Donald W. Noid

Semiclassical calculation of bound states in multidimensional systems with Fermi resonance

A method is devised to calculate eigenvalues semiclassically for an anharmonic system whose two unperturbed modes are 2:1 degenerate. For some special states the periodic energy exchange between unperturbed modes is found to be very large. The quantum mechanical wave functions are examined and a correlation with the classical trajectories is described, both for quasiperiodic and the stochastic cases. A method used in the literature for calculating the stochastic limit is tested and found to break down when the present anharmonic system is separable.

Symplectic integrators for large scale molecular dynamics simulations: A comparison of several explicit methods

We test the suitability of a variety of explicit symplectic integrators for molecular dynamics calculations on Hamiltonian systems. These integrators are extremely simple algorithms with low memory requirements, and appear to be well suited for large scale simulations. We first apply all the methods to a simple test case using the ideas of Berendsen and van Gunsteren. We then use the integrators to generate long time trajectories of a 1000 unit polyethylene chain. Calculations are also performed with two popular but nonsymplectic integrators. The most efficient integrators of the set investigated are deduced. We also discuss certain variations on the basic symplectic integration technique.

Continuum methods of mechanics as a simplified approach to structural engineering of nanostructures

Recent studies of potential components for nanomachines reveal that for a wide variety of structures, the rigidity of the structure is a key element in its proper performance. Vibrational analysis is an ideal way to study structural rigidity, but standard methods of molecular vibrational analysis are computationally prohibitive for nanostructures with large numbers of atoms. Herein, the vibration of nanotubes is used to demonstrate that continuum methods of vibrational analysis have potential utility in the engineering of nanostructures.

Computer experiments on the internal dynamics of crystalline polyethylene: Mechanistic details of conformational disorder

The atomistic details of the internal dynamics of a polyethylene‐like crystal are studied using molecular dynamics. Crystals with up to 6100 chain atoms have been studied for up to 30 ps. A microscopic description of the atomic motion has been examined and a link to available experimental data on the macroscopic and microscopic motion is provided. The results show that the onset of a significant population of rotational isomers is strongly altered by the intermolecular forces. Typical rates for the formation of isomers are 1010 to 1012 s−1 at 350 K (depending on the size of the simulated crystal, which changes the overall nature of the intermolecular forces) and increase exponentially with temperature. The large number of created defects causes a continuous decrease in the end‐to‐end distance. Specific defects, however, have extremely limited lifetime (i.e., those suggested by molecular mechanics calculations). These results suggest that at the temperatures where annealing or deformation of metastable crystals is possible, only randomly generated defects cause the macroscopically observed changes. The defects should move under the free enthalpy gradient set up within the crystal toward a more stable location. The activation energy required for motion which ultimately results in mass transport or lamellar thickening can be shown to be temperature and chain‐length dependent. The highly uncorrelated behavior of the creation and annealing of defects reveals the underlying chaotic nature of the ‘‘transition’’ from an ordered crystal to a conformationally disordered crystal (CONDIS crystal). In the simulated case, the transition to the conformationally disordered state occurs gradually, involving little or no cooperative motion. This continuous transition to the condis state was suggested earlier on the basis of experimental evidence and is expected to occur in many other polymers in addition to and at lower temperature than possible additional first‐order transitions to the condis state. Thermodynamic and kinetic parameters of the simulations have been determined and compared to the available experimental data with good agreement.The atomistic details of the internal dynamics of a polyethylene‐like crystal are studied using molecular dynamics. Crystals with up to 6100 chain atoms have been studied for up to 30 ps. A microscopic description of the atomic motion has been examined and a link to available experimental data on the macroscopic and microscopic motion is provided. The results show that the onset of a significant population of rotational isomers is strongly altered by the intermolecular forces. Typical rates for the formation of isomers are 1010 to 1012 s−1 at 350 K (depending on the size of the simulated crystal, which changes the overall nature of the intermolecular forces) and increase exponentially with temperature. The large number of created defects causes a continuous decrease in the end‐to‐end distance. Specific defects, however, have extremely limited lifetime (i.e., those suggested by molecular mechanics calculations). These results suggest that at the temperatures where annealing or deformation of metastable cry...

Semiclassical calculation of eigenvalues for a three‐dimensional system

A method utilizing integration along invariant curves on Poincares surfaces of section is described for the semiclassical calculation of eigenvalues for three and higher dimensional systems, supplementing thereby our previous work in two dimensions. The eigenvalues calculated for anharmonically coupled oscillators agree well with the exact quantum eigenvalues.

The classical mechanics of vibrational predissociation: A model based study of phase space structure and its influence on fragmentation rates

The classical dynamics pertinent to van der Waals molecule vibrational predissociation of a T‐shaped model for HeI2(B) is examined. An interesting phase space structure involving nonlinear resonances and stochastic motion is found. For low initial vibrational excitations of the I2 partner of the vdW complex the relevant part of phase space is dominated by quasiperiodic motion indicating a purely quantal mode of decay (‘‘dynamical tunneling’’), but for higher initial vibrational excitations van der Waals molecule predissociation is a classically allowed process. Classically determined rates of decay agree to within a factor of 3 with the rates calculated from quantum mechanics.

Uniform semiclassical theory of avoided crossings

Avoided crossings influence spectra and intramolecular redistribution of energy. A semiclassical theory of these avoided crossings shows that when primitive semiclassical eigenvalues are plotted vs a parameter in the Hamiltonian they cross instead of avoiding each other. The trajectories for each are connected by a classically forbidden path. To obtain the avoided crossing behavior, a uniform semiclassical theory of avoided crossings is presented in this article for the case where that behavior is generated by a classical resonance. A low order perturbation theory expression is used as the basis for a functional form for the treatment. The parameters in the expression are evaluated from canonical invariants (phase integrals) obtained from classical trajectory data. The results are compared with quantum mechanical results for the splitting, and reasonable agreement is obtained. Other advantages of the uniform method are described.

Fractal behavior in classical collisional energy transfer

A plot of final vibrational action vs initial vibrational phase for a two degree of freedom model for He + I2 collisions is examined and shown to exhibit a chattering region. The chattering region is shown to exhibit a very intricate structure, including an infinite number of regions of regularity which we term icicles. Structure is evident on all scales of examination and a fractal dimension close to 2 is obtained for some parts of the chattering region. The survival probability associated with the complexes shows an initial fast decay, due to the icicles, but can be roughly characterized over a longer and wider time range by a more slowly decaying exponential.

Neural network-graph theory approach to the prediction of the physical properties of organic compounds

A new computational scheme is developed to predict physical properties of organic compounds on the basis of their molecular structure. The method uses graph theory to encode the structural information which is the numerical input for a neutral network. Calculated results for a series of saturated hydrocarbons demonstrate average accuracies of 1--2% with maximum deviations of 12--14%.

Local mode predictions for excited stretching vibrational states of HCCD and H 12C 13CH

Calculation are performed for the stretching vibrational states of acetylene HCCD and H12C13H on the Oak Ridge computing systems. The results of these calculations agree with the recent observations by photo‐acoustic spectroscopy. (AIP)