Conceptual density functional theory properties

Huang, Y., Zhong, A., Rong, C., Xiao, X., and Liu, S. 2008. Structure, spectroscopy, and reactivity properties of porphyrin pincers A conceptual density functional theory and time-dependent density functional theory study. J. Phys. Chem. A 112 305-311. 

E = Si) and EN(R)CH=CHNR (e.g. 2, E = Si) (R = H, Bu ) have been reported " " it was concluded that there is significant p -p -delocalisation for the latter compounds. The relationship between stability, acid-base and spin properties, nucleophilicity and electrophilicity in a series of silylenes was studied by conceptual density functional theory." ... 

Conceptual density functional theory has been quite successful in providing quantitative definitions for popular qualitative chemical concepts like electronegativity , hardness and electrophilicity . It has also been found to be useful in providing firm theoretical bases for the associated electronic structure principles. Various global and local reactivity descriptors " have played an important role in analyzing bonding, reactivity, stability, interactions and aromaticity in a variety of many-electron systems as well as a host of their physico-chemical properties. 

J. Olah, T. Veszpermi, F. De Proft and P. Geerlings. Silylenes A unified picture of their stability, acid/base and spin properties, nucleophilicity, and electrophihcity via computational and conceptual density functional theory. J. Phys. Chem. A 111, 2007,10815. 

The three main approaches based on the single-particle density are the density functional theory (DFT), quantum fluid dynamics (QFD), and studying the properties of a system through local quantities in 3D space. In this chapter, we present simple discussions on certain conceptual and methodological aspects of the single-particle density for details, the reader may consult the references listed at the end of this chapter. 

In this section, it is shown that some properties and quantities arising from the noncomputational or conceptual side of density functional theory can be proposed as aromaticity measures. 

It is shown that Density Functional Theory offers both a conceptual and a computational tool for chemists in relating electronic structure of atoms and molecules to their properties both as isolated systems and upon interaction. The computational performance of DFT in the calculation of typical DFT quantities such as electronegativity and hardness and in the ev uation of atomic electronic affinities and molecular dipole and quadrupole momCTits is assessed. DFT concepts are discussed as such (a non finite difference evaluation of the electronic Fukui function, local softness and its use in similarity analysis of peptideisosteres and the nuclear Fukui function as a indicator of nuclear rearrangemCTits upon reaction) and in the context of principles (EEM, MHP, HSAB) for a variety of reactions involving the influence of solvent on the acidity of alcohols and the addition of HNC to dipolarophiles. 

Compared with density functional methods, Hartree-Fock-based approaches play a less important role in electronic structure calculations of solids and surfaces, although the exact treatment of the exchange terms is conceptually very appealing. The inclusion of electronic correlation effects in the form of perturbation theory, coupled cluster methods, or configuration interaction expansion is very well developed for the calculation of molecular properties. However, in most cases these approaches are not suited for solid state systems. 

Therefore, the conceptual ideas of kinetic theory rely on the assumption that the mean flow, transport and thermodynamic properties of a collection of gas molecules can be obtained from the knowledge of their masses, number density, and a probabilistic velocity distribution function. The gas is thus described in terms of the distribution function which contains information of the spatial distributions of molecules, as well as about the molecular velocity distribution, in the system under consideration. 

As an example, it has been pointed out that the Hamaker and Lifshitz theories assume (exphcitly and implicitly, respectively) that intensive physical properties of the media involved such as density, and dielectric constant, remain unchanged throughout the phase—that is, right up to the interface between phases. We know, however, that at the atomic or molecular level solids and liquids (and gases under certain circumstances) exhibit short-range periodic fluctuations they are damped oscillating functions. Conceptually, if one visualizes a hquid in contact with a flat solid surface (Fig. 4.8a), one can see that the molecules (assumed to be approximately spherical, in this case) trapped between the surface and the bulk of the liquid will have less translational freedom relative to the bulk and therefore be more structured. That structure will (or may) result in changes in effective intensive properties near the surface. 

In a series of impressive publications. Maxwell [95-98] provided most of the fundamental concepts constituting the statistical theory recognizing that the molecular motion has a random character. When the molecular motion is random, the absolute molecular velocity cannot be described deterministically in accordance with a physical law so a probabilistic (stochastic) model is required. Therefore, the conceptual ideas of kinetic theory rely on the assumption that the mean flow, transport and thermodynamic properties of a collection of gas molecules can be obtained from the knowledge of their masses, number density, and a probabilistic velocity distribution function. The gas is thus described in terms of the distribution function which contains information of the spatial distributions of molecules, as well as about the molecular velocity distribution, in the system under consideration. An important introductory result was the Maxwellian velocity distribution function heuristically derived for a gas at equilibrium. It is emphasized that a gas at thermodynamic equilibrium contains no macroscopic gradients, so that the fluid properties like velocity, temperature and density are uniform in space and time. When the gas is out of equilibrium non-uniform spatial distributions of the macroscopic quantities occur, thus additional phenomena arise as a result of the molecular motion. The random movement of molecules from one region to another tend to transport with them the macroscopic properties of the region from which they depart. Therefore, at their destination the molecules find themselves out of equilibrium with the properties of the region in which they arrive. At the continuous macroscopic level the net effect... 

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