The role of thermal fluctuations in the motion of a free body

The motion of a rigid body is described in Classical Mechanics with the venerable Euler's equations which are based on the assumption that the relative distances among the constituent particles are fixed in time. Real bodies, however, cannot satisfy this property, as a consequence of thermal fluctuations. We generalize Euler's equations for a free body in order to describe dissipative and thermal fluctuation effects in a thermodynamically consistent way. The origin of these effects is internal, i.e. not due to an external thermal bath. The stochastic differential equations governing the orientation and central moments of the body are derived from first principles through the theory of coarse-graining. Within this theory, Euler's equations emerge as the reversible part of the dynamics. For the irreversible part, we identify two distinct dissipative mechanisms; one associated with diffusion of the orientation, whose origin lies in the difference between the spin velocity and the angular velocity, and one associated with the damping of dilations, i.e. inelasticity. We show that a deformable body with zero angular momentum will explore uniformly, through thermal fluctuations, all possible orientations. When the body spins, the equations describe the evolution towards the alignment of the body's major principal axis with the angular momentum vector. In this alignment process, the body increases its temperature. We demonstrate that the origin of the alignment process is not inelasticity but rather orientational diffusion. The theory also predicts the equilibrium shape of a spinning body.Comment: 24 pages, 1 figure with Supplemental Materia

Linewidths and shifts of very low temperature CO in He: A challenge for theory or experiment?

The pressure broadening and shifting coefficients for pure rotational transitions of CO in a He bath gas at very low temperatures are calculated from the best available potential energy surfaces, and compared with very recent measurements by M. M. Beaky, T. M. Goyette, and F. C. De Lucia ͓J. Chem. Phys. 105, 3994 ͑1996͔͒. The results obtained for two recent empirical potentials determined from fits to Van der Waals spectra, and for a recent high quality purely ab initio surface, are consistent with one another. The best of the spectroscopic potentials also yields good agreement with high temperature virial coefficients and transport properties. Predictions from all three of these potentials agree with linebroadening and shifting measurements at temperatures above ϳ20 K, but are in substantial disagreement with the measurements at temperatures below 4 K. At present, the source of this discrepancy is not known

COLLISIONAL LINE BROADENING CALCULATIONS FOR HF-He

Author Institution: Guelph-Waterloo Centre for Graduate Work in Chemistry, University of WaterlooA study of collisional line broadening calculations using a variety of theoretical methods on an atom-diatom system has been performed. The full close coupled quantai calculation is compared with the centrifugal sudden approximation (CSA), the ``corrected'' centrifugal sudden approximation (CCSA), the infinite order sudden approximation (IOSA) and a semiclassical trajectory method for the HF-He interaction. The accuracy and relative cost of each method will be discussed

A semiclassical approach to intense-field above-threshold dissociation in the long wavelength limit. II. Conservation principles and coherence in surface hopping

This paper is a companion to our recently published semiclassical formalism for treating time-dependent Hamiltonians [J. Chem. Phys. 105, 4094 (1996)], which was applied to study the dissociation of diatomic ions in intense laser fields. Here two fundamental issues concerning this formalism are discussed in depth: conservation principles and coherence. For time-dependent Hamiltonians, the conservation principle to apply during a trajectory hop depends upon the physical origin of the electronic transition, with total energy conservation and nuclear momentum conservation representing the two limiting cases. It is shown that applying an inappropriate scheme leads to unphysical features in the kinetic energy of the dissociation products. A method is introduced that smoothly bridges the two limiting cases and applies the physically justified conservation scheme at all times. It is also shown that the semiclassical formalism can predict erroneous results if the electronic amplitudes for well-separated hops are added coherently. This is a fundamental problem with the formalism which leads to unphysical results if left unattended. Alternative schemes are introduced for dealing with this problem and their accuracies are assessed. Generalization of the well-known Landau-Zener formula to the time-dependent Hamiltonian case is derived, which allows one to significantly decrease the computational overhead involved with the numerical implementation of the semiclassical method. Finally, we show that in strong-field molecular dissociation a trajectory can \u201csurf\u201d a moving avoided crossing. In this case the hopping probability is a sensitive function of the interference between two closely spaced avoided crossing regions.Peer reviewed: YesNRC publication: Ye

A semiclassical approach to intense-field above-threshold dissociation in the long wavelength limit. II. Conservation principles and coherence in surface hopping

This paper is a companion to our recently published semiclassical formalism for treating time-dependent Hamiltonians [J. Chem. Phys. 105, 4094 (1996)], which was applied to study the dissociation of diatomic ions in intense laser fields. Here two fundamental issues concerning this formalism are discussed in depth: conservation principles and coherence. For time-dependent Hamiltonians, the conservation principle to apply during a trajectory hop depends upon the physical origin of the electronic transition, with total energy conservation and nuclear momentum conservation representing the two limiting cases. It is shown that applying an inappropriate scheme leads to unphysical features in the kinetic energy of the dissociation products. A method is introduced that smoothly bridges the two limiting cases and applies the physically justified conservation scheme at all times. It is also shown that the semiclassical formalism can predict erroneous results if the electronic amplitudes for well-separated hops are added coherently. This is a fundamental problem with the formalism which leads to unphysical results if left unattended. Alternative schemes are introduced for dealing with this problem and their accuracies are assessed. Generalization of the well-known Landau-Zener formula to the time-dependent Hamiltonian case is derived, which allows one to significantly decrease the computational overhead involved with the numerical implementation of the semiclassical method. Finally, we show that in strong-field molecular dissociation a trajectory can \u201csurf\u201d a moving avoided crossing. In this case the hopping probability is a sensitive function of the interference between two closely spaced avoided crossing regions.Peer reviewed: YesNRC publication: Ye

Inferring Parameters for an Elementary Step Model of DNA Structure Kinetics with Locally Context-Dependent Arrhenius Rates

Models of nucleic acid thermal stability are calibrated to a wide range of experimental observations, and typically predict equilibrium probabilities of nucleic acid secondary structures with reasonable accuracy. By comparison, a similar calibration and evaluation of nucleic acid kinetic models to a broad range of measurements has not been attempted so far. We introduce an Arrhenius model of interacting nucleic acid kinetics that relates the activation energy of a state transition with the immediate local environment of the affected base pair. Our model can be used in stochastic simulations to estimate kinetic properties and is consistent with existing thermodynamic models. We infer parameters for our model using an ensemble Markov chain Monte Carlo (MCMC) approach on a training dataset with 320 kinetic measurements of hairpin closing and opening, helix association and dissociation, bubble closing and toehold-mediated strand exchange. Our new model surpasses the performance of the previously established Metropolis model both on the training set and on a testing set of size 56 composed of toehold-mediated 3-way strand displacement with mismatches and hairpin opening and closing rates: reaction rates are predicted to within a factor of three for 93.4% and 78.5% of reactions for the training and testing sets, respectively