Quantum chemical equations methodology

The outlook given in this chapter on the theory of the second-order contracted Schrodinger equation and on its methodology has been aimed mostly at convincing the reader that this theory is not difficult to understand and that its methodology is now ready to be applied. That is, in the author s opinion, this methodology can be considered as accurate and probably more economical than the best standard quantum chemical computational methods for the study of states where the occupation number of spin orbitals is close to one or zero. 

The use of quantum chemistry to obtain the individual rate coefficients of a free-radical polymerization process frees them from errors due to kinetic model-based assumptions. However, this approach introduces a new source of error in the model predictions the quantum chemical calculations themselves. As is well known, as there are no simple analytical solutions to a many-electron Schrodinger equation, numerical approximations are required. While accurate methods exist, they are generally very computationally intensive and their computational cost typically scales exponentially with the size of the system under study. The apphcation of quantum chemical methods to radical polymerization processes necessarily involves a compromise in which small model systems are used to mimic the reactions of their polymeric counterparts so that high levels of theory may be used. This is then balanced by the need to make these models as reahstic as possible hence, lower cost theoretical procedures are frequently adopted, often to the detriment of the accuracy of the calculations. Nonetheless, aided by rapid and continuing increases to computer power, chemically accurate predictions are now possible, even for solvent-sensitive systems [8]. In this section we examine the best-practice methodology required to generate accurate gas- and solution-phase predictions of rate coefficients in free-radical polymerization. 

Ab initio methods solve the molecular Schrodinger equation associated with the molecular Hamiltonian based on different quantum-chemical methodologies that are derived directly from theoretical principles without inclusion of any empirical or semiempirical parameters in the equations. Though rigorously defined on first principles (quantum theory), the solutions from ab initio methods are obtained within an error margin that is qualitatively known beforehand thus all the solutions are approximate to some extent. Due to the expensive computational cost, ab initio methods are rarely used directly to study the physicochemical properties of flotation systems in mineral processing, but their application in developing force fields for molecular mechanics (MM) and MD simulation has been extensively documented. (Cacelli et al. 2004 Cho et al. 2002 Kamiya et al. 

Methodology. Unquestionably, the application of quantum mechanics to chemical bonding has revolutionized scientific thinking. In fact, the modern theoretical framework of chemistry rests on quantum physics. In principle, the Schrodinger equation may be solved for any chemical system. No prior knowledge of any analogous or related system is necessary. Exactly solvable problems are rare, due to the mathematical complexities recourse must then be made to approximate methods, and many powerful approaches have been devised. Generally, approximate solutions must suffice for the size of molecules of pharmaceutical interest. 

Is this the context in which the book of Mihai V. Putz, Quantum Structure-Activity Relationship Qu-SAR) add a plus-value and insight in QSAR methodology, especially in establishing the chemical-biological mechanism of interaction, so fulfilling the celebrated fifth amendment of the OECD-QSAR directives, otherwise very difficult to assess in general as based on a multivariate equation. To this aim, new theoretical approaches, like Spectral-SAR, propose purely algebraic alternatives... 

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