Rotation–torsion analysis of the Si2H6 infrared fundamental ν9, perturbed by excited torsional levels of the vibrational ground state

The lowest infrared active perpendicular fundamental ν₉ of disilane has been analysed on a Fourier transform spectrum between 320 and 430?cm^?1, at the spectral resolution of 0.0012?cm^?1. The rotation–torsion structure of this band is affected by x,y Coriolis interactions with excited torsional levels of the vibrational ground state, correlating with components of 3ν₄ and 4ν₄ in the high barrier limit. The interaction of ν₉ and 4ν₄, forbidden in the D_3d symmetry limit, is allowed between components of E torsional symmetry under the G₃₆(EM) extended molecular group, because of the large amplitude of the internal rotation motion. We could determine the values of the main vibration–rotation–torsion parameters of ν₉, interaction parameters, and the vibrational wavenumbers of the four torsional components of 3ν₄ and of the E_3d component of 4ν₄. The intrinsic torsional splitting of ν₉ is found to be smaller than in the ground vibrational state by 0.0066?cm^?1, in good agreement with our theoretical predictions. The possibility of observing the effects of D_3d-forbidden interactions in the spectra of ethane-like molecules is also discussed.     

Group-theoretical investigation of the tunneling splitting patterns of enolic acetylacetone

Extensive experimental and theoretical studies for enolic acetylacetone have been presented in the literature, but studies of the tunneling splitting patterns are still lacking. In this work we adopt the C_s symmetry equilibrium structure and apply a group-theoretical formalism to study the tunneling splitting pattern of the ground vibrational level of enolic acetylacetone. Enolic acetylacetone has three large-amplitude motions, one intramolecular hydrogen transfer and two methyl torsions. Therefore, the C_s structure of enolic acetylacetone has 18 (3 × 3 × 2) equivalent equilibrium molecular frameworks, nine (3 × 3) of them are from the two methyl torsions, and two are from the intramolecular hydrogen transfer. Tunneling motions among the 18 equivalent molecular frameworks split the ground vibrational level into eight sublevels: A₁, A₄, E₁, E₂, E₃, E₄, G(1) and G(2). In enolic acetylacetone the intramolecular hydrogen transfer induces a rearrangement of the CC, CO single and double bonds, and then triggers two additional 60° internal rotations, one in each of the two methyl groups attached to the hydrogen-bonded malonaldehyde ring. This interaction further complicates the tunneling splitting patterns and increases the difficulty of spectral analysis. In this work the influence of the intramolecular hydrogen transfer on the energy order of the eight sublevels is determined by a group-theoretical formalism.     

The adiabatic approximation as a diagnostic tool for torsion-vibration dynamics

The adiabatic separation of large-amplitude torsional motion from small-amplitude vibrations is applied as an aid in interpreting the results of fully coupled quantum calculations on a model methanol Hamiltonian. Comparison is made with prior work on nitromethane [D. Cavagnat, L. Lespade, J. Chem. Phys. 106 (1997) 7946]. Even though the torsional potentials are very different, both molecules show a transition from adiabatic to diabatic behavior when the CH stretch is excited to ν_CH = 4 or higher. In the adiabatic approximation, the effective torsional potentials for the various CH stretch vibrational states do not cross, but the CH vibrational amplitude moves from one bond to the next as a function of torsional angle. In the diabatic approximation, the effective torsional potentials do cross, but the distribution of the CH vibrational amplitude remains approximately constant in the vicinity of the crossing. The transition to diabatic behavior is promoted by the normal mode to local mode transition, and the relevant adiabatic and diabatic effective torsional potentials are determined by the torsion-vibration coupling. The torsion-vibration couplings in the four overtone manifolds considered (methanol OH, CH, nitromethane CH, and hydrogen peroxide OH) are large, reaching 265-500 cm⁻¹ by ν_XH = 6, and are of generally similar magnitude. The largest torsion-vibration couplings involve the first Fourier term in the torsional angle (cosγ for the CH stretch in methanol and the OH stretch in HOOH), whereas higher Fourier terms (cos2γ in nitromethane and cos3γ for the OH stretch of methanol) result in somewhat weaker coupling. Nonadiabatic matrix elements in methanol couple the torsional and vibrational energies and they exhibit a slow fall-off with coupling order.     

Torsional Line Splittings in the (ν4+ν8)−ν4 Hot Transitions of C2H6 between 1400 and 1510 cm

A detailed investigation of the high-resolution infrared spectrum of ethane revealed the occurrence of features belonging to the hot perpendicular system (ν₄+ν₈)−ν₄ between 1400 and 1510 cm⁻¹. Transition lines of the subbranches with K″ΔK from −7 to 4, exhibiting torsional splittings of several tenths of a cm⁻¹, were observed and measured in this region. The observed line splittings are strongly influenced by the interaction between the ν₄+ν₈ and 2ν₄+ν₁₂ states and change with the values of K″ΔK, depending on the zero-order energy separation of the interacting levels. We found by numerical extrapolation that splittings still occur far from resonance, showing that the intrinsic torsional splittings of the combining states ν₄+ν₈ and ν₄ are quite different. We determined the intrinsic torsional splitting of ν₄+ν₈ to be less than 0.083 cm⁻¹, compared with 0.236 cm⁻¹ estimated for the ν₄ state. This result is in agreement with the expected effects of torsional Coriolis and head-tail coupling and is consistent with previous observations on vibrationally degenerate states of ethane-like molecules.     

在不同应力下石墨烯中拉曼谱的G峰劈裂的变化

应用计及五阶近邻的力常数模型,研究了单轴应力下的石墨烯和芳香烃分子三明治型贴层的石墨烯中拉曼谱的G峰劈裂.计算结果表明对称性的降低解除了G峰对应的在Γ点的面内的纵波光学模声子和横波光学模声子能量简并,从而G峰劈裂为G⁺和G^- 两个峰.在单轴应力作用下,C—C键的伸长致使力常数减小,软化了面内的光学模声子,导致两个G峰都红移;芳香烃分子对石墨烯产生的沿分子长短边方向不同的应力作用,使得G峰对应的两支光学模声子的频率一支发生蓝移,而另一支发生红移.这解 关键词： 力常数模型 石墨烯 拉曼G峰劈裂     

Schwingungsspektrum von Magnesiumsulfat-Heptahydrat (Epsomit) und Cäsiumsulfat

As in the preceding paper [1], infrared reflection spectra of single crystals of orthorhombic MgSO₄·7H₂O and MgSO₄·7D₂O have been obtained at 300°K, 80°K, and at about 14°K in the region between 4000 cm^?1 and 400 cm^?1. By a Kronig-Kramers analysis, the frequencies of the infrared active transitions have been determined. The spectra and their temperature dependence are contrasted with reflection spectra of anhydrous, orthorhombic Cs₂SO₄, which show practically no temperature dependence. The spectra of the magnesium compounds show two prominent features: 1. In the region below 700 cm^?1, the low-temperature experiments show the existence of many distinct vibrational modes arising mainly from the coupled translational and librational motions of the water molecules. These observations will be discussed in the light of the results of the preceding paper [1]. 2. The internal vibrations of the SO₄-ions at about 1100 cm^?1 present a very interesting combination of two solid-state effects on vibrational states of molecules in crystals: a) The threefold degeneracy of this mode is lifted by the deformation of the molecule due to the asymmetric crystal field, and b) the coupling of four molecules in the unit cell (resonance or correlation-field coupling) results in a further splitting of each mode into four clearly separated states of which three are infrared active. The magnitude of this splitting is calculated with the Davydov-theory (Coulomb-interaction of the transition-dipoles), making use of the crystal structure and the experimentally determined strength of the transition dipoles. Considering the limitation of the model, fairly good agreement with the experiment is obtained.     

The high-resolution infrared spectrum of Si2H6: rotation–torsion analysis of the ν5 and ν7 fundamentals,and torsional splittings in the degenerate vibrational states

The infrared active ν₇ and ν₅ fundamentals of disilane, coupled by an x,y Coriolis interaction, have been analysed on a Fourier transform spectrum between 2120 and 2225?cm^?1, at the Doppler limited spectral resolution. A Fermi resonance with 2ν ₂?+?ν₉ affects the Δ K?=?1 side of ν₇, and both ν₇ and ν₅ show the effects of several additional localized perturbations. Line splittings in the ν₅ transitions are not observed, showing that the torsional splitting in the ν₅ excited state and in the vibrational ground state are almost equal. The intrinsic torsional splitting of ν₇ is found to be smaller than in the ground vibrational state by 0.0085?cm^?1. This splitting value and those found for the other two infrared active degenerate fundamentals, ν₈ and ν₉, follow the trend expected from our theoretical predictions. Exploratory numerical calculations show that the decrease of the torsional splittings, observed in the fundamental degenerate vibrational states of disilane, can actually be accounted for by the head–tail and torsional Coriolis coupling of all the degenerate vibrational fundamentals, in several torsional states.     

Torsional tunneling splittings in the v4 = 1 excited torsional state of Si2H6: analysis of hot bands accompanying fundamental transitions in the high resolution infrared spectrum

The (ν₄?+?ν₆)???ν₄, (ν₄?+?ν₈)???ν₄ and (ν₄?+?ν₉)???ν₄ hot infrared systems of disilane (Si₂H₆) have been analysed at high resolution, and the values of the relative vibration–rotation–torsion parameters have been determined. The torsional splitting is about 0.500?cm^?1 in the ν₄ and ν₄?+?ν₆ states, and decreases strongly in the vibrationally degenerate upper states ν₄?+?ν₈ (about 0.0272?cm^?1 on average) and ν₄?+?ν₉ (about 0.3019?cm^?1), consistent with theoretical predictions. Comparison between the vibrational wavenumbers of cold transitions and hot transitions originating in the excited torsional state v₄?=?1 allows one to determine the change of the fundamental torsional frequency ν₄ caused by the excitation of small amplitude vibrations. A remarkable increase in ν₄ of about 8.599?cm^?1 is found in the v₉?=?1 state (E_1d SiH₃-rocking mode, asymmetric to inversion in the staggered geometry), and this corresponds to an increase in the torsional barrier height in this excited fundamental vibrational state by about 48.77?cm^?1. The mechanism responsible for the decrease of the torsional splittings in the degenerate vibrational states is briefly outlined by means of second-order perturbation theory, using torsion-hindered vibrational basis functions of E_1d and E_2d symmetries for the degenerate modes.     

Torsional Splittings in Small-Amplitude Vibrational Fundamental States of Methanol-Type Molecules

Group-theoretical methods are used to show that inverted torsional splittings in fundamental levels of small-amplitude vibrations of methanol-like molecules can be parameterized and understood in terms of the energy level patterns induced when a pair of high-barrier torsionally split components of given v(t) and (t)A+(t)E symmetry species in the molecular symmetry group G(6) is allowed to interact with small-amplitude vibrational modes of symmetry (v)E. Such doubly degenerate (v)E vibrational modes arise rather naturally in G(6) (isomorphic with the point-group C(3v)) for those methyl-group vibrations in point-group-C(s) asymmetric tops such as CH(3)-CHO that are analogs of the degenerate methyl-group stretch, bend, and rocking vibrations in point-group-C(3v) symmetric tops such as CH(3)-C identical withC-H. The present group-theoretical treatment is somewhat different from, but (as a comparison of model parameters shows) still fundamentally similar to, the recent local mode explanation of inverted torsional splittings in the C-H stretching fundamental region in methanol. Copyright 2001 Academic Press.     

Calculation of the spin-lattice coupling coefficients in cubic symmetry

The relationships between spin-lattice coupling coefficients G₁₁, G₄₄ in cubic symmetry and the zero-field splittings in low symmetry have been put forward and hence the simple methods of calculating these coefficients from the formulae of zero-field splittings are given. According to these, the coefficient G₄₄ can be obtained very easily from two cases, one from the derivative of zero-field splitting D in trigonal symmetry with respect to the bonding angle β and another from the derivative of splitting E in rhombic symmetry with respect to the angle θ. So, one can, in a certain degree, check whether the formulae of D in trigonal field and E in rhombic field based on different mechanisms and models are consistent and reliable by comparing the formulae of G₄₄ obtained from the two cases.     

Unravelling overlaps and torsion-facilitated coupling using two-dimensional laser-induced fluorescence

Two-dimensional laser-induced fluorescence (2D-LIF) spectroscopy is employed to identify contributions to fluorescence excitation spectra that arise from both overlapping bands and coupling between zero-order states (ZOSs). Evidence is found for the role of torsional motion in facilitating the coupling between vibrations that particularly involves the lowest-wavenumber out-of-plane vibrational modes. The experiments are carried out on jet-cooled p-fluorotoluene, where the molecules are initially in the lowest two torsional levels. Here we concentrate on the 390–420?cm^?1 features in the S₁?←?S₀ excitation spectrum, assigning the features seen in the 2D-LIF spectrum, aided by separate dispersed fluorescence spectra. The 2D-LIF spectra allow the overlapping contributions to be cleanly separated, including some that arise from vibrational-torsional coupling. Various coupling routes open up because of the different symmetries of the lowest two torsional modes; these combine with the vibrational symmetry to provide new symmetry-allowed vibration-torsion (‘vibtor’) interactions, and the role of the excited m?=?1 torsional level is found to be significant.     

Increase in the probability of passing molecules through a cooled multichannel plate as induced by a high-power infrared laser

It has been found that molecules (e.g., SF₆, CF₃I) excited in a molecualr beam by intense infrared laser radiation into high vibrational states (with energy E _v ≥ 0.5–2.0 eV) pass through a multichannel metal plate, which is cooled to T _s ? 80–85 K and inclined to the beam axis, much more efficiently than unexcited (vibrationally cold) molecules. This property provides the possibility of separating excited and unexcited molecules in the beam. The method is described and the first experimental results are reported.     

The ν5 band of CH3CH3: High resolution stimulated Raman spectrum and global three band analysis

Rotationally resolved spectrum of ¹²CH₃¹³CH₃ in the region of ν₅ vibrational fundamental (CC stretch) was observed using stimulated Raman spectroscopy. This spectrum was analyzed with data from the ν₁₂ fundamental and transitions from the ν₆, 2ν₆-ν₆, and 3ν₆ torsional bands using a 3-state fit. One torsional component of the ν₅ fundamental is perturbed, interacting with its partner in the ν₆=4 of the torsional stack of the ground vibrational state. As for normal ethane, the coupling was successfully modeled using a Fermi-type interaction. The results mirror that of ¹²CH₃¹²CH₃ in that the inclusion of the Fermi-type interaction reduces the required number of terms in the Fourier expansion of the torsional potential for the ground vibrational state from three (in the 2-state fit) to one, only the term in the barrier height is required.     

Interaction of intense beams of highly vibrationally excited molecules with molecules (clusters) condensed on a cold surface

The interaction of intense beams of SF₆ and CF₃I molecules, excited by powerful IR laser radiation to high vibrational states (0.3 eV ≤ E _vib ≤ 2.0 eV), with molecules (clusters) condensed on a cold surface (T _s ≈ 80–85 K) has been studied. The probability that the excited and unexcited molecules are reflected from the cold metal surface covered by condensed molecules (clusters), as well as the probability that such excited and unexcited molecules are transmitted through a cooled multichannel metal plate and a converging cone oriented at an angle relative to the molecular beam axis, has been determined. Expressions for these probabilities of reflection and transmission as functions of the angle of incidence and the parameters of the exciting laser radiation and the molecular beam are obtained. It is shown that highly vibrationally excited molecules are reflected from the surface and transmitted through the plates and cones with a much higher probability than unexcited molecules. The results suggest that this phenomenon can be used for the separation of molecules in a beam with respect to isotope (or atomic) composition.     

Spectral and energetic characteristics of passing vibrationally excited SF6 molecules through a cooled multichannel plate

We study the spectral and energetic characteristics of SF₆ molecules excited in a pulsed molecular beam by intense IR laser radiation into high-lying vibrational states (with the energy E _v ≥ 0.3–2.0 eV) that pass through a multichannel metal plate that is cooled to T _s ? 80–85 K and is inclined to the beam axis. From comparison of the measured characteristics with the spectral and energetic characteristics of the IR multiphoton absorption of these molecules, we find that they correlate rather well with each other. The results obtained allow us to conclude that, due to different probabilities of passing vibrationally excited and unexcited molecules through the multichannel plate, it is possible to separate molecules in the beam with respect to their isotopic (component) composition.     

Symmetry and Fourier analysis of the ab initio-determined torsional variation of structural and Hessian-related quantities for application to vibration–torsion–rotation interactions in CH3OH

The aim of the present paper is to investigate the use of quantum chemistry calculations to obtain the torsional dependence of various structural and vibrational-force-field-related quantities that could help in estimating the vibration–torsion–rotation interaction terms needed to treat perturbations observed in the spectra of methanol-like molecules. We begin by using the Gaussian suite of programs to determine the steepest-descent path from a stationary point at the top of the internal rotation potential barrier in methanol to the equilibrium structure at the bottom of the barrier. This procedure requires determining the gradient ?V of the potential (as calculated in mass-weighted Cartesian coordinates) along the internal rotation path. In addition, we use the Gaussian suite to calculate the Hessian ??V along this path and to generate from these second derivatives the 3N ? 7 small-amplitude vibrational frequencies and the 3N Cartesian vibrational displacements for each of these vibrations. We then symmetrize the internal coordinates used in presenting the structures, gradients, Hessians and vibrational displacements along the path to take into account the periodic variation of the behavior of the three methyl hydrogen atoms H_i as they pass in turn through the C_s-plane of the HOC frame. The symmetrized linear combinations of the CH_i stretches, of the OCH_i bends, and of the HOCH_i dihedral angles of the methyl group depend on the internal rotation angle γ and they are determined by considering coordinate transformations from the G₆ permutation-inversion group appropriate for internally rotating methanol. This symmetrization procedure permits us to explore the feasibility of expressing the structures, gradients, Hessians, and vibrational displacement vectors along the internal rotation path as short Fourier series in γ, which is one of the main goals of this paper. In summary, we find that the symmetrized structures, gradients, and Hessians, as well as nine of the 11 projected vibrational frequencies and the vibrational displacement vectors for the three vibrations occurring primarily in the HOC frame can be expressed by short Fourier series expansions to their precision in the Gaussian output, and that these series involve only sin 3nγ or only cos 3nγ terms, as required by G₆ symmetry considerations. A preliminary discussion is given of why short Fourier expansions fail for the projected frequencies of the two methyl asymmetric stretches, and for the vibrational displacement vectors of the methyl group vibrational modes. Looking more closely at the symmetrized and projected 3N × 3N Hessian, we find algebraically that only elements in the (3N ? 7) × (3N ? 7) small-amplitude-vibrational block of the Hessian are useful for spectroscopic problems. Non-zero elements in the rest of the 3N × 3N symmetrized and projected Hessian cannot be converted into quantities needed for perturbation studies.     

Perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings

Various examples of perturbations in the vibration-rotation-torsion energy levels of an ethane molecule exhibiting internal rotation splittings are discussed, both from the point of view of the point group D_3d, appropriate when internal rotation tunneling effects cannot be observed, and from the point of view of the group $\text{G}{}_{36}{}^2$, appropriate when internal rotation tunneling in ethane leads to observable splittings in the spectrum. It is found, for perturbations allowed in both D_3d and $\text{G}{}_{36}{}^2$, that each of the two torsional components of the perturbed D_3d vibration-rotation level can in principle interact with a “corresponding” torsional component in the perturbing vibration-rotation level. It is found for perturbations forbidden in D_3d but allowed in $\text{G}{}_{36}{}^2$, which all occur between D_3d vibrational levels of different g, u parity, that only one of the two torsional components of the perturbed D_3d vibration-rotation level can interact with a corresponding torsional component in the perturbing vibration-rotation level. Some of the perturbations examined give intensity to otherwise forbidden transitions in such a way that perturbation-induced transitions can be used in conjunction with normally allowed transitions to determine the sum of the internal rotation splittings for two rotational levels differing in K by three units.     

Internal hydrogen bond,torsional motion,and molecular properties of 2-methoxyethylamine by microwave spectroscopy: Methyl barrier to internal rotation for 2-methoxyethanol

The microwave spectra of four substituted isotopic species of 2-methoxyethylamine (NH₂, NHD, NDH, ND₂) have been assigned. The molecule is found to exist in a gauche form with an intramolecular hydrogen bond of the NH?O type. The four possible sets of the amino hydrogen r_s corrdinates give different H?H distances, probably because the -NH₂ group is involved in large amplitude vibrations and because of changes in the heavy atom positions arising from the deuteration of the hydrogen bond. For the most abundant species many vibrational states have been analyzed and assigned to the two possible CO torsions in the molecule. A value V₃ = 3150 ± 50 cal/mol was found for the methyl torsional barrier and V₁ = 9 ± 3 kcal/mol for the other CO torsional barrier. A third set of observed vibrational satellites is probably assignable to the CC torsion. The determination of the dipole moment and of the quadrupole coupling constants gave values which were not in good agreement with those predicted from nonhydrogen bonded molecules. In addition a value V₃ = 3100 ± 100 cal/mol was calculated for the CH₃ torsional barrier in the related 2-methoxyethanol, using previous experimental data (Canad. J. Chem.50, 1149–1156 (1972)).     

Infrared transitions of C2D6 from v 4 to the interacting system v 4+ v 6, v 4+ v8, v 3+ 2v 4: rotational analysis,and torsional splitting in the v 3+ 2v 4 and v 3+ v 4 states

The hot infrared transitions of C₂D₆ from the υ₄(A_1u ) to the υ₄ + υ₆(A_2g ) and υ₄ + υ₈(E _g ) vibrational states, observed from 960 to 1180 cm^?1, have been rotationally analysed on a high-resolution Fourier transform spectrum (full width at half-maximum about 0·0030 cm^?1). The vibration-rotation interactions affecting the upper vibrational states are very similar to those of the corresponding cold system. A strong x,y Coriolis interaction between υ₄ + υ₆ and υ₄ + υ₈, with K-level crossing, generates large displacements of the rotational components of both vibrational states, tuning them to additional local resonances in several spectral regions. Thus l resonances with Δl = ±2, Δk = ±1 occur within υ₄ + υ₈. A x,y Coriolis-type resonance between υ₄ + υ₈(?l,K ? 1) and υ₃ + 2υ₄(K) occurs at K = 11,12,13, and a further coupling of υ₄ + υ₈(+l,K + 1) and υ₃ + 2υ₄(K + 3) is most effective at K = 11 and 12. These resonances induce torsional splittings on the perturbed levels of υ₄ + υ₈ and allow us to determine the torsional splittings in the υ₃ + 2υ₄ state. The vibration-rotation constants of υ₄ + υ₆, υ₄ + υ₈ and υ₃ + 2υ₄, several interaction parameters and the torsional splitting of υ₃ + 2υ₄ have been determined by least-squares fit of 1391 observed transition wavenumbers, with an overall standard deviation σ = 0·75 × 10^?3 cm^?1. The vibrational wavenumbers found for the four torsional components of (υ₃ + 2υ₄)? υ₄ are υ(E_3d) = 1040·961 82(809)cm^?1, υ(A_3d) = 1041·218 27(865)cm^?1, υ(E_3s) = 1041·225 23(662)cm^?1 and υ(A_1s) = 1041·407 77(633)cm^?1. These are anomalous for both the order of the torsional components and the magnitudes of their separations. We believe that this is mainly due to the interactions of υ₃ + 2υ₄ with the torsional manifolds with υ₃ = 0 and υ₃ = 2, through the vibration-torsion Hamiltonian term (?V ₆/?q ₃)q ₃cos (6γ)]/2. The further observation of a few doublets of υ₈ and υ₃ + υ₄ at resonance provides information on the torsional splitting of the latter state.