A density functional representation of quantum chemistry. I. Motivation and general formalism

Abstract

Abstract The molecular N ‐electron problem is formulated in terms of the particle density 𝔔( r ) = ∑σ( r − q n ) and its canonically conjugated field. Weyl's representation of the canonical commutation relations is used and a characteristic functional of the molecular system is introduced as the expectation value of Weyl's functional exp { i (α, Q) + i (β, P)}. The Hamiltonian equation of motion for the characteristic functional is derived and its cumulant approximation is discussed. The first paper is restricted to a general discussion, independent of a special choice of the Hamiltonian. The density functional representation may be considered as a step towards a formulation of a renormalized quantum chemistry. The lowest order cumulants of the characteristic functional are accessible to actual precision measurements; on the other hand, most experiments are correctly represented by a characteristic functional of the Gaussian type. The significance of the higher order correlations is neither theoretically nor experimentally disclosed yet, their possible importance for biological systems is mentioned, and the question is raised of how far quantum mechanics is empirically confirmed for extremely complex systems.