Density functional theory classification

Classification of Density Functional Theory Possibly Variationally... 

CLASSIFICATION OF DENSITY FUNCTIONAL THEORY POSSIBLY VARIATIONALLY VALID VERSUS HEURISTIC... 

This book is concerned with the quantum chemical methods for the calculations of electromagnetic properties of molecules. However, in detail only so-called ab initio quantum chemical methods will be discussed in Part III. As ab initio methods one normally describes those quantmn chemical methods that start from the beginning, i.e. methods that require the evaluation of all the terms in the Schrodinger or Dirac equation and do not include other experimentally determined quantities than the nuclear charges, nuclear masses, nuclear dipole and quadrupole moments and maybe positions of the nuclei. This is in contrast to the so-called semi-empirical methods where many of the integrals over the operators in the Hamiltonian are replaced by experimentally or otherwise determined constants. However, in the case of density functional theory (DFT) methods the classification is somewhat debatable. 

The focus in this chapter is on quantum chemical methods. These can be classified as semiempirical, ab initio, and density functional theory (DFT) methods. The latter ones usually involve empirical parameterization and, hence, sometimes are also considered as semiempirical methods. Alternatively, a distinction on the basic quantity - wave function (WF) or electronic density - can be made as wave-function-based methods (WFT) and DFT. In this classification scheme, wave-function-based methods include semiempirical as well as ah initio procedures. Although the impact of semiempirical methods on the progress of quantum chemistry can hardly be overestimated [13], their use now is mainly restricted to very large systems [14]. Thus, in the following the description of wave-function-based procedures will be restricted to ah initio methods. 

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... 

Semiempirical approaches to quantum chemistry are thus characterized by the use of empirical parameters in a quantum mechanical framework. In this sense, many current methods contain semiempirical features. For example, some high-level at initio treatments of thermochemistry employ empirical corrections for high-order correlation effects, and several advanced density functionals include a substantial number of empirical parameters that are fitted against experimental data. We shall not cover such approaches here, but follow the conventional classification by considering only semiempirical methods that are based on molecular orbital (MO) theory and make use of integral approximations and parameters already at the MO level. 

Bulat FA, Toro-Labbe A (2003) An extension of the Hammond postulate. Structural effects on the classification of chemical reactions. J Phys Chem A 107 3987-3994 Toro-Labbe A, Gutierrerez-Oliva S, Murray JS, Politzer P (2007) A new perspective on chemical and physical processes the reaction force. Mol Phys 105 2619-2625 Toro-Labbe A, Gutierrerez-Oliva S, Politzer P, Murray JS (2009) The reaction force a rigorously defined approach to analyzing chemical and physical processes. In Chattaraj PK (ed) Chemical reactivity theory a density functional view. CRC, Boca Raton, pp 293-302 90. Politzer P et al (2005) The reaction force three key points along an intrinsic reaction coordinate. J Chem Sci 117 467-472... 

In the emerging theory of interfacial thermodynamics, the properties of the thermodynamic functions (PVT or free energy quantities) at densities corresponding to thermodynamically unstable states play a crucial role. For example, the Interfacial tension is computed from a formula calling for Helmholtz free energy data at every density (composition) between the compositions of the bulk phases in equilibrium. A particular implication of the theory is that Method (a) of Professor Prausnltz s classification is useful for interfacial calculations of vapor-liquid systems, but Method (b) is not. For those interested in the interfacial theory to which I refer, the following papers and references therein may be useful ... 

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