Related papers: Optimized auxiliary functions for robust mitigatio…

Recent high resolution Compton scattering experiments clearly reveal that there are fundamental limitations to the conventional local density approximation (LDA) based description of the ground state electron momentum density (EMD) in…

We propose a multiconfigurational hybrid density-functional theory which rigorously combines a multiconfiguration self-consistent-field calculation with a density-functional approximation based on a linear decomposition of the…

One-body reduced density matrix functional theory (RDMFT) provides an alternative to Density Functional Theory (DFT), able to treat static correlation while keeping a relatively low computation scaling. Its disadvantageous cost comes mainly…

Self-interaction is a fundamental flaw of practical Kohn-Sham Density Functional Theory (KS DFT) approximations responsible for numerous qualitative and even catastrophic shortcomings. Whereas self-interaction is easy to characterize in…

The present work proposes to use density-functional theory (DFT) to correct for the basis-set error of wave-function theory (WFT). One of the key ideas developed here is to define a range-separation parameter which automatically adapts to a…

We combine density-functional theory with density-matrix functional theory to get the best of both worlds. This is achieved by range separation of the electronic interaction which permits to rigorously combine a short-range density…

We present an energy/entropy stable and high order accurate finite difference (FD) method for solving the nonlinear (rotating) shallow water equations (SWEs) in vector invariant form using the newly developed dual-pairing and…

We suggest a new method of calculation of the equilibrium correlation functions of an arbitrary order for the interacting Fermi-gas model in the frame of the static fluctuation approximation (SFA) method. This method based only on the…

We consider Galerkin finite element methods for semilinear stochastic partial differential equations (SPDEs) with multiplicative noise and Lipschitz continuous nonlinearities. We analyze the strong error of convergence for spatially…

We consider autonomous stochastic ordinary differential equations (SDEs) and weak approximations of their solutions for a general class of sufficiently smooth path-dependent functionals f. Based on tools from functional It\^o calculus, such…

The implementation of an efficient self-consistent field (SCF) method including both scalar relativistic effects and spin-orbit interaction in density functional theory (DFT) is presented. We make use of Gaussian-type orbitals (GTOs) and…

Modern density functional approximations achieve moderate accuracy at low computational cost for many electronic structure calculations. Some background is given relating the gradient expansion of density functional theory to the WKB…

In the present work, strong approximation errors are analyzed for both the spatial semi-discretization and the spatio-temporal fully discretization of stochastic wave equations (SWEs) with cubic polynomial nonlinearities and additive…

The quantum mechanical ground state of electrons is described by Density Functional Theory, which leads to large minimization problems. An efficient minimization method uses a selfconsistent field (SCF) solution of large eigenvalue…

For the large and chemically diverse GMTKN55 benchmark suite, we have studied the performance of density-corrected density functional theory (HF-DFT), compared to self-consistent DFT, for several pure and hybrid GGA and meta-GGA…

We study finite element approximations of second-order elliptic problems with measure-valued right-hand sides supported on lower-dimensional sets. The exact solution generally lacks $H^1$-regularity due to the source singularity, which…

For fast and accurate calculations of band gaps of solids, we present an {\it ab initio} method that extends the density functional theory plus on-site Hubbard interaction (DFT+$U$) to include inter-site Hubbard interaction ($V$). This…

We present the first mathematical analysis of stochastic density functional theory (DFT) in the context of the Hartree approximation. We motivate our analysis via the notion of nearly-optimal or $\tilde{O}(n)$ scaling with respect to the…

We consider the approximate solution of parametric PDEs using the low-rank Tensor Train (TT) decomposition. Such parametric PDEs arise for example in uncertainty quantification problems in engineering applications. We propose an algorithm…

Linear-scaling techniques for Kohn-Sham density functional theory (KS-DFT) are essential to describe the ground state properties of extended systems. Still, these techniques often rely on the locality of the density matrix or on accurate…