The definition of molecular structure

Before getting into a deeper analysis of the concept of resonance, we must define precisely what we understand by chemical structure . One of the most basic concepts in molecular quantum mechanics is the one of potential energy surface (PES). It allows us to define a molecular structure as an arrangement of nuclear positions in space. The definition of molecular structure depends on the validity of the Bom-Oppenheimer approximation for a given state. Actually, its validity is limited to selected portions of the entire Bom-Oppenheimer PES. When a state is described by one PES, we call it an adiabatic state. It is clear that the concept of chemical structure , depends on the existence of a previously defined molecular structure . Only adiabatic states have a molecular structure . From now on, we will always be dealing with adiabatic states. 

We here summarize the results of Bader et a/.118 which are concerned with the definition of molecular structure and with the extension of this concept, together with the associated concept of a bond, to the dynamic case. A precise description and physical interpretation of the making and breaking of chemical bonds is presented by these workers in a quantitative analysis of the evolution of molecular structure. The topological analysis of the dynamic system, as pointed out by Collard and Hall,119 falls naturally into the realm of an existing and elegant mathematical theory, the catastrophe theory of Thom.120... 

The problem is conventionally sidestepped by assuming that nuclear and electronic motions are decoupled, but despite many efforts this condition has never been shown to yield a rigid molecular shape either. The insurmountable problem is permutational invariance. In molecular-orbital calculations that decouple electronic from nuclear motion the nuclei are identified in order to support the definition of molecular structure, but then permutation of identical nuclei implies rearrangement of bonds and a new set of calculated electronic energies. There is little hope of ever overcoming these problems ... 

As discussed above and illustrated in Fig. 3.4, the partitioning of nuclear configuration space obtained as a result of the definition of molecular structure leads to the concept of a structure diagram. The space R is partitioned into a finite number of structural regions with their boundaries, as defined by the catastrophe set, denoting the configurations of unstable structures. This information constitutes a system s structure diagram, a... 

A new approach in the definition of "molecular structure" is introduced for natural humic substances and soil organic matter by proposing a model HA which represents a characteristic structural pattern for a large number of possible and likely structures. The crucial point is the adaptation, flexibility, and variability to decomposition and synthesis processes in the natural environment. 

Wilson, E. B. (1979). On the definition of molecular structure in quantum mechanics. International Journal of Quantum Chemistry, 13, 5. 

The main scientific disciplines of quantum chemistry and solid-state physics were developed by way of a mathematical simplification or approximation of the Schrodinger equation, known as the Born-Oppenheimer (B-O) approximation [1]. It does not only give the basis of almost all quantum chemical calculations, but it also provides the very concept of molecular structure [2]. There are two main contemporary trends in quantum chemistry that put a question mark over the B-O approximation and its role in the definition of (molecular) structure theories based on the incorporation of the centre-of-mass (COM) problem and applications in connection with the Jahn-Teller (J-T) effect. 

Lowdin, 1991] P.-O. Lowdin. On nuclear motion and the definition of molecular structure. 

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