Molecular system structure representation

A connection table has been the predominant form of chemical structure representation in computer systems since the early 1980s and it is an alternative way of representing a molecular graph. Graph theory methods can equally well be applied to connection table representations of a molecule. 

We describe here a new structure representation which extends the valence bond concept by new bond types that account for multi-haptic and electron-deficient bonds. This representation is called Representation Architecture for Molecular Structures by Electron Systems (RAMSES) it tries to incorporate ideas from Molecular Orbital (MO) Theory [8T]. 

A universal, computer oriented representation of the relevant structural features of molecular systems and their interconversion by chemical reactions is possible with the pairwise combinations (E, C) of BE-matrices and CC-matrices. The transformation... 

It is to be noted that the QSPR/QSAR analysis of nanosubstances based on elucidation of molecular structure by the molecular graph is ambiguous due to a large number of atoms involved in these molecular systems. Under such circumstances the chiral vector can be used as elucidation of structure of the carbon nanotubes (Toropov et al., 2007c). The SMILES-like representation information for nanomaterials is also able to provide reasonable good predictive models (Toropov and Leszczynski, 2006a). 

Simulation methods have been proved to be useful in the study of many different molecular systems, in particular in the case of flexible polymers chains [ 14]. According to the variety of structures and the theoretical difficulties inherent to branched structures, simulation work is a very powerful tool in the study of this type of polymer, and can be applied to the general problems outHned above. Sometimes, this utility is manifested even for behaviors which can be explained with simple theoretical treatments in the case of linear chains. Thus, the description of the theta state of a star chain cannot be performed through the use of the simple Gaussian model. The adequate simulation model and method depend strongly on the particular problem investigated. Some cases require a realistic representation of the atoms in the molecular models [10]. Other cases, however, only require simplified coarse-grained models, where some real mon-... 

So far, CG approaches offer the most viable route to the molecular modeling of self-organization phenomena in hydrated ionomer membranes. Admittedly, the coarse-grained treatment implies simplifications in structural representation and in interactions, which can be systematically improved with advanced force-matching procedures however, it allows simulating systems with sufficient size and sufficient statishcal sampling. Structural correlations, thermodynamic properties, and transport parameters can be studied. 

Mislow and Bickart (258) have recently discussed the properties, and specified the limitations and essential features, of models that can be used for the prediction of chirality of a molecular system. In the simplified and idealized representation of molecular stracture, nonessential features are deliberately left out the model summarizes some selected aspects of the system and completely disregards or even falsifies, others. The model must be adequate to the time scale in which the phenomenon is observed. In particular, in mobile conformational systems it should refer to a time-averaged structure. In other words, the model can have a higher symmetry than that observed under static conditions (e.g., by X-ray diffraction in the crystalline state or by NMR under slow exchange conditions) (259). 

Scheme 2.2 Schematic representation of a proton-jumping molecular system with fast enol-enolic equilibrium between structures la and lb.

Computer-Aided Property Estimation Computer-aided structure estimation requires the structure of the chemical compounds to be encoded in a computer-readable language. Computers most efficiently process linear strings of data, and hence linear notation systems were developed for chemical structure representation. Several such systems have been described in the literature. SMILES, the Simplified Molecular Input Line Entry System, by Weininger and collaborators [2-4], has found wide acceptance and is being used in the Toolkit. Here, only a brief summary of SMILES rules is given. A more detailed description, together with a tutorial and examples, is given in Appendix A. 

Similar to quantum mechanics, which can be formulated in terms of different quantities in addition to the traditional wave function formulation, in quantum chemistry a number of alternative tools are developed for this purpose, which may be useful in the context of the present book. We have already described different approximate models of representing the electronic structure using (many-electronic) wave functions. The coordinate and second quantization representations were employed to get this. However, the entire amount of information contained in the many-electron wave function taken in whatever representation is enormously large. In fact it is mostly excessive for the purpose of describing the properties of any molecular system due to the specific structure of the operators to be averaged to obtain physically relevant information and for the symmetry properties of the wave functions the expectation values have to be calculated over. Thus some reduced descriptions are possible, which will be presented here for reference. 

Qualitative valence-bond (VB) descriptions of the electronic structures of molecules are often able to provide "primitive patterns of understanding" [1] of the origin of various molecular properties. In this chapter, we shall give consideration to VB structures for some molecular systems that involve four active-space orbitals. The discussion will include VB formulations of the electronic structures of isolated molecules, reaction mechanisms, and types of "metallic orbitals" that can be used in VB representations for electron conduction in metallic lithium. For the latter topic, the results of STO-6G VB calculations are reported in order to make a provisional comparison of two conduction mechanisms. 

Chemical structure representation formats (e.g., InChl, Simplified Molecular Line Entry System [SMILES])... 

About 20 years ago, the theory of the be- and r-matrices, a global algebraic model of the logical structure of constitutional chemistry was formulated. This theory is the first direct mathematical approach to chemistry which also accentuates its dynamic aspect. The representation by mathematics comprises the individual objects of chemistry and also their relations, including their interconvertibility by chemical reactions. A decade later, the theory of the chemical identity groups was published in a monograph. It is a unified theory of stereochemistry that is primarily devoted to relations between molecular systems. 

The fourth paper in this volume is devoted to some extensions and generalizations of the algebra of the be- and r-matrices. The latter is only valid for the chemistry of molecular systems that are representable by integer bond orders and thus is not applicable to the great variety of molecules with multi-center bonds and delocalized electron systems. This deficiency is overcome by the introduction of the so-called extended be- and r-matrices the xbe- and xr-matrices. They contain additional rows/columns which refer to the delocalized electron systems. Some corresponding data structures are presented that also account for stereochemical aspects. 

We will in this section introduce the representation of the electronic wave function of the molecular system and describe how we determine the wave function of the quantum mechanical subsystem including interactions with the structured environment. We consider the situation where the MCSCF electronic wave function of the quantum mechanical subsystem is optimized while interacting with a classical system represented by charges, polarization sites and van der Waals sites. We start out by expressing the total electronic free energy for the QM/MM-system as... 

All intermolecular interactions can be adequately described, at least in principle, by multidimensional scalar and vector fields representing the energetics of a molecular system as functions of both intermolecular distances and orientations as well as intramolecular structure data. The visualization of these fields, however, has to be based on a three-dimensional picture or a two-dimensional projection because human pattern recognition ability is strongly related to the two- and three-dimensional world. Consequently, the multidimensional field has to be reduced to a two- or three-dimensional representation. In molecular science this can be done in many different ways. 

The above considerations also hold for different hierarchical descriptions of a system at a given level, i.e. the same level is traversed by an inner hierarchical organization because of different descriptions of the same elements. The molecular representations are hierarchical descriptions of the molecular system, therefore, derived from the different representations of the molecular structure several - molecular descriptors are calculated with different chemical information contents. 

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