Showing papers on "Fermi resonance published in 1988"

Fermi resonances and local modes in water, hydrogen sulfide, and hydrogen selenide

Abstract: A simple vibrational curvilinear internal coordinate Hamiltonian for bent H2X molecules is constracted by expanding the g matrix elements and the potential energy function in terms of the Morse variable y=1−exp(−ar) and retaining important local mode and Fermi resonance terms. The eigenvalues of this Hamiltonian are calculated variationally using Morse oscillator basis functions for the stretches and harmonic oscillator basis functions for the bend. The nonlinear least‐squares method is used to optimize the potential energy parameters. The model is applied to water, hydrogen sulfide, and hydrogen selenide. Experimental vibrational levels up to 18 500 cm−1 for five symmetrical isotopic species of water are reproduced with a standard deviation of about 4 cm−1. For both hydrogen sulfide and hydrogen selenide two symmetrical isotopic species were included in the optimization procedure and standard deviations of 1.0 and 0.66 cm−1 were obtained. The potential energy parameters obtained agree well with previous ...

Vibrational spectrum and potential energy surface of the CH chromophore in CHD3

Abstract: The rovibrational spectrum of trideutero‐methane has been measured at resolutions mostly close to the Doppler limit on an interferometric Fourier transform spectrometer from the lowest fundamental vibration to high overtones of the CH stretching vibration (wave numbers from 900 to 12 000 cm−1). The CH chromophore spectrum is fully assigned and interpreted by means of the tridiagonal Fermi resonance Hamiltonian for the coupled CH stretching and bending vibrations. The Hamiltonian predicts and also fits the visible spectrum up to 19 000 cm−1 measured by Scherer et al., Perry et al., and Campargue et al. The effective tridiagonal Hamiltonian is derived ab initio by means of MRD‐CI and full CI calculations of the potential surface of methane, a variational vibrational calculation in a normal coordinate subspace of the coupled CH stretching and bending motions and an approximate similarity transformation to tridiagonal form. Fits of the experimental results by the tridiagonal and the variational Hamiltonian le...

Structure and vibrational dynamics of the CO2 dimer from the sub‐Doppler infrared spectrum of the 2.7 μm Fermi diad

Abstract: Sub‐Doppler infrared spectra of two Fermi resonance coupled bands of carbon dioxide dimer have been obtained at 3611.5 and 3713.9 cm−1 using an optothermal molecular beam color‐center laser spectrometer. The band origins for the complexes are red shifted by approximately 1 cm−1 from the corresponding ν1+ν3/2ν02+ν3 CO2 bands. The higher frequency band is perturbed while the lower frequency band appears free of extraneous perturbations as determined from a precision fit to a Watson asymmetric rotor Hamiltonian. This fit and the observed nuclear spin statistical weights reveal that the complex is planar with C2h symmetry. The C‐‐C separation and C‐‐C–O angle are determined to be 3.599(7) A and 58.2(8)°, respectively. The nearest neighbor O‐‐C distance is 3.14 A which is the same as that found in the crystal. From the centrifugal distortion analysis the weak bond stretching and symmetric bending frequencies are estimated to be 32(2) and 90(1) cm−1. No interconversion tunneling is observed.

The C–H overtone spectra of acetylene: Bend/stretch interactions below 10 000 cm−1

Abstract: High resolution FT‐IR spectra of C2H2 have been obtained from 1800 to 10 000 cm−1. Over 1600 rovibrational transitions belonging to 30 vibrational bands were assigned and analyzed yielding band origins and rotational constants. Band centers from this and other studies were used to calculate various stretch/stretch and bend/stretch anharmonic coupling constants. Several resonances of the type between ν3 and (ν2+ν4+ν5)0 were analyzed, and an unperturbed value of ν3 was determined. This was combined with other data to obtain ωm, xm, and λ in the local mode basis. x–K relations were imposed to yield the normal mode constants for ν1 and ν3. Treatment of Darling–Dennison resonances in the first two overtone manifolds led to reassignments of previously reported spectra and to the discovery of a Fermi resonance involving overtones of ν3 and states containing ν1, ν2, and 2ν04. Calculated rotational constants and intensity data confirm the assignments and interactions treated in the vibrational analysis. Treatment ...

Optothermal‐infrared and pulsed‐nozzle Fourier‐transform microwave spectroscopy of rare gas–CO2 complexes

Abstract: Sub‐Doppler infrared spectra of Ne–CO2, Ar–CO2, and Kr–CO2 have been recorded near 3613 and 3715 cm−1, in the region of the 2ν02+ν3/ν1+ν3 Fermi diad of CO2, using an optothermal molecular‐beam color‐center laser spectrometer. In addition, pulsed‐nozzle Fourier‐transform microwave spectra are reported for the ground vibrational states of the complexes. The infrared and microwave spectra are consistent with T‐shaped complexes as shown originally by Steed, Dixon, and Klemperer for Ar–CO2.1 The infrared band origins for the Ar and Kr complexes are red shifted, from that of free CO2, by 1.09 and 0.95 cm−1 for Ar–CO2 and by 1.97 and 1.76 cm−1 for 84Kr–CO2. For Ne–CO2, blue shifts of 0.15 and 0.19 cm−1 are observed. The lower Fermi components are free of perturbations, whereas the upper components of Ar–CO2 and Kr–CO2 are perturbed. For Ar–CO2 the perturbation is strong, shifting the positions of the observed Q‐branch lines of the Ka =1←0 subband by as much as 500 MHz.

The S1–S0(1B2u–1Ag) transition of p‐difluorobenzene cooled in a supersonic free jet expansion. Excitation and dispersed fluorescence spectra, vibrational assignments, Fermi resonances, and forbidden transitions

Abstract: The vibronic spectroscopy of the S1(1B2u)–S0(1Ag) transition of p‐difluorobenzene (000 at 36 838 cm−1) cooled in a supersonic free jet expansion in argon has been reinvestigated in some detail. Analysis of over 50 vibronic transitions using fluorescence excitation and dispersed single vibronic level fluorescence spectroscopy has led to the establishment or confirmation of the assignments of 19 S1 and S0 frequencies, including eight previously unassigned S1 vibrational frequencies, and the reassignment of two S1 and one S0 frequencies. Several Franck–Condon forbidden transitions have been identified. Their activity in the S1–S0 spectrum is attributed to vibronic coupling involving higher lying electronic states. Forbidden transitions involving b3g modes, notably ν27 and ν26, derive their intensity from a higher lying 1B1u electronic state, via vibronic coupling that is analogous to that responsible for the 1B2u–1Ag transition in benzene. Numerous Fermi resonances in both the S1 and S0 states have been iden...

Spectroscopy and intramolecular dynamics of highly excited vibrational states of NH3

Abstract: Using the recently developed technique of microwave-detected, microwaveoptical double resonance, we have for the first time been able to assign the rotational structure in the local-mode progression of NH3. This work has resulted in a near doubling of the number of rotationally assigned bands of this well studied molecule. We have reproduced our observed spectrum with an effective vibrational Hamiltonian that includes both Darling–Dennison and Fermi resonance coupling between ν1, ν3 and 2ν4. Because these interactions were not included previously, we have also determined the first relible anharmonic constants for this molecule. We have used this effective Hamiltonian to determine the intramolecular dynamics of NH3 for ca. 1 ps.

Overtone spectra of C–H oscillators in cold molecules

Abstract: The C–H stretch overtone spectra of methane (5–0), ethylene (5–0 and 6–0), ethane (5–0 and 6–0), propyne (4–0 and 5–0 acetylenic and 5–0 methyl C–H stretches), allene (5–0), propane (5–0 and 6–0), cyclopropane (5–0 and 6–0), dimethyl ether (5–0), and isobutane (5–0) have been recorded at temperatures between 143 and 189 K, depending on the molecule. A comparison is made to the spectra obtained at room temperature, with the goal of improved understanding of the band shapes. The temperature dependence of most of the observed bands is found to be significantly less than that expected for ‘‘simple’’ bands. For these small to medium size hydrocarbons, the temperature independence of the overtone bands is found to correlate loosely with the density of states and with the degree of saturation. Other factors are important determinants of spectral widths and temperature independence as well, such as conformational inequivalence of the C–H oscillators, and the number and positions of the oscillators. It is concluded that the vast majority of hydrocarbon C–H stretch high overtone bands have upper states which are extensively mixed with other states. This is the case even for most of the relatively small hydrocarbons. This mixing produces a broadening effect and greatly increases the transition density, thereby diluting the oscillator strength of the rovibrational transitions from that of the zero‐order approximation. The Fermi resonance type of interaction appears to be of greater importance than the Coriolis type in determining the appearance of the high overtone bands.

Local mode and normal mode interpretations of the CH and CD stretching vibrational manifolds in C2H4 and C2D4

Abstract: The CH and CD stretching vibrational manifolds in C2H4 and C2D4 have been studied up to six and four quanta of excitation, respectively. They are interpreted in each case in terms of a minimum number of local mode parameters. In C2H4, perturbations arising from Fermi resonances are complex and involve both the C=C stretching and the CH2 scissoring vibrations, with the former itself being in close resonance with the in‐phase CH2 rocking overtone. Nevertheless, once all major resonances are taken into account, a self‐consistent set of vibrational parameters is determined, which reproduces observations well in both infrared and Raman spectra. In C2D4, no significant Fermi resonance complications are apparent, spectroscopic interpretation is straightforward, and approximations inherent in the simple local mode model may be tested. The local mode parameters determined for C2H4 and C2D4 obey closely their expected isotopic interdependences. Values determined for the interbond harmonic coupling parameters in each case are in excellent agreement with those predicted through the harmonic force constants of ethylene.

Effect of pressure and temperature on the Raman spectra of solid N2O

Abstract: High pressure Raman studies up to 18 GPa have been made on solid CO2 at room temperature and low temperatures. Changes in the spectral features of external modes are used to draw conclusions on the structural behavior under compression. Anharmonic contributions to the intermolecular potential and their pressure dependence are determined from the pressure and temperature shift of librational frequencies. Anharmonic contributions to the intramolecular potential are determined by pressure tuning of the Fermi resonance.

Temperature study of intra- and inter-molecular coupling and Fermi resonance constants in the Raman spectra of liquid water using Fourier deconvolution

Abstract: The structure of the Raman OH stretching band of water has been investigated from 4 to 90 °C using a Fourier deconvolution technique. The overlapped components in the isotropic and anisotropic spectra have been resolved. The information on the positions of the components in the deconvoluted spectra was used for calculation of the constants for intra- and inter-molecular coupling and Fermi resonance and for an estimation of the component frequencies according to the model presented. For the first time, the value of the asymmetric Fermi resonance constant and the temperature dependences of all coupling constants have been obtained. Their temperature behaviour is in good agreement with the data in the literature concerning the different phases of water. It was established that the intramolecular coupling constant increases and the intermolecular coupling constant decreases as the temperature increases. The Fermi resonance constant for symmetric components tends to decrease with increasing temperature. The decrease in the symmetric Fermi resonance interaction with increasing temperature is due to the increase in the distance between the unperturbed fundamental and overtone band positions. The asymmetric Fermi resonance constant tends to increase with increasing temperature and this determines the strengthening of the asymmetric Fermi resonance interaction, which exhibits a limiting value at high temperatures.

Investigation of fermi resonances in CHX3 molecules with an internal-coordinate hamiltonian

Abstract: A Hamiltonian for CHX3 molecules in terms of symmetrized curvilinear internal coordinates and their conjugate momenta has been derived and used to study the Fermi resonances between the CH stretching and HCX bending vibrations. The kinetic energy operator is obtained by expanding the G matrix in displacement coordinates and retaining the terms mos important for the Fermi resonance problem. This Hamiltonian is used to interpret the observed CH stretching and bending vibrational spectrum of flouromform, CHF3. Eigenvalues are calculated variationally using a separable basis set consisting of functions which are products of a Morse oscillator eigenfunction for the stretch and a two-dimensional harmonic oscillator wavefunction for the bend. Potential-energy parameters are optimized using the least-squares method. The energy levels up to N=v1+1/2v4= 6 (for A1 states) and 11/2 (for E states) can be fitted well (the standard deviation of the fit is 4.7 cm–1) and relative intensities show the correct behaviour as compared to experiment. Expressions for the tridiagonal parameters xsb and Φsbb are obtained in a closed form and evaluated for fluoroform. The results for CHF3 and CHD3 are also compared to results from ab initio calculations.

Sensitivity of intramolecular vibrational energy relaxation to stretch–bend potential energy coupling and stability of periodic orbits

Abstract: Stretch–bend coupling via 2:1 Fermi resonance is an important mechanism for rapid energy flow from overtone excited CH local mode states. To elucidate the role of potential energy coupling, we have studied the classical dynamics of a two‐mode stretch–bend Hamiltonian for the benzene fragment C3 H. The effects of attenuation of the CCH bend force constant by stretching of the CH bond on the short time (up to 0.12 ps) probability decay dynamics of the model system are in good qualitative accord with trends found previously in full scale classical trajectory simulations on planar benzene by Lu, Hase, and Wolf. Surfaces of section are used to study the classical phase space structure of the stretch–bend Hamiltonian. A close correlation between instability of the CH periodic orbit and exponential decay of probability is found, and relaxation rates can be estimated to good accuracy by linear stability analysis of the periodic orbit. Increasing the strength of the potential coupling stabilizes the CH periodic orbit, thereby suppressing overtone relaxation. There is therefore an effective cancellation of kinetic and potential stretch–bend coupling terms.

Semiclassical phase space evolution of Fermi resonance spectra

Abstract: The evolution of the semiclassical phase space of a Fermi resonance spectrum is investigated as the strength of the resonance coupling is varied between zero and the strong coupling limit. The phase space evolution gives information beyond that contained in the phase space profile of the experimental spectrum alone. The zero‐order phase space is found to be different in important respects from that of the pendulum model of a nonlinear resonance. In the weak coupling regime, the phase space evolution is essentially like that of a dynamical barrier picture. In the strong coupling regime of ‘‘intrinsic resonance,’’ the phase space structure is much different. Topology change appears to take place in a more discontinuous manner than in the weak coupling regime. The phase space evolution shows that some levels are problematic for an adiabatic switching treatment. The origin of some anomalous levels seen both in phase space profiles of experimental spectra and in semiclassical quantization studies is clarified.

Infrared studies of CH and CD stretching anharmonicity

Abstract: Progress is reported in the analysis of CH and CD stretching overtones and their accompanying Fermi resonances in C2H4, C2H3D, CH2CD2 and C2HD3. CH stretching overtone data have been obtained for a number of partially deuterated alkanes, halogenated alkanes, MeCN, MeC2H, MeNH2, Me2NH, MeOH and Me2O. Values of anharmonicity constants xii obtained from these are compared with the results of local-mode studies. A provisional Fermi resonance analysis of CH(CD3)3 is reported. The possiblity of a relationship between xii, ωi and CH dissociation energy is explored.

Neutron Scattering Investigation of Deuterated Crystalline Acetanilide

Abstract: Crystalline acetanilide (ACN) is a quasi-one-dimensional anharmonic solid characterized by soft hydrogen-bonded chains of ACN molecules. Recent theoretical interest in the dynamics of ACN stems from the observation of anomalies in the infrared and Raman internal mode spectra at low temperatures. In this context, several models have been discussed, involving, alternatively, Fermi resonances, topological defects or nonlinear localized (Davydov-type) excitations. We present inelastic neutron scattering results on acoustic mode dispersions in deuterated ACN. The measured elastic slopes are found to be strongly anisotropic, consistent with the one-dimensional character of the hydrogen-bonding. The temperature dependence of the longitudinal (LAy) and transverse (TAx) acoustic modes propagating along the chain direction is studied. The observed anharmonic shifts are substantial but not usually so. Furthermore, a systematic search for anomalous elastic or quasi-elastic diffuse scattering fails to yield evidence for structural disorder. On the basis of these results and of optical results on deuterated ACN, we conclude that a Fermi resonance mechanism is most likely to be at the origin of the reported optical anomalies.