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Time-dependent density functional theory continues to draw a large number of users in a wide range of fields exploring myriad applications involving electronic spectra and dynamics. Although in principle exact, the predictivity of the…
The accuracy of density-functional theory (DFT) is determined by the quality of the approximate functionals, such as exchange-correlation in electronic DFT and the excess functional in the classical DFT formalism of fluids. The exact…
We prove that the electron density function of a real physical system can be uniquely determined by its values on any finite subsystem. This establishes the existence of a rigorous density-functional theory for any open electronic system.…
We present conditional probability (CP) density functional theory (DFT) as a formally exact theory. In essence, CP-DFT determines the ground-state energy of a system by finding the CP density from a series of independent Kohn-Sham (KS) DFT…
When developing and assessing density functional theory methods, a finite basis set is usually employed. In most cases, however, the issue of basis set dependency is neglected. Here, we assess several basis sets and functionals. In…
The electron energy and density matrices in molecular systems are convex in respect of the number of particles. So that, the chemical descriptors based on their derivatives present the hamper of discontinuities for isolated systems and…
An often-cited fact regarding mixing or mixture distributions is that their density functions are able to approximate the density function of any unknown distribution to arbitrary degrees of accuracy, provided that the mixing or mixture…
The empirical and particle force-based models of granular segregation due to density differences among the species are compared in this work. Dependency of the empirical segregation parameters on the initial configuration, the observation…
Molecular simulations and biophysical experiments can be used to provide independent and complementary insights into the molecular origin of biological processes. A particularly useful strategy is to use molecular simulations as a modelling…
Probabilistic programs are typically normal-looking programs describing posterior probability distributions. They intrinsically code up randomized algorithms and have long been at the heart of modern machine learning and approximate…
We present new algorithms and fast implementations to find efficient approximations for modelling stochastic processes. For many numerical computations it is essential to develop finite approximations for stochastic processes. While the…
One of the potential applications of a quantum computer is solving quantum chemical systems. It is known that one of the fastest ways to obtain somewhat accurate solutions classically is to use approximations of density functional theory.…
This chapter provides a tutorial overview of first principles methods to describe the properties of matter at the ground state or equilibrium. It begins with a brief introduction to quantum and statistical mechanics for predicting the…
We introduce a new form of density functional theory for the {\em ab initio} description of electronic systems in contact with a molecular liquid environment. This theory rigorously joins an electron density-functional for the electrons of…
In this paper, we study numerical approximations of the ground states in finite temperature density functional theory. We formulate the problem with respect to the density matrices and justify the convergence of the finite dimensional…
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…
An exponential interaction is constructed so that one-dimensional atoms and chains of atoms mimic the general behavior of their three-dimensional counterparts. Relative to the more commonly used soft-Coulomb interaction, the exponential…
The formalism of Kohn and Sham uses a specific (model) hamiltonian which highly simplifies the many-electron problem to that of noninteracting fermions. The theorem of Hohenberg and Kohn tells us that, for a given ground state density, this…
It seems self-evident that a density functional calculation should be normalized to the number of electrons in the system. We present multiple examples where the accuracy of the approximate energy is improved (sometimes greatly) by…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…