Quantum-classical method separability assumption

The anisotropy of polymer erystals is eharacteristie of the orientation of intra- and intermoleeular interaetions, which is also reflected in a broad separation on the dynamical time scale. It is especially important in polymer crystals to be cognizant of the limitations imposed by either the assumptions on which a method is based (e.g., the quasiharmonic approximation for lattice dynamics) or the robustness of the simulation method (e.g., ergodicity of the simulation in Monte Carlo or molecular dynamics). In some instances, valuable checks on these assumptions and limitations (e.g., quantum mechanical vs. classical dynamics, finite size effects and anharmonicity) can and should be made by repeating the study using more than one method. 

In this method we assume that the various Xj-Y, bonds separating the quantum part from the classical one are represented by localized bond orbitals and that the electrons of the quantum part are represented by canonical molecular orbitals, expanded on the basis of the atomic orbitals defined on the quantum atoms and their nearest neighbours Y,. One could obtain such a situation by performing a unitary transformation on the molecular orbitals of the whole molecule (assumed to be known) and setting equal to zero the coefficients of the atomic orbitals defined on the atoms of the now classical part If the X, -Y, bonds have been chosen according to the criteria above defined, this simplification may not have a major importance. We make some additional assumptions ... 

---