Molecular-level descriptions

Analytical Approaches. Different analytical techniques have been appHed to each fraction to determine its molecular composition. As the molecular weight increases, complexity increasingly shifts the level of analytical detail from quantification of most individual species in the naphtha to average molecular descriptions in the vacuum residuum. For the naphtha, classical techniques allow the isolation and identification of individual compounds by physical properties. Gas chromatographic (gc) resolution allows almost every compound having less than eight carbon atoms to be measured separately. The combination of gc with mass spectrometry (gc/ms) can be used for quantitation purposes when compounds are not well-resolved by gc. 

The next level seeks a molecular description, and kinetics again makes a contribution. As will be seen in Chapter 5, the experimental kinetics provides information on both the energetics of the reaction (i.e., the height of the energy barrier on the reaction path) and the atomic composition of the transition state. Any proposed mechanism must therefore be consistent with the kinetic evidence. 

A study of the molecular descriptions provided by geneticists and molecular biologists reveals at least three different levels. The first can be illustrated by the schematic models of signal-transduction pathways. In such models, the precise shape of the different proteins, their atomic composition, is of no importance. Sometimes, only the name of the protein is given. What is important is the place of these proteins in the pathways, how they receive upstream signals and transfer them to downstream molecular components. 

Finally, the third level of molecular description can be illustrated by the complex formed between a transcription factor and the DNA molecule. In such a complex, the atoms involved in the interaction, the hydrogen bonds formed between the amino acids and the bases are shown, because this description, is necessary to explain the specificity of molecular recognition. 

Through these examples, I wanted to illustrate the fact that the expression molecular description can have at least three different meanings. These three levels of representation are not independent. For instance, the atoms and bonds that make up the jaws of RNA polymerase II can be described, as well as RNA polymerase II can be integrated, with transcription factors and DNA, in the general picture of the preinitiation transcription complex. However, in order to answer a specific question, one particular level of description is always more significant, better adapted than others, with a greater explanatory value. 

This impossibility of reducing a complex process to single macromolecules explains the co-existence of different levels of explanation in biologists molecular descriptions. This does not mean that the nature of the molecular components is of no importance, nor that the complex functions originate only from the rules of assembly of the different macromolecular components. The organization of living beings is based both on the precise nature of the molecular components and on the way that these molecular components are assembled. 

This homogeneity does depend both on the level of the molecular description and on the definition of the ad hoc molecular descriptors. 

These simple molecular orbital pictures provide useful descriptions of the structures and spectroscopic properties of planar conjugated molecules such as benzene and naphthalene, and heterocychc species such as pyridine. Heats of combustion or hydrogenation reflect the resonance stabilization of the ground states of these systems. Spectroscopic properties in the visible and near-ultraviolet depend on the nature and distribution of low-lying excited electronic states. The success of the simple molecular orbital description in rationalizing these experimental data speaks for the importance of symmetry in determining the basic characteristics of the molecular energy levels. 

In this section we shall first treat the simple molecular orbital description of pyridine. Each molecular energy level corresponds to a configuration, specified by the occupancy of individual molecular orbitals. Each molecular orbital has the symmetry species of an irreducible representation of the symmetry group, C2v The spatial symmetry of the overall molecular wave function is the direct product of the symmetry species of the occupied orbitals. 

Potential energy surfaces or profiles are descriptions of reactions at the molecular level. In practice, experimental observations are usually of the behaviour of very large numbers of molecules in solid, liquid, gas or solution phases. The link between molecular descriptions and macroscopic measurements is provided by transition state theory, whose premise is that activated complexes which form from reactants are in equilibrium with the reactants, both in quantity and in distribution of internal energies, so that the conventional relationships of thermodynamics can be applied to the hypothetical assembly of transition structures. 

In addition to being a function of T, the partition function is also a function of V, on which the quantum description of matter tells us that the molecular energy levels, , depend. Because, for single-component systems, all intensive state variables can be written as functions of two state variables, we can think of q(T, V) as a state function of the system. The partition function can be used as one of the independent variables to describe a single-component system, and with one other state function, such as T, it will completely define the system. All other properties of the system (in particular, the thermodynamic functions U, H, S, A, and G) can then be obtained from q and one other state function. 

In the theoretical description of regular polymers, the monoelectronic levels (orbital energies in the molecular description) are represented as a multivalued function of a reciprocal wave number defined in the inverse space dimension. The set of all those branches (energy bands) plotted versus the reciprocal wave number (k-point) in a well defined region of the reciprocal space (first Brillouin zone) is the band structure of the polymers. In the usual terminology, we note the analogy between the occupied levels and the valence bands, the unoccupied levels and the conduction band. 

Method (III) attempts to include a discrete molecular description of the solvent structure around a central solute molecule. The solute molecule is described, again, through a QM calculation while the spatial distribution, charge distribution, polarizabilities etc. of the adjacent part of the solvent is represented by a parametrized molecular mechanics (MM) model. The parametrization may be achieved through high level calculations on the isolated solvent molecules. 

The stereoelectronic representation (or lattice representation) of a molecule is a molecular description related to those molecular properties arising from electron distribution - interaction of the molecule with probes characterizing the space surrounding them (e.g. - molecular interaction fields). This representation is typical of - grid-based QSAR techniques. Descriptors at this level can be considered 4D-descriptors, being characterized by a scalar field, i.e. a lattice of scalar numbers associated with the 3D - molecular geometry. 

Fig.1 Description of a commonly encountered molecular energy level spectrum the singlet (S = 0) and triplet (S = 1) spectra have heen artificially separated...

Here the situation is very similar to that encountered in connection with the need for continuum (constitutive) models for the molecular transport processes in that a derivation of appropriate boundary conditions from the more fundamental, molecular description has not been accomphshed to date. In both cases, the knowledge that we have of constitutive models and boundary conditions that are appropriate for the continuum-level description is largely empirical in nature. In effect, we make an educated guess for both constitutive equations and boundary conditions and then normally judge the success of our choices by the resulting comparison between predicted and experimentally measured continuum velocity or temperature fields. Models derived from molecular theories, with the exception of kinetic theory for gases, are generally not available for comparison with the empirically proposed models. We discuss some of these matters in more detail later in this chapter, where specific choices will be proposed for both the constitutive equations and boundary conditions. 

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