Electron density models

Both space-filling and electron density models yield similar molecular volumes, and both show the obvious differences in overall size. Because the electron density surfaces provide no discernible boundaries between atoms (and employ no colors to highlight these boundaries), the surfaces may appear to be less informative than space-filling models in helping to decide to what extent a particular atom is exposed . This weakness raises an important point, however. Electrons are associated with a molecule as a whole and not with individual atoms. The space-filling representation of a molecule in terms of discernible atoms does not reflect reality, but rather is an artifact of the model. The electron density surface is more accurate in that it shows a single electron cloud for the entire molecule. 

Complementary spherical electron density model. D. M. P. Mingos and J. C. Hawes, Struct. Bonding (Berlin), 1985, 63,1 (93). 

Mildvan AS, Grisham CM (1974) The Role of Divalent Cations in the Mechanism of Enzyme Catalyzed Phosphoryl and Nucleotidyl. 20 1-21 Mingos DMP, Hawes JC (1985) Complementary Spherical Electron Density Model. 63 1-63 Mingos DMP, Johnston RL (1987) Theoretical Models of Cluster Bonding. 68 29-87 Mingos DMP, McGrady JE, Rohl AL (1992) Moments of Inertia in Cluster and Coordination Compounds. 79 1-54... 

An electron density model of sulfur dioxide shows low electron density blue) around the sulfur atom and high electron density red) on the oxygen atoms. 

Spin densities determine many properties of radical species, and have an important effect on the chemical reactivity within the family of the most reactive substances containing free radicals. Momentum densities represent an alternative description of a microscopic many-particle system with emphasis placed on aspects different from those in the more conventional position space particle density model. In particular, momentum densities provide a description of molecules that, in some sense, turns the usual position space electron density model inside out , by reversing the relative emphasis of the peripheral and core regions of atomic neighborhoods. 

Breneman, C. M., Thompson, T. R., Rhem, M., and Dung, M. (1995) Electron density modeling of large systems using the transferable atom equivalent method. Comp. Chem. 19, 161-179. 

A promising simplification has been proposed by Bader (1990) who has shown that the electron density in a molecule can be uniquely partitioned into atomic fragments that behave as open quantum systems. Using a topological analysis of the electron density, he has been able to trace the paths of chemical bonds. This approach has recently been applied to the electron density in inorganic crystals by Pendas et al. (1997, 1998) and Luana et al. (1997). While this analysis holds great promise, the bond paths of the electron density in inorganic solids are not the same as the more traditional chemical bonds and, for reasons discussed in Section 14.8, the electron density model is difficult to compare with the traditional chemical bond models. 

A closer comparison of bond valence and electron density models is not possible because of the different underlying assumptions of the models. The forces in the bond valence model act between structureless point atoms, but the forces in the electron density model are exerted by electrons on nuclei and vice versa. This basic difference makes it difficult to compare the two models in greater detail. They are best seen as complementary, the electron density model providing important information about the nature of the bonding between the atoms, the bond valence model providing a simple tool for predicting structure and properties, particularly in cases where the structure is complex. 

In Table 13, calculated and measured geometry data of substituted cyclopropanes are compared with predictions of the MO model of Clark andcoworkers (Table 14)33 and those of the electron density model by Cremer and Kraka (Table 15)97. From the comparison, it becomes clear that both models lead to similar predictions, but differ with regard to some... 

Vinylcyclopropane " The vinyl group can act both as m-donor and re-acceptor. This is indicated by lengthening of all ring bonds, where the vicinal bonds become longer than the distal bond. The same bond length pattern is obtained by considering the re-attractor propensity of the vinyl group on the basis of the electron density model. ... 

Summary. The electron density model of substituent-ring interactions functions better than the MO model, which is not surprising since the electron density covers all MO effects while any MO model will simplify orbital interactions by selecting just a few important... 

In the following two sections two approaches will be discussed where molecular fragments are represented by fuzzy electron density models. 

Another method is to calculate the molecular electronic electrostatic potential by replacing p(r ) in Eq. 19 by its multipole formulation (Eq. 8). The quantity obtained represents the electrostatic potential of a molecule removed from the crystal lattice. First calculations have been performed by the Pittsburgh group (Stewart, Craven, He, and co-workers) [43] electrostatic potential calculations were also derived from the Hansen Coppens [lib] electron density model [41,44], The atomic total electrostatic potential including nuclear contribution may be calculated as ... 

Two important tools of electron density modeling and shape analysis are the concepts of molecular isodensity contour, MIDCO G(K,a) and the associated density domain DD(K,a) [27], Here the nuclear arrangement (also called the nuclear configuration) is denoted by K, whereas the electron density threshold is denoted by a. Each MIDCO G(K,a) is the collection of all those points r of the three-dimensional space where the electron density p(K,r) of the molecule M of conformation K is equal to the threshold a. The density domain DD(K,a) is the collection of all points r where the electron density p(K,r) is greater than or equal to the threshold a. Using formal notations,... 

Halocyclopropanes. According to Clark and coworkers,F acts predominantly as cr-acceptor. If 71-donor ability is invoked for F, then controversial geometry effects are predicted by the MO model. Predictions by the electron density model of Cremer and Kraka are consistent, no matter whether cr-attractor or 7r-repeller ability of F is considered (Table 13). The other halogens are also cr-attractors/7r-repellers but their effects on the geometry of 1 decrease in the order... 

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