Coherence transfer processes in vibrational relaxation of polyatomic molecules in condensed media

The vibrational relaxation of a polyatomic molecule in a condensed host is studied by a consideration of two molecular vibrations. Relaxation processes, intermode coupling terms and vibrational frequency fluctuation contributions are retained. Population decay (T₁), dephasing (T₂), and coherence transfer rates are evaluated through second order in the limit where the host bath dynamics are rapid compared to these molecular timescales. The rates are expressed in terms of temperature and frequency dependent bath correlation functions. For the special case of a three level system (the ground state and ones where one of the two vibrational modes is excited) the important effects of anharmonicity are incorporated. It is shown that certain coherence transfer terms involve zero frequency bath correlation functions, so they should be larger than the high frequency ones which obey modified energy gap laws. A discussion is presented of the types of interactions which may contribute to these coherence transfer processes.     

Improved relations for vibrational relaxation in gases

Explicit expressions are presented for calculating vibration-to-translation (VT) energy conversion probabilities, essential in molecular laser isotope separation. VT conversions in molecular collisions occur by two mechanisms: (1) high-energy impact transfers prevailing at higher temperatures, and (2) Van der Waals-bonding encounters followed by (pre-)dissociations at lower temperatures. While mechanism (1) has been studied for over fifty years culminating in the Schwartz–Slawsky–Herzberg relation, a useful analytic expression for (2) has so far been lacking. An improved dimer formation theory developed by the author together with molecular pre-dissociation physics now provides a VT conversion relation for mechanism (2), which correctly predicts observations.     

Time-dependent quantum theory III. Model for vibrational relaxation in crystals

A one-dimensional model consisting of a “diatomic” spring attached on one side to a rigid wall and on the other side to a linear array of mass-springs is proposed as a model for the vibrational relaxation of small solute molecules in host lattices. A modification allowing a change in the equilibrium internuclear extension of the diatomic spring is also incorporated. The Hamiltonian divides naturally into pure diatomic, pure linear crystal, and the two mixed perturbation terms, one giving rise to stepwise vibrational cascade damping accompanied by phonon emission, and the other process, lattice relaxation, giving rise to phonon emission without any change of the quantum number of the diatomic spring. The cascade damping rate for a diatomic spring with a frequency less than the the maximum frequency of the linear crystal is calculated to second-order, and it is shown that the perturbation series converges in this range. An upper bound to the cascade damping rate for a diatomic spring with a frequency greater (i.e., 4.5 ×) than the cut-off frequency of the linear crystal is determined to be very small, λ ≦ 10⁴ sec ^?;1. The rate for the lattice relaxation process corresponds to a line-width λ = 6 cm ^?1 at ⁰K. An explanation for the thermal quenching of the low-temperature luminescence of SO₂ is based upon induced cascade-phonon emission.     

A study of molecular vibrational relaxation mechanism in condensed phase based upon mixed quantum-classical molecular dynamics. II. Noncollisional mechanism for the relaxation of a polar solute in supercritical water

Mixed quantum-classical molecular dynamics method has been applied to vibrational relaxation of a hydrophilic model NO in supercritical water at various densities along an isotherm above the critical temperature. The relaxation rate was determined based on Fermi's golden rule at each state point and showed an inverse S-shaped curve as a function of bulk density. The hydration number was also calculated as a function of bulk density based on the calculated radial distribution function, which showed a good correlation with the relaxation rate. Change of the survival probability of the solute vibrational state was analyzed as a function of time together with the trajectory of the solvent water and the interaction with it. We will show that the solvent molecule resides near the solute molecule for a while and the solvent contributes to the relaxation by the random-noiselike Coulombic interaction only when it stays near the solute. After the solvent leaves the solute, it shows no contribution to the relaxation. The relaxation mechanism for this system is significantly different from the collisional one found for a nonpolar solute in nonpolar solvent in Paper I. Then, the relaxation rate is determined, on average, by the hydration number or local density of the solvent. Thus, the density dependence of the relaxation rate for the polar solute in supercritical water is apparently similar to that found for the nonpolar solute in nonpolar solvent, although the molecular process is quite different from each other.     

Rotational—vibrational dipole transitions in HD

The transition moments are computed for several lines in the X¹Σ⁺_g state of HD. The results are obtained by taking into account interactions with Σ_u and Π_u states. It is shown that the latter influence appreciably the transition probabilities in the 00 band. The permanent dipole moment is also computed for several vibrational and rotational states.     

Intermolecular vibrational relaxation in liquids

The influence of intermolecular vibrational relaxation on dipole moment correlation functions, as obtained from IR band shapes, is discussed. It is explicitly shown that vibrational relaxation due to intermolecular interactions depends on the reorientational behaviour of the molecules in the liquid.Therefore, an a priori separation of the dipole moment correlation function into independent reorientational and vibrational factors is not generally possible. The implications for various procedures used to “correct” Raman and IR band shapes for vibrational relaxation are discussed.The expression derived for the intermolecular vibrational relaxation is used to calculate theoretically the effect of transition dipole-transition dipole coupling on dipole moment correlation functions.Experimental data obtained from isotopic dilution measurements support the interpretation of the isotopic dilution effect in terms of the transition dipole-transition dipole coupling.     

Rotational and translational relaxation times of quasi-elastic and rigid dumbbells elastically bound to polymer network junctions

The dynamics of a rigid rod located between fixed junctions of a polymer network is studied. Three approaches are used in the solution of this problem. The first is based on the viscoelastic model, where a rigid rod is simulated by an elastic dumbbell with a fixed average length; the second includes solution of equations of motion for projections of the rigid rod using the Lagrangian multipliers under the constraint condition; and the third involves solution of the diffusion equation in the presence of an elastic potential. The second and third approaches allow calculation of orientational relaxation times for rod projections under the action of a strong orienting field. The dependences of the relaxation times of orientational and translational motions of the rod projections on the coordinate axes and the orientational relaxation times of mean-square rod projections on the model parameters (the distances between fixed polymer network junctions, the length of the rigid rod, and the elastic coefficient characterizing the binding between the rod and the network) are found.     

Rotational relaxation in simple chain models

The rotational dynamics of chemically similar systems based on freely jointed and freely rotating chains are studied. The second Legendre polynomial of vectors along chain backbones is used to investigate the rotational dynamics at different length scales. In a previous study, it was demonstrated that the additional bond-angle constraint in the freely rotating case noticeably perturbs the character of the translational relaxation away from that of the freely jointed system. Here, it is shown that differences are also apparent in the two systems' rotational dynamics. The relaxation of the end-to-end vector is found to display a long time, single-exponential tail and a stretched exponential region at intermediate times. The stretching exponents beta are found to be 0.75+/-0.02 for the freely jointed case and 0.68+/-0.02 for the freely rotating case. For both system types, time-packing-fraction superposition is seen to hold on the end-to-end length scale. In addition, for both systems, the rotational relaxation times are shown to be proportional to the translational relaxation times, demonstrating that the Debye-Stokes-Einstein law holds. The second Legendre polynomial of the bond vector is used to probe relaxation behavior at short length scales. For the freely rotating case, the end-to-end relaxation times scale differently than the bond relaxation times, implying that the behavior is non-Stokes-Einstein, and that time-packing-fraction superposition does not hold across length scales for this system. For the freely jointed case, end-to-end relaxation times do scale with bond relaxation times, and both Stokes-Einstein and time-packing-fraction-across-length-scales superposition are obeyed.     

Rotational quantum changes accompanying vibrational relaxation in the 1Au state of glyoxal

Changes of the rotational quantum state occurring simultaneously (in one single collision step) with the deactivation of the torsional vibration ν₇ have been measured in glyoxal ¹A_u. Selective excitation of rotational levels in the vibronic level 7¹ was accomplished by means of a tunable dye laser. A near thermal distribution of rotational levels in the O⁰ state was attained as the result of a single collision. Intramolecular vibration-to-rotation transfer was not found. Similarly, a nearly thermalized distribution of rotational levels in the O⁰ state has been observed as the result of one single collision after selective excitation of a restricted number of rotational levels in the vibronic 8¹ state in the presence of different collision partners.     

On vibrational relaxation in liquid trimethylchlorosilane

Vibrational correlation functions and related spectral data were determined in several ways for the ν_s(SiCl) and sym-ν_s(Si(CH₃)₃) vibrations of liquid trimethylchlorosilane, from Raman bandshape analysis. The influence of isotopic composition and Fermi resonances on th accuracy of obtained correlation functions is discussed.     

Rotational and vibrational dynamics of ethylene in helium nanodroplets

Rotationally resolved infrared spectra are reported for the asymmetric C-H stretching fundamental bands of C(2)H(4) in helium nanodroplets, as well as two weak combination bands. The J=2 rotor levels are strongly shifted from the energies estimated from a rigid rotor calculation and can be accounted for with two centrifugal distortion constants. The excited states of the three bands with B(3u) symmetry are strongly coupled in the gas phase and exhibit lifetimes >100 ps in helium, with the upper member of the polyad exhibiting the shortest lifetime. In contrast, the nu(9) band (B(2u) symmetry) exhibits very broad, homogeneously broadened line profiles (full width at half maximum approximately 0.5 cm(-1)) corresponding to an excited state lifetime of approximately 10 ps. This short lifetime is presumed to be due to an efficient, solvent mediated vibration-to-vibration relaxation process. In addition, the absence of transitions to the 2(21) and 2(20) rotor levels in the nu(9) band suggests they form rotational resonances with the elementary modes of helium, resulting in very short excited state lifetimes of less than 2 ps.     

Reorientational and vibrational relaxation in liquid trichloracetonitrile

The first- and second-order reorientational correlation functions were determined from i.r. and Raman bandshapes of ν_s(CN)in liquid trichloracetonitrile and discussed in terms of the J-diffusion model. A consistent fit for G_1r(t) and G_2r(t) was possible for short times only (0–1.5 ps). The vibrational correlation functions, determined from Raman studies of the ν_s(CN) and ν_s(CC) bandshapes, are discussed in terms of recent theories of vibrational dephasing.     

Rotational mode participation in long-distance vibrational energy transfer in solids

It is shown that nonresonant vibrational energy transfer between molecules in solids can be greatly enhanced by participation of the rotational mode. This mechanism is predicted to dominate over multiphonon-assisted energy transfer for systems with a large mismatch (?10² cm^?1 between the vibrational energy spacings of the donor and the acceptor. Calculations based on this mechanism on the processes NH,ND(³Π,υ = 1) → ¹²CO, ¹³CO (in solid Ar) yield results in excellent agreement with the experimental isotope effects.     

A poisson equation for vibrational potentials of diatomic molecules

A Poisson equation for nuclear motions in diatomic molecules is derived. The working formula is whereV _α ² is the Laplacian operator for the position of nucleusα, W is the Born-Oppenheimer molecular energy, is the atomic number ofα, and ? _β (α) is the electronic charge density evaluated atα due to orbitals centered onβ. Harmonic, anharmonic and quartic equilibrium force constants are calculated using Hartree-Fock molecular and atomic electronic charge densities, for a number of first and second row diatomic molecules. A charge-model field gradient formula for harmonic force constants $$k_e = {3 \mathord{\left/ {\vphantom {3 {R_e^3 ,}}} \right. \kern-\nulldelimiterspace} {R_e^3 ,}}$$ wherek _e is the force constant andR _e the equilibrium internuclear distance, which offers general improvement over a similar formula due to Bratoz, is presented.     

Temperature dependence of vibrational relaxation in carbon tetrachloride

The temperature dependence of vibrational relaxation in carbon tetrachloride has been investigated from near the melting point to near the boiling point. The method of spontaneous Brillouin scattering has been used to determine the hypersonic frequencies and velocities as functions of temperature. The dispersion in the velocities are then compared with theoretical predictions in order to investigate the character of the relaxation.     

Light-scattering study of vibrational relaxation in liquid xylenes

Brillouin spectra obtained in dynamic light-scattering experiments are reported for the three isomeric xylenes (ortho-, meta-, and paradimethylbenzenes) between 288 and 363 K. Limiting sound velocities and relaxation times, as obtained from the polarized spectra using the theory developed by Mountain [J. Res. Natl. Bur. Stand. 70A, 207 (1966)], reveal the existence of a relaxation process. Our results suggest that the relaxation process in liquid xylenes has a purely vibrational nature. Vibrational-translational energy exchanges in xylenes are analyzed in terms of available molecular models and compared to those previously obtained for toluene and benzene. The results presented here confirm the important role played by the molecular geometry in the vibrational relaxation process, as the relative arrangement of the methyl groups has significant effect in determining the relaxing vibrational modes.