Molecular similarity quantum mechanical concepts

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

At the molecular level, shape is now reali d to be one of the most fundamental concepts of chemistry, even though it may be difficult to quantify [67], In 1980 the first quantum-mechanical measure of shape similarity for molecules was put forward by Carbo et al. [68]. This measure, which was intended to be of special use in molecular design studies, proved to be of seminal influence. For any two molecules, M and N, the similarity, S ns was defined as the ratio... 

The characterization of the interrelations between chemical bonding and molecular shape requires a detailed analysis of the electronic density of molecules. Chemical bonding is a quantum mechanical phenomenon, and the shorthand notations of formal single, double, triple, and aromatic bonds used by chemists are a useful but rather severe oversimplification of reality. Similarly, the classical concepts of body and surface , the usual tools for the shape characterization of macroscopic objects, can be applied to molecules only indirectly. The quantum mechanical uncertainty of both electronic and nuclear positions within a molecule implies that valid descriptions of both chemical bonding and molecular shape must be based on the fuzzy, delocalize properties of electronic density distributions. These electron distributions are dominated by the nuclear arrangements and hence quantum mechanical uncertainly affects electrons on two levels by the lesser positional uncertainty of the more massive nuclei, and by the more prominent positional uncertainty of the electrons themselves. These two factors play important roles in chemistry and affect both chemical bonding and molecular shape. 

In conclusion, it became evident to the physicists that the concept of isosterism, developed before quantum-mechanical theories, could not provide at the molecular level the same results as those that the periodic classification had provided for the elements, namely a correlation between electronic structure and physical and chemical properties. In the field of medicinal chemistry the isosterism concept, taken in its broadest sense, has proved to be a research tool of the utmost importance. The main reason for this is because isosteres are often much more alike in their biological than in their physical and chemical properties. An illustrative example is found in the comparison of oxazolidine-diones and hydantoins which possess different chemical reactivities, but present a similar antiepileptic profile (Fig. 13.2). 

As stated, the most important concept in molecular quantum similarity is the electron density. The idea of the electron density as the ultimate molecular descriptor is founded on the basic elements of quantum mechanics. It is the alldetermining quantity in DFT, and it holds a close relation to the wave function. It is therefore appropriate in this context to raise the question of whether the electron density can really be considered as the all-determining entity in quantum similarity studies. Clear indications of this conclusion were described by Flandy and are attributed to Wilson,although initial ideas can also be traced back to Born" and von Neumann." The electron density p(r) has several important features. First, integrated over all space, it gives the number of electrons ... 

In fact, one of the objectives of the book is to introduce nonexpert readers to modem computational spectroscopy approaches. In this respect, the essential basic background of the described theoretical models is provided, but for the extended description of concepts related to theory of molecular spectra readers are referred to the widely available specialized volumes. Similarly, although computational spectroscopy studies rely on quantum mechanical computations, only necessary aspects of quantum theory related directly to spectroscopy will be presented. Additionally, we have chosen to analyze only those physical-chemical effects which are important for molecular systems containing atoms from the first three rows of the periodic table, while we wiU not discuss in detail effects and computational models specifically related to transition metals or heavier elements. Particular attention has been devoted to the description of computational tools which can be effectively applied to the analysis and understanding of complex spectroscopy data. In this respect, several illustrative examples are provided along with discussions about the most appropriate computational models for specific problems. 

The concept of diabatic states dates back to the beginnings of molecular quantum mechanics, since it is implicit in the work of Landau and Zener on the electronic transitions occurring at a curve crossing (see Valence Bond Curve Crossing Models). Similar concepts underlie the drawing of correlation diagrams, first introduced by Hund and Mulliken around 1930, and subsequently exploited, among others, by Woodward and Hoffmann, to formulate their famous rules (see Photochemistry). 

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