The Concept of Molecular Structure

A fully quantum-mechanical treatment of nuclei is incompatible with the conventional notion of molecular structure. Nevertheless, it is possible to assign molecular structures to both spectroscopic and localized states, and even to nonstationary states with zero linear momentum. Such an assignment proceeds through the following steps [21]  

Topological analysis of p(2 R,t) for a given R and t, all the points in p(Z R,t) that are extremal with respect to the three-dimensional vector TL 

Identification of all the molecular structures compatible with (r,R,t), that is construction of a set (]j of all distinct equivalence classes of 7(R, t) . Two molecular graphs belong to the same equivalence class Qj if and only if they are homeomorphic [27,28]. The set Qj is finite, provided that the system under consideration consists of a finite number of particles (nuclei and electrons). 

The quantity P(Qj,t) constitutes the probability of the system in question being at the time t in a quantum-mechanical state compatible with the structure Qj. Obviously, Qj with the largest P(( j,t) is the dominant molecular structure or simply the molecular structure at that moment of time. Such a definition, aspects of which have been considered before [28,29], is fully quantum-mechanical in nature and does not rely on any particular approximation to (r,R,t). 

---

Testa, B., Kier, L. B. The concept of molecular structure in structure-activity relationship studies and drug design. Med. Res. Rev. 1991, 11, 35 8. 

The concept of molecular structure implies a reduction in the freedom of motion for the involved atoms. Thus an indirect strategy for identifying structured segments is to search for restricted motion for contiguous sets of amino acid residues. Relaxation of the 15N nucleus in the peptide bond provides a quantitative measure of the rates and angular range of motion experienced by individual amino acids under equilibrium conditions (Palmer, 2001). 

Perturbative reasoning can be used to justify conceptual models of chemistry that are far from evident in Eq. (1.1) itself. An important example is the concept of molecular structure - the notion that nuclei assume a definite equilibrium configuration R0, which determines the spatial shape and symmetry of the molecule. At first glance, this concept appears to have no intrinsic meaning in Eq. (El),... 

With its emphasis on the concepts of molecular structure and the relationship of structure to reactivity with all its implications, stereochemistry provides a unifying theme for the study of mechanism. This review will have served a useful purpose if it conveys this sense to the reader. 

Background Philosophy. Within the framework of the Born-Oppenheimer approximation (JJ ), the solutions of the Schroedin-ger equation, Hf = Ef, introduce the concept of molecular structure and, thereby, the total energy hyperspace provided that the electronic wave function varies only slowly with the nuclear coordinates, electronic energies can be calculated for sets of fixed nuclear positions. The total energies i.e. the sums of electronic energy and the energy due to the electrostatic re-... 

The hope of understanding the concept of molecular structure quantum-mechanically would obviously be at its most realistic for the smallest of molecules at the absolute zero of temperature. However, under these conditions completely different pictures emerge for the molecule in, either total isolation, or in a macroscopic sample. In the latter case the molecule appears embedded in a crystal, which is quantum-mechanically described by a crystal hamiltonian with the symmetry of the crystal lattice. The isolated molecule has a spherically symmetrical hamiltonian. The two models can obviously not define the same quantum molecule. 

Meyer, A. Y. Molecular Mechanics Alias Mass Points, in Theoretical Models of Chemical Bonding Atomic Hypothesis and the Concept of Molecular Structure Maksic, Z.B., Ed. Springer-Verlag Heidelberg, 1990, pp. 213-254. 

The concept of molecular structure, consisting of atoms and their mutual connections, is fundamental in chemical theory. Knowledge about... 

Inherent in the concept of molecular structure is the notion that properties of all kinds, chemical, physical and biological, must vary with structural change. At first the structure -property relationships (SPR) reported were qualitative. As quantitative measurements of... 

Although chemical theories are the framework within which molecular structure has been developed, experimental properties define the reference framework in which the concept or, better still, the concepts of molecular structure have been continuously verified, evaluated and modified. 

The years between 1860 and 1880 were characterized by a strong dispute about the concept of -> molecular structure, arising from the studies on substances showing optical isomerism and the studies of Kekule (1861-1867) on the structure of benzene. The concept of the molecule as a three-dimensional body was first proposed by Butlerov (1861-1865), Wislicenus (1869-1873), Van t Hoff (1874-1875) and Le Bel (1874). The publication in French of the revised edition of La chimie dans I espace by Van t Hoff in 1875 is considered a milestone in the three-dimensional conception of the chemical structures. 

Testa, B. and Kier, L.B. (1991). The Concept of Molecular Structure in Structure-Activity Relationship Studies and Drug Design. Med.Res.Rev., 11,35-48. 

For example, the Born-Oppenheimer approximation is ubiquitous. The separation of the electronic and nuclear motion is most often an excellent approximation. However, it is also fundamental to the concept of molecular structure. The model of fixed nuclei surrounded by electrons which accommodate almost instantly any change in the nuclear positions is basic to qualitative and quantitative discussions of molecular structure. 

In a nice review of an area that bears directly on this question, Weininger ("The Molecular Structure Conundrum Can Classical Chemistry be Reduced to Quantum Chemistry " Journal of Chemical Education, 61, 939-944 [1984]) has commented on the continuing disagreement between Woolley and Bader regarding the status of the concept of molecular structure, with others like Scerri and Mosini contributing to the debate. 

Molecular descriptors, tightly connected to the concept of molecular structure, play a fundamental role in scientific research, being the theoretical core of a complex network of knowledge. 

The history of molecular descriptors is closely related to the history of what can be considered one of the most important scientific concepts of the last part of the nineteenth century and the whole twentieth century, that is, the concept of molecular structure. 

Once the concept of molecular structure vas definitively consolidated by the successes of quantum-chemistry theories and the approaches to the calculation of numerical indices encoding molecular structure information vere accepted, all the constitutive elements for the take-off of QSAR strategies vere available. 

Thus, from the perspective of either of two major and widely received accounts of scientific explanation, chemists do not provide proper explanations for one of their most central concepts, the concept of molecular structure. These classical accounts of scientific explanations were part of a general thread in the philosophy of science that pinpointed the search for scientific explanations as one of the major tasks of science in general [see for instance (Nagel 1961)]. Hence, taking these accounts seriously, it seems that we have come back to Kant, who maintained that a great part, if not the whole of chemistry does not deserve to be classified as scientific (Kant 1984). We... 

Since each well is identified with a particular conformation, one sees that the time dependence of l (r) is akin to the concept of molecular structure. For example, consider the isomers ethyl alcohol and dimethyl ether. At an internal energy of 10 kcal/mol neither is a stationary state. The reason that structural attributes may be associated with each is because tunneling is very slow. Thus, a (0 that evolves slowly is similar to a stable molecular conformation. 

---