Distance geometry principles

Finally, Burkhard Luy, Andreas Frank and Horst Kessler discuss Conformational Analysis of Drugs by Nuclear Magnetic Resonance Spectroscopy . The determination and refinement of molecular conformations comprehends three main methods distance geometry (DG), molecular dynamics (MD) and simulated anneahng (SA). In principle, it is possible to exclusively make use of DG, MD or... 

In general, five different approaches can be distinguished and are applied to explore the conformational space of a molecule systematic searches, rule-based and data-based approaches (model building), random methods, genetic algorithms, distance geometry, and simulation methods. Some of the basic principles and ideas behind these concepts have already been described in the Secs. 2 and 3 of this article. In the following, the application of these concepts to conformational analysis and searches will be discussed. 

The basic principles of the distance geometry approach have been described in Sec. 3.4. There, it was mentioned that the embedding procedure can produce several molecular geometries that do not violate the preset distance restrictions. Therefore, distance geometry per se can be regarded as a conformational search method. 

This correction is carried out by using the scaled distance, d , based on the similitude principle proposed by Hopkinson in 1915, according to which when two explosive charges of similar geometry and of the same explosive but different sizes, detonate in the same atmosphere, similar pressure waves are generated at the same scaled distance. This principle can also be applied to two different explosives, taking into account the fact that two types of explosion with the same overpressure give rise to the same effects. Because overpressure is a function of the distance and two different explosions do not cause the same overpressure at the same distance from the center of the explosion, the scaled distance is defined as that at which the overpressure has the same value for both explosions. The scaled distance is related to the real distance and to the equivalent TNT mass by the cubic root law. 

B. Lambert and E. P. Mazzola, Nuclear Magnetic Resonarwe Spectroscopy, An Introduction to Principles, Applications, and Experimental Methods, Pearson Education, Upper Saddle River, NJ, 2004. (d) J. M. Blaney and J. S. Dixon, Distance Geometry in Molecular Modeling, Reviews in Computational Chemistry, Vol. 5, K. B. Lipkowitz and D. B. Boyd, Eds., Wiley, New York, 1994, p. 299. 

As shown in Fig. 6, there is a correlation between absorption spectrum and emission spectrum. Taking into consideration the Franck-Condon principle, which states that there is no motion of the atoms during an electronic transition, one has to differentiate between the two following possibilities in the one the geometry of the excited state is similar to the one of the ground state (same interatomic distances),... 

There are N(N-l)/2 distinct distances in a cluster of N atoms, disregarding symmetry-dictated equivalencies. This set of distances is of course redundant 3N-6 Cartesian coordinates are sufficient to determine molecular geometry, apart from the position of the center of mass and the orientation of the principle moments of inertia. 

Verify that the d0 values thus calculated show a relatively narrow distribution around a mean value close to 0.2 nm. Criticize or defend the following proposition As a mean center-to-center intermolecular spacing, this value is on the low side as a back-calculated parameter, however, it probably compensates for deviations from the assumed geometry, breakdown of Equation (33) at short distances, or other shortcomings of the molecular additivity principle. 

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