Given a vector space of microscopic quantum observables, density functional theory is formulated on its dual space. A generalized Hohenberg-Kohn theorem and the existence of the universal energy functional in the dual space are proven. In this context ordinary density functional theory corresponds to the space of one-body multiplication operators. When the operators close under commutation to f...

Density functional theory (DFT) has become the most popular by far of the panoply of methods in quantum chemistry and the reason for this is simple. Where other schemes had become bogged down in mindnumbingly expensive and detailed treatments of the electron correlation problem, DFT simply shrugged, pointed at the Hohenberg–Kohn theorem, and asserted that the correlation energy can be written a...

A recent article in The Intelligencer described in some detail the theory of non-well-founded sets for the purpose of being able to solve freely equations of the sort X = A × X with A fixed ([Barwise & Moss, 1991]). Of course, the empty set is a solution, but what was wanted was a non-empty solution (in fact, the largest solution, if such exists). If X were a non-empty solution and x ∈ X, then ...

The vacuum expectation value of the S-matrix is represented, following HORI, as a functional integral and separated according to 5Vac = exp( — i W) f D (p exp( —i / d x L w ) . Now, the functional integral involves only the part L w of the Lagrangian without derivatives and can be easily calculated in lattice space. We propose a graphical scheme which formalizes the action of the operator r = /...

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Kohn-Sham density functional theory (KS-DFT)[1, 2] is an efficient and usefully accurate electronic structure method, because it replaces the interacting Schrödinger equation with a set of single-particle orbital equations. Calculations with several hundred atoms are now routine, but there is always interest in much larger systems. Many such systems are treated by a lower-level method, such as ...