Absolute Entropy and Energy of Carbon Dioxide Using the Two-Phase Thermodynamic Model

The two-phase thermodynamic (2PT) model is used to determine the absolute entropy and energy of carbon dioxide over a wide range of conditions from molecular dynamics trajectories. The 2PT method determines the thermodynamic properties by applying the proper statistical mechanical partition function to the normal modes of a fluid. The vibrational density of state (DoS), obtained from the Fourier transform of the velocity autocorrelation function, converges quickly, allowing the free energy, entropy, and other thermodynamic properties to be determined from short 20-ps MD trajectories. The anharmonic effects in the vibrations are accounted for by the broadening of the normal modes into bands from sampling the velocities over the trajectory. The low frequency diffusive modes, which lead to finite DoS at zero frequency, are accounted for by considering the DoS as a superposition of gas-phase and solid-phase components (two phases). The analytical decomposition of the DoS allows for an evaluation of properties contributed by different types of molecular motions. We show that this 2PT analysis leads to accurate predictions of entropy and energy of CO_2 over a wide range of conditions (from the triple point to the critical point of both the vapor and the liquid phases along the saturation line). This allows the equation of state of CO_2 to be determined, which is limited only by the accuracy of the force field. We also validated that the 2PT entropy agrees with that determined from thermodynamic integration, but 2PT requires only a fraction of the time. A complication for CO_2 is that its equilibrium configuration is linear, which would have only two rotational modes, but during the dynamics it is never exactly linear, so that there is a third mode from rotational about the axis. In this work, we show how to treat such linear molecules in the 2PT framework

Absolute evaporation rates of non-rotating neutral PAH clusters

Clusters of polycyclic aromatic hydrocarbons (PAHs) have been proposed as candidates for evaporating very small grains, which are thought to be precursors of free-flying PAHs. Evaporation rates have been calculated so far only for species containing up to a few 100 C atoms, whereas interstellar PAH clusters could contain up to ~1000 C atoms. We present a method that generalises the calculation of the statistical evaporation rate of large PAH clusters and provides rates for species containing up to ~1000 C-atoms. The evaporation of non-rotating neutral homo-molecular PAH clusters containing up to 12 molecules from a family of highly symmetric compact PAHs is studied. Statistical calculations were performed and completed with molecular dynamics simulations at high internal energies to provide absolute values for the evaporation rate and distributions of kinetic energy released. The calculations used explicit atom-atom Lennard-Jones potentials in the rigid molecule approximation. A new method is proposed to take both inter- and intra-molecular vibrations into account. Without any parameter adjustment, the calculated evaporation rates agree well with available experimental data. We find that the non-rotation assumption has a limited impact on the evaporation rates. The photostability of PAH clusters increases dramatically with the size of molecules in the clusters, and to a lesser extent with the number of molecules in the clusters. For values of the UV radiation field that are typical of the regions where evaporating very small grains are observed, the smallest clusters in this study (~50 C-atoms) are found to be quickly photo-evaporated, whereas the largest clusters (~1000 C-atoms) are photostable. Our results support the idea that large PAH clusters are good candidates for evaporating very small grains.Comment: 13 pages, 10 figure

Gyration-radius dynamics in structural transitions of atomic clusters

This paper is concerned with the structural transition dynamics of the six-atom Morse cluster with zero total angular momentum, which serves as an illustrative example of the general reaction dynamics of isolated polyatomic molecules. It develops a methodology that highlights the interplay between the effects of the potential energy topography and those of the intrinsic geometry of the molecular internal space. The method focuses on the dynamics of three coarse variables, the molecular gyration radii. By using the framework of geometric mechanics and hyperspherical coordinates, the internal motions of a molecule are described in terms of these three gyration radii and hyperangular modes. The gyration radii serve as slow collective variables, while the remaining hyperangular modes serve as rapidly oscillating “bath” modes. Internal equations of motion reveal that the gyration radii are subject to two different kinds of forces: One is the ordinary force that originates from the potential energy function of the system, while the other is an internal centrifugal force. The latter originates from the dynamical coupling of the gyration radii with the hyperangular modes. The effects of these two forces often counteract each other: The potential force generally works to keep the internal mass distribution of the system compact and symmetric, while the internal centrifugal force works to inflate and elongate it. Averaged fields of these two forces are calculated numerically along a reaction path for the structural transition of the molecule in the three-dimensional space of gyration radii. By integrating the sum of these two force fields along the reaction path, an effective energy curve is deduced, which quantifies the gross work necessary for the system to change its mass distribution along the reaction path. This effective energy curve elucidates the energy-dependent switching of the structural preference between symmetric and asymmetric conformations. The present methodology should be of wide use for the systematic reduction of dimensionality as well as for the identification of kinematic barriers associated with the rearrangement of mass distribution in a variety of molecular reaction dynamics in vacuum

Molecular dynamics simulation of the fragile glass former ortho-terphenyl: a flexible molecule model

We present a realistic model of the fragile glass former orthoterphenyl and the results of extensive molecular dynamics simulations in which we investigated its basic static and dynamic properties. In this model the internal molecular interactions between the three rigid phenyl rings are described by a set of force constants, including harmonic and anharmonic terms; the interactions among different molecules are described by Lennard-Jones site-site potentials. Self-diffusion properties are discussed in detail together with the temperature and momentum dependencies of the self-intermediate scattering function. The simulation data are compared with existing experimental results and with the main predictions of the Mode Coupling Theory.Comment: 20 pages and 28 postscript figure

Importance Sampling in Rigid Body Diffusion Monte Carlo

We present an algorithm for rigid body diffusion Monte Carlo with importance sampling, which is based on a rigorous short-time expansion of the Green's function for rotational motion in three dimensions. We show that this short-time approximation provides correct sampling of the angular degrees of freedom, and provides a general way to incorporate importance sampling for all degrees of freedom. The full importance sampling algorithm significantly improves both calculational efficiency and accuracy of ground state properties, and allows rotational and bending excitations in molecular van der Waals clusters to be studied directly.Comment: Accepted for publication in Computer Physics Communication

Generalization of the Activated Complex Theory of Reaction Rates. II. Classical Mechanical Treatment

In its usual classical form, activated‐complex theory assumes a particular expression for the kinetic energy of the reacting system, one being associated with a rectilinear motion along the reaction coordinate. The derivation of the rate expression given in the present paper is based on the general kinetic‐energy expression. A rate equation of the customary form is obtained: k_rate = (kT/h)exp[−(F‡−F^r)/kT], where F‡ is the free energy of a system constrained to exist on a hypersurface in n‐dimensional space and Fr is the free energy of the reactants. The usual derivation is then reinterpreted, in terms of geodesic normal coordinates, to be somewhat more general than it appears. Normally, rotation—vibration interaction is neglected, as in the above derivation, although not in treatments of some special reactions in the literature for which the centrifugal potential is important. A derivation is given which includes the influence of this centrifugal potential but which omits Coriolis effects