Monte-Carlo Studies of Bosonic van der Waals Clusters

1995 ◽  
Vol 408 ◽  
Author(s):  
M. Meierovich ◽  
A. Mushinski ◽  
M. P. Nightingale
Keyword(s):  
Van Der Waals ◽  
Zero Point ◽  
Bound State ◽  
Van Der Waals Clusters ◽  
Point Energy ◽  
Jones Potential ◽  
Lennard Jones ◽  
Monte Carlo Studies ◽  
Simple Picture ◽  
Zeropoint Energy

AbstractIn a previous paper [1], we developed a form of variational trial wave function and applied it to van der Waals clusters: five or less atoms of Ar and Ne modeled by the Lennard-Jones potential. In addition, we tested the trial functions for a hypothetical, light atom resembling Ne but with only half its mass. We did not study atoms such as He4 with larger de Boer parameters, i.e., systems in which the zero point energy plays a more important role relative to the potential energy. This is the main purpose of the present paper. In fact, we study clusters to the very limit where the zeropoint energy destroys the ground state as a bound state. A simple picture of this un-binding transition predicts the power law with which the energy vanishes as the de Boer parameter approaches its critical value and the power of the divergence of the the size of the clusters in this limit. Our numerical results are in agreement with these predictions.

New applications of the genetic algorithm for the interpretation of high-resolution spectra

2004 ◽  
Vol 82 (6) ◽  
pp. 804-819 ◽  
Author(s):  
W Leo Meerts ◽  
Michael Schmitt ◽  
Gerrit C Groenenboom
Keyword(s):  
Genetic Algorithm ◽  
High Resolution ◽  
Van Der Waals ◽  
Computing Time ◽  
Zero Point ◽  
Building Blocks ◽  
Molecular Structures ◽  
High Resolution Spectroscopy ◽  
Van Der Waals Clusters ◽  
Point Energy

Rotationally resolved electronic spectroscopy yields a wealth of information on molecular structures in different electronic states. Unfortunately, for large molecules the spectra get rapidly very congested owing to close-lying vibronic bands, other isotopomers with similar zero-point energy shifts, or large-amplitude internal motions. A straightforward assignment of single rovibronic lines and, therefore, line position assigned fits are impossible. An alternative approach is unassigned fits of the spectra using genetic algorithms (GAs) with special cost functions for evaluation of the quality of the fit. This paper decribes the improvements we established on the GA method discussed before (J.A. Hageman, R. Wehrens, R. de Gelder, W.L. Meerts, and L.M.C. Buydens. J. Chem. Phys. 113, 7955 (2000)). In particular, we succeeded in obtaining a dramatic reduction in computing time that made it possible to apply the GA process in a large number of cases. A completely automated fit of a rotationally resolved laser-induced fluorescence spectrum without any prior knowledge of the molecular parameters can now be performed in less than 1 h. We demonstrate the power of the method on a number of typical examples such as very dense rovibronic spectra of van der Waals clusters and overlapping spectra due to different isotopomers. The discussed results demonstrate the extreme power of the GA in automated fitting and assigning of complex spectra. It opens the road to the analysis of complex spectra of biomolecules and their building blocks. Key words: high-resolution spectroscopy, genetic algorithm, biomolecules, structure, van der Waals clusters.

scholarly journals An analysis by adsorption of the surface structure of graphite

1937 ◽  
Vol 161 (907) ◽  
pp. 476-493 ◽  
Keyword(s):  
Energy Levels ◽  
Van Der Waals ◽  
Zero Point ◽  
Zero Point Energy ◽  
Energy Effect ◽  
Point Energy ◽  
Adsorbed Molecules ◽  
Lennard Jones ◽  
Vibrational Levels ◽  
Effects Of Temperature

The work to be described had as objectives: to measure accurately sets of isothermals of non-polar gases on an inert adsorbent as a function of temperature and of quantity adsorbed; then to employ these isotherms and heats to obtain a modified Langmuir isotherm capable of a general and quantitative application to surfaces of variable adsorption potential. Owing to a quantization of the energy levels of the interacting molecules, in the van der Waals potential energy hollow, the liquid hydrogens H 2 and D 2 (Urey and Teal 1935) or the hydrogens adsorbed on charcoal (Barrer and Rideal 1935) have different vapour pressures; The quanta are larger for H 2 than for D 2 and therefore it is easier to evaporate H 2 . A counteracting influence must be considered, however (Lennard-Jones and Devonshire 1936), which is the effect of the mass on the wave functions whose product determines the probability of evaporation. Calculation shows for a simple case a separation factor which diminishes with temperature at a rate less than the original zero-point energy theory requires, though the zero-point energy effect is the greater. One might expect similar considerations to apply to other adsorbed molecules held by van der Waals forces only, and by lowering the temperature to cause transitions to lower vibrational levels of the adsorbed molecules against the solid, making it more difficult to desorb them. No investigation of the magnitude of these effects has been made, and so it was regarded as important to look for effects of temperature on pure van der Waals heats of sorption.

scholarly journals Improved semiclassical model for real-time evaporation of matrix black holes

2021 ◽  
Author(s):  
David Berenstein ◽  
Yueshu Guan
Keyword(s):  
Black Hole ◽  
Real Time ◽  
Zero Point ◽  
Bound State ◽  
Quantitative Model ◽  
Point Energy ◽  
Yang Mills ◽  
Matrix Mechanics ◽  
Long Lifetime ◽  
Do So

In this paper, we study real-time classical matrix mechanics of a simplified [Formula: see text] matrix model inspired by the black hole evaporation problem. This is a step towards making a quantitative model of real-time evaporation of a black hole, which is realized as a bound state of D0-branes in string theory. The model we study is the reduction of Yang–Mills in [Formula: see text] dimension to [Formula: see text] dimensions, which has been corrected with an additional potential that can be interpreted as a zero-point energy for fermions. Our goal is to understand the lifetime of such a classical bound state object in the classical regime. To do so, we pay particular attention to when [Formula: see text]-particles separate to check that the “off-diagonal modes” of the matrices become adiabatic and use that information to improve on existing models of evaporation. It turns out that the naive expectation value of the lifetime with the fermionic correction is infinite. This is a logarithmic divergence that arises from very large excursions in the separation between the branes near the threshold for classical evaporation. The adiabatic behavior lets us get some analytic control of the dynamics in this regime to get this estimate. This divergence is cutoff in the quantum theory due to quantization of the adiabatic parameter, resulting in a long lifetime of the bound state, with a parametric dependence of order [Formula: see text].

Continuum Modeling of van der Waals Interaction Force Between Carbon Nanocones and Carbon Nanotubes

2011 ◽  
Vol 2 (3) ◽  
Author(s):  
F. Alisafaei ◽  
R. Ansari ◽  
H. Rouhi
Keyword(s):  
Carbon Nanotubes ◽  
Van Der Waals ◽  
Interaction Force ◽  
Van Der Waals Interaction ◽  
Continuum Modeling ◽  
Jones Potential ◽  
Carbon Nanocones ◽  
Single Walled Carbon ◽  
Lennard Jones ◽  
Walled Carbon Nanotubes

Using the Lennard–Jones potential, continuum modeling of the van der Waals potential energy and interaction force distributions are investigated for the eccentric and concentric single-walled carbon nanocones inside the single-walled carbon nanotubes. Furthermore, a new semi-analytical solution is presented to evaluate the van der Waals interaction of the nanocone located on the axis of the nanotube. Eccentric and concentric configurations of these nanostructures are also investigated to obtain the preferred position of the nanocone inside the nanotubes. Finally, the optimum radius of a carbon nanotube for which the preferred location of carbon nanocones is along the tube axis is found.

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