Related papers: Quasi-non-local gradient-level exchange-correlatio…
The role of exchange-correlation effects in non-equilibrium quantum transport through molecular junctions is assessed by analyzing the IV curve of a generic two-level model using self-consistent many-body perturbation theory (second Born…
In this work, we investigate stochastic quasi-Newton methods for minimizing a finite sum of cost functions over a decentralized network. In Part I, we develop a general algorithmic framework that incorporates stochastic quasi-Newton…
Local solutions for variational and quasi-variational inequalities are usually the best type of solutions that could practically be obtained when in case of lack of convexity or else when available numerical techniques are too limited for…
While the exact total energy of a separated open system varies linearly as a function of average electron number between adjacent integers, the energy predicted by semi-local density functional approximations curves upward and the…
The construction of meta generalized gradient approximations based on the density matrix expansion (DME) is considered as one of the most accurate technique to design semilocal exchange energy functionals in two-dimensional density…
The rigorous convergence analysis of adaptive finite element methods for regularized variational models of quasi-static brittle fracture in strain-limiting elastic solids is presented. This work introduces two novel adaptive mesh refinement…
We investigate the extent to which the nuclear transverse response to electron scattering in the quasielastic region, evaluated in the random-phase approximation can be described by ring approximation calculations. Different effective…
Recently, Tao and Mo (TM) proposed an accurate all-purpose nonempirical meta-generalized gradient approximation (meta-GGA). The exchange part was derived from the density matrix approximation, while the correlation part is based on a…
We present a global hybrid meta-generalized gradient approximation (meta-GGA) with three empirical parameters, as well as its underlying semilocal meta-GGA and a meta-GGA with only one empirical parameter. All of them are based on the new…
In the search for an accurate and computationally efficient approximation to the exact exchange potential of Kohn-Sham density functional theory, we recently compared various semilocal exchange potentials to the exact one [F. Tran et al.,…
These are introductory lectures to some aspects of the physics of strongly correlated electron systems. I first explain the main reasons for strong correlations in several classes of materials. The basic principles of dynamical mean-field…
The analytical gradient for periodic systems is presented, for the case of metallic systems. The total energy and the free energy are computed on the Hartree-Fock or density functional level, with the wave function being expanded in terms…
In this paper, we study convergence properties of the gradient Expectation-Maximization algorithm \cite{lange1995gradient} for Gaussian Mixture Models for general number of clusters and mixing coefficients. We derive the convergence rate…
A cardinal obstacle to understanding and predicting quantitatively the properties of solids and large molecules is that, for these systems, it is very challenging to describe beyond the mean-field level the quantum-mechanical interactions…
We rewrite the standard nodal virtual element method as a generalised gradient method. This re-formulation allows for computing a reliable and efficient error estimator by locally reconstructing broken fluxes and potentials on elemental…
Reviewing the semiclassical theory for the parametric level density fluctuations, we show that for large parametric changes the density correlation function, after rescaling, becomes universal and coincides with the leading asymptotic term…
We derive an explicit form for the electronic friction as felt by a molecule near a metal surface for the general case that molecule-metal couplings depend on nuclear coordinates. Our work generalizes a previous study by von Oppen et al…
The effective potential of electron--electron interaction and the two-particle \textquotedblleft density--density\textquotedblright\ correlation function have been calculated for a simple semiinfinite metal making allowance for the…
Quasilinear theory is often utilized to approximate the dynamics of fluids exhibiting significant interactions between mean flows and eddies. In this paper we present a generalization of quasilinear theory to include dynamic mode…
For the planar Navier--Lam\'e equation in mixed form with symmetric stress tensors, we prove the uniform quasi-optimal convergence of an adaptive method based on the hybridized mixed finite element proposed in [Gong, Wu, and Xu:…