Quantum chemistry separation

On the first level of the spatiotemporal scale are the QM and quantum chemical approaches. Most applications of quantum chemistry separate the motion of the nuclei from the motion of electrons. This treatment is called Bom-Oppenheimer (BO)... 

Although a separation of electronic and nuclear motion provides an important simplification and appealing qualitative model for chemistry, the electronic Sclirodinger equation is still fomiidable. Efforts to solve it approximately and apply these solutions to the study of spectroscopy, stmcture and chemical reactions fonn the subject of what is usually called electronic structure theory or quantum chemistry. The starting point for most calculations and the foundation of molecular orbital theory is the independent-particle approximation. 

The first basic approximation of quantum chemistry is the Born-Oppenheimer Approximation (also referred to as the clamped-nuclei approximation). The Born-Oppenheimer Approximation is used to define and calculate potential energy surfaces. It uses the heavier mass of nuclei compared with electrons to separate the... 

It is common that mechanochemical degradation involves scission of the macromolecule, so one basic question would be to inquire about the level of stress necessary to separate two chemical moieties which have been attached by a covalent bond. Besides the academic interest, the breaking strength of a covalent bond is associated with the ultimate properties of engineering materials and has attracted considerable attention since the beginnings of quantum chemistry. 

I have reported this last example not for the sake of completeness in our discussion, but to underline a different point. Quantum chemistry, in the work of CTOup 1 and even more in the work of group II, put the emphasis on some properties which by tradition are not object of direct experimental determination. Electron charge distribution and MEP arejust two examples. The use of these quantities by theoreticians has spurred the elaboration of experimental methods able to measure them. This positive feedback between theory and experiment is an indication that quantum and experimental chemistry do not live in separate worlds. 

Quantum mechanically, however, the diatomic molecule and the separated atoms at infinite distance are two distinct quantum systems having their own quantum states. The physical dissociation cannot be seen as a continuous process of extending a classical spring as nearly all textbooks in chemistry, physical chemistry and quantum chemistry suggest. This is quite contrary to the fundamentals of quantum mechanics itself. Before... 

Present quantum chemistry is mainly concerned with the calculation of bond energies. Accordingly, for the rest of this chapter we shall concentrate mainly on solvation enthalpies. The latter, being magnitudes composed of a lot of strongly interwoven effects, do not allow a simple separation of bulk and outer-shell influences. 

There are several possible ways of introducing the Born-Oppenheimer model " and here the most descriptive way has been chosen. It is worth mentioning, however, that the justification for the validity of the Bom-Oppenheimer approximation, based on the smallness of the ratio of the electronic and nuclear masses used in its original formulation, has been found irrelevant. Actually, Essen started his analysis of the approximate separation of electronic and nuclear motions with the virial theorem for the Coulombic forces among all particles of molecules (nuclei and electrons) treated in the same quantum mechanical way. In general, quantum chemistry is dominated by the Bom-Oppenheimer model of the theoretical description of molecules. However, there is a vivid discussion in the literature which is devoted to problems characterized by, for example, Monkhorst s article of 1987, Chemical Physics without the Bom-Oppenheimer Approximation... ... 

The direct variational solution of the Schrddinger equation after separation of the center of mass motion is in general possible and can be performed very accurately for three- and four- body systems such as (Kolos, 1969) and H2 (Kolos and Wolniewicz, 1963 Bishop and Cheung, 1978). For larger systems it is unlikely to perform such calculations in the near future. Therefore the usual way in quantum chemistry is to introduce the adiabatic approximation. The nonrelativistic hamiltonian for a diatomic N-electron molecule in the center of mass system has the following form (in atomic units). 

In the quantum mechanical description of molecules (atoms and clusters) one problem has been the identification and validity of adiabatic separations of electronic ip) md nuclear (R) coordinates [30] This problem has been with us ever since the Bom-Oppenheimer (BO) theory was published in 1927 [1,2]. But this approach, as implemented in quantum chemistry, has serious deceiving aspects. 

Primas, H. Separability in many-electron systems. In Modem quantum chemistry. Istanbul lectures. Sinanoglu, O. (ed.). New York Academic Press 1965 s°) Paldus, J., Ctzek, J. Relation of coupled-pair theory, Cl and some other many-body approaches. In Energy, Structure, and Reactivity. Proceedings of the 1972 Boulder Summer Research Conference on Theoretical Chemistry. Smith, D. W., McRae, W. B. (eds.). New York Wiley 1973, pp. 198-212... 

H. Primas. Separability in many electron systems, in Modem Quantum Chemistry. Istanbul Lectures ed. by O. Sinanoglu, Academic, New York, 1965. 

The theoretical tools of quantum chemistry briefly described in the previous chapter are numerously implemented, sometimes explicitly and sometimes implicitly, in ab initio, density functional (DFT), and semi-empirical theories of quantum chemistry and in the computer program suits based upon them. It is usually believed that the difference between the methods stems from different approximations used for the one- and two-electron matrix elements of the molecular Hamiltonian eq. (1.177) employed throughout the calculation. However, this type of classification is not particularly suitable in the context of hybrid methods where attention must be drawn to the way of separating the entire molecular system (eventually - the universe itself) into parts, of which some are treated explicitly on a quantum mechanical/chemical level, while others are considered classically and the rest is not addressed at all. That general formulation allows us to cover both the traditional quantum chemistry methods based on the wave functions and the DFT-based methods, which generally claim... 

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