Charge self-consistent many-body corrections using optimized projected localized orbitals

In order for methods combining ab initio density-functional theory and many-body techniques to become routinely used, a flexible, fast, and easy-to-use implementation is crucial. We present an implementation of a general charge self-consistent scheme based on projected localized orbitals in the projector augmented wave framework in the Vienna Ab Initio Simulation Package (VASP). We give a detailed description on how the projectors are optimally chosen and how the total energy is calculated. We benchmark our implementation in combination with dynamical mean-field theory: first we study the charge-transfer insulator NiO using a Hartree-Fock approach to solve the many-body Hamiltonian. We address the advantages of the optimized against non-optimized projectors and furthermore find that charge self-consistency decreases the dependence of the spectral function - especially the gap - on the double counting. Second, using continuous-time quantum Monte Carlo we study a monolayer of SrVO$_3$, where strong orbital polarization occurs due to the reduced dimensionality. Using total-energy calculation for structure determination, we find that electronic correlations have a non-negligible influence on the position of the apical oxygens, and therefore on the thickness of the single SrVO$_3$ layer.Comment: 11 pages, 6 figure

Rekurencyjna estymacja funkcji parametrycznych metodą najmniejszych kwadratów

W pracy uogólniora zostala technika rekurencyjnej estymacji funkcji parametrycznych metodą najmniejszych kwadratów w ogólnym modelu liniowym. Proponowana procedura umożliwia aktualizację estymatorów zarówno ze względu na dodatkową stochastyczną, jak i niestochastyczną informację o parametrach modelu.The technique of recursive least squares estimation for the standard regression model is extended lo the general linear model with possibly singular dispersion matrix of error term. It is shown how to update the minimum dispersion linear unbiased estimate of a given vector of parametric functions with respcct to additional sample data which are to be successively incorporated to the inference base

Rekurencyjna estymacja funkcji parametrycznych metodą najmniejszych kwadratów

W pracy uogólniora zostala technika rekurencyjnej estymacji funkcji parametrycznych metodą najmniejszych kwadratów w ogólnym modelu liniowym. Proponowana procedura umożliwia aktualizację estymatorów zarówno ze względu na dodatkową stochastyczną, jak i niestochastyczną informację o parametrach modelu.The technique of recursive least squares estimation for the standard regression model is extended lo the general linear model with possibly singular dispersion matrix of error term. It is shown how to update the minimum dispersion linear unbiased estimate of a given vector of parametric functions with respcct to additional sample data which are to be successively incorporated to the inference base.Zadanie pt. „Digitalizacja i udostępnienie w Cyfrowym Repozytorium Uniwersytetu Łódzkiego kolekcji czasopism naukowych wydawanych przez Uniwersytet Łódzki” nr 885/P-DUN/2014 zostało dofinansowane ze środków MNiSW w ramach działalności upowszechniającej nauk

Adjusting of estimates in general linear model with respect to linear restrictions

Concerning with the general linear model s{;y, X[beta], [sigma]2Vs}; and a set of the linear restrictions Hi[beta] = hi, i = 1, 2,..., which are to be successively incorporated into the model, a recursive formula for the best linear unbiased estimator of a given vendor of estimable parametric functions is derived.General linear model singular dispersion matrix linear restrictions recursive estimation best linear unbiased estimator

A note on using linear restrictions in a Gauss-Markov model

Nella nota si pongono condizioni necessarie e sufficienti per la dominanza, con riferimento al rischio matricielo, dello stimatore usuale dei minimi quadrati sullo stimatore dei minimi quadrati stocasticamente o non stocasticamente ristretto in un modello semplice di gauss Markov. I risultati ottenuti completano i criteri già noti in letteratura a proposito della dominanza, con riferimento al rischio matricielo, degli stimatori ristretti sullo stimatore usuale dei minimi quadrati