Theories of Electronic Structure

The result is that, to a very good approxunation, as treated elsewhere in this Encyclopedia, the nuclei move in a mechanical potential created by the much more rapid motion of the electrons. The electron cloud itself is described by the quantum mechanical theory of electronic structure. Since the electronic and nuclear motion are approximately separable, the electron cloud can be described mathematically by the quantum mechanical theory of electronic structure, in a framework where the nuclei are fixed. The resulting Bom-Oppenlieimer potential energy surface (PES) created by the electrons is the mechanical potential in which the nuclei move. Wlien we speak of the internal motion of molecules, we therefore mean essentially the motion of the nuclei, which contain most of the mass, on the molecular potential energy surface, with the electron cloud rapidly adjusting to the relatively slow nuclear motion. 

The Exclusion Principle is fundamentally important in the theory of electronic structure it leads to the picture of electrons occupying distinct molecular orbitals. Molecular orbitals have well-defined energies and their shapes determine the bonding pattern of molecules. Without the Exclusion Principle, all electrons could occupy the same orbital. 

W Kohn. Density functional theory of electronic structure. J Phys Chem 100 12974-12980, 1996. 

A different approach is adopted here. Within the LMTO-ASA method, it is possible to vary the atomic radii in such a way that the net charges are non-random while preserving the total volume of the system . The basic assumption of a single-site theory of electronic structure of disordered alloys, namely that the potential at any site R depends only on the occupation of this site by atom A or B, and is completely independent of the occupation of other sites, is fulfilled, if the net charges... 

Modern theories of electronic structure at a metal surface, which have proved their accuracy for bare metal surfaces, have now been applied to the calculation of electron density profiles in the presence of adsorbed species or other external sources of potential. The spillover of the negative (electronic) charge density from the positive (ionic) background and the overlap of the former with the electrolyte are the crucial effects. Self-consistent calculations, in which the electronic kinetic energy is correctly taken into account, may have to replace the simpler density-functional treatments which have been used most often. The situation for liquid metals, for which the density profile for the positive (ionic) charge density is required, is not as satisfactory as for solid metals, for which the crystal structure is known. 

Kohn, W., A. D. Becke, and R. G. Parr. 1996. Density Functional Theory of Electronic Structure. J. Phys. Chem. 100,12974. 

Equation 4.9 has been extensively applied to study the mechanisms of electrophilic (e.g., protonation) reactions, drug-nucleic acid interactions, receptor-site selectivities of pain blockers as well as various other kinds of biological activities of molecules in relation to their structure. Indeed, the ESP has been hailed as the most significant discovery in quantum biochemistry in the last three decades. The ESP also occurs in density-based theories of electronic structure and dynamics of atoms, molecules, and solids. Note, however, that Equation 4.9 appears to imply that p(r) of the system remains unchanged due to the approach of a unit positive charge in this sense, the interaction energy calculated from V(r) is correct only to first order in perturbation theory. However, this is not a serious limitation since using the correct p(r) in Equation 4.9 will improve the results. 

Among various theories of electronic structure, density functional theory (DFT) [1,2] has been the most successful one. This is because of its richness of concepts and at the same time simplicity of its implementation. The new concept that the theory introduces is that the ground-state density of an electronic system contains all the information about the Hamiltonian and therefore all the properties of the system. Further, the theory introduces a variational principle in terms of the ground-state density that leads to an equation to determine this density. Consider the expectation value (H) of the Hamiltonian (atomic units are used)... 

One requires both these perspectives to tackle all issues in the theory of electronic structure of molecules and their chemical reactivity. The wave function and... 

Harbola-Sahni approximation. Since these two approximations were derived by using completely different reasoning, their coincidence strongly enhances expectation that this function is very close to the exact v (r). See [35] for the latest review of the Harbola-Sahni work formalism approach to the theory of electronic structure. 

Thirty years after Hohenberg and myself realized the simple but important fact that the theory of electronic structure of matter can be rigorously based on the electronic density distribution n(r) a most lively conference was convened by Professor R. Nalewajski and his colleagues at the Jagiellonian University in Poland s historic capital city, Krakow. The present series of volumes is an outgrowth of this conference. 

The single-configuration mean-field theories of electronic structure neglect correlations among the electrons. That is, in expressing the interaction of an electron at r... 

The overall picture of the atom envisioned by Bohr was a dense nncleus of fixed charge surrounded by rings of electrons. The comphcated optical spectra and the simple x-ray spectra suggested that the ring closest to the nucleus was different than the outer rings. More theory and more observations were necessary to refine this picture, but the shell theory of electronic structure has persisted. 

Hartree-Fock theory is a rigorous ab initio theory of electronic structure and has a vast array of successes to its credit. Equilibrium structures of most molecules are calculated almost to experimental accuracy, and reasonably accurate properties (e.g., dipole moments and IR and Raman intensities) can be calculated from HF wave functions. Rela-... 

Vol. 29 N.D. Epiotis, Unified Valence Bond Theory of Electronic Structure Vlll, 305 pages. 1982. 

The general theory of electronic structure of complex systems and their PES are based on the tacit assumption that the basis orbitals are well defined orthonormal functions, which can be conveniently divided into two (or more if necessary) classes. The reality is much more tough and results in serious conceptual problems in all the existing packages offering hybrid modelization techniques in their respective menus. These have been addressed in the previous section. Now we address the meaning of the results obtained so far. In fact, up to this point, we obtained the description suitable for any hybrid QM/QM method. Within this context, the distribution of orbitals... 

Epiotis, N. D., Larson, J. R., and Eaton, H. L. (1982). Unified Valence Bond Theory of Electronic Structure, Lecture Notes in Chemistry, Vol. 29. Springer-Verlag, Berlin and New York. 

In this respect, chemistry does not differ from other sciences. Contemporary chemical research is organized around a hierarchy of models that aid its practitioners in their everyday quest for the understanding of natural phenomena. The building blocks of the language of chemistry, including the representations of molecules in terms of structural formulae [1], occupy the very bottom of this hierarchy. Various phenomenological models, such as reaction types and mechanisms, thermodynamics and chemical kinetics, etc. [2], come next. Quantum chemistry, which at present is the supreme theory of electronic structures of atoms and molecules, and thus of the entire realm of chemical phenomena, resides at the very top. 

Hehre, W. J., Ditchfield, R., Radom, L., and Pople, J. A., Molecular orbital theory of electronic structure of organic compounds. 5. Molecular theory of bond separation. J. Am. Chem. Soc. 92, 4796 801 (1970). 

Adams, W. H. (1962). Orbital theories of electronic structure. J. Chem. Phys. 37, 2009-18. 

Tsukada, M., J. Adachi, and C. Satoko (1983). Theory of electronic structure of oxide surfaces. Prog. Surf. Sci. 14, 113-74. 

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