Related papers: koopmans: an open-source package for accurately an…
Koopmans spectral functionals are a powerful extension of Kohn-Sham density-functional theory (DFT) that enable the prediction of spectral properties with state-of-the-art accuracy. The success of these functionals relies on capturing the…
The determination of spectral properties from first principles can provide powerful connections between microscopic theoretical predictions and experimental data, but requires complex electronic-structure formulations that fall outside the…
Koopmans-compliant functionals have been shown to provide accurate spectral properties for molecular systems; this accuracy is driven by the generalized linearization condition imposed on each charged excitation - i.e. on changing the…
Koopmans-compliant functionals provide an orbital-density-dependent framework for an accurate evaluation of spectral properties; they are obtained by imposing a generalized piecewise-linearity condition on the total energy of the system…
Koopmans spectral functionals aim to describe simultaneously ground state properties and charged excitations of atoms, molecules, nanostructures and periodic crystals. This is achieved by augmenting standard density functionals with simple…
Koopmans spectral functionals are a class of orbital-density-dependent functionals designed to accurately predict spectroscopic properties. They do so markedly better than their Kohn-Sham density-functional theory counterparts, as…
Koopmans-compliant functionals emerge naturally from extending the constraint of piecewise linearity of the total energy as a function of the number of electrons to each fractional orbital occupation. When applied to approximate…
Koopmans-compliant (KC) functionals have been shown to provide accurate spectral properties through a generalized condition of piece-wise linearity of the total energy as a function of the fractional addition/removal of an electron to/from…
Electronic-structure functionals that include screening effects, such as Hubbard or Koopmans' functionals, require to describe the response of a system to the fractional addition or removal of an electron from an orbital or a manifold.…
In approximate Kohn-Sham density-functional theory, self-interaction manifests itself as the dependence of the energy of an orbital on its fractional occupation. This unphysical behavior translates into qualitative and quantitative errors…
Data-driven spectral analysis of Koopman operators is a powerful tool for understanding numerous real-world dynamical systems, from neuronal activity to variations in sea surface temperature. The Koopman operator acts on a function space…
We introduce a spectral density functional theory which can be used to compute energetics and spectra of real strongly--correlated materials using methods, algorithms and computer programs of the electronic structure theory of solids. The…
This paper reports a theory of Koopman operators for a class of hybrid dynamical systems with globally asymptotically stable periodic orbits, called hybrid limit-cycling systems. We leverage smooth structures intrinsic to the hybrid…
We have proposed a method for correcting the Kohn-Sham eigen energies in the density functional theory (DFT) based on the Koopmans theorem using Wannier functions. The method provides a general approach applicable for molecules and solids…
Koopman operators provide a linear framework for data-driven analyses of nonlinear dynamical systems, but their infinite-dimensional nature presents major computational challenges. In this article, we offer an introductory guide to Koopman…
We introduce a general, variational scheme applied to Kohn-Sham density functional theory that allows for partitioning of the ground-state density matrix into distinct spectral domains, each of which spanned by an independent diagonal…
Koopman operator theory enables linear analysis of nonlinear dynamical systems by lifting their evolution to infinite-dimensional function spaces. However, finite-dimensional approximations of Koopman and transfer (Frobenius--Perron)…
Spectral decomposition of dynamical systems is a popular methodology to investigate the fundamental qualitative and quantitative properties of these systems and their solutions. In this chapter, we consider a class of nonlinear cooperative…
The Koopman operator provides a linear framework to study nonlinear dynamical systems. Its spectra offer valuable insights into system dynamics, but the operator can exhibit both discrete and continuous spectra, complicating direct…
This work introduces the use of the Koopman operator theory to generate approximate analytical solutions for the zonal harmonics problem of a satellite orbiting a non-spherical celestial body. Particularly, the solution proposed directly…