Search for the Most Stable Structures on Potential Energy Surfaces

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Title:Search for the Most Stable Structures on Potential Energy Surfaces
Creators:
Piela, Lucjan
Journal or Publication Title:
Collection of Czechoslovak Chemical Communications, 63, 9, pp. 1368-1380
Uncontrolled Keywords:Energy minimum, Bloch equation, Schrödinger equation, Gibbs free-energy principle, Stable structure, Fick's diffusion equation, Global optimization

Abstract

Smoothing techniques for global optimization in search for the most stable structures (clusters or conformers) have been a novel possibility for the last decade. The techniques turned out to be related to a variety of fundamental laws: Fick's diffusion equation, time-dependent and time-independent Schrodinger equations, Smoluchowski dynamics equation, Bloch equation of canonical ensemble evolution with temperature, Gibbs free-energy principle. The progress indicator of global optimization in those methods takes different physical meanings: time, imaginary time, Planck constant, or the inverse absolute temperature. Despite this large spectrum of physical phenomena, the resulting global optimization procedures have a remarkable common feature. In the case of the Gaussian Ansatz for the wave function or density distribution, the underlying differential equations of motion for the Gaussian position and width are similar for all these phenomena. In all techniques the smoothed potential energy function plays a central role rather than the potential energy function itself. The smoothed potential results from a Gaussian convolution or filtering out high frequency Fourier components of the original potential energy function. During the minimization, the Gaussian position moves according to the negative gradient of the smoothed potential energy function. The Gaussian width is position dependent through the curvature of the potential energy function, and evolves according to the following rule. For sufficiently positive curvatures (close to minima of the smoothed potential) the width decreases, thus leading to a smoothed potential approaching the original potential energy function, while for negative curvatures (close to maxima) the width increases leading eventually to the disappearance of humps of the original potential energy function. This allows for crossing barriers separating the energy basins. Some methods result in an additional term, which increases the width, when the potential becomes flat. This may be described as a feature allowing hunting for distant minima. <p>

Title:Search for the Most Stable Structures on Potential Energy Surfaces
Creators:
Piela, Lucjan
Uncontrolled Keywords:Energy minimum, Bloch equation, Schrödinger equation, Gibbs free-energy principle, Stable structure, Fick's diffusion equation, Global optimization
Divisions:Life and Chemical Sciences > Institute of Organic Chemistry and Biochemistry > Collection of Czechoslovak Chemical Communications
Journal or Publication Title:Collection of Czechoslovak Chemical Communications
Volume:63
Number:9
Page Range:pp. 1368-1380
ISSN:0010-0765
E-ISSN:1212-6950
Publisher:Institute of Organic Chemistry and Biochemistry
Related URLs:
URLURL Type
http://dx.doi.org/10.1135/cccc19981368UNSPECIFIED
ID Code:1387
Item Type:Article
Deposited On:06 Feb 2009 17:09
Last Modified:06 Feb 2009 16:09

Citation

Piela, Lucjan (1998) Search for the Most Stable Structures on Potential Energy Surfaces. Collection of Czechoslovak Chemical Communications, 63 (9). pp. 1368-1380. ISSN 0010-0765

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