Density domain approach

The Density Domain Approach to Functional Groups and Local Molecular Properties... 

Apparently, the concept of similarity plays an important role in the chemistry of functional groups. Motivated by the recent revival of interest in molecular similarity [7-39], we shall present a systematic approach towards a quantum chemical description of functional groups. There are two main components of the approach described in this report. The first component is shape-similarity, based on the topological shape groups and topological similarity measures of molecular electron densities[2,19-34], whereas the second component is the Density Domain approach to chemical bonding [4]. The topological Density Domain is a natural basis for a quantum... 

THE DENSITY DOMAIN APPROACH TO FUNCTIONAL GROUPS AND LOCAL MOLECULAR PROPERTIES... 

The density domain approach was first proposed [4] as a tool for the description of chemical bonding where the complete shape information of the molecular electron density was taken into account. Density domains are formal bodies of electron density clouds enclosed by MIDCOs defined by eq. (1) [or by eq. (2) if there is no need to specify the nuclear configuration K],... 

One of the exceptions, that offers an alternative to the conventional bond diagrams is the density domain approach [4,5] to chemical bonding. This approach is based on the following observation for a given molecule with a specified nuclear configuration K, the infinite family (DD(a,K) of density domains for the range (0, amax] of density thresholds,... 

One of the main advantages of the density domain approach is the introduction of a natural model for a quantum chemical representation of formal functional groups [1-3]. Consider the simplest case a single connected density domain DD(a,K) and all the nuclei contained within DD(a,K). The boundary MIDCO G(a,K) of the density domain DD(a,K) separates this subset of the nuclei of the molecule from the rest of the nuclei. This fact indicates that the nuclei embedded within DD(a,K), together with a local electronic density cloud surrounding them, represent a sub-entity of the molecule. This sub-entity has an individual identity, since for a range of density threshold values including the value a, the local electron density cloud is separable from the density cloud of the rest of the molecule. 

The Density Domain Approach (DDA) to chemical bonding has been proposed [109] as a tool that is able to describe the global properties as well as the fine details of the full, three-dimensional bonding pattern within molecular bodies. 

The Density Domain Approach to chemical bonding is based on the topological analysis of the dominant shape variations of the molecular body DD(a) [or, equivalently, those of the G(a) contour surface] regarded as a function of the density parameter a. 

One may summarize the essence of the approach as follows. The Density Domain Approach is a 3D topological tool for a comprehensive description of chemical bonding [ 09], By decreasing the contour parameter a from high values to zero, the various density domains DDj(a), that is, the parts of the body DD(a) become connected. The isodensity surface threshold values aj at which such connections occur are characteristic to the given configuration of the nuclei and to the electronic state. In actual computations, if the density domains are calculated by some ab initio technique, then the calculated aj values and the associated shapes of... 

For most practical applications, CIMM is used within the framework of local measures. These measures are based on local shape matrices or on the shape groups of local moieties, defined either by the density domain approach mentioned earlier, or by alternative conditions, such as the simple truncation condition replacing the "remainder" of the molecule by a generic domain [192], For proper complementarity, identity or close similarity of the patterns of the matched domains is an advantage, hence the parts Cl HM)) and Cl KM2) of the corresponding local shape codes are compared directly. For shape complementarity only the specified density range [bq - Aa, Bq + Aa] and a specified curvature range of the (a,b) parameter maps is considered. A local shape complementarity measure, denoted by... 

Shape codes [43,109,196,351,408]. The simplest topological shape codes derived from the shape group approach are the (a,b) parameter maps, where a is the isodensity contour value and b is a reference curvature against which the molecular contour surface is compared. Alternative shape codes and local shape codes are derived from shape matrices and the Density Domain Approach to functional groups [262], as well as from Shape Globe Invariance Maps (SGIM). 

Fi e 3 Two approximate isodensity surfaces of the butadiene molecule, obtained for density contour parameter values a = 0.25c/(a.u.) and a = 0.02c/(a.u.), respectively. Note that according to the density domain approach (DDA) to chemical bonding, all molecular fragments are bonded together at both density levels shown. 

Figure 4 Three cross sections of approximate isodensity surfaces of the butadiene molecule, obtained for density contour parameter values a 0.40e/(a.u.) aj = 0.30e/(a.u.), and a = 0.27e/(a.u.) respectively. Note that according to the density domain approach (DDA) to chemical bonding, no bonding occurs at density level (Zj, and only me pairs of carbon centers that are formally double bonded according to the conventional description are bonded at density level ai- Near the density level 03 the formal conjugated system of four carbon centers becomes bonded. However, for the manifestation of bonding of all nuclear centers of the molecule, a somewhat lower density level is required, as illustrated in Figure 3.

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