Molecular superposition methods

Abstract A mixed molecular orbital and valence bond (MOVE) method has been developed and applied to chemical reactions. In the MOVE method, a diabatic or valence bond (VE) state is defined with a block-localized wave function (ELW). Consequently, the adiabatic state can be described by the superposition of a set of critical adiabatic states. Test cases indicate the method is a viable alternative to the empirical valence bond (EVE) approach for defining solvent reaction coordinate in the combined qnantum mechanical and molecnlar mechanical (QM/MM) simulations employing exphcit molecular orbital methods. 

In benzene it is found by superposition of the five canonical configurations mentioned that each bond has a double bond character of 0.389 + 0.073 = 0.462. In view of the single o-bond always present one also speaks of total bond character equal to 1 -j- the double bond character. Though this bond character ( indice de liaison double , Daudel and Pullman) from the calculations based on the Valence Bond method is different from the bond order (Penney, Coulson), e.g. in the Molecular Orbital Method, both terms are frequently used without discrimination. In Pauling s earlier very simple concept (p. 210) the bond character of benzene is just 0.5 since there only the Kekule configurations are taken into account. 

Figure 4.1 Ligand-based virtual screening methods. The figure shows different computational methods for screening compound databases that take either a local or a global view on molecular structure. Molecular similarity methods that operate on molecular descriptors, histogram representations, superposition or (reduced) molecular graphs evaluate molecular structure globally. By contrast, local structural features are explored by substructure and pharmacophore searching or QSAR modeling.

For hydrogen-treated M0S2, possible hydrogen species are shown in Fig. 7.31 with their calculated vibration frequencies according to the atom superposition and electron delocalization molecular orbital method [134]. Typical spectra of hydrogen-treated RuS2 and M0S2 [130,131] are shown in Fig. 7.32. 

In this chapter only QSAR methods which use physicochemical or structural features of molecules will be discussed, while in Chapter 25 3D-QSAR approaches will be presented. These so-called 3D-QSAR techniques, e.g. CoMFA, use the basic statistical principles, such as partial least squares (PLS), of QSAR methods, but in addition use the three-dimensional characteristics of a molecule specifically related to electronic, steric and lipophilic field effects. In these methods the molecular superposition believed relevant to binding to the target is crucial. 

The molecular orbital method is a very flexible and often successful tool for analyzing electronic structure-dependent properties. Its deficiencies are intimately connected with the treatment of superpositions of configurations. In particular, the molecular orbital model is not satisfactory when the overlap between relevant valence orbitals on adjacent atoms is smaller than 1/2. This result was particularly well illustrated by Coulson and Fischer in their well-known study of the hydrogen molecule, and it is relevant for the molecular orbital treatment of TT-electron systems, where the typical overlap is in the range 1/3-1/4. Evidence has also been presented for the insufficiency of the PPP-model when... 

Some of the first quantum-mechanical descriptions of the electrochemical interface were developed by Anderson, utilizing an atom superposition and electron delocalization molecular orbital method (ASED-MO) to generate potential surfaces for the reactant and product states using a cluster model of the electrode surface [27,32,34,49,50]. The activation barrier and equilibrium potential were extracted from the potential surfaces in a manner reminiscent of Marcus theory [51]. Recently, this approach has been... 

Fig. 3.4. With a multi-frequency measurement, frequencies beyond the measurable range of the DMA can be achieved by using the superposition method. Employing the Williams-Landel-Ferry (WLF) equation, and with a treatment of the data, designated as the method of reduced variables or time-temperature superposition (TTS) it is possible to overcome the difficulty of extrapolating limited laboratory tests at shorter times to longer-term, more real world conditions. The underlying bases for TTS are that the processes involved in molecular relaxation or rearrangements in viscoelastic materials occur at accelerated rates at higher temperatures and that there is a direct equivalency between time (the frequency of the measurement) and temperature.

Boon et al. also studied several chiral molecules, which included again two amino acids (Ala and Leu) and CHFClBr, a prototype of chiral molecules. Ab initio total molecular electron densities yielded both Euclidean distances and Carbo indices between the enantiomers of these molecules. Molecular superposition was performed with, on the one hand, a manual alignment based on chemical intuition and the QSSA method, on the other hand. When analyzing the tables of the work by Boon et al. and comparing the results to the work by Mezey et al., similar values for the Euclidean distances between the two enantiomers appear for Ala and Leu, which once again illustrates the power of the ASA promolecular densities to yield quantum similarity measures in good agreement with those obtained from ab initio calculations. 

The reader will appreciate that the problem of molecular superposition is a difficulty with many 3D-QSAR methods. The comparative molecular moment analysis (CoMMA) method overcomes this obstacle by calculating descriptors based on the 3D structures without reference to a common orientation frame. ... 

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