Quantum-dressed Classical Mechanics

Abstract

Classical mechanics is known often to offer a good description of molecular dynamical processes and hence this approach is widely used to simulate the dynamics of molecular systems. Classical mechanics allows for simulation of large systems. Large means in this connection systems consisting of several thousands of atoms or molecules. The reason for this is that the computational effort in classical dynamics scales about linearly with the size of the system, i.e. with the number of atoms N. Hence, within the classical mechanical description it is therefore possible to simulate phenomena as for instance protein folding or phase transitions. However, for a number of dynamical processes the classical mechanical description appears to be insufficient. In general this is so for what could be called “rare events”, i.e. processes which have probabilities of the order 10⁻³ or smaller. Such processes could for instance be reactions where a barrier has to be tunneled through or state resolved vibrational or electronic transitions which are classically forbidden. By classically forbidden we understand processes which for dynamical reasons do not occur in classical mechanics. Thus, for a large class of problems involving for instance chemical reactions with activation barrier, vibrational and electronic transitions we will have to use the correct description, namely the quantum description. However, the quantum mechanical approach has the problem that the computationally effort scales exponentially as 10^3N, i.e. even today problems with N=3~4 (three to four atoms) can only be solved “exactly” if one or more of the atoms are hydrogen atoms.