Collisional Depolarization of the Luminescence of Asymmetric Top Molecules in the Gas Phase

To describe the collisional depolarization of the luminescence of asymmetric top polyatomic molecules, integral and integrodifferential forms of master equations, in which the effect of collisions is determined by the conditional probabilities of an instantaneous error of rotational phase variables, have been obtained. A symmetry analysis of the master equations has been performed, and it has been shown that in the general case the evolution of optically induced anisotropy is given by five independent relaxation components. The kinetic equations derived are initial equations for specific calculations of the anisotropy relaxation in various collisional models. They make it possible to study the influence of the angular momentum transfer efficiency on the orientational relaxation of anisotropy in a wide range of buffer medium densities: from free rotation to binary collisions in the gas and then to rotational diffusion.     

Influence of steric hindrance on luminescence anisotropy of resonance dipole–dipole transfer of electronic excitation energy

An orientation factor is calculated and the effect of steric hindrance in the donor and acceptor molecules is found for the efficiency of resonance dipole–dipole transfer of electronic energy. General expressions for the acceptor luminescence anisotropy under such conditions in isotropic media (gases and liquids) are obtained taking into account orientational relaxation in ensembles of donors and acceptors. It is shown that the luminescence anisotropy of an acceptor with significant steric hindrance can increase by more than an order of magnitude compared with the case with no hindrance.     

Collisional Relaxation of the Optically Induced Dichroism of Complex Molecules in a Gas Phase

The transformation of molecular rotation with rise of the buffer gas pressure is studied. The evolution of the optically induced anisotropy is measured for perylene and 1,4-di[2-(5-phenyloxazolyl)]benzene (POPOP) in pentane at high pressures. The orientational relaxation is shown to be governed not only by the buffer gas pressure (which determines the collision frequency), but also by the efficiency of the collisional angular momentum transfer. The orientational relaxation of perylene falls in between the predictions of the strong (J diffusion) and weak (Fokker–Planck equation) collision models. The situation is found to be closer to the latter, and four collisions with pentane are approximately necessary for randomization of the perylene angular momentum. The orientational relaxation of POPOP in the vicinity of the critical liquid–gas point is demonstrated to be almost independent of the pentane pressure in the range 45–130 atm, which is a manifestation of rotational diffusion. Generally, it was found that perylene rotates more freely than POPOPdeed, under the pentane pressure of the order of 50 atm, the rotation of POPOP is highly damped and is described by the diffusion equation. On the other hand, the orientational relaxation of perylene under pentane pressures of about 100 atm exhibits characteristic features arising due to inertial effects.     

Dynamics of optically induced anisotropy in an ensemble of asymmetric top molecules in the gas phase

A complex theoretical and experimental investigation of the evolution of optically induced anisotropy in an ensemble of free asymmetric tops under collisionless conditions is performed. The dynamics of the orientational correlation functions is studied and the results of femtosecond measurements of the relaxation of the anisotropy of perylene fluorescence in the gas phase are reported. The results obtained are interpreted in terms of the theory developed. It is shown that, in contrast to steady-state anisotropy, the time kinetics of optically induced anisotropy yields more complete and typical data on the dynamics of vector correlations in an ensemble of molecules.     

A CNDO/2 calculation on the radical formed on electron irradiation of mesitylene

Mori's method is applied to the calculation of the collective molecular orientation correlation functions which are of interest in light scattering and dielectric relaxation. The case of liquids composed of asymmetric top molecules is discussed. For the collective variables, the usual ‘rotational diffusion’ assumptions do not yield the single-particle rotational diffusion results unless there exists no orientational order in the medium. This point is discussed with regard to the results of some recent light scattering and dielectric relaxation experiments.     

Orientational relaxation of pheophorbide-a molecules in the ground and in the first excited state measured by transient dichroism spectroscopy

We report on transient dichroism spectroscopy carried out on pheophorbide-a in ethanol to measure the response time of the pump-beam induced anisotropy after selective excitation at high excitation levels. From the observed time behaviors of induced absorption, transient amplification, and of the bleaching signal, the orientational relaxation times of pheophorbide-a in the first excited singlet state and in the ground state were obtained separately to be 370 and 250 ps, respectively. It is found that pheophorbide-a behaves like a spherical rotor in the first excited state, while in the ground state randomization of molecules is dominated by the rotation around its quasi-symmetry axis. Because of rotation free measurement of ordinary transient absorption spectra fail in the case of ground state depletion, the observed orientational relaxation time of the ground state have to be taken into account to fit the bleaching kinetics obtained from transient absorption spectra very well to determine the intersystem crossing yield of pheophorbide-a to be 0.46.     

Efficiency of the structure analysis of complex molecules in the gas phase by their optical rotation

It was shown in the dipole approximation of optical rotation that in the general case only in orientationally anisotropic vapors is the rotational force dependent on the intramolecular orientation of both the electric and magnetic dipole moments. Expressions relating the optical rotational force to the intramolecular orientation of these moments, the orientational distribution in an anisotropic ensemble, and the configuration of a measurement have been obtained. Calculated dependences of the rotational force on the intramolecular orientation of the magnetic moment at a fixed electric moment and “rotational force excitation spectra” obtained for different types of rigid asymmetric top molecules and rotational contours are presented. It is proposed to measure the intramolecular orientation of the electric and magnetic dipole moments with the use of the rotational force normalized to that detected in the case of observation at a “magic” angle to the direction of the exciting light electric vector. Institute of Molecular and Atomic Physics of the Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 6, pp. 843–849, November–December, 1998.     

Rotational diffusion and orientation relaxation of rodlike molecules in a biaxial liquid crystal phase

The longitudinal relaxation time and the complex dielectric polarizability of rod-like molecules with dipole moment parallel to the long axis in a biaxial nematic liquid crystal are calculated using as model the rotational Brownian motion in a mean field potential so reducing the problem to a solution of a set of linear differential-recurrence relations for statistical moments (the appropriate equilibrium orientational correlation functions). The solution of this set is obtained by matrix continued fractions. Moreover, simple analytic equations (based on the exponential separation of the time scales of the intrawell and overbarrier (interwell) relaxation processes), allowing one to understand the qualitative behavior of the system and accurately predicting the longitudinal complex polarizability for wide range of the barrier height and anisotropy parameters, are proposed.     

Analytical approach to the study of molecular rotation in liquids

The rotational thermal motion of molecules is investigated by the combined use of the stochastic rotation operator, the Euler-Langevin equations of Brownian motion and the Krylov-Bogoliubov method of solving nonlinear differential equations. The results are applied to dielectric relaxation by orientational polarization and to nuclear magnetic relaxation by a variety of mechanisms.     

Diffusion of nanoparticles in a rarefied gas

It is suggested to describe the diffusion of nanoparticles in rarefied gases in terms of the kinetic theory. For this purpose, the potential of interaction between a carrier gas molecule and a dispersed particle is constructed by summing the interactions of the given gas molecule with all atoms (molecules) of the dispersed particle. With this potential, a formula for the diffusion coefficient of the dispersed nanoparticle is derived. The dependence of the diffusion coefficient on the radius and temperature is studied. Analytical results are compared with experimental data. The well-known experimental Cunningham-Millikan correlation is shown to apply only in the range of near-room temperatures, for which the parameters of this correlation were determined.     

Anisotropy of ensembles of free polyatomic photoisomers

In order to describe the polarization response of an ensemble of molecules undergoing structural transformations (photoisomerization) under collisionless conditions, we have calculated the orientational correlation functions. We assume that changes in molecular structure can be considered as instantaneous on the molecular rotation scale. We have obtained general expressions for the anisotropy when the original molecule and the photoisomer are asymmetric tops. We have performed anisotropy calculations for steady-state experimental conditions and a number of limiting situations, when the characteristic times of the photoreaction are much shorter or much longer than the molecular reorientation times and when the original molecule and the photoisomer are planar tops. We have shown that detecting the polarization response allows us to estimate the characteristic times of the photoreaction and to determine the intramolecular orientation of the transition dipole moments for transitions with absorption and emission of light. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 73, No. 5, pp. 582–587, September–October, 2006.     

Maximum entropy principle for rarefied polyatomic gases

The aim of this paper is to show that the procedure of maximum entropy principle for the closure of the moments equations for rarefied monatomic gases can be extended also to polyatomic gases. The main difference with respect to the usual procedure is the existence of two hierarchies of macroscopic equations for moments of suitable distribution function, in which the internal energy of a molecule is taken into account. The field equations for 14 moments of the distribution function, which include dynamic pressure, are derived. The entropy and the entropy flux are shown to be a generalization of the ones for classical Grad’s distribution. The results are in perfect agreement with the recent macroscopic approach of extended thermodynamics for real gases.     

Polarization-luminescence studies of the structure and molecular dynamics of smectic and nematic mesophases

The liquid crystal 50B7A in the smectic A and nematic phases was studied by the method of polarization luminescence. The order parameters P₂ and P₄ were determined from the experimental values of the luminescence spectrum both neglecting and taking into account relaxation processes in the liquid crystal. The orientational distribution function of the molecules in the ground and excited states are constructed. The orientational relaxation time (10^–9 sec for the nematic and smectic A phases) is calculated. The results obtained are compared with calculation of the rotational relaxation time determined from the coefficient of diffusion for the related compound EBBA.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 8, pp. 39–43, August, 1987.     

Relaxation contribution to shear moduli of the low-temperature phase of solid C60

The relaxation contribution of the molecular reorientation in an elastic field of an acoustic wave to the effective shear moduli is calculated in the framework of the phenomenological two-level model of orientational states in the low-temperature phase of solid C₆₀. The polarity of the rotation axis of C₆₀ molecules and the possible existence of orientational domains in the structure of the low-temperature phase are taken into consideration. The estimates obtained are compared with the available experimental data.     

Higher-order quadrature-based moment methods for kinetic equations

Kinetic equations containing terms for spatial transport, body forces, and particle–particle collisions occur in many applications (e.g., rarefied gases, dilute granular gases, fluid-particle flows). The direct numerical solution of the kinetic equation is usually intractable due to the large number of independent variables. A useful alternative is to reformulate the problem in terms of the moments of the velocity distribution function. Closure of the moment equations is challenging for flows sufficiently far away from the Maxwellian limit. In previous work, a quadrature-based third-order moment closure was derived for approximating solutions to the kinetic equation for arbitrary Knudsen number. A key component of quadrature-based closures is the moment-inversion algorithm used to find the non-negative weights and velocity abscissas. Here, a robust inversion procedure is proposed for three-component velocity moments up to ninth order. By reconstructing the velocity distribution function, the spatial fluxes in the moment equations are treated using a kinetic-based finite-volume solver. Because the quadrature-based moment method employs the moment transport equations directly instead of a discretized form of the kinetic equation, the mass, momentum and energy are conserved for arbitrary Knudsen and Mach numbers. The computational algorithm is tested for the Riemann shock problem and, for increasing Knudsen numbers (i.e. larger deviations from the Maxwellian limit), the accuracy of the moment closure is shown to be determined by the discrete representation of the spatial fluxes.     

Effect of molecular structure nonrigidity on anisotropy of dipole absorption cross section

The influence of the nonrigidity of free complex asymmetric top molecules on the anisotropy of the absorption cross section over various rotational configurations has been studied under conditions where the total angular momentum is conserved. It is shown that the nonrigidity-induced cross section anisotropy is maximal for the optical transition with the dipole moment collinear to the axis of the molecule’s mean moment of inertia and rapidly decreases with the rise of the intramolecular flexibility. For all types of tops, disturbances from internal motions are stronger in the region where the principal axes of inertia are collinear with the total rotational angular momentum.     

Vibration-internal rotation-rotation Hamiltonian of an asymmetric top molecule with C3v internal rotor

An expression for the kinetic energy part of the vibration-torsion-rotation Hamiltonian of an asymmetric top molecule containing a C_3v internal rotor has been derived. The terms for various interactions in the molecule, viz. Coriolis interaction between rotation (both overall and internal rotation) and vibration, centrifugal distortion and anharmonicity of molecular vibrations induced by the internal, and overall rotation of the molecule, have been formulated. For a planar molecule with C_s symmetry we have obtained the vibrationally averaged rotation-internal rotation Hamiltonian. Diagonalization of this Hamiltonian for a particular vibrational state will yield the rotation-internal rotation energy levels and hence the transition frequencies. These data will be useful for analysis of high-resolution infrared spectra obtained by laser or Fourier transform spectroscopy of nonrigid molecules with internal rotor. We also present a set of quartic centrifugal distortion coefficients associated with rotation and internal rotation. These data will be helpful for evaluation of vibrational potential constants of the orthorhombic asymmetric top molecules.     

Luminescence quenching kinetics upon diffusion-accelerated dipole-dipole energy transfer for a realistic condensed-matter model

The hard-sphere model is considered as a more realistic condensed-matter model. In this model, the radial distribution function of molecules in a medium, used for calculations of luminescence decay kinetics, takes into account the short-range order in fluids and has the shape of damped oscillations. It is assumed that the motion of donor and acceptor molecules in a solution for the lifetime of the excited state of the donor is described by the diffusion equation, while the luminescence quenching occurs due to the long-range dipole-dipole energy transfer. It is shown that, if diffusion coefficients are small, the kinetics determined in this study hardly differs at all from the traditional kinetics. At intermediate and large diffusion coefficients, this difference becomes significant and should be taken into account in estimating the Förster energy transfer radius and diffusion coefficients from experimental luminescence decay curves.     

Rapidly progressing photophysical and photochemical relaxation processes in complex organic molecules

Using methods of high-speed kinetic laser spectroscopy, we investigated the dynamics and mechanisms of rapidly progressing relaxation processes in multiatomic molecules. We separated intra- and intermolecular channels of relaxation of the vibrational energy of excitation by the rate of transformation of nonstationary absorption spectra in a picosecond range of times. The role of highly excited electronic states in the process of electronic-vibrational relaxation in molecules of the class of phenazines was ascertained. Applying femtosecond light pulses in a real time scale, we recorded the dynamics of the decay of optically induced anisotropy in rarefied vapors of organic compounds. Several mechanisms of transfer of a hydrogen atom in the process of formation of free radicals in photoreduction of ketones were established. The dynamics of formation of inter- and intramolecular exciplexes in binary gas-phase systems was investigated. We determined the mechanisms of intramolecular dissociation of a C–O chemical bond in spiropyrans and xanthene dyes. Photodissociation of S–S bonds in molecules of disulfides was studied. The possibility of the existence of states with intramolecular charge transport with a twisted configuration for organic free radicals is shown. To whom correspondence should be addressed. Institute of Molecular and Atomic Physics of the National Academy of Sciences of Belarus, 70, F. Skorina Ave., Minsk, 220072, Belarus. Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 65, No. 5, pp. 635–661, September–October, 1998.