Molecular Vibrational Relaxation Research Articles

Studies of molecular motions and vibrational relaxation in acetonitrile. I. Raman spectral studies of the ν 1 ν 3 and 2ν 3 bands in the

Raman spectroscopic studies on acetonitrile in the liquid and in dilute solutions have been used to investigate the vibrational relaxation-processes wh

The sliding filament model of muscle contraction: II. The energetic and dynamical predictions of a quantum mechanical transducer model

A theoretical model of a molecular energy transducing unit designed for the production of mechanical work is constructed and its consequences examined and compared with the experimentally determined myothermal and dynamic properties of vertebrate striated muscle. The model rests on a number of independent assumptions which include: the almost instantaneous generation of mechanical force by the occurrence of a radiationless transition between vibronic states of the transducer (crossbridge) at a point of potential energy surface crossing; transmission of this force to the load via the active sites on the thin filament by means of non-bonding repulsive forces, no energy being required for detachment; “detachment” consists of a second radiationless transition at a lower energy point than the first force generating transition, the energy difference appearing largely as work. The method of force generation completely avoids problems such as the “force-rate dilemma” which occur repeatedly in any discussion where state populations are near-Boltzmann and also leads without further arbitrary assumptions to such concepts as “attached but non force-producing states” and strongly position dependent “attachment” and “detachment” rate constants since these can only be appreciable near potential energy surface crossings. The kinetics and energetics of a transducer of this type operating cyclically and converting ATP → ADP + P i are considered and shown to lead to length-tension and energetic behaviour very similar to that exhibited by vertebrate striated muscle, both for contraction and stretching. The existence of a limiting tension for stretching is predicted by the model as is the decrease of the rate of enthalpy release rate below the isometric value. At the limiting tension the rate of enthalpy release by the transducers is virtually zero, as observed. However, the stretching only inhibits the ATP hydrolysis, the cyclic synthesis from ADP and work being impossible with this model. The response to rapid length step changes automatically contains the asymmetry observed experimentally (with respect to lengthening and shortening) and arbitrary assumptions over and above those giving adequate explanation of the steady-state properties are not required. The asymmetry arises mainly as a consequence of the non-bonded pushing action of the crossbridges. This same assumption predicts the occurrence of an asymmetric thermoelastic ratio for active muscle with respect to stretching and contraction. The quantitative aspects of the model are satisfactory as it simultaneously reconciles the numerical magnitudes of macroscopic quantities such as isometric tension, maximum contraction velocity, limiting tension sustainable on stretching, isometric heat rate and resting heat rate with molecular parameters such as the filament and crossbridge periodicities, molecular vibrational relaxation rates, recurrence times for the radiationless transitions occurring, etc. This is achieved without any parameter optimization and only a very much smaller number of unknown parameters than the number of observed results accounted for. Many of the entities occurring in the model cycle (vibronic states of crossbridges, ATP, etc.) appear to be in one-to-one correspondence with many of the kinetic entities postulated to account for the biochemical kinetic results obtained for the actomyosin ATPase system in vitro. Finally, the rigor state has to be viewed in a different way from the conventional one; on the basis that the present model states which are part of the contraction cycle but sparsely populated during the latter (and hence are of chemical kinetic but not dynamical importance) are heavily populated during the rigor state. The mechanical properties of the rigor state would then be determined by these molecular states which would be very short-lived during the contraction cycle. If this is correct the rigor state could yield much more information about inaccessible parts of the contraction cycle than is presently supposed. The model leads one to expect a rather different response to quick length step changes in the rigor state from that of the active state, in contrast to current interpretations in terms of a large number of attached crossbridges, unable to detach due to the absence of ATP.

Metallic reflection in a crystalline polymethinium dye and in crystalline TCNQ: Theory of the damping

Metallic reflection occurs in molecular crystals when a stopping band associated with a strong molecular electronic transition emerges. Variations in reflectivity over the band are studied here theoretically for two cases—1,5-bis (dimethylamino)pentamethinium perchlorate (BDP) and tetracyanoquinodimethane (TCNQ). The variations are described by a frequency dependent damping term Γ (ω) in the expression for the polarizability. For the case of one molecule per unit cell (BDP), the observed reflection band shape can be matched using a theoretical expression iΓ (ω) = (γ2/N) Σk 1/(ω−ωk−Δ), where γ is a molecular vibrational relaxation constant and Δ is the frequency of a single active vibration. The variation of ωk with k is approximated by the long-wave method. For the case of two molecules per unit cell (TCNQ) a more complicated expression is obtained which predicts a reflection spectrum richer in structure than in the case of one molecule per unit cell. The number and location of features in the theoretical spectrum match those in the observed spectrum reasonably well.

Effects of reorientational and vibrational relaxation on linewidth of resonance Raman spectral lines

The theory of line-shape analysis of Raman bands in terms of a molecular reorientation correlation function and vibrational relaxation is extended to be applicable to resonant Raman spectroscopy (RRS) where the Raman tensor may be unsymmetric. A line shape analysis of the spectral power density is presented in terms of the three Raman tensor invariants for each of the four measurable polarizations of incident and scattered light: parallel, perpendicular, co-rotating and contra-rotating. A specific example of a symmetric top molecule with antisymmetric Raman tensor is treated.

Dynamics of molecular reorientational motion and vibrational relaxation for symmetric top molecules in the liquid phase

Detailed studies of the molecular relaxation processes in pure liquid t-butyl chloride (TBC) and t-butyl bromide (TBB) and in solutions in carbon tetrachloride and in n-hexane have been made using several experimental techniques. Single particle reorientational motions perpendicular to the symmetry axis were studied using Raman scattering and a comparison of these results with those obtained from depolarized Rayleigh scattering allowed an evaluation of the importance of correlations in orientation between pairs of molecules in the two systems, also, collision induced scattering was not found to be significant. Additional cross comparisons of related data obtained using infrared absorption and dipolar absorption were made. In all cases, the original experimental data were subjected to Fourier transform analyses so that the time evolution of the resulting correlation functions could be studied. In general, at short times the reorientational motions are inertial, but at long times exponential decay of the correlation functions is observed. The mechanism of vibrational relaxation in TBC and TBB was also studied by analysis of the correlation functions corresponding to the isotropic Raman scattering in the pure liquids and in solution. In addition, an efficient computational model for the theoretical calculation of any orientational vectorial correlation function has been developed. The theoretical correlation functions could be compared directly with those determined experimentally.

Dynamics of molecular reorientational motion and vibrational relaxation in liquids. Chloroform

Vibrational and rotational (dipole and second−order tensor) correlation functions were obtained by Fourier inversion of infrared and Raman vibrational band contours of the three ∥ and one ⊥ fundamental of liquid CHCl3, CDCl3, and isotopically pure CH35Cl3. All correlation functions are nonexponential at short times and approximately exponential for long times. The symmetry axis of the molecule reorients by ’’free’’ jumps of about 1/3 rad, turning through a root−mean−square angle of 1 radian within 2psec by about 13 orientational jumps. Computer simulations show that J diffusion is too fast beyond 1 psec and that M diffusion fits the data up to 4 psec (τJ = 0.12 psec); thereafter, M diffusion is too slow. The Raman rotational correlation time is approximately equal to the NMR quadrupolar correlation time; the infrared rotational correlation time is only 0.75 of a corresponding dielectric relaxation time. Vibrational relaxation in the symmetric near−infrared carbon−hydrogen stretch is of the same order of importance as rotational relaxation; however, the dynamics of the vibrational relaxation of this mode do not support the presence of ’’hydrogen bonding’’ in the neat liquid. In the symmetric far−infrared carbon−chlorine deformation mode, vibrational relaxation is of considerably lesser significance than rotational relaxation throughout the whole time domain, whereas the rate of vibrational relaxation of the symmetric midinfrared carbon−chlorine stretch is intermediate to those of the other two symmetric fundamentals. None of these modes obeys vibrational energy dissipation or resonance vibrational energy transfer mechanism induced by dipole−dipole interaction. The ratios of the derived polarizability tensor elements, which are required to evaluate the rotational correlation function of the degenerate mode (carbon−hydrogen deformation), were computed from formulations relating them to the bond polarizabilities: It appears that its Raman and infrared correlation function does not contain the same vibrational correlation function and that the respective contour is determined essentially by nonorientational relaxation processes. An extensive analysis of the experimental errors inherent in our Raman band contour determinations is presented, as well as a critical comparison of our conclusions with previous results in the literature.

Density and temperature effects on the molecular reorientation and vibrational relaxation in liquid methyl iodide

The reorientational correlation function for liquid methyl iodide has been measured by analysis of the Raman 526 cm−1 ν3 (a1) band as a function of pressure up to 2.5 kbar within the temperature range 0 to 90°C. These reorientational correlation functions have been obtained from the anisotropic component of the vibrational Raman scattered light using a method of Fourier deconvolution. Density and viscosity of methyl iodide over the same range of temperatures and pressures have also been determined. In order to obtain information about the effects of density and temperature on the internal C3 rotation of the methyl group the NMR deuteron spin-lattice relaxation times in liquid methyl iodide-d3 have been measured under the same experimental conditions. In addition the vibrational relaxation rates have been determined from the isotropic Raman band shapes. The Raman experiments enable us to calculate the reorientational correlation function describing the reorientational motion of the CH3I molecules about an axis perpendicular to the main symmetry axis for the following cases: (i) constant density ρ-variable temperature; (ii) constant T-variable ρ; and (iii) constant pressure-variable T. Activation energies and activation volumes for the reorientation process are also discussed. All experimental results show unambiguously the large effects of density on molecular motions and the importance of constant density experiments. Assuming a rotational diffusion process the Raman data furnish the rotational diffusion constant D⊥. By using this D⊥ and the experimental NMR deuteron spin-lattice relaxation times in CD3I we calculate the rotational diffusion constant, D∥, characterizing the internal rotation of the methyl group about the symmetry axis. In order to interpret the experimental data we propose that the deuteron field gradient deviates from the C–D bond axis. Both the rotational diffusion model and the Langevin model treatments of the internal rotation indicate very strong inertial effects in the methyl group rotation. As the density changes the rotation of the methyl group about the C3 axis remains largely unaffected. In this study it has also been possible to obtain the vibrational relaxation rate 1/τvib from the isotropic component of the vibrational Raman band shape. The experimental results can be summarized as follows: (i) as ρ increases the relaxation rate increases; (ii) as T increases at constant ρ, 1/τvib remains approximately constant, and (iii) at constant pressure increasing T causes a significant decrease in the vibrational relaxation rate. The experimental data are discussed in terms of a binary collision model as developed by Litovitz and the time between collisions is estimated from the Enskog theory, the cell model, and the J-diffusion model. Based on our earlier results we assume a temperature dependence of the effective hard sphere diameter in order to explain the experimental trends in the vibrational relaxation rate. On the basis of this study one arrives at a conclusion of general validity that any serious experimental attempt to characterize the molecular dynamics in a liquid must include the separation of the effects of density and temperature on the molecular motions.

Effect of vibrational relaxation of molecules on dissociating air characteristics behind a strong shock front

Molecular vibrational relaxation has a considerable effect on the dissociation rate in a gas consisting of molecules of a single type [1]. In gas mixtures such as air, vibrational relaxation also affects the other reaction rates, which may be important in solving several problems of hypersonic aerodynamics. This is due to the fact that in air at temperatures above 5000° the vibrational excitation of nitrogen molecules and the dissociation of oxygen molecules proceed almost simultaneously. We study the effect of vibrational relaxation on the conditions behind a strong shock front.

Molecular collision cross sections and vibrational relaxation in carbon dioxide

Molecular collision cross sections and vibrational relaxation in carbon dioxide

Molecular collision cross sections and vibrational relaxation in carbon monoxide

A method for the calculation of cross sections for processes involving the exchange of vibrational and translational energy on collision of molecules with internally structureless particles is described. On the assumption that the excited molecule is a simple harmonic vibrator and that the molecular interaction potential may be represented by a spherically symmetric Lennard-Jones function, the partial wave scattering equations have been obtained in a form suitable for direct numerical integration. Coupling between any selected number of energetically accessible molecular vibrational states can be retained in this calculation. The collision cross sections are then derived in terms of the asymptotic phases and the amplitudes of the numerical solutions.