The vibrational structures of furan, pyrrole, and thiophene cations studied by zero kinetic energy photoelectron spectroscopy

The vibrational structures of the electronic ground states ((approximately)X (2)A(2)) of furan, pyrrole, and thiophene cations have been studied by zero kinetic energy (ZEKE) photoelectron spectroscopic method. In addition to the strong excitations of the symmetric a(1) vibrational modes, other three symmetric vibrational modes (a(2), b(1), and b(2)) have been observed unambiguously. These results which cannot be explained by the Franck-Condon principle illustrate that the vibronic coupling and the Coriolis coupling may play important roles in understanding the vibrational structures of the five-membered heterocycle cations. The vibrationally resolved ZEKE spectra are assigned with the assistance of the density function theory calculations, and the fundamental frequencies for many vibrational modes have been determined for the first time. The first adiabatic ionization energies for furan, pyrrole, and thiophene were determined as 8.8863, 8.2099, and 8.8742 eV, respectively, with uncertainties of 0.0002 eV.     

A theoretical anharmonic study of the infrared absorption spectra of FHF-, FDF-, OHF-, and ODF- anions

Anharmonic vibrational frequencies, equilibrium bond lengths, rotational constants, and vibrational absorption spectra have been calculated for the triatomic anions, FHF(-) and OHF(-), and the heavier isotopomers FDF(-) and ODF(-). The triatomic anions are assumed to maintain a collinear configuration throughout all calculations, so only the symmetric (nu(1)) and asymmetric (nu(3)) stretching modes are considered. The two-dimensional permanent dipole surfaces and potential energy surfaces are then constructed along bond coordinates, using high-level ab initio methods. Fundamental and combination bands are obtained from the vibrational eigenfunctions, resulting in anharmonic frequencies, which can be compared with the available theoretical and experimental data. The agreement is very good, especially for the pure symmetric modes, while the asymmetric ones show larger discrepancies, presumably due to the neglected coupling between stretching and bending modes. Strong inverse anharmonicity is found in the level spacing of the asymmetric modes, for both FHF(-) and OHF(-) anions. The calculated mixed modes (nnu(1)+mnu(3), n, m=0-3) also agree reasonably with the few available experimental data, supporting our model. Based on the vibrational eigenfunctions, isotope effects are also rationalized. Infrared absorption spectra are calculated from the dipole autocorrelation function for FHF(-) and FDF(-), and for OHF(-) and ODF(-). Peak locations and relative intensities are assigned in terms of the fundamental and mixed transitions.     

Quasibound continuum states in SiF4 (D2A1) photoionization: photoelectron-vibrational coupling

The authors report a fully vibrationally resolved photoelectron spectroscopy investigation of a nonplanar molecule studied over a range of excitation energies. Experimental results for all four fundamental vibrational modes are presented. In each case significant non-Franck-Condon effects are seen. The vibrational branching ratio for the totally symmetric mode nu1+ is found to be strongly affected by resonant excitation in the SiF4+ (D2A1) photoionization channel. This is shown to be the result of two distinct shape resonances, which for the first time have been both confirmed by theoretical calculations. Vibrationally resolved Schwinger photoionization calculations are used to understand the vibronic coupling for the photoelectrons, both using ab initio and harmonic vibrational wave functions.     

Mode-specific photoelectron scattering effects on CO2(+)(C2Sigmag+) vibrations

Using high-resolution photoelectron spectroscopy, we have determined the energy dependent vibrational branching ratios for the symmetric stretch [v+ = (100)], bend [v+ = (010)], and antisymmetric stretch [v+ = (001)], as well as several overtones and combination bands in the 4sigmag(-1) photoionization of CO2. Data were acquired over the range from 20-110 eV, and this wide spectral coverage highlighted that alternative vibrational modes exhibit contrasting behavior, even over a range usually considered to be dominated by atomic effects. Alternative vibrational modes exhibit qualitatively distinct energy dependences, and this contrasting mode-specific behavior underscores the point that vibrationally resolved measurements reflect the sensitivity of the electron scattering dynamics to well-defined changes in molecular geometry. In particular, such energy-dependent studies help to elucidate the mechanism(s) responsible for populating the symmetry forbidden vibrational levels [i.e., v+ =( 010), (001), (030), and (110)]. This is the first study in which vibrationally resolved data have been acquired as a function of energy for all of the vibrational modes of a polyatomic system. Theoretical Schwinger variational calculations are used to interpret the experimental data, and they indicate that a 4sigmag-->ksigmau shape resonance is responsible for most of the excursions observed for the vibrational branching ratios. Generally, the energy dependent trends are reproduced well by theory, but a notable exception is the symmetric stretch vibrational branching ratio. The calculated results display a strong peak in the vibrational branching ratio while the experimental data show a pronounced minimum. This suggests an interference mechanism that is not accounted for in the single-channel adiabatic-nuclei calculations. Electronic branching ratios were also measured and compared to the vibrational branching ratios to assess the relative contributions of interchannel (i.e., Herzberg-Teller) versus intrachannel (i.e., photoelectron-mediated) coupling.     

Quasi-classical trajectory study of the role of vibrational and translational energy in the Cl(2P) + NH3 reaction

A detailed state-to-state dynamics study was performed to analyze the effects of vibrational excitation and translational energy on the dynamics of the Cl((2)P) + NH(3)(v) gas-phase reaction, effects which are connected to such issues as mode selectivity and Polanyi's rules. This reaction evolves along two deep wells in the entry and exit channels. At low and high collision energies quasi-classical trajectory calculations were performed on an analytical potential energy surface previously developed by our group, together with a simplified model surface in which the reactant well is removed to analyze the influence of this well. While at high energy the independent vibrational excitation of all NH(3)(v) modes increases the reactivity by a factor ≈1.1-2.9 with respect to the vibrational ground-state, at low energy the opposite behaviour is found (factor ≈ 0.4-0.9). However, when the simplified model surface is used at low energy the independent vibrational excitation of all NH(3)(v) modes increases the reactivity, showing that the behaviour at low energies is a direct consequence of the existence of the reactant well. Moreover, we find that this reaction exhibits negligible mode selectivity, first because the independent excitation of the N-H symmetric and asymmetric stretch modes, which lie within 200 cm(-1) of each other, leads to reactions with similar reaction probabilities, and second because the vibrational excitation of the reactive N-H stretch mode is only partially retained in the products. For this "late transition-state" reaction, we also find that vibrational energy is more effective in driving the reaction than an equivalent amount of energy in translation, consistent with an extension of Polanyi's rules. Finally, we find that the non-reactive events, Cl((2)P)+NH(3)(v) → Cl((2)P) + NH(3)(v'), lead to a great number of populated vibrational states in the NH(3)(v') product, even starting from the NH(3)(v = 0) vibrational ground state at low energies, which is unphysical in a quantum world. This result is interpreted on the basis of non-conservation of the ZPE per mode.     

Jet-cooled infrared spectroscopy in slit supersonic discharges: symmetric and antisymmetric CH2 stretching modes of fluoromethyl (CH2F) radical

The combination of shot noise-limited direct absorption spectroscopy with long-path-length slit supersonic discharges has been used to obtain first high-resolution infrared spectra for jet-cooled CH2F radicals in the symmetric (nu1) and antisymmetric (nu5) CH2 stretching modes. Spectral assignment has yielded refined lower- and upper-state rotational constants and fine-structure parameters from least-squares fits to the sub-Doppler line shapes for individual transitions. The rotational constants provide indications of large amplitude vibrational averaging over a low-barrier double minimum inversion-bending potential. This behavior is confirmed by high-level coupled cluster singles/doubles/triples calculations extrapolated to the complete basis set limit and adiabatically corrected for zero point energy. The calculations predict a nonplanar equilibrium structure (theta approximately 29 degrees, where theta is defined to be 180 degrees minus the angle between the C-F bond and the CH2 plane) with a 132 cm(-1) barrier to planarity and a vibrational bend frequency (nu(bend) approximately 276 cm(-1)), in good agreement with previous microwave estimates (nu(bend) = 300 (30) cm(-1)) by Hirota and co-workers [Y. Endo et al., J. Chem. Phys. 79, 1605 (1983)]. The nearly 2:1 ratio of absorption intensities for the symmetric versus antisymmetric bands is in good agreement with density functional theory calculations, but in sixfold contrast with simple local mode CH2 bond dipole predictions of 1:3. This discrepancy arises from a surprisingly strong dependence of the symmetric stretch intensity on the inversion bend angle and provides further experimental support for a nonplanar equilibrium structure.     

Intermolecular vibrations of fluorobenzene-Ar up to 130 cm(-1) in the ground electronic state

Sixteen intermolecular vibrational levels of the S(0) state of the fluorobenzene-Ar van der Waals complex have been observed using dispersed fluorescence. The levels range up to ～130 cm(-1) in vibrational energy. The vibrational energies have been modelled using a complete set of harmonic and quartic anharmonic constants and a cubic anharmonic coupling between the stretch and long axis bend overtone that becomes near ubiquitous at higher energies. The constants predict the observed band positions with a root mean square deviation of 0.04 cm(-1). The set of vibrational levels predicted by the constants, which includes unobserved bands, has been compared with the predictions of ab initio calculations, which include all vibrational levels up to 70-75 cm(-1). There are small differences in energy, particularly above 60 cm(-1), however, the main differences are in the assignments and are largely due to the limitations of assigning the ab initio wavefunctions to a simple stretch, bend, or combination when the states are mixed by the cubic anharmonic coupling. The availability of these experimental data presents an opportunity to extend ab initio calculations to higher vibrational energies to provide an assessment of the accuracy of the calculated potential surface away from the minimum. The intermolecular modes of the fluorobenzene-Ar(2) trimer complex have also been investigated by dispersed fluorescence. The dominant structure is a pair of bands with a ～35 cm(-1) displacement from the origin band. Based on the set of vibrational modes calculated from the fluorobenzene-Ar frequencies, they are assigned to a Fermi resonance between the symmetric stretch and symmetric short axis bend overtone. The analysis of this resonance provides a measurement of the coupling strength between the stretch and short axis bend overtone in the dimer, an interaction that is not directly observed. The coupling matrix elements determined for the fluorobenzene-Ar stretch-long axis bend overtone and stretch-short axis bend overtone couplings are remarkably similar (3.8 cm(-1) cf. 3.2 cm(-1)). Several weak features seen in the fluorobenzene-Ar(2) spectrum have also been assigned.     

Inversion Vibrational Energy Levels of PH3+(X2A2") Calculated by a New Two-dimension Variational Method

A new 2-D variational method is proposed to calculate the vibrational energy levels of the symmetric P-H stretching vibration (v1) and the symmetric umbrella vibration (inversion vibration) (v2) of PH₃⁺(X²A₂") that has the tunneling effect. Because the symmetric internal Cartesian coordinates were employed in the calculations, the kinetic energy operator is very simple and the inversion vibrational mode is well characterized. In comparison with the often used 1-D model to calculate the inversion vibrational energy levels, this 2-D method does not require an assumption of reduced mass, and the interactions between the v1 and v2 vibrational modes are taken into consideration. The calculated vibrational energy levels of PH₃⁺ are the first reported 2-D calculation, and the average deviation to the experimental data is less than 3 cm^-1 for the first seven inversion vibrational energy levels. This method has also been applied to calculate the vibrational energy levels of NH₃. The application to NH₃ is less successful, which shows some limitations of the method compared with a full dimension computation.     

Vibrational structure of vinyl chloride cation studied by using one-photon zero-kinetic energy photoelectron spectroscopy

The vibrational structure of vinyl chloride cation, CH(2)CHCl+ (X(2)A' '), has been studied by vacuum ultraviolet (VUV) zero-kinetic energy (ZEKE) photoelectron spectroscopy. Among nine symmetric vibrational modes, the fundamental frequencies of six modes have been determined. The first overtone of the out-of-plane CH(2) twist vibrational mode has been also measured. In addition to these, the combination and overtone bands of the above vibrational modes about 4500 cm(-1) above the ground state have been observed in the ZEKE spectrum. The vibrational band intensities of the ZEKE spectrum can be described approximately by the Franck-Condon factors with harmonic approximation. The ZEKE spectrum has been assigned based on the harmonic frequencies and Franck-Condon factors from theoretical calculations. The ionization energy (IE) of CH(2)CHCl is determined as 80705.5 +/- 2.5 (cm(-1)) or 10.0062 +/- 0.0003 (eV).     

Quantitative prediction of gas-phase 19F nuclear magnetic shielding constants

Benchmark calculations of (19)F nuclear magnetic shielding constants are presented for a set of 28 molecules. Near-quantitative accuracy (ca. 2 ppm deviation from experiment) is achieved if (1) electron correlation is adequately treated by employing the coupled-cluster singles and doubles (CCSD) model augmented by a perturbative correction for triple excitations [CCSD(T)], (2) large (uncontracted) basis sets are used, (3) gauge-including atomic orbitals are used to ensure gauge-origin independence, (4) calculations are performed at accurate equilibrium geometries [obtained from CCSD(T)/cc-pVTZ calculations correlating all electrons], and (5) vibrational averaging and temperature corrections via second-order vibrational perturbation theory (VPT2) are included. For the CCSD(T)/13s9p4d3f calculations corrected for vibrational effects, mean and standard deviation from experiment are -1.9 and 1.6 ppm, respectively. Less elaborate theoretical treatments result in larger errors. Consideration of relative shifts can reduce the mean deviation (through an appropriately chosen reference compound), but does not change the standard deviation. Density-functional theory calculations of absolute and relative (19)F nuclear magnetic shielding constants are found to be, at best, as accurate as the corresponding Hartree-Fock self-consistent-field calculations and are not improved by consideration of vibrational effects. Molecular systems containing fluorine-oxygen, fluorine-nitrogen, and fluorine-fluorine bonds are found to be more challenging than the other investigated molecules for the considered theoretical methods.     

Vibrational spectroscopy of protonated imidazole and its complexes with water molecules: ab initio anharmonic calculations and experiments

The results of anharmonic frequency calculations on neutral imidazole (C3N2H4, Im), protonated imidazole (ImH+), and its complexes with water (ImH+)(H2O)n, are presented and compared to gas phase infrared photodissociation spectroscopy (IRPD) data. Anharmonic frequencies are obtained via ab initio vibrational self-consistent field (VSCF) calculations taking into account pairwise interactions between the normal modes. The key results are: (1) Prediction of anharmonic vibrational frequencies on an MP2 ab initio potential energy surface show excellent agreement with experiment and outstanding improvement over the harmonic frequencies. For example, the ab initio calculated anharmonic frequency for (ImH+)(H2O)N2 exhibits an overall average percentage error of 0.6% from experiment. (2) Anharmonic vibrational frequencies calculated on a semiempirical potential energy surface fitted to ab initio harmonic data represents spectroscopy well, particularly for water complexes. As an example, anharmonic frequencies for (ImH+)H2O and (ImH+)(H2O)2 show an overall average deviation of 1.02% and 1.05% from experiment, respectively. This agreement between theory and experiment also supports the validity and use of the pairwise approximation used in the calculations. (3) Anharmonic coupling due to hydration effects is found to significantly reduce the vibrational frequencies for the NH stretch modes. The frequency of the NH stretch is observed to increase with the removal of a water molecule or replacement of water with N2. This result also indicates the ability of the VSCF method to predict accurate frequencies in a matrix environment. The calculation provides insights into the nature of anharmonic effects in the potential surface. Analysis of percentage anharmoncity in neutral Im and ImH+ shows a higher percentage anharmonicity in the NH and CH stretch modes of neutral Im. Also, we observe that anharmonicity in the NH stretch modes of ImH+ have some contribution from coupling effects, while that of neutral Im has no contribution whatsoever from mode-mode coupling. It is concluded that the incorporation of anharmonic effects in the calculation brings theory and experiment into much closer agreement for these systems.     

Excited state ab initio and Franck-Condon simulation of S1 → S0 fluorescence excitation spectra of p-, m-, and o-difluorobenzenes

Although difluorobenzenes (DFBs) are well-known organic molecules to understand the electronic structure and spectroscopy of benzene and its derivatives, few theoretical investigations have been performed to simulate their fine spectra and assign their vibrational bands. In this work, the fluorescence excitation (FEX) spectra of the first excited singlet states for three DFBs molecules (para-, meta- and ortho-difluorobenzene) were simulated by the Franck-Condon calculations with the displaced harmonic oscillator approximation plus the distorted correction. The calculated results indicated that the spectral profiles of three DFBs are primarily described by the Franck-Condon progression of their totally symmetric vibrational modes. Specifically, it is found that modes v(3) and v(5) of para-DFB, v(8) and v(9) of meta-DFB, and ortho-DFB play the most important roles in the fluorescence spectra. By taking into account the contributions of the distorted effect, we could assign most of the dominant overtones from the nontotally symmetric vibrational modes, and the results agree well with the experimental assignments. Some inferred and unassigned vibrational transitions in experiment were confirmed according to the present calculated results. In addition, in the simulated fluorescence spectra, we tentatively assigned several combination bands with relative moderate intensity and weak vibrational lines which appeared in the experimental observations but the corresponding assignments were not given. The present work reproduced satisfactorily the experimental FEX spectra of p-, m-, and o-DFBs derivatives and provided a useful method to simulate the FEX spectra of dihalogenated benzene molecules.     

On the number of significant mode-mode anharmonic couplings in vibrational calculations: Correlation-corrected vibrational self-consistent field treatment of di-, tri-, and tetrapeptides

A computational study is made of the number of important anharmonic mode-mode couplings in the context of vibrational calculations for di-, tri-, and tetrapeptides. The method employed is the correlation-corrected vibrational self-consistent field (CC-VSCF) algorithm, which includes correlation effects between different vibrational modes. It is found that results of good accuracy can be obtained in calculations that include only N log N mode-mode coupling terms, where N is the number of modes. This simplification significantly accelerates CC-VSCF calculations for large molecules. A criterion based on the characteristics of the normal-mode displacements is employed to predict a priori unimportant coupling terms. The criterion is tested statistically using Spearman's rank correlation coefficient. The results are illustrated by calculations for several di-, tri-, and tetrapeptides using semiempirical PM3 potential surfaces. These results are analyzed and a statistical model for error estimation is given. The decrease in the number of included coupling from N(2) to N log N opens possibilities of anharmonic vibrational calculations for large peptides.     

Time-resolved spectroscopy of silver nanocubes: observation and assignment of coherently excited vibrational modes

The response of single crystal, cubic silver particles to ultrafast laser-induced heating has been examined experimentally and theoretically. The transient absorption traces display clear modulations due to coherently excited vibrational modes. Nanocube samples with edge lengths smaller than 50 nm show a single modulation, whereas samples larger than 50 nm show two vibrational modes. The results are compared to finite element calculations, where the cubes are modeled as having cubic crystal symmetry with the principal axes parallel to the sides of the particle. The action of the laser pulse is treated in two ways, first, as creating a uniform initial strain. In this case the predominant mode excited is the breathing mode. The period of this mode is in reasonable agreement with the vibrational periods measured for the smaller cubes and with the higher frequency modulation observed for the larger cubes. A nonuniform initial strain is also considered, which could arise from nonuniform heating for particles larger than the optical skin depth of the metal. In this case the predominant mode excited is a nontotally symmetric mode. The calculated periods from this analysis are in reasonable agreement with the lower frequency modulations observed for the larger samples. The results from this study show that, to within the accuracy of these measurements, the elastic constants of cubic silver nanoparticles are the same as bulk silver.     

Evaporatively cooled M+ (H2O)Ar cluster ions: infrared spectroscopy and internal energy simulations

Rotationally resolved IR spectra of M+ (H2O)Ar cluster ions for M=Na, K, and Cs in the O-H stretch region were measured in a triple-quadrupole mass spectrometer. Analysis of the spectra yields O-H stretch vibrational band origins and relative IR intensities of the symmetric and asymmetric modes. The effect of the alkali-metal ions on these modes results in frequency shifts and intensity changes from the gas phase values of water. The A-rotational constants are also obtained from the rotational structure and are discussed. Experimentally, the temperatures of these species were deduced from the relative populations of the K-rotational states. The internal energies and temperatures of the cluster ions for Na and K were simulated using RRKM calculations and the evaporative ensemble formalism. With binding energies and vibrational frequencies obtained from ab initio calculations, the average predicted temperatures are qualitatively consistent with the experimental values and demonstrate the additional cooling resulting from argon evaporation.     

pH-dependent Raman study of pyrrole and its vibrational analysis using DFT calculations

Raman spectra of pyrrole in aqueous medium at different pH values, 2.5, 5.5, 7.5 and 10.5 were recorded in the two spectral regions, 1,040-1,160 cm(-1) and 3,300-3,360 cm(-1) and pH dependence of the linewidth, peak position and intensity of the Raman bands corresponding to the ring breathing and symmetric nu(N-H) stretching modes were examined. A linear pH dependence of the peak positions for the ring breathing mode and a maximum at nearly neutral pH (7.5) for the symmetric nu(N-H) normal mode is observed, whereas the linewidth (FWHM) shows almost no variation with the change of pH. A slight decrease in the wavenumber position of the nu(N-H) mode at pH value >7.5 indicates that the influence of deprotonation is small, which results from a weak interaction between the reference molecule and the surrounding environment. The density functional theory (DFT) calculations were made primarily to obtain the optimized geometry and vibrational spectra of pyrrole in the ground electronic state using B3LYP functional and the highest level basis set 6-311++G(d,p). The assignments of the normal modes of pyrrole were made on the basis of potential energy distribution (PED). The calculations were also performed on protonated and deprotonated structures of pyrrole.     

End-cap effects on vibrational structures of finite-length carbon nanotubes

Vibrational structures of C60-related finite-length nanotubes, C(40+20n) and C(42+18n) (1 < or = n < or = 4), in which n is, respectively, the number of cyclic cis- and trans-polyene chains inserted between fullerene hemispheres, are analyzed from density functional theory (DFT) calculations. To illuminate the end-cap effects on their vibrational structures, the corresponding tubes terminated by H atoms C(20n)H20 and C(18n)H18 (1 < or = n < or = 5) are also investigated. DFT calculations show a broad range of vibrational frequencies for the finite-size nanotubes: high-frequency modes (1100-1600 cm(-1)) containing oscillations along tangential directions (tangential modes), medium-frequency modes (700-850 cm(-1)) whose oscillations are located on the edges or end caps, and low-frequency modes (300-600 cm(-1)) involving oscillations along the radial directions (radial modes). Broadening of the calculated frequencies is due to the number of nodes in the standing waves of normal modes in the finite-size tubes. In the capped tubes, calculated vibrational frequencies are insensitive to the number of chains (n), whereas in the uncapped tubes, most vibrational frequencies change significantly with an increase in tube length. The discrepancy in the size dependency is reasonably understood by their C-C bonding networks; the capped tubes have similar bond-length alternation patterns within the polyene chains irrespective of n, whereas the uncapped tubes have various bond-deformation patterns. Thus, DFT calculations illuminate that the edge effects have strong impacts on the vibrational frequencies in the finite-size nanotubes.     

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.     

The emergence of collective vibrations in cluster models: quantum chemical study of the methyl-terminated Si(111) surface

In this paper we present structures and harmonic vibrational frequencies for the methylated silicon (111) surface from quantum chemical calculations using both cluster models and periodic boundary conditions. The results from both calculations are in very good agreement with experimentally determined frequencies. We demonstrate that relatively small cluster models already show the emergence of collective vibrational modes and provide a general method for the assignment of vibrational frequencies for extended surfaces from cluster models. Finally, we discuss a vibrational mode that results from the coupling between near-surface phonons and the silicon-carbon bending modes.