Related papers: The Role of the Basis Set: Assessing Density Funct…
Density functional theory has become the workhorse of quantum physics, chemistry, and materials science. Within these fields, a broad range of applications needs to be covered. These applications range from solids to molecular systems, from…
We present a broadly-applicable, physically-motivated first-principles approach to determining the fundamental gap of finite systems. The approach is based on using a range-separated hybrid functional within the generalized Kohn-Sham…
Density functional theory can be extended to excited states by means of a unified variational approach for passive state ensembles. This extension overcomes the restriction of the typical density functional approach to ground states, and…
We develop the theory justifying the application of the density-based basis-set correction (DBBSC) method to double-hybrid approximations in order to accelerate their basis convergence. We show that, for the oneparameter double hybrids…
In this review we provide a rigorous and self-contained presentation of one-body reduced density-matrix (1RDM) functional theory. We do so for the case of a finite basis set, where density-functional theory (DFT) implicitly becomes a 1RDM…
I describe the foundation of a Density Functional Theory approach to include pairing correlations, which was applied to a variety of systems ranging from dilute fermions, to neutron stars and finite nuclei. Ground state properties as well…
The Hohenberg-Kohn theorem of density functional theory (DFT) for the case of electrons interacting with an external magnetic field (that couples to spin only) is examined in more detail than previously. A unexpected generalization is…
An alternative definition of the concept is given of functional dependence among the attributes of the relational schema in the Relational Model, this definition is obtained in terms of the set theory. For that which a theorem is…
Constraints on cosmological parameters are often distilled from sky surveys by fitting templates to summary statistics of the data that are motivated by a fiducial cosmological model. However, recent work has shown how to estimate the…
Estimating the ratio of two probability densities from a finite number of observations is a central machine learning problem. A common approach is to construct estimators using binary classifiers that distinguish observations from the two…
This paper reviews the functional aspects of statistical learning theory. The main point under consideration is the nature of the hypothesis set when no prior information is available but data. Within this framework we first discuss about…
The fundamental measure density functional theory for hard spheres is generalized to binary mixtures of arbitrary positive and moderate negative non-additivity between unlike components. In bulk the theory predicts fluid-fluid phase…
A set of bi-orthogonal potential-density basis functions is introduced to model the density and its associated gravitational field of three dimensional stellar systems. Radial components of our basis functions are weighted integral forms of…
A density functional theory (DFT) framework is presented that links functional derivatives of free-energy functionals to non-linear static density response functions in quantum many-body systems. Within this framework, explicit expressions…
A classical density functional theory is applied to study solvation of solutes in water. An approx- imate form of the excess functional is proposed for water. This functional requires the knowledge of pure solvent direct correlation…
Time-dependent density-functional theory (TDDFT) is an extension of ground-state density-functional theory which allows the treatment of electronic excited states and a wide range of time-dependent phenomena in the linear and nonlinear…
Machine learning has now become an integral part of research and innovation. The field of machine learning density functional theory has continuously expanded over the years while making several noticeable advances. We briefly discuss the…
In this paper we give a method, based on the characteristic function of a set, to solve some difficult problems of set theory in undergraduate research.
This article addresses a fundamental problem faced by the ab initio community: the lack of an effective formalism for the rapid exploration and exchange of new methods. To rectify this, we introduce a novel, basis-set independent,…
In this paper we give a brief review of semiparametric theory, using as a running example the common problem of estimating an average causal effect. Semiparametric models allow at least part of the data-generating process to be unspecified…