Vibrational Coupling Constants Research Articles

Vibrational excitation at high energies and potential-surface models

Models for studying systems provided by an atom and a diatomic molecule by means of high-energy vibrational excitation were constructed and discussed. The use of the inverse scattering treatment to recover the potential from the scattering data for multidimensional potential surfaces was demonstrated by examining the quantum-mechanical rainbow, or the nonmonotone behavior of the scattering probability as a function of quantum number, using the uniform quasiclassical approximation for the T scattering amplitude in terms of the action angle variable. Expressions for differential elastic cross sections were derived and evaluated. The analysis with made it possible to estimate the vibrational coupling constant in the molecular collision potential and to explain the behavior of the rainbow peak as a function of collision energy.

The 2 ν1 + ν3 and 3 ν3 bands of 14N 16O 2

The spectra of the 2 ν 1 + ν 3 and 3 ν 3 bands of 14N 16O 2 have been recorded by means of high-resolution Fourier transform spectroscopy and have been extensively analyzed. The (2 0 1) and (0 0 3) rotational levels deduced from the analysis have been reproduced within the experimental uncertainty using a Hamiltonian which takes into account the Coriolis interaction coupling the vibrational states of the diads {(2 2 0), (2 0 1)} and {(0 2 2), (0 0 3)}. Finally, precise sets of vibrational energies, and spin-rotation, rotational, and coupling constants have been derived for these vibrational states.

The assignment of fundamental vibrations of BEDT-TTF and BEDT-TTF- d8

The i.r. and Raman spectra of bis(ethylenedithio)tetrathiafulvalene (BEDT-TTF) and BEDT-TTF- d 8, are reported. All fundamental vibrations are assigned using the correlations between the data obtained and those for compounds containing BEDT-TTF fragments. A comparative normal coordinate analysis was done. The results can be used for calculation of the electron-intramolecular vibrational coupling constants of superconductive BEDT-TTF based charge-transfer complexes.

Synthesis, Vibrational Spectra and Normal Coordinate Analysis of Cesium-Hexathiohypodiphosphate Cs4P2S6

The title compound has been prepared by elemental synthesis at high temperatures and also by reaction of Na4P2S6 · 6H2O with CsCl in aqueous solution. Both reaction products have closely related vibrational spectra which are assigned on the basis of a P2S6 4- anion with perturbed D3d symmetry. A normal coordinate analysis has been performed using a force Field with 4 initial force constants. The refined force Field, potential energy distribution (PED), mean amplitudes of vibration and Coriolis coupling constants are given.

Butterfly motion of isolated perylene in its ground and first excited singlet states

Vibrational frequencies and Franck-Condon factors derived from laser-induced fluorescence spectra of jet-cooled perylene obtained by Tramer and co-workers are presented for the two lowest-frequency out-of-plane deformation modes. Potential functions are calculated for the “butterfly” mode in the ground and first excited singlet electronic states. The molecule appears to be planar in both cases. A simplified force constant analysis shows that the rigidity of the molecule and the vibrational coupling constant between the two naphthalene entities increase significantly in the excited state.

Accurate electron-molecular vibration coupling constants from powders optical spectra: TCNQ and TTF

A simple but accurate method is proposed for the experimental determination of electron — molecular vibration (e-mv) coupling constants from the optical spectra of powdered samples of dimerized, segregated stack organic quasi-one-dimensional radical salts. By re-examining various TCNQ-based compounds a transferable set of coupling constants is obtained for this key molecular structure. The application of our method to TTF Br salt leads to TTF e-mv coupling constants which nicely compare with those determined from TTF-Chloranil.

Optical and infrared properties of tetramethyltetraselenafulvalene [(TMTSF)2X] and tetramethyltetrathiafulvalene [(TMTTF)2X] compounds

The electronic structure of the organic conductors bis-tetramethyltetraselenafulvalene-$X$ [${(\mathrm{TMTSF})}_{2}X$] and bis-tetramethyltetrathiafulvalene-$X$ [${(\mathrm{TMTTF})}_{2}X$] has been investigated by means of polarized optical and infrared reflectance measurements. Analysis of plasma edges in reflectance is used to extract information on transfer integrals. Measurements of infrared reflectance provide information on the energy of charge-transfer processes and on electron-molecular vibration coupling. Far-infrared measurements allow comparison with low-frequency transport properties, and give clues to the transport mechanisms. The main results may be summarized as follows: The ${(\mathrm{TMTSF})}_{2}X$ class of materials has chain-axis transfer integrals of order 0.25 eV at 300 K and 0.28 eV at 30 K. The $b$-axis transfer integral is found to vary from 18 to 24 meV for different $X$. The ${(\mathrm{TMTTF})}_{2}X$ class has a chain-axis transfer integral of the order 0.18-0.20 eV. No $b$-axis plasma edge is observable. The infrared conductivity spectra of the materials consist of a broad electronic band with superimposed vibrational fine structure. The band is centered at 300 ${\mathrm{cm}}^{\ensuremath{-}1}$ in the best ${(\mathrm{TMTSF})}_{2}X$ conductors and at 2200 ${\mathrm{cm}}^{\ensuremath{-}1}$ in ${(\mathrm{TMTTF})}_{2}$P${\mathrm{F}}_{6}$, an organic conductor of moderate conductivity. The electron-molecular vibration coupling constants for TMTSF and TMTTF appear to be qualitatively similar to those of TTF (tetrathiafulvalene). A new feature is the observation of considerable coupling to modes involving methyl groups, suggesting that a sizable charge density is located near these groups. The electronic band in ${(\mathrm{TMTSF})}_{2}$P${\mathrm{F}}_{6}$ sharpens at low temperature, and a pseudogap at 180 ${\mathrm{cm}}^{\ensuremath{-}1}$ is formed at temperatures above the metal-insulator transition. This behavior is discussed in terms of a possible spin-density-wave contribution to the conductivity. The spin-density-wave amplitude is estimated to be $0.02{\ensuremath{\mu}}_{B}$.

Electron–Molecular Vibration Coupling in Trimerized Organic Ion‐Radical Semiconductors

AbstractThe totally‐symmetric (ag) internal molecular vibrational excitations in a trimer are considered. The mode corresponding to the charge transfer (CT) between non‐centric molecules is shown to be responsible for the indirect IR activity. The trimer MO calculations in the site occupation representation are simplified and the symmetry of the basis states is taken into account. Eigenstates and eigenvalues of the molecular trimer with two radical electrons are calculated as a function of the transfer integral, t, and the Coulomb „on‐site”︁ repulsion, U. The following interpretation of the absorption spectrum of the cesium salt of tetracyanoquinodimethane Cs2(TCNQ)3 is given: the 1.4 eV peak is attributed to intratrimer charge transfer excitation, the less than 0.6 eV peak corresponds to the electronic transition between neighbouring trimers. The electron–molecular vibration coupling constants and Hubbard parameters U and t are evaluated for Cs2(TCNQ)3.

Measured and predicted band model parameters of BF 3( v3) at high temperatures

Two experimental techniques were used to determine the high temperature infrared absorption coefficients of the v 3 band of BF 3. A high temperature flow tube fitted with a multipass infrared absorption cell was used to determine the BF 3 absorption coefficients at 295, 585, 870, 1150, and 1440K. BF 3 was also used in a flame emission-absorption apparatus to determine the BF 3 absorption coefficients at 2400 K. A generalized formulation for predicting the S/d and 1/ d band model parameters of symmetric top perpendicular bands of MX 3 molecules is presented. The effect of including nuclear spin statistics in computing the S/d and 1/ d band model parameters is considered. It is shown that nuclear spin statistic̆s effect only the 1/ d parameter and are significant only for the case of zero nuclear spin. A number of practical considerations, which arise in designing a computer algorithm to calculate the S/d and 1/ d parameters, are discussed. Comparisons of the theoretical and experimental BF 3 absorption coefficients are made. Good agreement between theory and experiment at all temperatures was obtained by adjusting only two vibrational energy coupling constants, χ 23 and χ 34 . Predicted S/d and 1/ d band model parameters at 300, 600, 900, 1200, 1500, 2000, 2500, and 3000 K are presented.

Schwingungsberechnungen der käfigstrukturierten Moleküle P4Se3 , AS4S3, As4Se3 und PAs3S3 / Molecular Vibration Analysis of the cage-like Molecules P4Pe3, As4S3, As4Se3 and PAs3S3

Abstractn The P4Se3, As4S3, As4Se3 and PAs3S3 molecules are supposed to have a cage-structure of the C3V symmetry. Normal coordinate analyses for these molecules were performed, based on a very simple initial force field transferred from P4S3. The force field was refined by adjusting the symmetry force constants to fit exactly observed frequencies. The force fields were used to calculate the mean amplitudes of vibration and Coriolis coupling constants. The standard thermodynamical functions from spectroscopic data are also given.

The 2ν2, ν1 and ν3 bands of D216O. The ground state (000) and the triad of interacting states {(020), (100), (001)}

Three spectra of D216O between 2170 and 3090 cm−1 have been recorded with a Fourier transform spectrometer having a resolution of about 5 × 10−3 cm−1. A careful analysis of the bands 2ν2, ν1, and ν3 has led to a largely extended and more precise set of rotational levels belonging to the vibrational states (000), (020), (100), and (001). From this set, we have then been able to determine improved rotational constants for the ground state (000) and precise vibrational energies, rotational and coupling constants for the three interacting states (020), (100), and (001). The Fermi-type interaction between (020) and (100) as well as the Coriolis-type interactions between (100) and (001) and between (020) and (001) have been explicitly taken into account. Many vibrorotational resonances were detected and are discussed.

Towards the experimental determination of the fundamental microscopic parameters of organic ion-radical compounds

The electron transfer integral t, the on-site Coulomb repulsion U and the linear electron-molecular vibration (EMV) coupling constants { g α} are microscopic parameters fundamental in the understanding of the physical properties of organic ion-radical compounds. For those compounds in which the ion-radical molecules are present as quasi-isolated dimers, we demonstrate that all of these parameters may be measured via polarized optical reflectance. The role of U in suppressing the EMV coupling is stressed.

Force field study op some hexahalide ions

AbstractThe force field study of some hexahalide ions (Mm6−n) is attempted by the method of Redington and Aljibury. The angle parameter has been fixed for all the ions to obtain the symmetrised force constants. Mean amplitudes of vibration and Coriolis coupling constants have also been evaluated. The results are discussed in detail.

Relaxation effects accompanying core ionization in diatomic molecules

The influence of electronic relaxation on the bond-length charges following inner-shell ionisation in diatomic molecules is studied. CO and N 2 are treated explicitly. Transition operators are used for predicting renormalized vibrational coupling constants and slopes of relaxation energy surfaces.

Electron–vibration interactions in benzene and deuterobenzene

An exactly solvable model of the linear interaction of molecular vibrations with the electronic states of molecules is utilized to describe the intensity distributions in band systems observed in the ultraviolet photoelectron and ultraviolet absorption spectra of C6H6 and C6D6. From this analysis, the linear coupling constants describing the vibration-induced energy shifts of the 1e1g(π), 3e2g(σ), and 3a1g(σ) one-electron orbitals and of the 1B2u excited state are determined. These coupling constants also are calculated using the spectroscopic CNDO/S2 molecular-orbital model of Lipari and Duke and the vibrational normal modes of Whiffen. The sensitivity of the calculated coupling constants to the precise form of the molecular orbital model is shown to be substantial. The CNDO/S2 model provides a semiquantitative (±50%) description of the measured coupling constants, whereas prior CNDO models (e.g., CNDO/2) predict values for these quantities deviating by as much as an order of magnitude from the measured ones. Although only linear electron–vibration coupling constants can be extracted from observed ultraviolet absorption and photoelectron spectra, the associated quadratic coupling constants can be evaluated using the molecular-orbital model. This analysis indicates that the linear terms dominate the nuclear-relaxation-induced energy shifts for one-electron orbitals but that the quadratic terms can predominate for excited electronic states. The calculated linear and quadratic coupling constants for the 1e2u(π*), 1e1g(π), 3e2g(σ), 1a2u(π), 3a1g(σ) orbitals and the 1B2u, 1B1u, and 1E2u electronic states are given for all 30 independent molecular vibrations of C6H6 and C6D6.

A many-body approach to the vibrational structure in molecular electronic spectra. II. Application to nitrogen, carbon monoxide, and formaldehyde

The theory developed in the preceding paper is applied to calculate the vibrational structure in optical absorption and electron impact spectra of N2 and CO and in the photoelectron spectra of H2CO and D2CO. In addition, the vibrational structure of a recently measured shake-up line in the photoelectron spectrum of N2 is computed. The influence of anharmonicity effects on the Franck–Condon factors is discussed and a very simple scheme to take these effects into account is proposed. The one-particle approximation is shown to provide a fairly accurate picture in most cases. For formaldehyde many-body effects are incorporated into the vibrational coupling constants, leading to an improved agreement with experiment for all bands. The assignment of the third and the fourth ionization potential of formaldehyde, which has been controversial, is clarified.

A theoretical photoelectron spectrum of cyanogen by a Green-function method

A Green-function method is used to calculate a photoelectron spectrum of C 2N 2 including the vibrational structure. The calculated spectrum and the experimental spectrum are in good agreement. It is found that the second band is due to ionization of the 5 a g electron. In addition predictions are made concerning the ionization potentials and vibrational structure of low lying bands which have not yet been measured. The ionization potentials obtained in the different orders of the perturbation expansion of the self-energy part are discussed as well as the influence of many-body effects on the vibrational coupling constants.

On the vibrational structure in inner-shell ionization spectra by a many-body approach

The vibrational structure due to the ionization of inner-shell electrons is calculated for methane and carbon monoxide. The vibrational coupling constants are renormalized by going up to second order perturbation theory. It is found that for core electrons the renormalization is essential. The results are compared with experimental spectra.

Selected valence electron split‐shell molecular orbital calculations on the diatomic interhalogen molecules

AbstractSelected valence electron split‐shell molecular orbital calculations have been performed on the diatomic interhalogen molecules in order to obtain their binding energies, equilibrium internuclear distances, vibrational force constants, dipole moments and nuclear quadrupole coupling constants. The results are compared with the corresponding closedshell values and with those of some previous semiempirical and nonempirical all valence electron calculations. It is observed that the selected valence electron split‐shell molecular orbital method which involves the least amount of computations yields results in better agreement with experiment than other methods.

Mean amplitudes of vibration and Coriolis coupling constants for the ammoniaboron trifluoride complex

Mean amplitudes of vibration and Coriolis coupling constants for the ammoniaboron trifluoride complex