Vibronic Selection Rules Research Articles

Interaction between overall and internal rotation below, near, and above the summit of a torsional barrier: 1nπ* methylglyoxal

The effects of rotation–torsion interactions on the rotational structure of torsional vibronic bands in an electronic spectrum are examined, and a computer program to calculate the relevant energies and transition intensities is described. Rotationally resolved type C bands in the 1nπ* spectrum of methylglyoxal are reported and interpreted. Since the torsional conformation of methylglyoxal differs in the two electronic states, a long progression of bands is observed, involving levels well below, near, and above the 190 cm−1 S1 torsional barrier. The rotation–torsion interaction increases rapidly towards the free rotor limit as the barrier is approached. Observed effects include energy shifts and the appearance of transitions forbidden by rigid rotor or torsional vibronic selection rules.

The dynamical crystal field model of selective vibronic coupling in d-d spectra

The dynamic crystal field operators, corresponding to the normal point-charge displacements in an octahedral complex are analyzed in detail. The strict equivalence of absolute versus relative coordinate treatments is established. The resulting formalism is applied to the intensity distribution in the vibronic side bands of the sharp line luminescence spectra ofd3 complexes. Thereby special attention is given to the role of spin-orbit coupling and to the elastic properties of the molecular force field. Using the closure procedure, the relative intensities of the side bands may be expressed in terms of a single dynamic crystal field parameter. These expressions provide a simple rationalization of the observed vibronic selection rules, entirely within the framework of dynamic crystal field theory.

Effective Hamiltonian for a molecule in a magnetic field

The definition of operations of the rotation group, point group, etc., is modified so that the redefined operations leave the Hamiltonian for a molecule placed in a magnetic field invariant. The modified groups are used to devise a method by which one can systematically derive the types of terms, with regard to rotational, electron-spin, and magnetic-field dependence as well as vibronic selection rules, that can occur in the effective Hamiltonian for a molecule in a magnetic field. The method is applied to the case of a C 3 v molecule with the specific example of CH 3O.

Hamiltonian for a D3 h molecule in an electric field

The effective Hamiltonian for a D 3 h molecule placed in an electric field is discussed in terms of the rotational and electric-field dependence as well as the vibronic selection rules by means of the group-theory-based method presented previously [ J. Mol. Spectrosc., 125, 258–273 (1987)]. Operators occurring in the effective Hamiltonian are discussed in connection with various energy terms, vibration-rotation interactions, rotational transitions allowed by vibrationally as well as centrifugal-distortion induced dipole moments, etc. The Stark effect in the NH 3 molecule with inversion doubling is also discussed.

Hamiltonian for a symmetric-top molecule in an electric field

A method is presented by which one can systematically derive the types of terms, with regard to rotational as well as electric-field dependence and vibronic selection rules, that can occur in the effective Hamiltonian for a symmetric-top molecule placed in a homogeneous electric field. Rotation and molecular point groups somewhat modified from the ordinary ones are used for the derivation. The method is applied to the case of a C 3 v molecule as an example, yielding a list of the operators occurring in the effective Hamiltonian with an electric-field dependence up to the second order.

Vibronic spectra ofGd3+in metaphosphate glasses: Comparison with Raman and infrared spectra

Vibronic sidebands associated with the /sup 6/P/sub 7/2/..-->../sup 8/S/sub 7/2/ transition of Gd/sup 3 +/-doped metaphosphate glasses are observed using line-narrowed fluorescence techniques. Glasses having metal cations of different mass and charge (La,Al,Mg,Ba) are examined. Vibronic spectra, which probe vibrations about the rare-earth element site, are compared with polarized Raman scattering data and the infrared dielectric constant obtained from near-normal reflectance measurements. Results indicate that in metaphosphate glasses vibronic selection rules are similar to HV (vertical height) Raman selection rules. The wavelengths and relative intensities of peaks in the high-frequency portion of the vibronic spectra change with respect to corresponding peaks in the Raman spectra when the mass and/or charge of Gd/sup 3 +/ differs significantly from that of the metal cation.

Luminescence spectra and electronic levels of osmium(IV) in cubic and quasi-tetragonal symmetry

Power luminescence spectra of Os(IV) doped in Rb 2SnCl 6 (cubic) and K 2SnCl 6 (mono-clinic) at 10 K have been measured. Three spectral regions attributable to transitions into the spin-orbit components of the 3 T 1 g ground term have been investigated by Lorentzian band analyses. Vibronic selection rules and relative band intensities for K 2SnCl 6: Os 4+, in which the site symmetry of osmium ions is almost tetragonal, indicate that the spin-orbit levels resulting from 3 T 1 g have the order Γ 1<Γ 4<Γ 3<Γ 5. Ligand field results including complete configuration interaction calculated with appropriate sets of parameters are in accordance with this sequence. A band was detected in the lattice mode region which was significantly altered in frequency upon temperature variation (10–120 K). This transition has been explained by a combination of two photons, involving a promoting mode and a soft mode, which induces the phase transition of the host crystal at 255 K.

Vibronic intensities and rotational line strength factors for the three-photon absorption spectrum of ammonia

A perturbation theory approach is used to analyze the rovibronic structure of the three-photon resonant absorption of ammonia. The vibronic selection rules are presented in a convenient pyramid mnemonic in terms of irreducible representations of the rotation group and of the D3h point group. The analysis is presented for each possible situation, namely, all three photons are different, two photons are identical and one different, and all three photons are identical. The experimentally important case of three identical photons implies only two polarizations and two vibronic tensor elements for each symmetry type. With both the B̃ and C̃′ systems of ammonia one expects a ratio of 5 to 2 in the absorbance for circularly versus linearly polarized light for the N, O, S, and T branches. For the P, Q, and R branches one expects a 21 to 4 ratio of the weight-1 versus weight-3 tensor contributions to the C̃′ system in linearly polarized light (21 to 6 for B̃). Weight-1 terms are absent with circularly polarized light. These predictions are confirmed experimentally. The complete set of rotational line strength factors for three-photon absorption are given in algebraic form for the first time. The combination of vibronic factors, rotational line strengths, and statistical weights allows one to predict the three-photon absorption spectrum. Such calculated spectra are presented for ammonia at 45 K and they compare very favorably with the experimental spectra for both the B̃ system (a perpendicular band) and for the C̃′ system (a parallel band) in both linearly and circularly polarized light.

Vibronic analysis of TRSVL fluorescence spectra from glyoxal: General activity

The vibrational structure comprising 15 time-resolved single vibronic level (TRSVL) fluorescence spectra from the 1 A u - 1 A g transition in glyoxal vapor was analyzed in order to (1) establish the vibronic selection rules operative in fluorescence, (2) reveal which normal modes are most active in determining the general vibronic structure in fluorescence, and (3) confirm the assignments of major absorption transitions. The general vibronic activity observed in these TRSVL spectra provides a basis by which to identify previously unrecognized absorption and fluorescence activity in the less active modes as well as excited-state perturbations and resonances. These latter topics are addressed in detail in subsequent papers.

Analysis of the vibronic spectrum of chromium doped strontium titanate

The fluorescence spectrum of chromium-doped strontium titanate was measured as a function of temperature. The low-energy vibronic sideband of the $R$ lines at low temperatures was analyzed to determine the one-phonon and multiphonon contributions to the observed spectral profile. The one-phonon spectrum appears to be predominantly forced electric dipole in nature. Vibronic selection rules appropriate for such transitions were determined, and by comparison with neutron scattering and infrared absorption data more than 30 peaks in the vibronic spectrum can be tentatively identified with transitions involving specific phonon modes. Numerous low-frequency peaks are observed in the high-energy vibronic sideband, many of which cannot be associated with known vibrational modes. Using a simple long-wavelength phonon approximation, a phonon density of states is obtained and found to compare quite well to that determined from analyzing neutron scattering data. The temperature dependences of the widths of the zero-phonon lines and local mode were investigated using several phonon distributions including the effective density of phonon states obtained from the vibronic sideband. Low-frequency modes appear to make the dominant contribution to the broadening of the zero-phonon lines, whereas both low- and high-frequency phonons are active in broadening the local mode.

Relative intensities in the vibronic Zeeman effect in cubic crystals

Vibronic Zeeman intensity ratios are predicted for circularly polarized light propagation parallel to an externally applied magnetic field along [100] and [111] directions. A unique relative-intensity pattern is predicted for each type of site-symmetry vibration appearing in vibronic Zeeman patterns involving ${T}_{1g}$ or ${T}_{2g}$ electronic states. Experimental results in fields up to 62.8 kOe show semiquantitative agreement in most cases with predicted results for the ideal case of a limiting approximation in which ${T}_{1u}$ and ${T}_{2u}$, etc., site-symmetry vibrations are not degenerate. Such degeneracy, rather than accidental, is typical of that required by the space-group symmetry of the crystal, and leads to departures from the limiting intensity ratios. Measurements of the departure from the limiting ratios can lead to the determination of the relative contribution of degenerate ${T}_{1u}$, ${T}_{2u}$, etc., site-symmetry vibrations. This information should provide quantitative data beyond that of zero-field vibronic intensity profiles in testing models for lattice-dynamics calculations applied to the vibronic interaction, or in evaluating necessary parameters of such models. Ideal $\frac{\ensuremath{\pi}}{\ensuremath{\sigma}}$ vibronic intensity ratios for ${D}_{3d}$ distortion of a cubic crystal field in zero magnetic field are also presented which explain certain observed polarizations not predicted by exact vibronic selection rules.

The electronic structure of square-planar nickel(II) and copper(II) complexes

The polarized single crystal spectra of Ni(DACO) 2 (ClO 4) 2 2H 2O and Cu(DACO)2· 2H 2O indicate that the d orbital energy level order is d x 2-y 2 >d xy>d xz, d yz>d z 2 in both cases. The simple vibronic selection rules for D 4h symmetry apply quite well and simple ligand field calculations fit the observed spectra reasonably well. The crystal structure of Ni(DACO) 2 (ClO 4) 2·2H 2O has been determined. It crystallizes in the triclinic space group P 1 with a = 8.586(6), b = 9.324(2), c = 16.863(4)Å, α = 156.34(2)°, β = 86.80(2)°, γ = 92.86°; V = 540.95Å 3 one formula unit per unit cell. The structure was solved and refined by conventional techniques, based on 525 reflections measured with a scintillation counter (Mo Kα radiation); the final R value was 0.087. The coordination of the nickel is strictly planar and square within experimental error. The x axis positions are effectively blocked with no coordination in that direction. Thus the metal is effectively exactly D 4h square planar

One-electron energy levels in Cu(H2O)4TiF6,NH4F

The polarized single-crystal electronic spectra, measured at ambient, liquid-nitrogen, and liquid-helium temperatures, and single-crystal e.p.r. spectra, measured at ambient temperature and 96 K, of Cu(H2O)4TiF6,NH4F are reported. The data indicate C4h effective symmetry with hydrogen-bonding playing an important role in determining the electronic structure. Because the vibronic selection rules for C4h are not definitive with respect to the order of the orbitals, band assignments are made by the extrapolation of data from previously reported complexes to the present case. The suggested one-electron orbital sequence is dx2–y2 > dz2 > dxy > dxz,dyz.

Vibrational analysis of the first ultraviolet band system of aniline

Vibrational structure associated with the 2940-Å band system of aniline vapor has been analyzed in some detail, and results are included for the − d 2, − d 5, and − d 7 isotopes. It is shown that the ω(NH 2) vibration is strongly anharmonic in the ground state, having the small-large alternation of quanta characteristic of a vibration occurring in a double-minimum potential. The data are consistent with an angle of about 46° between the ring-to-N bond and the NH 2 plane in the electronic ground state. The same vibration is not harmonic in the upper electronic state, though its anharmonic character is less strongly marked there than in the ground state. The data for the upper state are compatible with a double-minimum potential having a very small maximum for the all-coplanar configuration, but the evidence is not conclusive. All that can be said definitely is that ∂ 3 V( q)∂ q 3 ≠ 0 for a considerable range of q to either side of q = 0. The term quasiplanar is proposed to cover this situation, a few other examples of which can be found in the literature. A complete classification of the vibronic sublevels of aniline is accomplished using a group G 8 of order eight; but the torsional splittings are not resolved in the electronic spectrum so that the practically useful group is G 4, a sub-group of G 8 . G 4 is isomorphous with the point group C 2 v . The vibronic selection rules are discussed.

The 2750-Å electronic band system of phenol: Part I. The in-plane vibrational spectrum

The banded absorption of phenol vapor in the region 2500–2900 Å has been extensively analyzed and the vibrational structure associated with the in-plane modes has been interpreted. Vibronic selection rules and the symmetry classification of states is discussed in the framework of a molecular symmetry group G 4, isomorphous with the point group C 2 v . The spectrum comprises a strong, allowed system of bands polarized in the plane of the molecule perpendicular to an axis grazing the O-atom (“short axis”), and a group of much weaker, forbidden subsystems polarized along this axis (“long axis”). All a 1 vibration frequencies of the phenyl group in the excited state of phenol have been assigned and measured. The vibrations principally active in the forbidden subsystems are 6 b ( b 2 ring deformation), 9 b ( b 2 CH bending) and 7 b ( b 2 CH stretching), all of which correlate with e 2 g modes of benzene. The forbidden subsystems collectively have similar intensity (10 4 f = 8) to the corresponding 2600-Å bands of benzene (10 4 f = 14), though the phenol mode 6 b is relatively less effective in intensity borrowing than mode 6 of benzene. Intensity distribution in the a 1 progressions is consistent qualitatively with a geometry change on excitation encompassing ( i) a generalized increase in CC bond distance, ( ii) a decrease in CO distance, and ( iii) some increase in quininoid character in the aromatic ring. An a priori calculation of allowed and forbidden intensities is attempted, using the Herzberg-Teller theory with the inclusion of higher terms. It is shown that terms in the conventional Herzberg-Teller expansion contribute alternately to the intensity of the allowed and forbidden systems, so that only terms 1, 3, 5, ⋯ give rise to nonzero values in an allowed subsystem, while only terms 2, 4, ⋯ have nonzero values in a forbidden subsystem. However, quantitative results are not satisfactory, probably owing to inaccuracies in the electronic wave functions.

Vibronic Selection Rules at Special Points of the Brillouin Zone: Pr3+ in LaCl3

The method of obtaining vibronic selection rules is described for an isolated impurity rare earth or actinidetype ion in a rare earth or actinide salt for various symmetry points of the Brillouin zone. The method is applied to Pr3+ in LaCl3 and the results used to further interpret the vibronic spectrum previously reported by Richman, Satten, and Wong. It is shown that in addition to the region around k=0, the region about the plane kz=0 is also probably the most important for the vibronic transitions. The points K and K′ are shown to lead to the same type of spectrum as the point at k=0.

Lattice Vibrations of LaCl3 and LaBr3 from Vibronic Spectra

The polarized vibronic spectra of PrCl3 and PrBr3, as well as Pr3+ in LaCl3 and LaBr3, were observed. The theory of vibronic transitions for the dilute salt is shown to predict a spectrum which closely resembles the vibronic spectrum of the pure salt, in agreement with experiment. Approximations valid when the optical vibrational branches of the crystal are flat leading to k=0 selection rules are shown to lead to agreement with the spectra fairly well, although slight violations in selection rules occur and can readily be explained. Tentative identifications of crystalline modes of vibration are assigned partly with the help of polarization data and vibronic selection rules, partly by consideration of frequency shift in comparing the chloride and bromide vibronic spectra, partly from Raman scattering data, and partly with the aid of the far-infrared absorption data of Buchanan, Murphy, and Caspers. The vibronic data in turn help refine the interpretation of the far-infrared results. The difference between longitudinal and transverse vibrating frequencies is discussed.

Species Classification and Rotational Energy Level Patterns of Non-Linear Triatomic Molecules

With the object of making existing knowledge more readily available, the quantized energy levels of symmetrical and asymmetrical tops are discussed from the viewpoint of their classification into species defined by symmetry operations; and simple species nomenclatures are proposed. These are then applied in a discussion of the rotational levels of symmetrical non-linear triatomic molecules A${\mathrm{B}}_{2}$. With S${\mathrm{O}}_{2}$ as an example, the pattern of rotational levels is studied as a function of the apex angle $2\ensuremath{\alpha}$ (near-prolate-symmetrical case for large $\ensuremath{\alpha}$, oblate or near-oblate case for intermediate $\ensuremath{\alpha}$, second near-prolate case for small $\ensuremath{\alpha}$). The classification of the over-all wave functions with respect to behavior for exchange of equal nuclei and for inversion is then considered. This gives rise to level patterns like those of diatomic and linear molecules in the first near-prolate case, but of interesting unfamiliar types (expected also in molecules such as B${\mathrm{Cl}}_{3}$ or N${\mathrm{H}}_{3}$) in the oblate case, and of relatively unfamiliar types (known for the molecule ${\mathrm{H}}_{2}$CO) in the second near-prolate case. Rotational-vibrational and rotational-electronic perturbations are discussed in relation to the species classifications. The concept of gyrovibronic species, and a corresponding nomenclature, are introduced. Top selection rules are discussed, using a convenient tabular formulation. Tables are given, for the case of symmetry ${C}_{2\ensuremath{\nu}}$, showing what types of transitions are allowed by the vibronic selection rules for every type of electronic transition, allowed or forbidden; the use of these tables is illustrated by application to the near-ultraviolet absorption spectrum of formaldehyde. Finally, non-linear ABC molecules are considered.