Quantum mechanics method definition

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. 

The ET processes under discussion here correspond by definition to pure ET, in which molecular or medium coordinates may shift (the polaron response) [17], but no overall bonding rearrangements occur. More complex ET processes accompanied by such rearrangements (e.g., coupled electron/proton transfer and dissociative ET) are of great current interest, and many theoretical approaches have been formulated to deal with them, including quantum mechanical methods based on DC treatment of solvent [31,32],... 

Explicit definitions for the response tensors are arrived at by quantum-mechanical methods. Allowing for the notation of equations (1) and (2), we used the expressions... 

In this review, we will deal with molecular properties obtained via quantum mechanical methods where comparison with experiment when available will be made. Note, however, that not all properties considered are amenable to experiment. We will in particular show how the study of aromaticity can benefit a lot from density functional theory (DFT). " During the past decade, this theory has received enormous attention and gained a lot of popularity in the quantum chemistry community. Although some theories were developed in the past using the electron density (for a review, see, e.g., ref 44), it obtained its definitive status after the formulation of two theorems proven by Hohenberg en Kohn in 1964, putting forward the electron density as the basic variable... 

There is a tendency to use the term molecular mechanics (MM) as opposite to quantum mechanics, therefore including all classical dynamics methods, such as energy minimization, Monte Carlo, and molecular dynamics. Sometimes it is used to describe only the energy minimization method using empirical force field (potential) or it is even used to refer to the quantum mechanical method specifically, emphasizing its use for molecular motion. Nevertheless, we will focus on the second definition of molecular mechanics (43-45). In this approach, a molecule is viewed as a collection of particles (atoms) held together by simple harmonic or elastic forces. Such forces are defined in terms of potential energy... 

The heat of formation is the energy released as heat when atoms situated at theoretically infinite distance approach, bind, and form the molecule of interest. The core includes, by definition, the atomic nucleus and the electrons that do not participate in chemical bonds, that is, the nonvalence electrons. The semiempirical method PM6 estimates the heat of formation as the sum of the total repulsion energy of the cores and the total heat of formation of the atoms. Each semiempirical quantum mechanics method calculates, in its own manner, the energy of repulsion of the cores and utilizes a different set of values for the atomic heat of formation. Consequently, the values of the heat of formation determined for the same molecule by different semiempirical... 

Evaluation of equations (5.76) and (5.78) via diagrammatic or conventional quantum-mechanical methods results in the explicit spin-independent CCD equations, given elsewhere. The definitions... 

At a physical level. Equation 35 represents a mixing of all of the possible electronic states of the molecule, all of which have some probability of being attained according to the laws of quantum mechanics. Full Cl is the most complete non-relativistic treatment of the molecular system possible, within the limitations imposed by the chosen basis set. It represents the possible quantum states of the system while modelling the electron density in accordance with the definition (and constraints) of the basis set in use. For this reason, it appears in the rightmost column of the following methods chart ... 

The definition of "concepts" must be accompanied by explicit recipes for computing them is actual cases. There is no more space in theoretical chemistty for "driving forces", "effects, etc. not accompanied by specific rules for their quantification. The impact of a new "concept will be greater if the rules of quantifications are not restricted to ad hoc methods, but related to methods of general use in molecular quantum mechanics. A concept based exclusively on some specific features of a given method, e g. the extended Hiickel method, is less robust than a concurrent concept which may be quantified also using other levels of the theory. 

By definition, a mixed quantum-classical method treats the various degrees of freedom (DoF) of a system on a different dynamical footing—for example, quantum mechanics for the electronic DoF and classical mechanics for the... 

The usefulness of spectral densities in nonequilibrium statistical mechanics, spectroscopy, and quantum mechanics is indicated in Section I. In Section II we discuss a number of known properties of spectral densities, which follow from only the form of their definitions, the equations of motion, and equilibrium properties of the system of interest. These properties, particularly the moments of spectral density, do not require an actual solution to the equations of motion, in order to be evaluated. Section III introduces methods which allow one to determine optimum error bounds for certain well-defined averages over spectral densities using only the equilibrium properties discussed in Section II. These averages have certain physical interpretations, such as the response to a damped harmonic perturbation, and the second-order perturbation energy. Finally, Section IV discusses extrapolation methods for estimating spectral densities themselves, from the equilibrium properties, combined with qualitative estimates of the way the spectral densities fall off at high frequencies. 

A structure for a system is represented in quantum mechanics by a wave function, usually called a function of the coordinates that in classical theory would be used (with their conjugate momenta) in describing the system. The methods for finding the wave function for a system in a particular state are described in treatises on quantum mechanics. In our discussion of the nature of the chemical bond we shall restrict our interest in the main to the normal states of molecules. The stationary quantum states of a molecule or other system are states that are characterized by definite values of the total energy of the system. These states are designated by a quantum number, repre-... 

The following definition of computational chemistry was published in 1985 (6) quantitative modeling of chemical behavior on a computer by the formalisms of theoretical chemistry. Some quantum theoreticians naturally would like to see computational chemistry as a subset of their field (7). However, today the number of scientists employed as computational chemists well exceeds the number employed as theoreticians (8). A recent textbook author (9) views computational chemistry as encompassing not only quantum mechanics, but also molecular mechanics, [energy] minimization, simulations, conformational analysis, and other computer-based methods for understanding and predicting the behavior of molecular systems. ... 

Thus, we have attempted to give, in the present appendix, an idea of the various methods of determining classical and quantum mechanical polarization moments and some related coefficients. We have considered only those methods which are most frequently used in atomic, molecular and chemical physics. An analysis of a great variety of different approaches creates the impression that sometimes the authors of one or other investigation find it easier to introduce new definitions of their own multipole moments, rather than find a way in the rather muddled system of previously used ones. This situation complicates comparison between the results obtained by various authors considerably. We hope that the material contained in the present appendix might, to some extent, simplify such a comparison. 

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