Topological approach

Finally, an alchemical free energy simulation is needed to obtain the free energy difference between any one substate of system A and any one substate of system B, e.g., Ai- In practice, one chooses two substates that resemble each other as much as possible. In the alchemical simulation, it is necessary to restrain appropriate parts of the system to remain in the chosen substate. Thus, for the present hybrid Asp/Asn molecule, the Asp side chain should be confined to the Asp substate I and the Asn side chain confined to its substate I. Flat-bottomed dihedral restraints can achieve this very conveniently [38], in such a way that the most populated configurations (near the energy minimum) are hardly perturbed by the restraints. Note that if the substates AI and BI differ substantially, the transfomnation will be difficult to perform with a single-topology approach. 

This topological approach with connectivity indices has been extended by Bicerano [58] to a point where many of the physical properties of the polymer can be estimated from empirical predictive equations. Bicerano correlated connectivity indices with group contribution values in order to develop a model equation for a specific property [58]. The usefulness of Bicerano s equations is that they can be extended to predict the same property values for new interested polymers. 

As we mentioned in the introduction, the topological approach is very convenient here, as it is possible to eliminate the independent variable between the differential equations... 

Microreactors find new niches, Achema Daily/Chemical Engineering, June 1997 Conclusions on IMRETl micro-reactor exhibitors at ACHEMA 1997 expert opinions industry s commitment general advantages of micro flow views on commercialization extended list of leading institutes and companies activities topological approach numbering-up [226],... 

Leherte, L., Fortier, S., Glasgow, J. and Allen, F.H. (1994) Molecular scene analysis application of a topological approach to the automated interpretation of protein electron-density maps, Acta Cryst., D50, 155-166 and references therein. 

The mechanisms by which an inhibitor adds to an oxidized hydrocarbon exerts its influence may differ depending on the reaction conditions. If the rate constants of the elementary reactions of RH, InH, R02 , In, ROOH, and 02 are known, the kinetics of the inhibited oxidation of RH can mathematically be described for any conditions. However, such an approach fails to answer questions how the mechanism of inhibited oxidation is related to the structure and reactivity of InH, RH, and R02 or what inhibitor appears the most efficient under the given conditions, and so on. At the same time, these questions can easily be clarified in terms of a topological approach whose basic ideas are the following [43-45,70-72] ... 

A. Graovac, I. Gutman and N. Trinajstic, Topological Approach to the Chemistry of Conjugated Molecules, Springer-Verlag, Berlin, 1972. 

Prunell, A. (1998) A topological approach to nucleosome structure and dynamics. The linking number paradox and other issues. Biophys. J. 74, 2531-2544. 

The study of chemical reactions requires the definition of simple concepts associated with the properties ofthe system. Topological approaches of bonding, based on the analysis of the gradient field of well-defined local functions, evaluated from any quantum mechanical method are close to chemists intuition and experience and provide method-independent techniques [4-7]. In this work, we have used the concepts developed in the Bonding Evolution Theory [8] (BET, see Appendix B), applied to the Electron Localization Function (ELF, see Appendix A) [9]. This method has been applied successfully to proton transfer mechanism [10,11] as well as isomerization reaction [12]. The latter approach focuses on the evolution of chemical properties by assuming an isomorphism between chemical structures and the molecular graph defined in Appendix C. 

Initially, the topological approach has been widely used only for the analysis of theoretical charge densities. Theoretical analysis allows us to consider two atoms as bonded, whereas experiments show only their spatial proximity (x-ray or neutron diffraction), changes in the vibrational behavior of an H-X bond involved in interaction, changes in magnetic shielding of target nuclei (NMR), and so on. 

Manceau, A. Combes, J.M. (1988) Structure of Mn and Fe oxides and oxyhydroxides a topological approach by EXAFS. Phys. Chem. Min. 15 283-295... 

The topological approach is an extension of simpler gronp contribntion efforts, as it can inclnde contributions of higher order, where gronp contribntions are essentially... 

The topological approach of Ranada and Trueba, the general relativistic approach of Sachs, and the 0(3) electrodynamics are interlinked and shown to be based on the concept of Faraday s lines of force. 

Finally, if we abandon Hiickel s topological approach altogether and consider more elaborate quantum-mechanical approaches, the concept of aromaticity derived purely from a consideration of -electrons becomes blurred and tends to disappear completely. In fact, allelectron methods allow the calculation of aromatic properties (Section V,B) of a given substance without introducing explicitly the concept of aromaticity. Certain authors, notably Dewar,19 have published resonance energies derived from self-consistent field molecular-orbital (SCF-MO) calculations, and these could be used as a measure of aromaticity. 

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