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Int. J. Mol. Sci. 2009, 10(11), 4816-4940; doi:10.3390/ijms10114816
Review

Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems

Received: 3 September 2009 / Revised: 23 October 2009 / Accepted: 2 November 2009 / Published: 10 November 2009
(This article belongs to the Special Issue Applications of Density Functional Theory)
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Abstract

The density matrix theory, the ancestor of density functional theory, provides the immediate framework for Path Integral (PI) development, allowing the canonical density be extended for the many-electronic systems through the density functional closure relationship. Yet, the use of path integral formalism for electronic density prescription presents several advantages: assures the inner quantum mechanical description of the system by parameterized paths; averages the quantum fluctuations; behaves as the propagator for time-space evolution of quantum information; resembles Schrödinger equation; allows quantum statistical description of the system through partition function computing. In this framework, four levels of path integral formalism were presented: the Feynman quantum mechanical, the semiclassical, the Feynman-Kleinert effective classical, and the Fokker-Planck non-equilibrium ones. In each case the density matrix or/and the canonical density were rigorously defined and presented. The practical specializations for quantum free and harmonic motions, for statistical high and low temperature limits, the smearing justification for the Bohr’s quantum stability postulate with the paradigmatic Hydrogen atomic excursion, along the quantum chemical calculation of semiclassical electronegativity and hardness, of chemical action and Mulliken electronegativity, as well as by the Markovian generalizations of Becke-Edgecombe electronic focalization functions – all advocate for the reliability of assuming PI formalism of quantum mechanics as a versatile one, suited for analytically and/or computationally modeling of a variety of fundamental physical and chemical reactivity concepts characterizing the (density driving) many-electronic systems.
Keywords: density matrix and functionals; Feynman integral; partition function; electronegativity; chemical action and hardness; Fokker-Planck equation; electronic localization density matrix and functionals; Feynman integral; partition function; electronegativity; chemical action and hardness; Fokker-Planck equation; electronic localization
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Putz, M.V. Path Integrals for Electronic Densities, Reactivity Indices, and Localization Functions in Quantum Systems. Int. J. Mol. Sci. 2009, 10, 4816-4940.

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