A density functional representation of quantum chemistry. II. Local quantum field theories of molecular matter in terms of the charge density operator do not work

Abstract

AbstractsA comprehensive review of the attempts to rephrase molecular quantum mechanics in terms of the particle density operator and the current density or phase density operator is given. All pertinent investigations which have come to our attention suffer from severe mathematical inconsistencies and are not adequate to the few-body problem of quantum chemistry. The origin of the failure of these attempts is investigated and it is shown that a realization of a local quantum field theory of molecular matter in terms of observables would presuppose the solution of many highly nontrivial mathematical problems.Dans une revue dttaillte de la IittCrature nous exposons les tentatives de reformuler la mtcanique quantique molCculaire directement ? i I'aide des optrateurs de densitt de particules, de courant ou de phase. Tous les travaux consider& comportent dimportantes inconsistences mathkmatiques et ne sont pas adaptables au problkme pluricorps de la chimie quantique. A la suite d'une Ctude sur les raisons de cet Cchec on montre que la rtalisation d'une thCorie de champs quantique local en termes d'observables implique la rtsolution de nombreux problkmes mathkmatiques qui w i t loin5 d'ctre triviauu.

Energy Density Functional Theory of Many-Electron Systems

“…is a very difficult one (Primas, 1967;Primas and Schleicher, 1975;Schleicher and Primas, 1975). In order to illustrate some of its complications it is instructive to carry out a detailed comparative analysis between the real t(r) == t( [-y(r; r'll; r) and its local density forms tn· ([p(r)]; T) and tTF ([p(r) ) since the latter varies in an infinite interval, including positive and negative values and produces all the local peculiarities of the quantum kinetic energy (for example, see Figure 4.20, we plot t(l), tw and tTF for the Hartree-Fock ground-state of the neon atom.…”

Approximating quasi‐particle density functional calculations of small active clusters: Strong electron correlation effects

“…It is known that quantum chemistry of conservative and unbounded-in3Dspace molecules is well defined in the framework of the nonrelativistic quantum mechanics of a finite number of electrons and nuclei. The naive model has been an important reason for the success of practical quantum chemistry [5,6]. But the simple "superm~lecular~~ approach gives us the only possibility for description on equal terms of both the conservative intramolecular forces between constituent parts of a single molecule and dissipative intermolecular forces between "different molecules," which are, in turn, constituent parts of the supermolecule [l-31.…”