Deductive molecular mechanics

DEDUCTIVE MOLECULAR MECHANICS BRIDGING QUANTUM AND CLASSICAL MODELS OF MOLECULAR STRUCTURE... 

In the previous sections we performed a sequence of moves intended to bridge the gap between an approximate QM description of molecular electronic structure and a classical representation of the PES of organic molecules suitable for further parametriza-tion and simplifications in order to reach a scheme similar to molecular mechanics i.e. classical force fields. This construct can be qualified as deductive molecular mechanics (DMM) as each of its components has a transparent counterpart in the underlying... 

In the previous chapters, we developed an approach which can be used to put the process of developing mechanistic descriptions of PES (i.e. of developing MM force fields) on a rational basis. Deductive molecular mechanics [2-4] (DMM) allows us to develop a form of the MM force fields to analyze the form of the electronic wave function relevant to the physical picture of the electronic structure of the considered class of molecules. In this chapter we apply the previously developedDMM approach to analytical derivation of the QM based form of the force fields involving the nontransition metal atoms. 

Reprinted from A.L. Tchougreeff. Deductive molecular mechanics as applied to develop QM/MM picture of dative and coordination bonds. J. Mol. Struct. (THEOCHEM), 632, 91, 2003 with permission of Elsevier. 

A. L. Tchougreeff and A. M. Tokmachev Deductive molecular mechanics of sp carbon atom, Int. J. Quantum Chem.., submitted. 

The two ways of learning - deductive and inductive - have already been mentioned. Quite a few properties of chemical compounds can be calculated explicitly. Foremost of these are quantum mechanical methods. However, molecular mechanics methods and even simple empirical methods can often achieve quite high accuracy in the calculation of properties. These deductive methods are discussed in Chapter 7. 

Osmotic Work. It is characteristic of living cells that they maintain nonequilibrium values of the concentrations of certain solutes on opposite sides of membranes, particularly ions such as Na and K. It is this nonequHibrium distribution of ions that probably is responsible for the electrical potentials developed by living organisms. Again, although thermodynamic data do not lead to deductions about molecular mechanisms, they provide limiting values with which any mechanism must be consistent. We shall discuss the thermodynamic aspects of osmotic work in detail when we have developed the methods requited to deal with solutions. 

Fattorusso and co-workers identified a component of wormwood called artar-borol. Correlation spectroscopy (COSY) and rotating frame nuclear overhauser effect spectroscopy (ROESY) experiments allowed for deduction of four possible diastereomeric structures of artarborol, 2-5. Low energy conformers of 11-14 were obtained through a molecular mechanics (MM) search. These conformers were screened to identify those having a dihedral angle of around 90 for the C-8 and C-9 protons due to a low coupling constant between these protons. Only conformers of 11 and 13 satisfied this criterion. Next, five low energy conformers, two... 

An example illustrates the point Suppose a blind person stands before an undulated model surface. She must find the deepest basins on this surface by throwing balls on it. She detects height acoustically. Even if this person has a very sophisticated technique of throwing balls on the surface, different runs will lead to different results. She does not deduce the deepest basin on the surface.11 In the same way, the actual process of deriving stable conformations by molecular mechanics is not entirely deductive.12... 

Hence the attempt to subsume molecular mechanics under the DN-model of scientific explanation fails. It fails twice First, the stun of the force-field potentials used in molecular mechanics calculations does not have the status of a proper scientific law and the derivation of the strain energy of a molecule by molecular mechanics is not nomological. Second, the conformational search required to find stable conformations is stochastic and not deductive. 

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. 

From this assumption stems the common use of the term "molecular mechanics" to describe the elementary use of empirical functions in conformational analysis. This similarity to macroscopic bodies made of elastic springs created the common impression as if empirical energy functions are "classical". In fact, empirical methods of describing molecular energies are distinct from molecular orbital methods of quantum chemistry not by being "classical", but by their being empirical guesses not based on any deductive principle, whether classical or quantum mechanical. 

These deductions from basic facts of observation interpreted according to the rigorous laws of thermodynamics do not alone offer an insight into the structural mechanism of rubber elasticity. Supplemented by cautious exercise of intuition in regard to the molecular nature of rubberlike materials, however, they provide a sound basis from which to proceed toward the elucidation of the elasticity mechanism. The gap between the cold logic of thermodynamics applied to the thermoelastic behavior of rubber and the implications of its... 

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. 

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