Related papers: Reconsidering Power Functional Theory
Density functional theory is usually formulated in terms of the density in configuration space. Functionals of the momentum-space density have also been studied, and yet other densities could be considered. We offer a unified view from a…
This article presents a reformulation of the Theory of Functional Connections: a general methodology for functional interpolation that can embed a set of user-specified linear constraints. The reformulation presented in this paper exploits…
We review some of the basic mathematical results about density functional theory.
Density Functional Theory (DFT) is one of the most widely used methods for "ab initio" calculations of the structure of atoms, molecules, crystals, surfaces, and their interactions. Unfortunately, the customary introduction to DFT is often…
The restoration of particle number within Energy Density Functional theory is analyzed. It is shown that the standard method based on configuration mixing leads to a functional of both the projected and non-projected densities. As an…
The ongoing replication crisis in science has increased interest in the methodology of replication studies. We propose a novel Bayesian analysis approach using power priors: The likelihood of the original study's data is raised to the power…
Usually, density functional models are considered approximations to density functional theory, However, there is no systematic connection between the two, and this can make us doubt about a linkage. This attitude can be further enforced by…
This note states and proves a representation theorem for regular quantity functions, based on the theory of quantity spaces, thereby giving a new perspective on dimensional analysis and the classical $\pi$ theorem.
Potential functional approximations are an intriguing alternative to density functional approximations. The potential functional that is dual to the Lieb density functional is defined and properties given. The relationship between…
Though calculations based on density functional theory (DFT) are used remarkably widely in chemistry, physics, materials science, and biomolecular research and though the modern form of DFT has been studied for almost 60 years, some…
In a recent paper [Phys. Rev. A 77, 062511 (2008)], it was advocated to modify the variational principle for the action-integral functional in the Runge-Gross foundation of time-dependent density-functional theory. This was criticised in a…
We establish a new generalized Taylor's formula for power fractional derivatives with nonsingular and nonlocal kernels, which includes many known Taylor's formulas in the literature. Moreover, as a consequence, we obtain a general version…
Force fields are usually formulated directly in nuclear configuration space, whereas density functional theory is naturally formulated in terms of external potentials, densities, and variational duality. We show that exact force fields are…
The derivation is studied in relation with the space of Schwartz of functions. This paper has been withdrawn by the author.
This work introduces a new functional series for expanding an analytic function in terms of an arbitrary analytic function. It is generally applicable and straightforward to use. It is also suitable for approximating the behavior of a…
We consider the set of power functions defined on the set of positive real number, and their linear combinations. After recalling some properties of the gamma function, we give two general definitions of derivatives of positive and negative…
This article has been published as a chapter in "Chemical Reactivity Theory: A Density Functional View", ed. P. K. Chattaraj (CRC Press, New York, 2009), ch. 8, p. 105. In it, an overview of the relationship between time-dependent DFT and…
The rich and diverse dynamics of particle-based systems ultimately originates from the coupling of their degrees of freedom via internal interactions. To arrive at a tractable approximation of such many-body problems, coarse-graining is…
We prove a stronger version of Jarden's Theorem for recurrence of powers of recursive functions
A density-functional theory is developed based on the Maxwell--Schr\"odinger equation with an internal magnetic field in addition to the external electromagnetic potentials. The basic variables of this theory are the electron density and…