ABSTRACT
Abstract ....................................................................................................402 12.1 Introduction.....................................................................................402 12.2 The Essence of the Monte Carlo method ........................................403 12.3 Monte Carlo Method as a General Integration Technique ..............406 12.4 Molecular Descriptors Calculated by Means of the Monte Carlo
method ............................................................................................408 12.4.1 Molecular Volume .............................................................408 12.4.2 Molecular Surface .............................................................413 12.4.3 Synthetic Descriptors of Molecular Size and Shape.........417 12.4.4 Steric Static Integral Parameter ........................................421 12.5 Descriptors for the Accessibility of Molecular Surface and the
Dynamics of the Molecular Structure .............................................429 12.6 Simulations of the Copolymerization Reactions based on the
Monte Carlo Method.......................................................................433 12.6.1 Introduction.......................................................................433 12.6.2 Implementing Monte Carlo Models on Computers ..........436 12.6.4 Simulation of Copolymerization Reactions ......................441 12.7 Description of the IRS Computer Program ....................................442 12.8 Conclusions ....................................................................................444 Keywords .................................................................................................446 References ................................................................................................446
In this chapter, we intend to review our contributions to the field of molecular descriptors calculated by Monte Carlo method. We begin with a short description of the fundamentals of Monte Carlo method and its general application as a stochastic integration technique for objects in an N-dimensional space. We describe the structural descriptors of molecular shape and size, which have been developed by us in the approximation of hard-spheres (i.e., the molecule is considered as a collection of relatively impenetrable atomic spheres, positioned at their Cartesian coordinates and having radii equal to van der Waals (vdW) radii). The simulation of the copolymerization reactions is also included, as another example of usefulness of the Monte Carlo method in other areas of theoretical research. The applications of these molecular descriptors are discussed in each chapter.
