Loge Theory

Comparatively little space will therefore be devoted to some rather recent approaches, such as the plasma model of Bohm and Pines, the two-body interaction method developed by Brueckner in connection with nuclear theory, Daudel s loge theory, and the method of variation of the second-order density matrix. This does not mean that these methods would be less powerful or less impor-... 

So, the loge theory provides the best justification of Lewis ideas. For example, it is found that the six electrons of the BH molecule are distributed two by two in core, bond, and lone-pair loges. This result corresponds to the classical (Lewis) formula ... 

The loge theory leads also to a unified description of the various types of chemical bonds (Daudel and Veillard, 1970). 

The loge theory proposes to divide the spatial region into cells. These latters are determined by maximizing the probability for that a given number of electrons be in a given cell [23-25]. One can also minimize the missing information about the system (containing the cells). 

It should be finally recalled, that the Loge Theory has made a vital connection between the Information Theory and the theory of electronic structure [142], i.e., a... 

Some pioneering efforts relating Information Theory to electronic structure and properties of molecules can be already found in the seminal papers by Daudel in the framework of loge theory [6, 7], subsequently followed by Mezey [8] and reexamined later by Nalewajski [9], The studies of Mezey [10] and Avnir [11] on symmetry and chirality-related problems in molecules, and in other very diverse fields (e.g., image and texture analysis), are also examples of applications of informational measures on specific aspects of shape, disorder, and complexity. 

Abstract The paper presents maximum probability domains (MPDs). These are regions of the three dimensional space for which the probability to find a given number of electrons is maximal. In order to clarity issues hidden by numerical uncertainties, some simple models are used. They show that MPDs reproduce features which one would expect using chemical intuition. For a given number of electrons, there can be several solutions, corresponding to different chemical situations (e.g. different bonds). Some of them can be equivalent, by symmetry. Symmetry can produce, however, alternative solutions. The models show that MPDs do not exactly partition space, and they can also be formed by disjoint subdomains. Finally, an example shows that a partition of space, as provided by loge theory, can lead to situations difficult to deal with, not present for MPDs. 

It was shown that using the missing information function, as it is done in loge theory, can produce unwanted results. 

Eq. (3.9) arises from the absolute rate theory and can be expressed in the following logarithmic form, using the numeric values of the Boltzmann constant k, the gas constant R, the Planck constant h, and loge [108]. 

The derivation is much more complicated than those outlined previously, especially when the quantum version is considered. Both versions are a vast improvement on the previous theories, and predict that 1 /klst versus 1/[A] should be a curve, and that the plot of loge kx versus 1/7 should be linear. Both predictions are verified by experiment. 

If the theory is adequate, then a plot of loge kohs versus I should be linear with slope = -zaZb e2 /4 tt Sq IcT. 

Stehling MK, Niedermeyer M, Laub G (1997) [Contrast medium enhanced magnetic resonance angiography. Theory, technique and practical implementation], Radio-loge 37 501-507... 

Daudel and co-workers (Daudel 1953, 1968 Daudel et al. 1955 Aslangul et al. 1972) were the first to provide a definition of the localization of electrons based solely upon information contained in the state function. They proposed that information theory (Shannon 1948) be used to define the best division of a system into regions or loges . According to this theory our knowledge about a given system is a maximum when the missing information function /(F ,Q) is minimized where... 

Using the definition of the best loges as the ones which minimize l(P , 12), Daudel et al. (1974) applied this theory to a number of diatomic and triatomic molecules containing up to six electrons, namely, LiH, BeH", BH, and BeH2. 

Another empirical extension suggested that there should be a term such as Dcactuai loge actuai This term will come into prominence in the later theories of Fuoss and Onsager (1957 and later) and other workers (see Sections 12.10 and 12.17). 

R. Daudel, S. Odiot, and H. Brion, C.R. Acad. Sci. Paris, 238,458 (1954). La notion de loge et la signification geometrique de la notion de couche dans le cortege electronique des atomes. H. Brion, R. Daudel and S. Odiot,/. Chim. Phys., 51, 553 (1954). Theorie de la localisabilite des corpuscules. TV. Emploi de la notion de loge dans I etude des liaisons chimiques. 

He emphasized that quantum chemistry was built upon many chemical concepts, often inherited from classical chemical theories. K-electrons, L-electrons, valence electrons, 7c- or (7-electrons, localized or delocalized electrons, bonds, and so forth, were certainly incompatible with the quantum mechanical ideas of indistinguishability and nonlocality but had proved to be very useful tools for chemists and had been appropriated by quantum chemists (Daudel 1952). Hence, he argued, they should be given alternative formulations compatible with the new physics. Such was the case of the concept of "loge" introduced by Daudel and his students to explain quantum-... 

---