Wilson Notation Research Articles

Theoretical Calculation of the Geometry and Vibrational Frequencies of Triphenylmethane

Raman spectra of polycrystalline triphenylmethane (TPM) are recorded at room temperature in the range 4000–400 cm–1. The optimum structure and vibrational (Raman and IR) spectra of TPM are calculated using the B3LYP/6-311G(d,p) approximation. Theoretical modes and bands corresponding to them in the experimental Raman spectrum are assigned to stretching and bending vibrations of certain bonds in the TPM molecule based on visualization of the vibrations. Most bands, in particular, the strongest ones in the Raman spectra of TFM, are due to vibrations in monosubstituted benzene rings. Some of the theoretical modes and the corresponding experimental bands are assigned to benzene modes in Wilson notation.

Resonance-Enhanced Raman Scattering of Ring-Involved Vibrational Modes in the (1)B(2u) Absorption Band of Benzene, Including the Kekule Vibrational Modes ν(9) and ν(10).

Resonance Raman spectroscopy provides much stronger Raman signal levels than its off-resonant counterpart and adds selectivity by excitation tuning. Raman preresonance of benzene has been well studied. On-resonance studies, especially at phonon-allowed absorptions, have received less attention. In this case, we observe resonance of many of the vibration modes associated motion of the carbons in the ring while tuning over the (1)B2u absorption, including the related ν9 (CC stretch Herzberg notation, ν14 Wilson notation) and ν10 (CH-parallel bend Herzberg notation, ν15 Wilson notation) vibrational modes along with the ν2 (CC-stretch or ring-breathing Herzberg notation, ν1 Wilson notation) mode and multiples of the ν18 (CCC-parallel bend Herzberg notation, ν6 Wilson notation) vibrational mode. The ring-breathing mode is found to mix with the b2u modes creating higher frequency composites. Through the use of an optical parametric oscillator (OPO) to tune through the (1)B2u absorption band of liquid benzene, a stiffening (increase in energy) of the vibrational modes is observed as the excitation wavelength nears the (1)B2u absorption peak of the isolated molecule (vapor) phase. The strongest resonance amplitude observed is in the 2 × ν18 (e2g) mode, with nearly twice the intensity of the ring-breathing mode, ν2. Several overtones and combination modes, especially with ν2 (a1g), are also observed to resonate. Raman resonances on phonon-allowed excitations are narrow and permit the measurement of vibrations not Raman-active in the ground state.

Surface‐enhanced Raman scattering from polystyrene on gold clusters

AbstractSurface‐enhanced Raman scattering (SERS) constitutes a spectroscopic method of rapidly growing importance, and polystyrene is a widely used compound of great industrial importance. In this work, SERS data were obtained from polystyrene samples prepared by vapor deposition of gold and plasma‐induced polymerization of styrene gas. A thorough examination of this data is presented. The relationships between sample preparation parameters, gold‐cluster morphology, and SERS intensity were elucidated. Using Wilson's notation, vibrations were assigned to all bands between 250 and 1750 cm−1 in the ordinary Raman and SERS spectra of polystyrene. The correct assignment of these bands would be a significant achievement because they have been controversial in the literature for ∼30 years. Our assignments were made by reviewing the literature and comparing the assignments found there to spectral data acquired during this study; they were confirmed using density functional theory (DFT) calculations performed on the styrene monomer. The orientation of polystyrene's phenyl ring, relative to the gold surface, was determined. It has been suggested that reactions involving silver catalyze polystyrene degradation during SERS, but we found that silver is not necessary for the degradation to occur. Copyright © 2009 John Wiley & Sons, Ltd.

An excited state ab initio and multidimensional Franck–Condon analysis of the A B12←X A11 band system of fluorobenzene

This work combines high level ab initio calculations with multidimensional Franck-Condon calculations to refine and augment previous assignments of the lower wavenumber region of the A (1)B(2) <-- X (1)A(1) band system of fluorobenzene. The strength of the assignment has been greatly assisted by the use of zero electron kinetic energy spectroscopy in a series of pump-probe experiments where the response of the molecule to selective excitation in specific modes prior to ionization has been studied. The net result of this analysis is the reassignment of 7 of the 12 previously assigned bands in the region below about 1000 cm(-1) using a strategy that aims to trace the origins of excited state normal modes of fluorobenzene to the well-known Wilson modes of benzene by taking full account of the Duschinsky mixing that accompanies electronic excitation. Duschinsky normal mode analyses of the ground and first excited states of fluorobenzene as well as the electronic ground state of fluorobenzene cation have shown that the common use of the benzene Wilson notation to describe normal modes of this prototypical benzene derivative is highly questionable, particularly following electronic excitation and ionization.

Lignin Radicals in the Plant Cell Wall Probed by Kerr-Gated Resonance Raman Spectroscopy

Lignin radicals are crucial intermediates for lignin biosynthesis in the cell wall of vascular plants. In this work they were for the first time, to our knowledge, selectively observed in wood cell walls by laser-based Kerr-gated resonance Raman spectroscopy, and the observations were supported by density functional theory prediction of their vibrational properties. For dry wood cells a lignin radical Raman band is observed at 1570 cm −1 irrespective of species. For wet beech cells they were generated in situ and observed at 1606 cm −1. DFT/B3LYP/6-31+G(d) modeling results support that in beech they are formed from syringyl (S) phenolic moieties and in spruce from guaiacyl (G) phenolic moieties. The observed lignin radical band is predicted as G is ∼1597 cm −1 and S is ∼1599 cm −1, respectively, and is assigned the (Wilson notation) ν 8a phenyl ring mode. The RR band probes lignin radical properties, e.g., spin density distribution, and these respond to charge polarization or hydrogen bonding to proximate water molecules. These observations can be crucial for an understanding of the factors that control cell wall structure during biosynthesis of vascular plants and demonstrate the unique potential of RR spectroscopy of lignin radicals.

The Jahn-Teller effect in the lower electronic states of benzene cation. III. The ground-state vibrations of C6H6+ and C6D6+.

New mass analyzed threshold ionization (MATI) spectra of the molecules C(6)H(6) (+) and C(6)D(6) (+) have been collected using tunable vacuum ultraviolet (VUV) single photon excitation from the neutral ground state and also using two-photon excitation through the 6(1) vibration of the (1)B(2u) S(1) state. Emphasis was placed on obtaining accurate relative intensities of the vibrational lines in order to use this information in the vibronic analysis. The MATI spectra collected from VUV (S(0) originating state), triplet (T(1)), and resonant two photon (S(1)) excitation schemes were compared with Jahn-Teller calculations employing the classical model of Longuet-Higgins and Moffitt to obtain the Jahn-Teller coupling parameters of 3 of the 4 linearly active modes (e(2g) modes 6-9 in Wilson's notation). Franck-Condon factors, including the effects of geometry changes, were calculated from the vibronic wave functions and used to identify the lines in the various spectra. It is found that most of the lines with substantial intensity can be understood using only the modes 1, 6, 8, and 9. Weaker peaks are due to various non-e(2g) modes, but these do not derive intensity through Jahn-Teller coupling. When the effects of geometry change were included, simulations of the spectra from the calculated vibrational energies and intensities were close to the experimental spectra. This verifies the applicability of the model to the understanding of the vibrational structure of this type of molecule, but some variations indicate directions for further improvement of the model.

High resolution FTIR spectra and analysis of the ν11 fundamental band of [formula omitted

A high resolution FTIR (apodized instrumental bandwidth 0.004 cm −1 FWHM) spectrum has been measured for the isotopically pure benzene molecule 13 C 6 H 6 in the range 600–850 cm −1 . Accurate molecular constants have been obtained for the fundamental vibration ν 11 (Wilson's notation, which is used here; ν 4 according to Herzberg's notation) of 13 C 6 H 6 with band center at 672.12930(5) cm −1 . Several hot-bands have been analyzed as well. Improved ground state constants have been deduced from a fit of ground state combination differences.

Hydrogen-Bonded Pyridine−Water Complexes Studied by Density Functional Theory and Raman Spectroscopy

Density functional theory (DFT) at the B3LYP/6-31++G(d,p) level was employed to obtain the optimized geometries and vibrational spectra of several pyridine(Py)−water(W) complexes with stoichiometric ratios ranging from 2:1 (Py2W) to 1:3 (PyW3). The harmonic vibrational wavenumbers of pyridine ring modes and the fundamental modes of water were calculated in order to examine the influence of hydrogen bonding on the normal modes of both pyridine and water upon complexation. The Raman spectra in the wavenumber region 960−1060 cm-1 covering the ring modes ν1 and ν12 of pyridine (in Wilson's notation) as a function of pyridine mole fraction were recorded. The integrated Raman intensities in the isotropic components of the spectra were used to determine the relative concentration of “free” pyridine molecules in close neighborhood with other Py−W complexes. The combination of both experimental wavenumbers yielding the overall shift induced by the entirety of hydrogen-bonded complexes in the mixture and the DFT-derived vibrational wavenumbers of the isolated species provides the possibility to probe concentration profiles as a function of pyridine mole fraction. The examination of the concentration dependence of line widths reveals that the counter competing influences of different dynamic processes are simultaneously present in this binary mixture.

The Limitations to Employing the Vibrational Assignment Notation of an Aromatic Homocycle to Its Heterocyclic Analogues

Abstract While the use of the WILSON notation of benzene may be employed to describe the fundamentals of substituted benzenes and azine N-oxides, the loss of three degrees of freedom for each aza-substitution makes application of the WILSON notation to azines more difficult, often resulting in an inconsistent application when compared with analogous substituted benzenes. This practice is examined in light of the description for pyridine, pyrazine and γ-substituted pyridines and some azine N-oxides. Several changes are recommended for the description of the “lost” C-H vibrations in azines and for the out-of-plane vibrations of γ-substituted pyridines.

The benzene ground state potential surface. IV. Discrimination between multiple E1u force field solutions through infrared intensities

Accurate values for integrated intensities of the infrared active 13C6H6 fundamentals, ν18, ν19, ν20, and ν11 (Wilson notation) have been measured and redetermined for ν18 and ν19 in C6H6 and C6D6. The 13C6H6 intensities are I18=6.52±0.15, I19=12.60±0.20, I20=55.6±1, and I11=74.6±3 km/mol. Unlike C6H6 and C6D6, interfering transitions in 13C6H6 are minor and these intensities can be used as a critical test for theoretical predictions of atomic polar tensors. The ν18 intensities in C6H6 and C6D6 (7.48±0.15 and 7.09±0.14 km/mol, respectively) and the ν19 intensity in C6D6 (2.51±0.12 km/mol) are measured to be substantially lower than the literature values. The qualitative intensity pattern of benzene in-plane fundamentals uniquely discriminate among the eight possible real E1u force field solutions obtained from frequency information alone. Isotopically invariant dipole moment derivatives, ∂μ/∂S18a, ∂μ/∂S19a, and ∂μ/∂S20a are 0.494±0.005, 0.395±0.016, and 0.770±0.008 D/Å, respectively, obtained from the 13C6H6 experimental intensities and the complete experimental force field of Part II. Using these quantities and the L−1 matrix (Table III), dipole moment gradients for C6H6 become ∂μ/∂Q018a =+0.298, ∂μ/∂Q019a =+0.371, and ∂μ/∂Q020a =+0.814 D/Å. Mode decomposition matrices expressing normal modes of benzene in terms of isotopically labeled molecule modes have been used to definitively determine the C6H6 dipole gradient signs. The signs are in agreement with theoretical calculations. The D6 isotopic labeling effect on C6H6 ν18 intensity provides a sensitive test of E1u force field quality and reveals the inadequacy of present theoretical force field approaches. Ab initio atomic polar tensors have been obtained both at the HF level, using several basis sets up to the 6-311+G(d,p) and at the MP2 level up to the 6-31+G(d) basis set. The dipole derivative for the CC stretch is highly sensitive to both basis set (particularly diffuse functions) and correlation effects. Qualitative CH and CC stretching dipole derivative and intensity predictions by the MP2/6-31+G(d) calculation are encouraging (i.e., within 15% of the experimental values). However, the same calculation yields 20% and 45% errors for the CH bending dipole derivative and fundamental intensity, respectively.

Direct measurements of vibrational predissociation of p-difluorobenzene–argon

We have measured rates of vibrational predissociation from 12 vibrational levels of S1 p-difluorobenzene–argon (pDFB–Ar) by time-resolved two-color multiphoton ionization. Three features of our results are particularly surprising. First, the vibrational predissociation rate does not necessarily increase with additional quanta in a given ring vibrational mode. Second, direct excitation of the presumed reaction coordinate, the van der Waals stretch, may decrease the vibrational predissociation rate. Third, pDFB mode 8 (mode 16a in the Wilson notation) shows a large vibrational frequency shift upon complexation, as in other aromatic-argon complexes, but in pDFB it is at most weakly active in vibrational predissociation, in striking contrast to the other systems. These results are inconsistent with available simple theories of vibrational predissociation. We also find that the vibrational predissociation lifetime exceeds 2.7 ns even at 1634 cm−1 excess vibrational energy, where rapid vibrational energy redistribution has been predicted. Where direct comparison is possible, the rates we measure are about 40% lower than those obtained in time-integrated experiments by Parmenter and co-workers.

The benzene ground state potential surface. II. Harmonic force field for the planar vibrations

A complete harmonic force field in terms of nonredundant coordinates has been generated from experimental frequencies for D6h, D3h, and D2h isotopically labeled benzenes and degenerate mode Coriolis constants predicting broken symmetry labeled benzene frequencies to ±0.1% and Coriolis constants to ±0.01 units, on the average. Exact solutions have been obtained for the six E1u force constants from D6h symmetry frequency data with the inclusion of 13C6H6 information. Some modes (e.g., the e2g mode ν8, in Wilson notation) are significantly altered from previous experimental force field predictions, rationalizing unclearly understood vibronic features of phosphorescence and two-photon spectra. A conundrum regarding the e1u Coriolis constant for ν18 (Wilson notation) is identified: no harmonic force field is capable of predicting the reported experimental magnitudes for this constant for both C6H6 and C6D6. The Pulay et al. scaled ab initio force field is in qualitative agreement with the experimental field for every symmetry class, with significant quantitative discrepancies involving CH stretching constants.

Vibrational mean-square amplitude matrices—I

Mean-square amplitudes of vibration in the theory of small harmonic vibrations of polyatomic molecules are studied. The quantities are treated as a kind of vibrational constants, similarly to the familiar treatment of harmonic force constants. After including certain interaction terms to form the mean-square amplitude matrix Σ, it was possible to develop two secular equations, the former one involving the matrices Σ and G−1, the latter one the matrices Σ and F. Here F and G are used for the energy matrices in Wilson's notation. Applications of the secular equations, including the ordinary one involving F and G, are discussed, and an isotope rule for the mean-square amplitude matrix elements is evaluated. Ultimately some approximation methods for computing mean-square amplitude matrices are reported, and are based on approximate expressions for the hyperbolic cotangent.