Fermi Resonance Interaction Research Articles

Vacuum ultraviolet pulsed field ionization-photoelectron study of OCS in the energy range of 15–19 eV

Vacuum ultraviolet pulsed field ionization-photoelectron (PFI-PE) spectra for OCS have been obtained in the energy range 15.0–19.0 eV, covering the vibronic bands of OCS+ (A 2Π, B 2Σ+, and C 2Σ+). The ionization energies for the formation of the ground vibrational levels of OCS+ (A 2Π3/2, A 2Π1/2, B 2Σ+, and C 2Σ+) from the ground OCS(X 1Σ+) state have been determined as 15.0759±0.0005 eV, 15.0901±0.0005 eV, 16.0403±0.0005 eV, and 17.9552±0.0005 eV, respectively. We have also generated the theoretical adiabatic three dimensional potential energy functions (PEFs) for OCS+(A 2Π) by employing the complete active space self-consistent field and internally contracted multireference configuration interaction methods. Using these PEFs, the spectroscopic constants and low-lying rovibronic energy levels for OCS+(A 2Π) are calculated variationally. These calculations have made possible the identification of many PFI-PE vibronic bands for OCS+(A 2Π), which are originated from vibronic and Fermi resonance interactions. Owing to the different equilibrium geometries between the OCS+(A 2Π) and OCS(X 1Σ+) states, the PFI-PE spectrum for OCS+(A 2Π) exhibits a long vibronic progression extending well above the OCS+(B 2Σ+) state. On the contrary, the PFI-PE spectra for OCS+ (B 2Σ+ and C 2Σ+) are overwhelmingly dominated by the ground (0,0,0) bands, exhibiting only weak vibrational progressions.

The carbonhydrogen stretching region of the Raman spectra of 1,6-hexanediamine: N-deuteration, ionisation and temperature effects

The Fermi resonance interaction between the methylene symmetric CH stretching mode and appropriate binary combinations involving the methylene bending mode in the Raman spectra of polyamines, namely in 1,6-hexanediamine derivatives, under different conditions of deuteration and ionisation of the head amino groups and varying temperature has been analysed. The tentative assignment of the observed bands in the CH stretching region of the registered Raman spectra is reported and the ratio of the Raman intensities of the symmetric stretching to the antisymmetric fundamentals is considered in its possible relation to the order/disorder of the skeletal hydrocarbon chains, from the all- trans prevailing geometry in the solid state at lower temperatures to the increasing amount of gauche arrangements on heating and melting.

Coherent Raman and Infrared Studies of Sulfur Trioxide

High-resolution (0.001 cm−1) coherent anti-Stokes Raman scattering (CARS) was used to observe the Q-branch structure of the IR-inactive ν1 symmetric stretching mode of 32S16O3 and its various 18O isotopomers. The ν1 spectrum of 32S16O3 reveals two intense Q-branches in the region 1065–1067 cm−1, with surprisingly complex vibrational–rotational structure not resolved in earlier studies. Efforts to simulate this with a simple Fermi-resonance model involving ν1 and 2ν4 states do not reproduce the spectral detail, nor do they yield reasonable spectroscopic parameters. A more subtle combination of Fermi resonance and indirect Coriolis interactions with nearby states, 2ν4(1=0, ±2), ν2+ν4(1=±1), 2ν2(1=0), is suspected and a determination of the location of these coupled states by high-resolution infrared measurements is under way. At medium resolution (0.125 cm−1), the infrared spectra reveal Q-branch features from which approximate band origins are estimated for the ν2, ν3, and ν4 fundamental modes of 32S18O3, 32S18O216O, and 32S18O16O2. These and literature data for 32S16O3 are used to calculate force constants for SO3 and a comparison is made with similar values for SO2 and SO. The frequencies and force constants are in excellent agreement with those obtained by Martin in a recent ab initio calculation.

The two-component bands at about 4500 and 800 cm −1 in infrared spectra of hydroxyl-containing silicas. Interpretation in terms of Fermi resonance

The band at about 4550 cm −1 in the near-infrared (IR) spectra of OH-containing high-surface area silicas is known to resolve into a doublet under certain experimental conditions. The interpretation of this by Tsyganenko [Zh. Fiz. Khim. (Moscow) 56 (1982) 2330], which has received no recognition so far, is advocated and is elaborated as follows: (1) there is Fermi resonance interaction between the SiOH bending fundamental and a doubly excited vibration giving rise to a mixed-state doublet around 800 cm −1, (2) the Fermi doublet propagates in the near IR in combinations with the OH stretching vibration (≈3750 cm −1). From a review of available IR transmission, inelastic neutron scattering (INS), and Raman scattering experimental data and model densities of vibrational states it is inferred that the doubly excited state causing Fermi resonance is likely to be either the first overtone of the bridging-oxygen rocking mode (400 cm −1 in the density of vibrational states) or the binary summation of the bridging-oxygen symmetric stretching in bent Si–O–SiOH units (the D 1 Raman band near 490 cm −1, in the interpretation of Mulder et al.) with the A ′ component of the Si–OH wagging mode (expected at about 300 cm −1). In the near-IR spectra of OH-containing vitreous silica and natural opals, the irregular shape of the band near 4500 cm −1, as argued, has a similar origin.

Orbital angular momentum (Renner–Teller) effects in the Πi2 ground state of silicon methylidyne (SiCH)

The ground state vibrational energy levels of jet-cooled SiCH and SiCD have been studied by a combination of laser-induced fluorescence and wavelength-resolved fluorescence techniques. The radicals were produced by a pulsed electric discharge at the exit of a supersonic expansion using tetramethylsilane or methyltrichlorosilane as the precursor. Emission spectra have been obtained by pumping both perpendicular and parallel (vibronically induced) bands, providing complementary information on the Si–C stretching and Si–C–H bending modes. Ground state energy levels up to 4000 cm−1 have been assigned and fitted using a vibrational Hamiltonian that incorporates Renner–Teller, spin–orbit, vibrational anharmonicity, and Fermi resonance interactions. The validity of the derived parameters has been tested using the isotope relations.

Threshold Behavior of Strongly Localized Nonlinear Modes in Crystals with Fermi Resonance Interaction

We report the existence of strongly localized modes in thin films and crystals with Fermi resonance interaction between vibration modes of molecules. Several families of bright and dark localized modes are investigated theoretically in two-and three-dimensional systems. Simple theoretical estimations are confirmed by numerical calculations. It is shown that in higher dimensions the solutions exist which do not have their one-dimensional analogs. The strongly localized Fermi resonance modes demonstrate the threshold behavior in any dimension in contrast to the nonlinear lattices with cubic interaction between sites.

Theoretical investigations of proton-bound cluster ions.

Several proton-bound cluster ions have been studied by means of coupled cluster calculations with large basis sets. Among these are complexes of a krypton or xenon atom with the cations HCO+, HN2+ and HNCH+. Various spectroscopic properties have been calculated in all cases. Effects of vibrational anharmonicity are particularly pronounced for the intramolecular stretching vibrations of Kr...HN2+ and Xe...HN2+. The proton stretching vibration of (N2)H+(N2) is predicted around 800 cm-1, with a large transition dipole moment of 1.15 D. Both (N2)H+(N2) and (HCN)H+(NCH) have linear centrosymmetric equilibrium structures. Those of (OC)H+(CO) and (HCC-)H+(CCH-) are asymmetric with barrier heights to the centrosymmetric saddle points of 382 and 2323 cm-1, respectively. The dissociation energy of the anionic complex Cl-...HCCH is calculated to be Do = 3665 cm-1, 650 cm-1 larger than the corresponding value for Br-...HCCH. The complex between a fluoride ion and acetylene is more strongly bound and shows strongly anharmonic behaviour, similar to the bihalides FHF- or ClHCl-. Strong Fermi resonance interaction is predicted between nu 3 (approximately proton stretch) and 2 nu 4 (first overtone of intermolecular stretch).

Anharmonic force field for methanol

An ab initio quartic anharmonic force field for methanol has been calculated at the equilibrium position using the CCSD(T) method for the structure and the harmonic potential energy surface, and the MP4(SDQ) method for the anharmonic part of the surface. A triple zeta basis set was employed with symmetrized curvilinear internal valence coordinates in all calculations. The internal coordinate force field constants have been transformed into force constants in the dimensionless normal coordinate representation for various isotopomers. Vibrational term values for CH3OH, CH3OD, CD3OH, and CD3OD have been obtained using second order perturbation theory. Particular care has been devoted to the inclusion of Fermi resonance interactions between different vibrational states. A good accuracy has been achieved in the calculation of the fundamentals for all the isotopomers, the mean absolute error being 5.8 cm−1.

Double-contact ion-molecule binding: Infrared characterization of the ionic H bonds to formic acid in the I−⋅HCOOH complex

We report mid-IR predissociation spectra of the I−⋅HCOOH⋅Arm(m=1–4) ion-acid complexes. The spectra are consistent with a planar structure where both hydrogens are engaged in ionic H bonds. Upon binding to the ion, the OH stretching fundamental displays a much more dramatic redshift (792 cm−1) than that of the CH stretch (99 cm−1), giving rise to a complex series of bands in the 2750–2950 cm−1 region. The contributions of the CH and OH stretches to the spectrum are isolated by recording spectra of the I−⋅DCOOH and I−⋅HCOOD species, which reveal that the OH stretching vibration is accompanied by combination bands involving soft modes while the CH stretch spectrum is dominated by a single feature. Some of the complexity in the I−⋅HCOOH spectrum arises from a strong Fermi resonance interaction between the v=1 level of the OH stretch and an overtone or combination band involving CH motion. We compare this behavior to that of the previously reported I−⋅CH3OH and I−⋅H2O complexes.

Stereochemical Equivalence of PIII-Bonded Hydrogen Atoms and |SeIV Lone Electron Pairs in Sr(H2PO3)2 and Sr(HSeO3)2

Sr(H2PO3)2 and Sr(HSeO3)2 have been characterized by means of single crystal X-ray diffraction and FT-IR absorption spectroscopy. The IR spectra exhibit split AB band systems in the OH stretching mode region due to Fermi resonance interactions of the ν(OH) with the in-plane bending modes of the hydroxyl groups. The compounds crystallize in a new structure type and are isotypic, if the P-bonded hydrogen atoms of Sr(H2PO3)2 and the lone electron pairs of Sr(HSeO3)2 are considered to be equivalent. The coordination of Sr is that of a distorted square antiprism. The SrO8 polyhedra share three common edges and are additionally connected via O−X−O bonds of the isolobal XO2OH− ions (X = HPIII, |SeIV) of tetrahedral and trigonal (ψ-tetrahedral) configuration, respectively. The resulting layers ∞2[Sr(XO2OH)2] are connected via circular hydrogen bond systems of tetrameric [XO2OH−]4 groups of a cyclooctane like chair topology. Both the P-bonded hydrogen atoms and the lone electron pairs of the HPIIIO2OH− and the |SeIVO2OH− ions, respectively, form channels along [001] and induce the same crystal structure. This is new for acid salts of the type MII(XO2OH)2·nH2O with X = HPIII and |SeIV.

Torsional motion and vibrational overtone spectroscopy of methanol

An internal coordinate Hamiltonian model has been constructed to model torsional motion in the OH stretching vibrational overtone region of methanol, CH3OH. The model includes harmonic couplings between OH and CH stretching vibrations and Fermi resonance interactions between OH stretches and COH bends and between CH stretches and CH2 bends. A symmetrized basis set has been used to form block diagonal Hamiltonian matrices with strong resonance couplings off-diagonal. Observed torsional levels of the excited vibrational states have been used as data in a least squares optimization of the model parameters, some of which have been estimated by ab initio calculations. The experimentally observed increase in the effective torsional barrier in moving to highly excited OH stretching states has been explained by the model.

A Fermi resonance study in H 12C 14NH 19F based on gas phase far infrared spectroscopy

A static gas phase far infrared spectroscopic investigation of seven hot bands involving the intermolecular bend ν 1 7 in the hydrogen-bonded species HCN-HF has been performed. The information obtained from a rovibrational analysis of these hot bands is combined with previously available microwave and infrared spectroscopic data to reinvestigate Fermi resonance interactions of 2 ν 0 7 with ν 4 and 3 ν 1 7 with ν 4 + ν 1 7. Corresponding Fermi resonance shifts of 2.31(5) cm −1 and 3.04(9) cm −1 were calculated respectively. Anharmonic constants x 77 = − 1.228(3) cm −1 and g 77 = 1.136(3) cm −1 were also determined and compared with values of value of x 77 = − 2.29 cm −1 and g 77 = 1.06 cm −1 evaluated by Amos [R.D. Amos, J.F. Gaw, N.C. Handy, E.D. Simandiras and K. Somasundram, Theoret. Chim. Acta, 71 (1987) 41] from an ab initio calculation.

Reactions of Laser-Ablated Nickel Atoms with Dioxygen. Infrared Spectra and Density Functional Calculations of Nickel Oxides NiO, ONiO, Ni2O2, and Ni2O3, Superoxide NiOO, Peroxide Ni(O2), and Higher Complexes in Solid Argon

Laser-ablated nickel atoms react with dioxygen to form the primary oxides NiO and ONiO, some of which combine to form the secondary oxides Ni2O2 and ONiONiO during condensation in excess argon at 10 K. The insertion product dioxide ONiO is linear based on natural nickel and 18O isotopic substitution and DFT calculations. Annealing produces the cyclic adducts reported in earlier thermal nickel experiments and the new NiOO superoxide species, which are characterized by isotopic shifts and DFT structure and frequency calculations. In addition, dioxygen complexes with NiO and ONiO were also observed. Finally, the matrix provides sharp bands and the resolution to observe nickel isotopic splittings which characterize the Fermi-resonance interaction in the ONiOO and (O2)Ni(O2) molecules.

Rotationally resolved spectrum of the C 2Πu←X 2Πg electronic transition of C−4 via resonant two-photon detachment spectroscopy

The C 2Πu←X 2Πg electronic transition of C−4 has been studied by both one-color and two-color resonant two-photon detachment (R2PD) spectroscopy. The one-color spectrum reveals vibrational structure in the excited anion state. Transitions due to excitations in one of the symmetric stretching modes as well as the bending modes are observed. Spectral resolution in the one-color experiment is limited by power broadening; using two-color R2PD, rotationally resolved spectra of the origin and 210 bands of the C 2Πu←X 2Πg transition are obtained. Molecular constants determined by fitting the rotationally resolved spectra are generally in good agreement with a recent ab initio calculation by Schmatz and Botschwina [Int. J. Mass. Spec. Ion. Proc. 149, 621 (1995)]. Perturbations in the 210 band are attributed to Fermi resonance interactions in the C 2Πu state.

Dye laser excitation studies of the à 2Π(100)/(020)–X̃ 2Σ+(020)/(000) bands of CaOD: Analysis of the à 2Π(100)∼(020) Fermi resonance

The CaOD à 2Π(100)/(020)–X̃ 2Σ+(020)/(000) bands have been rotationally analyzed via high resolution laser excitation. All measured line positions have been included in a global matrix deperturbation that takes account of the Renner–Teller, spin–orbit, and Fermi resonance interactions occurring in the Ã(100)(020) 2Π vibronic manifold. The corresponding bands of CaOH were studied previously; in the present work, two new CaOH subbands, Ã(020)κ 2Π–X̃(020), were recorded, and the complete data set for CaOH has been refitted using the improved model reported in this paper. The Fermi resonance parameter for CaOD has been determined as ‖W1‖=5.2707(22) cm−1; for CaOH, the newly determined value, ‖W1‖=10.3256(5) cm−1 is very close to that determined originally. The (100)∼(020) Fermi interaction in the X̃ 2Σ+ state has also been investigated for both isotopomers. The vibrational dependence of the Renner–Teller parameter εω2 has been characterized, yielding values of the anharmonic quartic parameter, ĝ4=−0.1002(3) and −0.0666(5) cm−1 for CaOH and CaOD, respectively. The ‘‘harmonic’’ Renner–Teller parameters are thus deduced as εω2=−35.6622(19) and −26.5605(31) cm−1 for CaOH and CaOD, respectively. The equilibrium bond lengths, molecular force constants and Coriolis coupling constants for both the à and X̃ states have been evaluated.

Nonlinear optical vibrations in organic superlattices with interface Fermi resonance

Abstract We discuss the nonlinear dynamics of organic superlattices in the case of interface Fermi resonance, which occurs when the energy ℏ ω c of excitation on one side of each interface is approximately equal to 2ℏ ω b , where ℏ ω b is the excitation energy on the other side of the interface. We demonstrate that the Fermi resonance interaction across each interface gives rise in the classical limit to nonlinear plane waves propagating through the superlattice. A general form of the dispersion law has been found. The peculiarities of this dispersion law are discussed in several particular cases.

Mode-selective photoisomerization in 5-hydroxytropolone. I. Experiment

Laser-induced fluorescence excitation, dispersed fluorescence, and population labeling spectra of the S0–S1 transition of 5-hydroxytropolone (5-HOTrOH) have been recorded in a supersonic free jet. In the ground state, the two in-plane orientations of the 5-OH substituent produce two isomers, syn and anti relative to the 2-OH. Population labeling is used to identify transitions in the spectrum originating from the syn and anti zero-point levels. In the excited electronic state where 2-OH H-atom tunneling is expected to be more facile, the single vibronic level dispersed fluorescence spectra identify excited state levels with widely varying syn–anti character. Many of the levels in the low-energy region of the spectrum are nearly pure syn or anti in character, thereby showing little coupling to the isomerization reaction coordinate. Other levels are strongly syn–anti mixed via Fermi resonance interactions. A few levels exhibit strong syn–anti mixing despite being relatively isolated from other levels. These levels have strong syn–anti coupling matrix elements which reflect a strong coupling to the reaction coordinate. Analysis of the dispersed emission identifies a ‘‘promoter’’ vibrational mode W, with syn (anti) ground-state frequency 336 (337) cm−1 which appears to play a key role in coupling syn and anti levels. The accessibility of excited state levels of mixed character makes it possible to efficiently and reversibly isomerize 5-hydroxytropolone in a highly mode-specific fashion.

Overtone Spectroscopy of CHD3 in Liquid Argon Solutions

AbstractThe vibrational overtone spectrum of CHD3 has been obtained in liquid argon solutions at temperatures around 94 K. The spectra of C‐H and C‐D overtones below 10000 cm−1 were obtained with a Fourier transform spectrophotometer operating in the near‐infrared region and a low temperature cell. The C‐H spectrum around Δv = 5 was recorded using a resonant photoacoustic technique at cryogenic temperatures. The absorption bands were computer deconvoluted to obtain the peak absorption frequency, the band‐width, and the area of some important bands. Due to the small frequency shift of the absorption bands in solution with respect to the gas phase frequencies, the assignment of the transitions was made by comparison with experimental and calculated gas phase frequencies. The calculation of gas phase frequencies and vibrational states was made using the pure local mode model for the isolated C‐H bond and the Harmonically Coupled Anharmonic Oscillator (HCAO) model for the three equivalent C‐D bonds. In order to test the Fermi resonance interaction between C‐H stretching and bending vibrations, the absorption bands and relative intensities in solution were used to obtain the parameters of an effective Fermi resonance Hamiltonian. The values of the parameters obtained in solution and gas phase are very close in magnitude. The optimized parameters of the Fermi resonance Hamiltonian give a good description of the frequencies and relative intensities of the C‐H absorption bands in solution.

Fermi Resonance Interface Modes: Propagation along the Interfaces

We discuss the nonlinear dynamics of an interface between two layers of organic semiconductors in the case of a Fermi resonance which occurs when the energy ha' of excitation on one side of the interface is approximately equal to 2hob with hab being the excitation energy on the other side. We develop the theory of quantum Fermi resonance interface modes (FRIM) propagating along the interface and demonstrate that the Fermi resonance interaction across the interface also gives rise to classical nonlinear plane waves propagating along the interface and in some cases to 2D solitons localized at the interface.

Effects of X3 frame vibrations on the CH chromophore in CHX3 type molecules: Harmonic coupling in curvilinear internal coordinate approach

Effects of harmonic coupling between X3 frame vibrations and the CH stretching and bending vibration chromophore in CHX3 type molecules have been investigated using a curvilinear internal coordinate model. The CH chromophore Hamiltonian used consists of a Morse oscillator Hamiltonian for the CH stretching vibration, two-dimensional isotropic harmonic oscillator Hamiltonian for the CH bending vibration, anharmonic bending terms, and Fermi resonance interaction terms between the stretching and bending vibrations. Van Vleck perturbation theory is used to take the harmonic coupling terms between the CH chromophore and the X3 frame vibrations into account. Analytical matrix elements for the perturbation theory contributions have been derived. The model has been applied to vibrational energy level and infrared absorption intensity data for CHD3. Potential energy parameters for the CH chromophore have been optimized by a nonlinear least-squares method. The model reproduces the experimental data well. Only small changes in the potential parameters are observed when the coupling terms due to D atom motions are introduced into the model. The overall conclusion is that it is a good first approximation to ignore the effects of harmonic coupling between the CH chromophore and the X3 frame vibrations in the curvilinear internal coordinate model for the CH chromophore in CHX3 type molecules.