Local Mode Theory Research Articles

Observation and Analysis of the Δv=5 Stretch Overtone Band Transition of 15NH3

The absorption spectra of the Δv=5 stretch overtone band transition of 15NH3 in the visible region (648 nm band) are observed by the photoacoustic method for the first time. The resolution is 0.01 cm-1. The observed Stark spectra at electric field high enough to resolve M components are helpfully employed in assignment of the rotation and inversion transitions. The vibrational level structure is well explained in terms of the local mode theory. The rotational constants and isotope shift are obtained.

Recent developments in the local mode theory of overtone spectra

Recent developments in the local mode theory of overtone spectra

Interpretation of overtone light-absorption lines in polystyrene

The intensities of the overtone vibrational transitions of a C-H oscillator are calculated using the Morse potential. The local-mode theory enabled comparison of the data obtained with the experimentally observed intensities of the light-absorption lines in substituted styrenes and complete identification of the spectrum of overtone transitions in them.

Structure and vibrational spectroscopy of the water dimer using quantum simulation

A method is described for calculating the vibrational frequencies of a molecular cluster using a combination of quantum simulation and local-mode variational theory. The method is applied to the water dimer and results are compared with normal-mode theory, frozen field local-mode theory, and with experiment. It is shown that the new approach is more rapidly convergent than the other techniques. Also, providing a suitable potential surface is available, the method is readily applicable to other molecular clusters.

SCF calculations of the CH-stretching overtone intensities in dichloromethane within the local mode model

Oscillator strengths for the CH-stretching components of the overtone spectrum of dichloromethane are calculated for ΔvCH ≤4. The calculations use local mode theory to obtain the vibrational wave functions and SCF theory, with a number of different basis sets, to obtain the dipole moment functions. A comparison with experimental results shows the calculations can reproduce the relative ordering of the oscillator strengths as a function of the particular vibrational state, and give a reasonably quantitative account of the magnitude of the intensities, even with simple split-valence basis sets.

ChemInform Abstract: Theoretical Description of the Overtone Spectra of Acetaldehyde Using the Local Mode Approach.

The overtone spectra of the C–H bonds of the methyl group of acetaldehyde are analyzed using a coupled oscillator local mode theory. The higher energy absorption band of each overtone region is assigned to the in‐plane C–H methyl bond while the lower energy absorption band is assigned to the two out‐of‐plane methyl C–H bonds. We conclude that the two out‐of‐plane methyl group C–H bonds are weaker and have longer bond lengths than the corresponding in‐plane C–H bond. This observation is in agreement with predictions based on the trans effect theory. The calculations exemplify the problem of assigning overtone spectra based on relative intensities. In particular, the lower energy band of the methyl C–H group is calculated to be more intense than the higher energy band irrespective of assignment. This theoretical prediction is associated with the importance of oscillator coupling via the kinetic energy matrix element.

Theoretical description of the overtone spectra of acetaldehyde using the local mode approach

The overtone spectra of the C–H bonds of the methyl group of acetaldehyde are analyzed using a coupled oscillator local mode theory. The higher energy absorption band of each overtone region is assigned to the in-plane C–H methyl bond while the lower energy absorption band is assigned to the two out-of-plane methyl C–H bonds. We conclude that the two out-of-plane methyl group C–H bonds are weaker and have longer bond lengths than the corresponding in-plane C–H bond. This observation is in agreement with predictions based on the trans effect theory. The calculations exemplify the problem of assigning overtone spectra based on relative intensities. In particular, the lower energy band of the methyl C–H group is calculated to be more intense than the higher energy band irrespective of assignment. This theoretical prediction is associated with the importance of oscillator coupling via the kinetic energy matrix element.

The infrared predissociation spectra of water clusters

Infrared predissociation spectra of water clusters have been measured in the frequency range 3000–3800 cm−1 using a molecular beam–color center laser apparatus. The transition from a spectrum resembling that of liquid water to that of the dimer is clearly seen. Detailed theoretical analyses using normal mode theory, local mode theory, and a quantum simulation method are used to interpret the spectrum in terms of a potential surface that includes both intramolecular and intermolecular degrees of freedom.

Observation of the ν 3 → (2ν 3, A 1) band of methane

Double-resonance spectra were recorded for several rotational sublevels of the (2ν 3, A 1) vibrational level of methane. The observed vibrational energy is 5968.1 cm −1, in good agreement with local-mode theory. The effective rotational constant for this level was found to be 5.31 cm −1. This unexpectedly high value could involve interactions with lower vibrational levels.

The high-resolution visible overtone spectrum of acetylenea)

Direct, gas-phase overtone spectra of states corresponding to five and six quanta of C–H stretch have been obtained for four isotopically substituted acetylenes in the region 14 900–18 500 cm−1. Peak positions of individual rotation–vibration lines were determined to a precision of about 0.003 cm−1. A total of 39 bands are analyzed: 16 for 12C2H2; 14 for 13C2H2; five for 12C13CH2; and four for 12C2HD. The rotational structure of the bands is fit to a semirigid rotor Hamiltonian. However, the bands suffer from severe rotational perturbations, with typical matrix elements being on the order of 0.3 cm−1 or less. The error in the determined band origins varies between 0.001 and 0.1 cm−1, depending on the degree of perturbation. Precision rotational constants are also determined for the observed bands. The vibrational term values cannot be adequately explained in terms of the usual slightly anharmonic normal mode expansion. Even though acetylene represents an intermediate case between the local mode and normal mode limits, the simple local mode theory described by Child and Lawton [M. S. Child and R. T. Lawton, Faraday Discuss. 71, 273 (1981)] can be used to rationalize many aspects of the spectrum—e.g., the splitting of the states ‖005g011〉 and ‖005u011〉 is found to be only 0.44 cm−1. The intermediate character of acetylene is seen upon single deuterium substitution. The state corresponding to five quanta of 12C–H stretch shifts about 100 cm−1 to the blue, a result which is certainly anomalous from the point of view of intuitive local mode theory. The band origins for the observed Σ–Σ transitions for all four acetylenes studied are found to be in good agreement with the results of a recent variational calculation [L. Halonen, M.S. Child, and S. Carter, Mol. Phys. 47, 1097 (1982)]. It is also observed that the anharmonic shifts of the sequence band transitions are quite large—for the v=5 overtone band, the sequence bands are shifted 74 cm−1 fo the Πg bend and 39 cm−1 for the Πu bend.

Photoacoustic spectroscopy of vibrational overtones in polyatomic molecules

Intracavity gas-phase photoacoustic spectroscopy is used to study the near IR and visible overtone spectra of propylene, 2-butene, 2-methyl-2-butene, 2,3-dimethyl-2-butene, acetone, 2-butanone, and 3-pentanone. The spectra are described in terms of the local-mode theory of vibrations as the absorption of loosely coupled anharmonic C-H oscillators within the molecule.

Light scattering study of phase transitions in ferroelectric tris-sarcosine calcium chloride and its brominated isomorphs

Abstract Raman data are presented for the soft optical phonon in brominated tris-sarcosine calcium chloride, together with a model calculation based upon the local-mode theory of Thomas and of Lines and Glass. Under the assumption that the parameter describing the coupling of sarcosine and chlorine motions varies monotonically with bromination, the calculation describes the observed variation of Curie temperature with bromine concentration, including the presence of a critical concentration at which the ferroelectric transition disappears.

Comments on the concept of universal intensities in local mode theory

Tetramethylsilane (TMS) Spectra were obtained with a Cary 14-spectropholometer. The intensities in the primary C-H LM overtones and the neighboring sidebands of TMS are given and discussed in terms of the Universal cconcept of intensities. (AIP)

A general local-mode theory for high energy polyatomic overtone spectra and application to dichloromethane

A new model is developed to describe the overtone spectra of polyatomic molecules containing XH n moieties. The infrared absorption is described as corresponding to excitation of localized modes of vibration rather than a set of symmetry allowed combinations of anharmonic normal modes. The possibility of assigning new bands in the more complex regions of the overtone spectra which involve combinations of both stretching and bending modes is examined and illustrated using the overtone spectrum of ammonia. The overtone spectrum of dichloromethane is recorded in the range λ = 9260 Å to λ = 5300 Å, and the CH overtone bands at 8850 Å, 7223 Å, and 6165 Å corresponding to the Δ v CH = 4, 5, and 6 overtones are identified. Specific features of these bands are discussed in detail in relation to the model. The common features and simplicity of the Δ v CH = 4 overtone bands of a series of halomethanes and ethanes are also interpreted in terms of the model.

Infrared absorption of silicon isotopes in gallium phosphide

Infrared absorption measurements at ∼80°K on 28Si- and (28Si+30Si)-doped GaP grown by liquid-phase epitaxy and compensated by electron irradiation are presented. Several new bands are observed with samples containing the mixed isotopes. The observed frequencies of 28Si-related bands agree with previously reported values, and the isotopic shifts for 30Si-related bands agree with values calculated from local mode theory. The results indicate that one band is attributable to a defect containing two Si atoms on nonequivalent sites, presumably nearest-neighbor substitutional pairs. The present measurements confirm the previous observations of a much larger concentration of pairs than that predicted by random statistics.

Infrared absorption of mixed silicon isotope pairs in gallium arsenide

The infrared absorption of GaAs doped with 28Si, 30Si, or 28Si + 30Si and compensated by 6Li diffusion or electron irradiation is reported. Isotopic shifts close to those predicted from local-mode theory are observed for all the silicon defect bands in 30Si-doped GaAs from frequencies previously reported for 28Si-doped material. a new band is observed at 456 cm−1 for the sample containing both 28Si and 30Si, and is attributed to (28Si–30Si) pairs. The frequency of the new band is in accord with simple theory, and its presence confirms the observation of the nearest-neighbor silicon pairs. The results indicate, however, that the indentification of one of the three absorption bands previously attributed to the 28Si pairs is questionable. The experimental result also indicates that an absorption band at 369 cm−1 previously observed in electron-irradiated samples in indeed due to a silicon-related defect.

Equivalent Circuit and Loss Invariant for Helicon Mode Semiconductor Devices

A basic nonreciprocal two-port component in the HF range is considered consisting of two spatially orthogonal coils wound on an indium antimonide slab. A dc magnetic field is impressed perpendicular to the axes of the coils. Local helicon mode theory, assuming a single type of carrier, is used to derive the frequency-dependent network matrix of the device. From this matrix a broadband equivalent circuit is synthesized, which contains one gyrator. The resultant network structure is then analyzed to arrive at a loss invariant or figure of merit for the nonreciprocal device and the invariant is found to be frequency independent. This loss invariant is used to calculate the minimum possible insertion loss of an isolator formed by imbedding the helicon mode element in the most general lossless reciprocal circuit. The minimum loss is shown to be Minimum insertion loss = <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">10 \log \left( 1 + \frac{1}{u^{2}} \right) dB</tex> , where <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">u</tex> is the tangent of the Hall angle in the InSb slab. Two-port experimental measurements were made (using a low-frequency embodiment of a microwave directional coupler) over the frequency band 5-15 MHz to verify the equivalent circuit and the value of the invariant. These data provided reasonable verification of the equivalent circuit, the invariant, and the minimum loss figure. A circuit for a minimum insertion loss isolator was constructed, and at fields of 2600 and 5600 gauss the measured minimum insertion loss at room temperature was found to be 2.8 and 1.5 dB, respectively. This data compares with the theoretically predicted figures of 3.1 and 1.0 dB. These results are all under infinite isolation conditions. A derivation is given to show the optimum benefits to be obtained by trading reduced isolation for improved insertion loss. Finally, the theory of invariance is employed to derive expressions for the minimum insertion loss of a helicon mode gyrator and three-port circulator.