Fermi Resonance Research Articles

SMALL CARBONACEOUS MOLECULES, ETHYLENE OXIDE (c-C2H4O) AND CYCLOPROPENYLIDENE (c-C3H2): SOURCES OF THE UNIDENTIFIED INFRARED BANDS?

We suggest that small carbonaceous molecules (SCMs) may be the sources of the unidentified infrared bands (UIRs) and the underlying continuum. We show that the IR spectroscopy of ethylene oxide (EO, c-C2H4O) and cyclopropenylidene (CP, c-C3H2) closely correlates with the major UIR bands at 3.3, 6.2, 7.7, 8.6, and 11.2 μm, the often seen strong bands at 12.7 and 16.4 μm, as well as many minor features. The differences in band locations and shapes between laboratory EO absorption spectra and astrophysical UIR emission spectra are attributed to vibrational anharmonicity, Fermi resonance splitting of nearly degenerate vibration levels, and rotational envelope narrowing due to the low temperatures in space. The excitation mechanism is absorption of UV radiation, primarily Lyα, by SCMs. Photon trapping for this very optically thick transition enhances the absorption by several orders of magnitude. Our abundance analysis for NGC 7027 reveals that the SCM abundance, relative to H2, is ~3 × 10–9 which compares well to radio measurements of the CP abundance range of ~10–9-10–7. The origin of the UIR continuum is discussed in terms of emission from vibrationally and rotationally hot SCM UV photodissociation products and UV excitation of rotationally hot SCM species. Radio lines of CP have been seen in numerous astronomical objects, most displaying the UIR bands. EO is also seen, but in fewer objects, none displaying the UIR bands. We theorize that in UIR objects, EO is formed on, and primarily resides on, carbonaceous grains, precluding radio detection of rotational lines. We suggest laboratory experiments, astronomical observations, and theoretical investigations to further evaluate the SCM mechanism for the UIR bands and continuum.

Vibrational Energy Transport in Peptide Helices after Excitation of C−D Modes in Leu-d10

Vibrational energy transport in a short 3(10)-helical peptide is studied by time-resolved femtosecond infrared spectroscopy. The C-D vibrations of decadeuterated leucine incorporated in the helical chain are excited, and the subsequent flow of vibrational energy through the helix is monitored by employing C horizontal lineO probes at various distances from the heat source as local thermometers. The C-D modes are not resonant to the C horizontal lineO modes, neither directly nor through any Fermi resonance, thereby suppressing resonant energy transfer directly along the C horizontal lineO oscillators of the peptide backbone. In contrast to our previous work (J. Phys. Chem. B 2008, 112, 9091), we no longer find any substantial difference in the vibrational energy transport efficiency after high- or low-energy excitation. That is, the heat diffusion constant of (2.0 +/- 0.5) A(2) ps(-1) is the same as that after depositing vibrational energy through the ultrafast internal conversion of a covalently bound chromophore.

Fermi resonance and strong anharmonic effects in the absorption spectra of the ν-OH ( ν-OD) vibration of solid H- and D-benzoic acid

The vibrational spectra of polycrystalline benzoic acid (BA) and its deuterated derivative were studied over the wide frequency region 4000–10 cm −1 by IR and Raman methods. A theoretical analysis of the hydrogen bond frequency region and calculations at the B3LYP/6-311++G(2d, 2p) level for the benzoic acid cyclic dimer in the gas phase were made. In order to study the dynamics of proton transfer two formalisms were applied: Car–Parrinello Molecular Dynamics (CPMD) and Path Integrals Molecular Dynamics (PIMD). It was shown that the experimentally observed very broad ν-OH band absorption is the result of complex anharmonic interaction: Fermi resonance between the OH-stretching and bending vibrations and strong interaction of the ν-OH stretching with the low frequency phonons. The theoretical analysis in the framework of such an approach gave a good correlation with experiment. From the CPMD calculations it was confirmed that the O–H⋯O bridge is not rigid, with the O⋯O distance being described by a large amplitude motion. For the benzoic acid dimer we observed stepwise (asynchronous) proton transfer.

Spectral Intensity Patterns and Vibrational Phase Space Structure

We examine patterns of absorption intensity in two-mode systems with a 2:1 Fermi resonance in an intensity model based on the effective fitting Hamiltonian. We relate these patterns to the Fermi resonance phase space structure and catastrophe map. Each of the four zones of the catastrophe map has a phase sphere structure with a certain number of distinct regions. For each zone, we find that for every region on the sphere, there is a distinct region in the intensity pattern.

Pathways for H2O Bend Vibrational Relaxation in Liquid Water

The mechanism of the H2O bend vibrational relaxation in liquid water has been examined via classical MD simulations and an analysis of work and power contributions. The relaxation is found to be dominated by energy flow to the hindered rotation of the bend excited water molecule. This energy transfer, representing approximately 2/3 of the transferred energy, is due to a 2:1 Fermi resonance for the centrifugal coupling between the water bend and rotation. The remaining energy flow (approximately 1/3) from the excited water bend is dominated by transfer to the excited water molecule's first four water neighbors, i.e., the first hydration shell, and is itself dominated by energy flow to the two water molecules hydrogen (H)-bonded to the hydrogens of the central H2O. The energy flow from the produced rotationally excited central molecule is less local in character, with approximately half of its rotational kinetic energy being transferred to water molecules outside of the first hydration shell, whereas the remaining half is preferentially transferred to the two first hydration shell water molecules donating H-bonds to the central water oxygen. The overall energy flow is well described by an approximate kinetic scheme.

Re-evaluation of the T2KK physics potential with simulations including backgrounds

The Tokai-to-Kamioka-and-Korea (T2KK) neutrino oscillation experiment under examination can have a high sensitivity to determine the neutrino mass hierarchy for a combination of relatively large ( ∼ 3.0°) off-axis angle beam at Super-Kamiokande (SK) and small ( ∼ 0.5°) off-axis angle at L ∼ 1,000 km in Korea. We elaborate previous studies by taking into account smearing of reconstructed neutrino energy due to finite resolution of electron or muon energies, nuclear Fermi motion and resonance production, as well as the neutral current π0 production background to the νμ → νe oscillation signal. It is found that the mass hierarchy pattern can still be determined at 3σ level if sin22θRCT ≡ 4|Ue3|2(1 − |Ue3|2) ≳ 0.08(0.09) when the hierarchy is normal (inverted) with 5 × 1021} POT (protons on target) exposure, or 5 years of the T2K experiment, if a 100 kton water Čerenkov detector is placed in Korea. The π0 backgrounds deteriorate the capability of the mass hierarchy determination, whereas the events from CC nuclear resonance productions contribute positively to the hierarchy discrimination power. We also find that the π0 backgrounds seriously affect the CP phase measurement. Although δMNS can still be constrained with an accuracy of ∼ ±45° (±60°) at 1σ level for the normal (inverted) hierarchy with the above exposure if sin22θRCT ≳ 0.04, CP violation can no longer be established at 3σ level even for δMNS = ±90° and sin22θRCT = 0.1. About four times higher exposure will be needed to measure δMNS with ±30° accuracy.

Some applications of stochastic averaging method for quasi Hamiltonian systems in physics

Many physical systems can be modeled as quasi-Hamiltonian systems and the stochastic averaging method for quasi-Hamiltonian systems can be applied to yield reasonable approximate response statistics. In the present paper, the basic idea and procedure of the stochastic averaging method for quasi Hamiltonian systems are briefly introduced. The applications of the stochastic averaging method in studying the dynamics of active Brownian particles, the reaction rate theory, the dynamics of breathing and denaturation of DNA, and the Fermi resonance and its effect on the mean transition time are reviewed.

Phase Transition in CCl4 under Pressure: a Raman Spectroscopic Study

High-pressure Raman studies at room temperature are performed on CCl4 up to 13 GPa. The Raman bands of the internal modes (v2, v4 and v1) show entirely positive pressure dependence. The slopes dω/dP of the internal modes exhibit two sudden changes at 0.73 GPa and 7.13 GPa, respectively. A new lower frequency mode (225 cm−1) appears at 3.03 GPa, and the splitting of v2, v3 and v4 occurs at about 7.13 GPa. Moreover, Raman spectra of Fermi resonance show that the relative position of the v1 + v4 combination and the v3 fundamental firstly interchanges corresponding to that at ambient pressure, then the v1 + v4 combination disappears in the gradual process of compression. It is indicated that the pressure-induced phase transition from CCl4 II to CCl4 III occurs at 0.73 GPa, and CCl4 III undergoes a transition to CCl4 IV below 3.03 GPa. Further CCl4 IV transforms in a new high-pressure phase at about 7.13 GPa, and the symmetry of the new high-pressure phase is lower than that of CCl4 IV. All the transitions are reversible during decompression.

Ab initio calculation of cubic force constants in formamide monomer, formamide dimer, formic acid dimer and their D, D2 and D4 derivatives. An estimation of fermi resonance and intra-intermolecular coupling

We report preliminary results of the ab initio calculations in the 4-31G basis set of cubic force constants in normal modes for the HCONH2 and DCONH2 monomers, and a series of cyclic dimers (HCONH2)2, (HCOND2)2, (HCOOH)2, and (HCOOD)2. These include diagonal cubic constants and nondiagonal constants, describing Fermi resonances between X—H(D) stretching modes and overtones of other vibrations, and couplings between intra- and intermolecular modes. Results allow us to interpret experimental Fermi resonance observed in the infrared spectrum of the HCONH2 monomer. Diagonal anharmonicities improve an agreement between experimental and calculated frequencies for the dimers. The calculation shows that the coupling between the X—H(D) and X …. Y stretching vibrations is substantially stronger in the formic acid dimers than in the formamide dimers.

Multiple coherent states for first-principles semiclassical initial value representation molecular dynamics

A multiple coherent states implementation of the semiclassical approximation is introduced and employed to obtain the power spectra with a few classical trajectories. The method is integrated with the time-averaging semiclassical initial value representation to successfully reproduce anharmonicity and Fermi resonance splittings at a level of accuracy comparable to semiclassical simulations of thousands of trajectories. The method is tested on two different model systems with analytical potentials and implemented in conjunction with the first-principles molecular dynamics scheme to obtain the power spectrum for the carbon dioxide molecule.

Theoretical interpretation of the infrared spectra of the hydrogen bond

A theory is presented which describes the energy and intensity distribution in the infrared spectra of the hydrogen-bonded systems. The effect of Fermi resonance on the form of spectra is studied for an individual hydrogen bond and for a cyclic dimer. The theory is used to calculate the IR transitions in the spectra of hydrogen-bonded crystals, including the deuterium effect and changes due to different polymorphic forms of crystals.

Experimental and theoretical study of the polarized infrared spectra of the hydrogen bond in 3‐thiophenic acid crystal

This article presents the results of experimental and theoretical studies of the v(O-H) and v(O-D) band shapes in the polarized infrared spectra of 3-thiophenic acid crystals measured at room temperature and at 77 K. The line shapes are studied theoretically within the framework of the anharmonic coupling theory, Davydov coupling, Fermi resonance, direct and indirect damping, as well as the selection rule breaking mechanism for forbidden transitions. The adiabatic approximation allowing to separate the high-frequency motion from the slow one of the H-bond bridge is performed for each separate H-bond bridge of the dimer and a strong nonadiabatic correction is introduced via the resonant exchange between the fast-mode excited states of the two moieties. The spectral density is obtained within the linear response theory by Fourier transform of the damped autocorrelation functions. The approach correctly fits the experimental line shape of the hydrogenated compound and predicts satisfactorily the evolution in the line shapes with temperature and the change in the line shape with isotopic substitution.

Theoretical study of the νO–H IR spectra for the hydrogen bond dimers from the polarized spectra of glutaric and 1-naphthoic acid crystals: Fermi resonances effects

A full quantum theoretical model is proposed to study the ν O–H experimental IR line shapes of polarized crystalline glutaric and 1-naphthoic acid dimer crystals at room and liquid nitrogen temperatures. This work is an application of a previous model [M. E-A. Benmalti, D. Chamma, P. Blaise, and O. Henri-Rousseau, J. Mol. Struct. 785 (2006) 27–31] by accounting for Fermi resonances. The approach is dealing with the strong anharmonic coupling, Davydov coupling, multiple Fermi resonances between the first harmonics of some bending modes and the first excited state of the symmetric combination of the two ν O–H modes and the quantum direct and indirect relaxation. Numerical results show that mixing of all these effects allows to reproduce satisfactorily the main features of the experimental IR line shapes of crystalline hydrogenated and deuterated glutaric and 1-naphthoic acid crystals and are expected to provide efficient of Fermi resonances effects.

New Interpretation of the CH Stretching Vibrations in Imidazolium-Based Ionic Liquids

In ionic liquids composed of alkyl-substituted imidazolium cations and weakly coordinating anions such as bis(trifluoromethanesulfonyl)imide, (CF(3)SO(2))(2)N(-), the stretching vibrations of the imidazolium CH groups are shown to interact by Fermi resonance with the overtones and the combination of two in-plane ring vibrations. This new assignment, based on isotopic substitutions and anharmonic frequency calculations for gas phase cations, implies that these imidazolium cations do not establish any strong and directional C-H...anion hydrogen bond.

Stretch-bend combination polyads in the à 1A u state of acetylene, C 2H 2

Rotational analyses are reported for a number of newly-discovered vibrational levels of the S 1- trans (Ã 1A u) state of C 2H 2. These levels are combinations where the Franck–Condon active ν 2 ′ and ν 3 ′ vibrational modes are excited together with the low-lying bending vibrations, ν 4 ′ and ν 6 ′ . The structures of the bands are complicated by strong a- and b-axis Coriolis coupling, as well as Darling–Dennison resonance for those bands that involve overtones of the bending vibrations. The most interesting result is the strong anharmonicity in the combinations of ν 3 ′ ( trans bend, a g ) and ν 6 ′ (in-plane cis bend, b u ). This anharmonicity presumably represents the approach of the molecule to the trans– cis isomerization barrier, where ab initio results have predicted the transition state to be half-linear, corresponding to simultaneous excitation of ν 3 ′ and ν 6 ′ . The anharmonicity also causes difficulty in the least squares fitting of some of the polyads, because the simple model of Coriolis coupling and Darling–Dennison resonance starts to break down. The effective Darling–Dennison parameter, K 4466, is found to increase rapidly with excitation of ν 3 ′ , while many small centrifugal distortion terms have had to be included in the least squares fits in order to reproduce the rotational structure correctly. Fermi resonances become important where the K-structures of different polyads overlap, as happens with the 2 13 1 B 1 and 3 1 B 3 polyads ( B = 4 or 6). The aim of this work is to establish the detailed vibrational level structure of the S 1- trans state in order to search for possible S 1- cis ( 1A 2) levels. This work, along with results from other workers, identifies at least one K sub-level of every single vibrational level expected up to a vibrational energy of 3500 cm −1.

Two-Dimensional Infrared Spectroscopy of Intermolecular Hydrogen Bonds in the Condensed Phase

Hydrogen bonding plays a key role in the structural, physical, and chemical properties of liquids such as water and in macromolecular structures such as proteins. Vibrational spectroscopy is an important tool for understanding hydrogen bonding because it provides a way to observe local molecular geometries and their interaction with the environment. Linear vibrational spectroscopy has mapped characteristic changes of vibrational spectra and the occurrence of new bands that form upon hydrogen bonding. However, linear vibrational spectroscopy gives very limited insight into ultrafast dynamics of the underlying molecular interactions, such as the motions of hydrogen-bonded groups, energy dissipation and delocalization, and the fluctuations within hydrogen-bonded structures that occur in the ultrafast time domain. Nonlinear vibrational spectroscopy with its femtosecond time resolution can discern these dynamic processes in real time and has emerged as an important tool for unraveling molecular dynamics and for quantifying interactions that govern the vibrational and structural dynamics of hydrogen bonds. This Account reviews recent progress originating from third-order nonlinear methods of coherent multidimensional vibrational spectroscopy. Ultrafast dynamics of intermolecular hydrogen bonds are addressed for a number of prototype systems: hydrogen-bonded carboxylic acid dimers in an aprotic liquid environment, the disordered fluctuating hydrogen-bond network of liquid water, and DNA oligomers interacting with water. Cyclic carboxylic acid dimers display a rich scheme of vibrational couplings, resulting in OH stretching absorption bands with highly complex spectral envelopes. Two-dimensional spectroscopy of acetic acid dimers in a nonpolar liquid environment demonstrates that multiple Fermi resonances of the OH stretching mode with overtones and combination tones of fingerprint vibrations dominate both the 2D and linear absorption spectra. The coupling of the OH stretching mode with low-frequency hydrogen-bonding modes leads to additional progressions and coherent low-frequency hydrogen-bond motions in the subpicosecond time domain. In water, the 2D spectra reveal ultrafast spectral diffusion on a sub-100 fs time scale caused by the ultrafast structural fluctuations of the strongly coupled hydrogen-bond network. Librational motions play a key role for the ultrafast loss of structural memory. Spectral diffusion rates are enhanced by resonant transfer of OH stretching quanta between water molecules, typically occurring on a 100 fs time scale. In DNA oligomers, femtosecond nonlinear vibrational spectroscopy resolves NH and OH stretching bands in the highly congested infrared spectra of these molecules, which contain alternating adenine-thymine pairs. Studies at different levels of hydration reveal the spectral signatures of water molecules directly interacting with the phosphate groups of DNA and of a second water species forming a fluctuating environment around the DNA oligomers. We expect that the application of 2D infrared spectroscopy in an extended spectral range will reveal the intrinsic coupling between water and specific functional units of DNA.

Catastrophe map and the role of individual resonances in C2H2 bending dynamics

A catastrophe map analysis is presented of the birth of new modes in bifurcations of the normal modes of the acetylene pure bending system using a spectroscopic fitting Hamiltonian that is nonseparable with multiple resonances. The map splits into two independent maps for subspaces defined by the resonance frequency conditions. Nonetheless, both resonance couplings act on each of the resonance subspaces, since the system is nonseparable. With this generalized notion of independent resonances, the map accounts for partial resemblances to single resonance models but maintains the full complexity inherent in the nonseparable Hamiltonian. This suggests a way to extend both the generalized Fermi resonance and the catastrophe map analysis to systems with higher degrees of freedom.

The role of H-bonded chelate rings in the organization of liquid crystalline 2-hydroxyazobenzenes

Polarized infrared spectra of 4-chloro-2′-hydroxy-4′-hexyloxyazobenzene were studied from 25 to 120 °C encompassing transitions from the crystalline to the isotropic phase. The behavior of the ν(OH), δ(OH), and γ(OH) bands is analyzed. Based on the DFT calculations and on linear dichroism spectroscopy, it was concluded that the core-to-core interaction between hydrogen-bonded chelate rings is responsible for changes in intensity and shape of the bands. A pseudo-band at ca. 620 cm −1 is discussed based on Fermi resonance between the ν(OH) and γ(OH) modes. A general analysis is presented with respect to the directions of the transition moments of the particular modes.

Self-Assembly of Hydrogensquarates: Crystal Structures and Properties

The self-assembly of the hydrogensquarates is elucidated by means of linear-polarized infrared (IR-LD) spectroscopy of oriented colloids in nematic host and the so-called reducing-difference procedure for polarized IR-LD spectra interpretation. The scopes and limitation are discussed on five novel derivatives of squaric acid and its anions, that is, 2-chloro-3-aminopyridinium hydrogensquarate (1), bis (1,2,3,4-tetrahydroquinolinium) squarate (2), bis hydrogensquarate dihydrate salt of 4-(aminomethyl)pyridine (3), N-(2-ammoniumethyl)-piperazinium monohydrate hydrogensquarate squarate (4), and 3-nitropyridinium hydrogensquarate monohydrate (5), respectively. The structures of these compounds 1-5 were solved by means of single-crystal X-ray diffraction, and the crystallographic data were used for the experimental elucidation of the corresponding IR spectra of crystals with respect to studying Fermi-resonance (FR), Davydov splitting (DS), and Fermi-Davydov (FD) as well as Evans' hole effects. The various motifs for self-assembly of squaric acid and its anions in the organic crystals are discussed together with their IR-spectroscopic properties.

Mode-Specific Vibrational Energy Relaxation of Amide I′ and II′ Modes in N-Methylacetamide/Water Clusters: Intra- and Intermolecular Energy Transfer Mechanisms

The mode-specific vibrational energy relaxation of the amide I' and amide II' modes in NMA-d(1)/(D(2)O)(n) (n = 0-3) clusters were studied using the time-dependent perturbation theory at the B3LYP/aug-cc-pvdz level. The amide modes were identified for each cluster based on the potential energy distribution of each mode. The vibrational population relaxation time constants were derived for the amide I' and II' modes. Results for the amide I' mode relaxation of NMA-d(1)/(D(2)O)(3) agree well with previous experimental results. The energy relaxation pathways were identified, and both intra- and intermolecular mechanisms were found to be important. The amide II' mode was identified in the energy transfer pathways from the excited amide I' mode of NMA-d(1)/(D(2)O)(n) (n = 1-3) clusters. The modes associated with methyl group deformation were found to play a role in the mechanism of energy transfer from both excited amide I' and II' modes. The kinetics of energy flow in the cluster were examined by solving a master equation describing the vibrational energy relaxation process from excited system mode as a multistep reaction with the third order Fermi resonance parameters as the reaction rate constants. The intramolecular energy transfer mechanism was found to dominate the short time energy flow dynamics, whereas the intermolecular mechanism was found to be dominant at longer times.