. With this representation, the calculation of a polyatomic Franck–Condon integral involves evaluation of matrix elements exclusively within the ground electronic state vibrational manifold. Application of both methods is made to the A0n vibronic series of the 1A1g→1B2u symmetry-forbidden electronic transition of benzene. Relative intensities calculated by either method agree well with observed values. However, the computational efficiencies of the two methods are found to be markedly different, with the perturbation method being the least efficient.

Magnetic circular dichroism studies. Part 55. The aliphatic nitro chromophore

The magnetic circular dichroism (m.c.d.) of twelve nitroalkanes is reported. For several of these compounds two distinct m.c.d. bands are observed in the 240–350 nm region. The presence of these bands is interpreted in terms of two electronic transitions, viz. a σ→π* transition at ca. 320 nm and an n→π* transition at ca. 270–280 nm. The magneto-optical B values for the σ→π* transition appear to be small in magnitude throughout the series of compounds; the B values for the n→π* transition are generally much larger in magnitude and are sensitive to alkyl substitution and to solvent effects. A qualitative interpretation of the spectra is given in terms of the effects of static and structural–vibrational perturbations on the m.c.d. associated with symmetry-forbidden transitions. Solvent effects observed in the m.c.d. spectra of the nitroalkanes are also discussed.

Investigation of low-lying electronic states in nitromethane by electron-impact spectroscopy

Low energy, variable angle, electron-impact energy-loss spectra of nitromethane have been obtained. A previously unreported singlet → triplet excitation with maximum intensity at 3.8 eV energy loss is observed and its relevance to the gas phase photochemistry of nitromethane is discussed. An additional weak transition with maximum intensity at 4.45 eV energy loss is tentatively assigned to a symmetry-forbidden transition.

Polyene spectroscopy: Vibronic evidence for a forbidden transition in DECA-2,4,6,8-tetraene

The dimethylpolyene deca-2,4,6,8-tetraene was studied by absorption, fluorescence excitation and fluorescence spectroscopy in glasses at 77 K and in n-alkane crystals at 4.2 K. A strong transition to a 1B u excited state is observed with an origin at 32400 cm −1 in isopentane at 77 K and at 31280 cm −1 in n-undecane at 4.2 K. A weak transition to a 1A g excited state is observed with an origin at 28738 cm −1 in the n-undecane matrix. The radiative fluorescence lifetime is 500 ns. In undecane the transition from the ground state to the 1A g excited state exhibits a classic Herzberg—Teller vibronic pattern indicating a symmetry forbidden transition.

A theoretical investigation of symmetry-forbidden transitions in magnetic circular dichroism and electronic spectra of benzene

In this paper, the vibronic coupling calculation in the π-electron framework has been carried out for 〈B2u‖?′vc‖E1u〉, 〈A1g‖?′vc‖B2u〉, and 〈B1u‖?′vc‖E1u〉 of benzene by using the so-called linear displacement method. Our method differs from that of Liehr’s by the fact that in our calculation all multicenter integrals have been evaluated exactly. The vibronic coupling matrix elements obtained have then been applied to calculate the magnetic rotational strengths and dipole strengths of symmetry-forbidden transitions 1A1g→1B1u and 1A1g→1B2u and the electronic matrix elements involved in radiationless transitions. It is well known that the 1A1g→1B2u transition is symmetry-forbidden in MCD and uv spectra and becomes allowed through the mixing of both B1u and B2u states with the E1u state through the E2g modes of vibration. We have developed a method for determining the dipole strengths and magnetic rotational strengths associated with each individual E2g promoting mode from the experimental MCD and uv spectra. Theoretical and experimental results are compared.

Study of vibronic, spin-orbit and vibronic-spin-orbit couplings of formaldehyde with applications to radiative and non-radiative processes

With the recent availability of large amounts of experimental data, theoretical models of radiative and nonradiative processes can be tested in detail. For this purpose, the absolute calculation of radiative and non-­radiative rate constants is required. The expression for the non-radiative rate constant consists of two parts, one from the electronic motion (the pro­moting part) and the other from the nuclear motion (the statistical part). All recent theoretical work has been focused on the calculation of the non-radiative rate constant of one single vibronic state relative to another so that the promoting part of the rate constant is cancelled and hence has been concerned mainly with the Franck–Condon factor calculation (the statistical part of the rate constant). That the calculation of the statistical part of the rate constant cannot provide a critical test for a theory of radiationless transitions is obvious. In the present investigation, the theory of radiationless transitions to be tested is that originally proposed by Robinson and Frosch and later developed by Lin & Bersohn, Siebrand & Henry, Freed, Nitzan & Jortner and Fischer. According to this theory, one way to calculate the promoting part of the non-radiative rate constant is to invoke the vibronic coupling for the internal conversion and to invoke the vibronic coupling plus the spin-orbit coupling and/or the vibronicspin-orbit coupling for the intersystem crossing. A numerical calculation is carried out for the internal conversion 1 A 2 → 1 A 1 and the intersystem crossing 1 A 2 → 3 A 2 of formaldehyde by using simple m. os. For radiative transitions, we calculate the lifetimes of the states, 3 A 2 ( n ↔ π * ), 1 A 2 ( n ↔ π * ), 1 B 1 ( n ↔σ*), and 1 A 1 ( π ↔ π * ). The corresponding transition moments are given. For symmetry forbidden transitions, we compared the Herzberg–Teller theory with the importance of the correc­tion to the breakdown of the adiabatic approximation. It is shown that for formaldehyde, the B.–O. correction is approximately one order of magnitude smaller than the first order vibronic coupling.

Electron-impact excitation of H2O and D2O at various scattering angles and impact energies in the energy-loss range 4.2–12 eV

The electron-impact excitation of H2O and D2O has been studied at electron energies close to threshold and at large scattering angles in order to enhance spin and/or symmetry forbidden electronic transitions; and at energies far from threshold and at small scattering angles to enhance optically allowed transitions. The energy-loss range covered is 4.2–12 eV. From a comparison of the present measurements and recent, accurate ab initio calculations, several new assignments of electronic transitions in both H2O and D2O have been made or suggested. Also suggested are future works which could be carried out in order to unravel the complex Rydberg spectra above 11 eV.

ChemInform Abstract: ELECTRONIC SPECTROSCOPY OF PROPADIENE (ALLENE) BY ELECTRON IMPACT

Chemischer InformationsdienstVolume 6, Issue 26 Physical Organic Chemistry ChemInform Abstract: ELECTRONIC SPECTROSCOPY OF PROPADIENE (ALLENE) BY ELECTRON IMPACT OREN A. MOSHER, OREN A. MOSHERSearch for more papers by this authorWAYNE M. FLICKER, WAYNE M. FLICKERSearch for more papers by this authorARON KUPPERMANN, ARON KUPPERMANNSearch for more papers by this author OREN A. MOSHER, OREN A. MOSHERSearch for more papers by this authorWAYNE M. FLICKER, WAYNE M. FLICKERSearch for more papers by this authorARON KUPPERMANN, ARON KUPPERMANNSearch for more papers by this author First published: July 1, 1975 https://doi.org/10.1002/chin.197526063AboutPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat No abstract is available for this article. Volume6, Issue26July 1, 1975 RelatedInformation

Study of the Franck-Condon and Herzberg-Teller Approximations

Using the Born-Oppenheimer parameter lambda = (m/M)(1/4) as a perturbation parameter, we find that for allowed transitions, the zeroth order approximation of the spectral intensity gives rise to the Condon approximation, the first order vibronic coupling and anharmonic effect appear in the first order approximation of the spectral intensity, which gives us the non-Condon scheme, and only the intensity of the transitions of totally-symmetric modes with nonvanishing normal coordinate displacements is affected by the inclusion of the first order vibronic coupling and anharmonic effect. For symmetry-forbidden but vibronic-allowed transitions, the first nonvanishing term of the spectral intensity is second order with respect to lambda and the B-O couplings do not appear in the calculation of the spectral intensity until the fourth order approximation with respect to lambda; in this case, other high order vibronic couplings and anharmonic effect are competing with the B-O couplings.

Energy dependence of radiative rates in isolated molecules

The energy dependence of the radiative rate constant of single vibronic states has been determined. Symmetry allowed and symmetry forbidden transitions are considered. In all cases the radiative rate constant depends linearly on the number of quanta excited in a given mode.

Halogénoacétates de cuivre(II): 2° Partie. Étude magnétique et spectroscopique

Electronic spectra of chloro- and bromoacetates of copper (II) (hydrated and as addition compounds with ethyl acetate) have been obtained in the solid state at 298 °K and 77 °K. The results are discussed and compared with magnetic susceptibility measurements. The band at about 27.5 kK. is present in the monomers and in the dimers and cannot be used to characterize the dimer species. It is assigned to the npπ → d x 2−y 2 symmetry forbidden transition.