Zero point energy problem

D. Zero-Point Energy Problem and Level Density... 

If an intrinsically-RRKM molecule with many atoms is excited non-randomly, its initial classical non-RRKM dynamics may agree with the quantum dynamics for the reasons described above. But at longer times, after a micro-canonical ensemble is created, the classical unimolecular rate constant is much larger than the quantum value, because of the zero-point energy problem. Thus, the short-time unimolecular dynamics of a large molecule will often agree quite well with experiment if the molecule is excited non-randomly. The following is a brief review of two representative... 

W. H. Miller, W. L. Hase, and L. Darling, A. simple model for correcting the zero point energy problem in classical trajectory simulations of polyatomic molecules, J. Chem. Phys. 91 2863 (1989). 

J. Bowman, B. Gazdy, and Q. Sun, A. method to constrain vibrational energy in quasiclass-ical trajectory calculations, J. Chem. Phys. 91 2859 (1989) R. Alimi, A. Garcia-Vela, and R. B. Gerber, A remedy for zero-point energy problems in classical trajectories a combined semiclassical/classical molecular dynamics algorithm, J. Chem. Phys. 96 2034 (1992). 

Increases in computer power and improvements in algorithms have greatly extended the range of applicability of classical molecular simulation methods. In addition, the recent development of Internal Coordinate Quantum Monte Carlo (ICQMC) has allowed the direct comparison of classical simulations and quantum mechanical results for some systems. In particular, it has provided new insights into the zero point energy problem in many body systems. Classical studies of non-linear dynamics and chaos will be compared to ICQMC results for several systems of interest to nanotechnology applications. The ramifications of these studies for nanotechnology applications will be discussed. 

Recent concerns about overly chaotic motion in classical system [7] and the zero point energy problem [8] have led us to begin to explore the limitations of classical MD simulation. In the context ofnano-fluidic systems, this would translate into whether or not it would be possible to study shock and pressure waves at the nanometer size scale using MD simulation. Of course, MD simulation has enabled reasonably accurate calculations of fluid viscosities [9] however, the phenomenon of fluid Viscosity, at the atomic level, does not require coherent energy transfer. 

Of course, many of the essential features of a liquid are preserved in classical simulations. What determines these liquid properties more than the total energy is energy differences with respect to thermal motion, external forces, and so on. In the context of classical-quantum correspondence, it is important to note that any liquid is an unbound system and so the zero point energy problem has far less significance in considerations of liquid structure than in the problems... 

Although the mapping approach provides an in principle consistent classical description of nonadiabatic dynamics, the formulation has been shown to suffer seriously from the zero-point energy problem. This is because in the mapping formalism the electronic oscillators are constrained to the ground... 

Isotopic substitution in the Cl + system leads to a normal isotope effect, i.e., [A (light)]/[A (heavy)] > 1. In other systems this ratio is less than 1—the so-called inverse isotope effect. The isotope effect is determined by the difference between the shape of the potential-energy surface at the reactant configuration and at the pass. Ignoring vibrational excitation, the ratio (9.24) reflects differences in zero point energies (Problem 9.15). In the example considered the zero point energy of the activated complex is less than that of the reactants—the activated complex is floppy. ... 

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