Related papers: Koopmans spectral functionals in periodic-boundary…
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…
Over the past decade we have developed Koopmans functionals, a computationally efficient approach for predicting spectral properties with an orbital-density-dependent functional framework. These functionals impose a generalized piecewise…
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 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-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 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 (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…
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 presence of spin-orbit coupling or non-collinear magnetic spin states can have dramatic effects on the ground-state and spectral properties of materials, in particular on the band structure. Here, we develop non-collinear…
Every invertible, measure-preserving dynamical system induces a Koopman operator, which is a linear, unitary evolution operator acting on the $L^2$ space of observables associated with the invariant measure. Koopman eigenfunctions represent…
We provide an overview of the Koopman operator analysis for a class of partial differential equations describing relaxation of the field variable to a stable stationary state. We introduce Koopman eigenfunctionals of the system and use the…
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 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…
The Koopman operator framework holds promise for spectral analysis of nonlinear dynamical systems based on linear operators. Eigenvalues and eigenfunctions of the Koopman operator, so-called Koopman eigenvalues and Koopman eigenfunctions,…
The performance of density functional theory depends largely on the approximation applied for the exchange functional. We propose here a novel screened exchange potential for semiconductors, with parameters based on the physical properties…
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…
Functionals that strive to correct for such self-interaction errors, such as those obtained by imposing the Perdew-Zunger self-interaction correction or the generalized Koopmans' condition, become orbital dependent or orbital-density…
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)…
The method of using periodic approximations to compute the spectral decomposition of the Koop- man operator is generalized to the class of measure-preserving flows on compact metric spaces. It is shown that the spectral decomposition of the…