Deductive molecular mechanics derived from

The word actual is important, because one could object that the fact that the minima are stable in fact is deduced from statistical mechanics and that the conformational search is just a vehicle to find these minima. The search does not affect the deductive character of the derivation. (I am grateful to Ansgar Beckermann for this objection) Yet, this is the wrong perspective. My claim is that, in order to find out what the term explanation means one has to have a close look at what scientist actually do when they explain. In the case of Molecular Mechanics they do not derive, they search. 

Parallel with the phenomenological development, an alternative point of view has developed toward thermodynamics, a statistical-mechanical approach. Its philosophy is more axiomatic and deductive than phenomenological. The kinetic theory of gases naturally led to attempts to derive equations describing the behavior of matter in bulk from the laws of mechanics (first classic, then quanmm) applied to molecular particles. As the number of molecules is so great, a detailed treatment of the mechanical problem presents insurmountable mathematical difficulties, and statistical methods are used to derive average properties of the assembly of molecules and of the system as a whole. 

The obvious question is this What conditions should be imposed Without a molecular or microscopic theory for guidance, there is no deductive route to answer this question. The application of boundary conditions then occupies a position in continuum mechanics that is analogous to the derivation of constitutive equations in the sense that only a limited number of these conditions can be obtained from fundamental principles. The rest represent an educated guess based to a large extent on indirect comparisons with experimental data. In recent years, insights developed from molecular dynamics simulations of relatively simple... 

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