Quantum similarity approach

Ponec, R., Amat, L. and Carb6-Dorca, R. (1999). Molecular Basis of Quantitative Structure-Properties Relationships (QSPR) A Quantum Similarity Approach. J.Comput.Aid.Molec. Des., 13,259-270. 

Molecular similarity, in turn, was expressed in the next step, directly on the topological representations of shapes, and at this level, quantum similarity is not involved directly. Using differential and algebraic topological representations of molecular shapes had several advantages when compared to the direct Quantum Similarity approach ... 

Hence while the topological shape analysis and shape similarity measures do not truly represent a Non-Quantum Similarity approach, nevertheless, in practical terms, they offer a powerful alternative. 

Ponec R, Amat L, Carbo-Dorca R. Molecular basis of quantitative structure-properties relationships (QSPR) a quantum similarity approach. J Comput-Aided Mol Des 1999 13 259-270. 

Molecular Basis of Quantitative Structure-Properties Relationships (QSPR) A Quantum Similarity Approach. 

Thus, for a transition between any two vibrational levels of the proton, the fluctuation of the molecular surrounding provides the activation. For each such transition, the motion along the proton coordinate is of quantum (sub-barrier) character. Possible intramolecular activation of the H—O chemical bond is taken into account in the theory by means of the summation of the probabilities of transitions between all the excited vibrational states of the proton with a weighting function corresponding to the thermal distribution.3,36 Incorporation in the theory of the contribution of the excited states enabled us in particular to improve the agreement between the theory and experiment with respect to the independence of the symmetry factor of the potential in a wide region of 8[Pg.135]

In 1973161, Rinaldi and Rivail proposed an approach that combines the quantum-mechanical level of description of chemical molecules with the macroscopic concept of the reaction field. A similar approach was introduced by Tapia and Goscinski in 1975162. 

By its size, this chapter fails to address the entire background of MQS and for more information, the reader is referred to several reviews that have been published on the topic. Also it could not address many related approaches, such as the density matrix similarity ideas of Ciosloswki and Fleischmann [79,80], the work of Leherte et al. [81-83] describing simplified alignment algorithms based on quantum similarity or the empirical procedure of Popelier et al. on using only a reduced number of points of the density function to express similarity [84-88]. It is worth noting that MQS is not restricted to the most commonly used electron density in position space. Many concepts and theoretical developments in the theory can be extended to momentum space where one deals with the three components of linear momentum... 

We are on our way testing if similar approaches can be applied to other, larger molecules such as pyrrole, thus with the hope to find regular patterns, supported by pseudo quantum numbers, allowing to frame the whole rovibrational structure, and therefore the IVR. 

Unlike molecular mechanics, the quantum mechanical approach to molecular modelling does not require the use of parameters similar to those used in molecular mechanics. It is based on the realization that electrons and all material particles exhibit wavelike properties. This allows the well defined, parameter free, mathematics of wave motions to be applied to electrons, atomic and molecular structure. The basis of these calculations is the Schrodinger wave equation, which in its simplest form may be stated as ... 

The key differences between the PCM and the Onsager s model are that the PCM makes use of molecular-shaped cavities (instead of spherical cavities) and that in the PCM the solvent-solute interaction is not simply reduced to the dipole term. In addition, the PCM is a quantum mechanical approach, i.e. the solute is described by means of its electronic wavefunction. Similarly to classical approaches, the basis of the PCM approach to the local field relies on the assumption that the effective field experienced by the molecule in the cavity can be seen as the sum of a reaction field term and a cavity field term. The reaction field is connected to the response (polarization) of the dielectric to the solute charge distribution, whereas the cavity field depends on the polarization of the dielectric induced by the applied field once the cavity has been created. In the PCM, cavity field effects are accounted for by introducing the concept of effective molecular response properties, which directly describe the response of the molecular solutes to the Maxwell field in the liquid, both static E and dynamic E, [8,47,48] (see also the contribution by Cammi and Mennucci). 

The last fundamental aspect characterizing PCM methods, i.e. their quantum mechanical formulation, is presented by Cammi for molecular systems in their ground electronic states and by Mennucci for electronically excited states. In both contributions, particular attention is devoted to the specific aspect characterizing PCM (and similar) approaches, namely the necessity to introduce an effective nonlinear Hamiltonian which describes the solute under the effect of the interactions with its environment and determines how these interactions affect the solute electronic wavefunction and properties. 

The idea of constrained dynamics performed for a set of points along such a reaction path , i.e. for a set of fixed values of the reaction coordinate, A, is not specific to MD. Similar approaches have been commonly used in computational studies based on static quantum-chemical calculations. Such approaches are known as linear transit calculations, reaction path scans, etc. A set of constrained geometry optimizations with the constraint driving the system from reactants to products is a popular way to bracket a transition state, for instance. 

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