Generalized Simulated Annealing Geometry Optimization and Conformational Geometry Optimization and Conformational

Introduction

It is well known that, in general, a molecular system can exist in different conformational geometries, which are three-dimensional arrangements of atoms in a structure. The number of conformations increases with the molecule size. In particular, molecules of biological and pharmacological interest present thousands of local minima (or conformations). The great difficulty, in this subject, is to find global minima and not to get trapped in one of the many local minima. This fact has led to the appearance of different theoretical methods, in quantum chemistry[1], to describe the molecular conformations as well as to obtain the optimized geometry.

In general, theoretical methods are based on the gradient descent approach. It is known that the gradient method indistinctly provides both global and local minima, consequently, to find the global minimum, the brute-force strategy has been the usual tool.

Recently, the so-called simulated annealing methods have demonstrated important successes in the description of a variety of global extremization problems. Simulated annealing methods have attracted significant attention as suitable for optimization problems of large scale, especially those where a desired global minimum is hidden among many local minima. The basic aspect of the simulated annealing method is its analogy with thermodynamics, especially with the way that liquids freeze and crystallize, or metals cool and anneal. The first nontrivial solution along this line was provided by Kirkpatrick et al [2, 3] for classical systems, and also extended by Ceperley and Alder [4] for quantum systems. It strictly follows the quasi-equilibrium Boltzmann-Gibbs statistics using a Gaussian visiting distribution, and is sometimes referred to as Classical Simulated Annealing (CSA) or Boltzmann machine . The next interesting step in this subject was Szu and Hartley's proposal [5] to use a Cauchy-Lorentz visiting distribution, instead of a Gaussian one. This algorithm is referred to as the Fast Simulated Annealing (FSA) or Cauchy machine.

In recent years, some authors [6, 7] have applied the Boltzmann machine to describe molecular conformations and the associated global minima.

On the other hand, it has been recently proposed [8] a Generalized Simulated Annealing (GSA) approach which closely follows the recently Generalized Statistical Mechanics [9, 10]; it contains both Boltzmann and Cauchy machines as particular cases, with the supplementary bonus of providing an algorithm which is even quicker than that of Szu and Hartley. Recently, this method has been applied with success in different subjects; Genetics [11], Traveling Salesman Problem [12], Fitting curves by Simulated Annealing [13]

We propose in this work the use of this generalized algorithm in order to describe molecular conformations and to optimize the molecular geometry. To illustrate this, we make a coupling between a semi-empirical quantum program (MOPAC-package) [14] and the GSA routine.

In the next section, we discuss the algorithm used for recovering the global minima. Then, we present results concerning a variety of molecular structures followed by conclusions.

Generalized Simulated Annealing Geometry Optimization and Conformational Geometry Optimization and Conformational