Search results for "Stationary point"

Are most of the stationary points in a molecular association minima? Application of Fraga's potential to benzene-benzene

1993

The importance of characterizing the stationary points of the intermolecular potential by means of Hessian eigenvalues is illustrated for the calculation of the benzene–benzene interaction using an atom-to-atom pair potential proposed by Fraga (FAAP). Two models, the standard one-center-per atom and another using three-centers-per atom due to Hunter and Sanders, are used to evaluate the electrostatic contributions and the results are compared. It is found in both cases that although using low-gradient thresholds allows optimization procedures to avoid many stationary points that are not true minima computing time considerations makes the usual procedure of using high-gradient thresholds [sa…

AMYR 2: A new version of a computer program for pair potential calculation of molecular associations

1998

AMYR is a computer program for the calculation of molecular associations using Fraga's pairwise atom-atom potential. The interaction energy is evaluated through a 1R expansion. The electrostatic energy is calculated through either the one-centre-per atom or the three-centres-per atom model by Hunter and Sanders. A pairwise dispersion energy term is included in the potential and corrected by a damping function. The program carries out energy minimizations through variable metric methods. The new version allows for the stationary point analysis of the intermolecular potential by means of the Hessian eigenvalues. Although using low-gradient thresholds optimization procedures to avoid many stat…

Online Hyperparameter Search Interleaved with Proximal Parameter Updates

2021

There is a clear need for efficient hyperparameter optimization (HO) algorithms for statistical learning, since commonly applied search methods (such as grid search with N-fold cross-validation) are inefficient and/or approximate. Previously existing gradient-based HO algorithms that rely on the smoothness of the cost function cannot be applied in problems such as Lasso regression. In this contribution, we develop a HO method that relies on the structure of proximal gradient methods and does not require a smooth cost function. Such a method is applied to Leave-one-out (LOO)-validated Lasso and Group Lasso, and an online variant is proposed. Numerical experiments corroborate the convergence …

An ab initio study of the unimolecular decomposition mechanism of formamidine. 4-31G Characterization of potential energy hypersurface

1991

Ab initio MO calculations have been carried out for the unimolecular decomposition of formamidine. The Hartree–Fock method in LCAO approximation with the 4-31G basis set was used. The 4-31G potential hypersurface has been further studied. The stationary points (R, TS, and P) were localized. A reaction analysis by correlation of bond-order indices and localized molecular orbitals demonstrated that the decomposition is an asynchronous process. The TS can be described as four-membered ring.

UNIQUENESS OF PERIODIC SOLUTIONS OF THE LIENARD EQUATION

1981

This chapter analyzes the uniqueness of periodic solutions of the Lienard equation. It considers the Lienard equation = y − F ( x ) and y = − x where F (0) = 0 , F ( x ) ∈ Lip( R ). The chapter discusses the existence of periodic solutions. It highlights that the origin is the only stationary point of the system = y − F ( x ) and y = − x , and therefore all nontrivial periodic solutions must circle around the origin. The existence of at least one periodic solution is proved by constructing a Poincare–Bendixson domain. The chapter also emphasizes that to prove the uniqueness of periodic solutions, additional assumptions are also needed. In the literature there are numerous uniqueness results…

Modelling and Simulation of Stationary Point Processes

2008

A new algorithm for the kinetic data analysis

2000

Abstract In this paper, a new algorithm for the kinetic data analysis is presented. The main objective of the algorithm is to retrieve the maximum information concerned with a multi-response complex chemical system evolving in time, in order to retrieve the rate constants (calibration problem) or the initial concentration of species. As a difference with other data treatments found in the literature, the algorithm is able to estimate the uniqueness and reliability of the calculated rate constants. This task is carried out by analyzing of the principal components of the sensitivity coefficients with regard to the rate constants. The analysis allows understanding whether the located stationar…