Isotropic Raman Spectra Research Articles

Raman band shapes of a three-level vibrational system for a bath represented by a two-state stochastic process

The isotropic Raman spectrum of the molecule described by a three-level vibrational system has been simulated for a bath modeled as a two-state stochastic process. The influence of the energy relaxation as well as the dephasing on the spectrum is demonstrated for different modulation speeds of the bath. The cumulant expansion and the projection-operator formalism description of the isotropic spectrum have been studied. The results show that the projection-operator method provides an accurate description of these spectra for all modulation speeds whereas the cumulant expansion technique reproduces the spectra in the fast modulation limit only.

Isotropic and anisotropic Raman spectra of interacting modes in liquids

A liquid sample consisting of a set of molecules with interacting modes perturbed by intermolecular interaction is considered. Based on the Mori projection-operator formalism expressions for isotropic and anisotropic spectra are derived. Application of the theory permits the determination of the parameters which characterize the relaxation processes and intramolecular coupling, e.g., Fermi interaction, in liquids.

On the isotropic Raman spectra of isotopic binary mixtures

A theory is developed for the isotropic Raman spectrum of nondegenerate modes in polyatomic binary mixtures. Particular emphasis is attached to isotopic binary mixtures and the problem of dipolar resonant transfer. The thermodynamic state dependences of spectral features are investigated in some detail. Attention is focused on quantities which are experimentally accessible by isotopic dilution experiments, in particular the frequency shift of the spectrum consequent upon isotopic dilution, and also the resultant changes in spectral second moments. The theory is compared with some existing experiments on specific systems, and a number of predictions are made which are capable of being tested experimentally.

Raman spectral studies of the dynamics of ions in molten LiNO3–RbNO3 mixtures. II. Vibrational dephasing: Roles of fluctuations of coordination number and concentration

The isotropic Raman spectra of the ν1 (A′1) mode of NO−3 ions are measured in molten LiNO3–RbNO3 mixtures at various concentrations and at temperatures from 478 to 750 K. The isotropic Raman bandwidth Γiso is found to increase almost linearly with the mole fraction c(Li+) of LiNO3, from 9–13 cm−1 for molten RbNO3 to 26–27 cm−1 for molten LiNO3. Vibrational correlation functions are analyzed on the basis of a model of simultaneous homogeneous and inhomogeneous vibrational dephasing. The contribution of inhomogeneous dephasing was found to be negligibly small in mixtures of c(Li+)≲0.33. While in mixtures of concentrations c(Li+)≳0.5, homogeneous and inhomogeneous processes are found to give comparable contributions to the total vibrational widths, where the latter contribution increases as the temperature decreases. The observed isotropic Raman bands are asymmetric. The asymmetry parameter α=Γ1/Γh , where Γ1 and Γh are the half-widths at half-maximum height of the low and high frequency sides of the band, is larger than one in molten LiNO3 and RbNO3, while α is smaller than one in molten mixtures of concentrations c(Li+)=0.33–0.67. This concentration dependent asymmetry is found to arise predominantly from coordination number fluctuation, i.e., fluctuation of the environmental cation number of a reference NO−3 ion, while concentration fluctuation in the coordination sphere plays a minor role. A model of local environmental states in a molten mixture, which assumes a linear change of vibrational frequency with neighboring cation numbers, is presented. The observed spectral asymmetry can be interpreted by assuming that the equilibrium distribution has a peak at the small coordination number side in pure molten LiNO3 and RbNO3, while the distribution peak shifts to the high coordination number side in molten mixtures.

Fermi resonance - the theory of isotropic and anisotropic Raman spectra in dilute solutions

Raman scattering from dilute solution was studied limiting considerations to one active molecule, in which the Fermi resonance occurs, interacting with the molecules of an inert solvent. For such a system, the isotropic and anisotropic correlation functions ⧸CFs⧸ for symmetric top molecule have been calculated and examples of Fermi resonance spectra ⧸FRS⧸ are presented.

Long-range conformational structure and low-frequency isotropic Raman spectra of some highly disordered chain molecules

ADVERTISEMENT RETURN TO ISSUEPREVArticleNEXTLong-range conformational structure and low-frequency isotropic Raman spectra of some highly disordered chain moleculesR. G. Snyder and S. L. WunderCite this: Macromolecules 1986, 19, 2, 496–498Publication Date (Print):February 1, 1986Publication History Published online1 May 2002Published inissue 1 February 1986https://doi.org/10.1021/ma00156a051RIGHTS & PERMISSIONSArticle Views143Altmetric-Citations19LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (375 KB) Get e-Alerts Get e-Alerts

Raman investigations of collective vibrational motions in van der Waals liquids

Recent investigations of collective vibrational motions in pure van der Waals liquids and in their isotopic mixtures are reviewed. Experimental data are enumerated first. The theory is presented later, separately, for non-composite and composite bands of both isotropic and anisotropic Raman spectra. It is shown that isotropic Raman processes are partially coherent and contain information about collective vibrational motions in liquids. In turn, anisotropic Raman processes are incoherent in the zero-order description and their study is less important in the present context.

Extended measurement and assignment of isotropic Raman transitions in the ν1 region of 12CD4

AbstractThe isotropic Raman spectrum of 12CD4 is presented in the range from 2101 to 2113 cm−1, thus covering the ν1(A1) Q‐branch and part of the ν2 + ν4(F1 + F2) Q‐branch. Experimental results for the 2101‐2108 cm−1 range were obtained using the ‘inverse Raman spectroscopy’ technique and have been published previously. New measurements in the 2108 cm−1‐2113 cm−1 range were obtained using the very similar ‘stimulated Raman gain spectroscopy’ technique. In both spectra the resolution is limited by the Doppler width of the lines. Formally, only transitions to the upper state of the ν1 band are allowed in isotropic Raman scattering, but strong resonances enhance transitions to the upper state of ν2 + ν4. An effective Hamiltonian which takes these resonances into account was used to interpret the spectra and led to the assignment of all significant lines. In all, 165 Raman transitions were assigned, and these transitions are fitted by the model Hamiltonian with a standard deviation of 0.008 cm−1.

Isotropic Raman study of rotation-vibration coupling for a system of free asymmetric top molecules

A theory is proposed to investigate the effects of rotation-vibration coupling on the isotropic Raman spectra of a system of free asymmetric top molecules. Appropriate time correlation function is given in the case of adiabatic evolution of the quantum mechanical vibrational motion. The problem is exactly soluble although the results are only available in a numerical form.

Studies of vibrational relaxation in liquid methyl iodide

The intermolecular coupling contribution to the vibrational relaxation function for v 2 of methyl iodide has been deduced using the method of isotopic dilution. The band widths, correlation functions and frequency shifts of both isotropic and anisotropic spontaneous Raman spectra have been studied at 295 and 205 K for solutions of 0·1 mole fraction of CH3I in CD3I and in CS2. Although isotopic dilution leads to a considerable decrease in the rate of vibrational relaxation, neither the corresponding first moment changes nor the I vv-I VH frequency shifts very large. This implies that neither permanent dipole nor other intermolecular interactions lead to appreciable liquid phase ‘order’ in CH3I. This is understood in terms of a model of the intermolecular coupling potential which shows that, for weak ‘order’, the second moment is affected much more than the first moment. Our results for CH3I are different from those predicted by a recently published theory of intermolecular coupling in pure liquids (albeit for unspecified potentials) which predict large frequency shifts on isotopic dilution.

On the vibrational frequency correlation in liquids: Raman study of aqueous thiocyanate solutions

The vibrational frequency correlation functions 〈ω(0) ω(t)〉 are calculated from isotropic Raman spectra for the CN stretching mode of the SCN− anion in aqueous LiSCN, NaSCN, and KSCN solutions, at concentrations 1–10 M, and at temperatures of 30, 55, and 80 °C. The experimental 〈ω(0) ω(t)〉 shows rapid relaxation within a particular environment on a subpicosecond time scale, accompanied by constant positive correlation. It is concluded that the homogeneous dephasing is due to the fast relaxation of 〈ω(0) ω(t)〉, and that the inhomogeneous dephasing comes from the static positive correlation, which should be attributed to a distribution of environments persisting over the time scale of Raman probe. The analysis of 〈ω(0) ω(t)〉 confirms that the inhomogeneous broadening increases with decreasing temperature, with increasing salt concentration, and in the order KSCN<NaSCN<LiSCN.

The lineshape of motion-averaged isotropic Raman spectra

The conventional Kubo model can be used to describe the spectrum modulation by slow to fast motion, i.e. even in the range of applicability of perturbation theory. However, the Kubo model assumes the gaussian shape of static spectra. A model free of this assumption has been used to show that experimental data can be interpreted provided the initial static spectrum has non-gaussian wings.

Contributions of self and distinct pair vibrational correlation functions to isotropic and anisotropic Raman spectra of the ν 2(A 1) band of liquid CD 3I

The isotropic and anisotropic Raman spectra of a pure liquid and a dilute isotopic solution are compared. In the light of the theories of Tarjus and Bratos, the experimental results allow a quantitative separation of the self and distinct pair vibrational contributions to the isotropic spectrum of the pure substance. It is found that the anisotropic spectrum depends only on the self vibrational term.

Homogeneous and inhomogeneous vibrational dephasing processes in aqueous thiocyanate solutions

The vibrational correlation functions are calculated from the isotropic Raman spectra for the CN stretching mode of SCN- anions in aqueous LiSCN, NaSCN and KSCN solutions, at concentrations 1–10 M and at temperatures 30, 55 and 80°C. These correlation functions are analysed on the basis of a model of simultaneous homogeneous and inhomogeneous vibrational dephasing, and both the homogeneous and inhomogeneous broadening contributions are extracted. The CN mode in aqueous thiocyanate solutions is found to be inhomogeneously broadened to various degrees depending on cation species, concentration and temperature. The homogeneous contribution increases and the inhomogeneous contribution decreases with increasing temperature because of increased molecular motion. Increase of salt concentration is found to develop inhomogeneity, probably because the strong interaction in concentrated solutions results in long lived local structures. An increase of inhomogeneous and a decrease of homogeneous broadening contributions with increasing salt concentration compensate in KSCN solutions. However, in LiSCN and NaSCN solutions, the increase of inhomogeneous contribution dominates the homogeneous contribution, which leads to concentration broadening. The band in 10 M LiSCN solution at 30°C, which is the broadest of all the CN bands investigated here, is found to be broadened only by the inhomogeneous process.

Binary theory of dephasing in liquid solutions. II. Motion-transformed isotropic Raman spectra

Abstract The non-markovian theory of encounters is applied to calculations of impurity dephasing kinetics, corresponding Raman spectra and their moments. The theory is checked against the model of suddenly switched interactions and then applied to linewidth calculations under dynamic and stochastic dephasing. The former occurs for isotropic short- or long-range interactions. The latter takes place in the case of anisotropic dipole—dipole interactions modulated by fast rotation. Within perturbation theory the line is stated to be motion-narrowed in the former case and independent of translational motion in the latter case. If the interaction is strong, the line is motion-broadened in both cases but in different ways depending on whether the interaction was switched on by a jump or by continual diffusion. Perturbation theory becomes inapplicable to impurity dephasing much earlier than is conventionally assumed.

The ν2 + ν4 and 2 ν2 isotropic Raman bands of 12CH 4

The purely isotropic Raman spectrum of the ν 1 band, the ν 2 + ν 4 band (enhanced through interaction with ν 1), and the 2 ν 2 band of 12CH 4 was obtained with a spectral resolution of 0.30–0.35 cm −1 from exposures with different orientations of the linearly polarized exciting light. The ν 2 + ν 4 and 2 ν 2 bands show partially resolved rotational structure. The spectra are interpreted in terms of a model which takes explicitly into account vibrational and rovibrational interactions with other vibrational states, using molecular constants determined primarily from infrared spectra. The computed contours are in excellent agreement with the experimental ones and the observed and calculated peak wavenumbers agree within one tenth of the spectral resolution limit, except for a small region near the ν 1 band. The good overall agreement represents an independent check on the overall correctness of the previously reported molecular constants. A detailed discussion is given of the contributions to the intensities of individual transitions from the three transition moment matrix elements, which in an isolated-band model are the intensity parameters of the ν 1, 2 ν 4, and 2 ν 2 isotropic bands, respectively.

The 2ν4 isotropic and anisotropic Raman bands of CH4

AbstractThe Raman spectrum of the very weak 2ν4 band of CH4 has been recorded in the region 2460–2675 cm−1 with a spectral resolution of about 0.30 cm−1 and with two different orientations of the linearly polarized exciting light relative to the direction of observation. The two exposures are used to obtain the purely isotropic and the purely anisotropic Raman spectrum of the band. The two spectra are interpreted in terms of a model which takes explicitly into account vibrational and rotation‐vibrational interactions with other vibrational states. Using molecular constants determined primarily from infrared spectroscopy, theoretical contours are calculated which agree very satisfactorily with the experimental ones. For the isotropic spectrum it is found that two different values of the ratio between the 2ν4(A1) and the ν1 transition moment matrix elements reproduce the spectrum equally well. It is shown that the major part of the intensity in the isotropic and anisotropic Raman spectrum is borrowed from the ν1(A1) and the ν3(F2) fundamentals, respectively, through Fermi‐type interactions, and it is also shown that the 2ν4 isotropic Raman band would have been 4–6 times more intense, if the 2ν4(A1) transition moment matrix element had been negligible.

Raman Spectrum of n-Propylamine in Cyclohexane

Abstract Polarized (Isotropic) Raman spectra of the N-H valence region of n-propylamine have been recorded as a function of concentration in cyclohexane. Statistical analysis of the data using non-linear least squares techniques revealed the presence of a fourth spectral band in this region, not observed in an earlier IR study. This latter peak has been assigned to vibrations of monomers in the liquid. The resolved spectral parameters are consistent with a picture of diminishing molecular association upon dilution of the amine in this non-polar solvent.

ChemInform Abstract: A THEORETICAL MODEL FOR THE INTERACTING UPPER STATES OF THE ν1, ν3, 2ν2, ν2 + ν4, AND 2ν4 BANDS IN METHANE

Abstract The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν1, ν3, 2ν2, ν2 + ν4, and 2ν4 bands in methane are reviewed, and the major vibration-rotation interactions (H30, H 40 , H 21 , H 31 , H 22 ) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2ν4 isotropic Raman spectrum of 12CH4, leading to a very good agreement between the experimental and calculated spectra.

A theoretical model for the interacting upper states of the ν1, ν3, 2 ν2, ν2 + ν4, and 2 ν4 bands in methane

The effective vibration-rotation Hamiltonians complete to fourth order in the Amat-Nielsen scheme for the upper states of the ν 1, ν 3, 2 ν 2, ν 2 + ν 4, and 2 ν 4 bands in methane are reviewed, and the major vibration-rotation interactions ( H 30, H ̃ 40 , H ̃ 21 , H 31 , H ̃ 22 ) connecting the different vibrational states are discussed. Explicit matrix elements in a basis of harmonic oscillator-symmetric rotor basis functions are given for the purely vibrational terms and for the vibration-rotation interactions. Expressions for spectral intensities of infrared and Raman spectra are presented, and the selection rules and transition moment matrix elements are stated. A computer program is described which, incorporating all these features, can be used for prediction of infrared and Raman spectra and for determination of molecular constants from observed spectra by a least-squares routine. As an example the program is applied to the 2 ν 4 isotropic Raman spectrum of 12CH 4, leading to a very good agreement between the experimental and calculated spectra.