Energy equipartitioning in the classical time-dependent Hartree approximation

In the classical time-dependent Hartree approximation (TDH), the dynamics of a single molecule is approximated by that of a ‘‘field’’ (each field being N ‘‘copies’’ of the molecule which are transparent to one another while interacting with the system via a scaled force). It is shown that when some molecules are represented by a field of copies, while other molecules are represented normally, the average kinetic energy of the system increases linearly with the number of copies and diverges in the limit of large N. Nevertheless, the TDH method with appropriate energy scaling can serve as a useful means of enhancing the configurational sampling for problems involving coupled systems with disparate numbers of degrees of freedom.