The molecular cobalt fluorides CoF2, CoF3 and CoF4 are studied and compared by employing different basis sets as well as Quantum Information Theory (QIT) to investigate their correlation effects. ...These prototypical monomers may be systematically extended in size yielding a novel quasi 1‐dimensional, strongly correlated model system consisting of cobalt atoms bridged by oxygen atoms and fluorine termination on both ends. Accurate correlation energies are obtained using Full Configuration Interaction (FCI) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) calculations and the results are compared to Coupled Cluster and Density Matrix Renormalization Group (DMRG) energies. The analysis indicates the cobalt atom requires a larger number of one‐electron basis functions than fluorine and the use of localized molecular orbitals may facilitate calculations for the extended systems.
Based on DMRG and FCIQMC calculations, electron correlation effects in cobalt fluorides are studied by analyzing orbital entanglement and application of different one‐electron basis set sizes. The results may be leveraged in calculations of related, larger systems.
Abstract
The molecular cobalt fluorides CoF
2
, CoF
3
and CoF
4
are studied and compared by employing different basis sets as well as Quantum Information Theory (QIT) to investigate their correlation ...effects. These prototypical monomers may be systematically extended in size yielding a novel quasi 1‐dimensional, strongly correlated model system consisting of cobalt atoms bridged by oxygen atoms and fluorine termination on both ends. Accurate correlation energies are obtained using Full Configuration Interaction (FCI) and Full Configuration Interaction Quantum Monte Carlo (FCIQMC) calculations and the results are compared to Coupled Cluster and Density Matrix Renormalization Group (DMRG) energies. The analysis indicates the cobalt atom requires a larger number of one‐electron basis functions than fluorine and the use of localized molecular orbitals may facilitate calculations for the extended systems.
Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches ...to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap (“sloppy”) DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one‐body MoI calculations.
Accurate treatment of electron correlation determines the quality of quantum chemical calculations. A systematic investigation in terms of the contributing orbitals can lead to new insights for new methods with improved computational scaling. Two different approaches to quantify correlation effects are compared, and ways to exploit their different computational cost are discussed.
The traditional wavepacket interferometry for nuclear densities is extended to nuclear flux densities. Accordingly, a molecule vibrating in an electronic excited state may be prepared such that at a ...given time, the nuclear densities correspond to a broad distribution of the molecular bond, from short to long distances, which is subdivided into a chain of lobes. We discover that neighbouring lobes, or groups of lobes, may flow towards alternating directions, implying alternating bond stretches and bond compressions. The corresponding nuclear flux densities may be controlled by appropriate parameters of the two laser pulses, which generate the underlying interferences. Similar patterns of the nuclear densities and flux densities may also be created by a single laser pulse, which may cause interferences of the overlapping tail and head of a wavepacket as they run towards or away from a turning point, respectively. The phenomena are demonstrated for the model system I
2
(B).
Understanding electron correlation is crucial for developing new concepts in electronic structure theory, especially for strongly correlated electrons. We compare and apply two different approaches ...to quantify correlation contributions of orbitals: Quantum Information Theory (QIT) based on a Density Matrix Renormalization Group (DMRG) calculation and the Method of Increments (MoI). Although both approaches define very different correlation measures, we show that they exhibit very similar patterns when being applied to a polyacetelene model system. These results suggest one may deduce from one to the other, allowing the MoI to leverage from QIT results by screening correlation contributions with a cheap ("sloppy") DMRG with a reduced number of block states. Or the other way around, one may select the active space in DMRG from cheap one-body MoI calculations.
The dissociation of \(\rm N_2\) and \(\rm N_2^+\) has been studied by using the \emph{ab initio} Density Matrix Renormalization Group (DMRG) method. Accurate Potential Energy Surfaces (PES) have been ...obtained for the electronic ground states of \(\rm N_2\) (\(\rm X^1\Sigma_g^+\)) and \(\rm N_2^+\) (\(\rm X^2\Sigma_g^+\)) as well as for the \(\rm N_2^+\) excited state \(\rm B^2\Sigma_u^+\). Inherently to the DMRG approach, the eigenvalues of the reduced density matrix (\(\rho\)) and their correlation functions are at hand. Thus we can apply Quantum Information Theory (QIT) directly, and investigate how the wave function changes along the PES and depict differences between the different states. Moreover by characterizing quantum entanglement between different pairs of orbitals and analyzing the reduced density matrix, we achieved a better understanding of the multi-reference character featured by these systems.
We shed light on wicked problems in the German energy transition. Our methods consist of a multiple-case study and multi-criteria analysis, utilising the wicked problems theoretical framework ...introduced by Horst Rittel and Melvin Webber 1973. "Dilemmas in a General Theory of Planning." Policy Sciences 4 (2): 155-169. Accessed August 20, 2019. https://doi.org/10.1007/BF01405730. Results from the energy supply, heating/cooling, transport, and industry sectors illustrate where and how the 10-point frame of wicked problems manifests in the German energy transition. The four cases exhibit more wicked tendencies in the governance domain than the technical domain and differ in their degrees of technology maturity, policy regulation, and knowledge states. We do not find that the German energy transition is inherently wicked. However, wickedness unfolds through the social setting into which technical solutions of the energy transition are embedded. We aim to highlight these intricacies and encourage scrutinising these wicked facets early on.
Superconducting fault current limiters (SCFCLs) are new and attractive devices to limit short-circuit currents in power systems. In recent years, the technical feasibility of SCFCLs in medium voltage ...applications was successfully demonstrated in several field tests. In high voltage power systems the application of SCFCLs is very attractive too, because at this voltage level conventional devices to limit short-circuit currents are hardly applicable and system studies showed considerable economical benefits. Therefore, a German project started recently to develop a first 110 kV, 1.8 kA prototype of a resistive SCFCL. A magnetic triggered resistive concept using MCP-BSCCO 2212 bulk material will be used for the demonstrator. This paper reports about the conceptual design of this SCFCL and the project status. Focus is given on the main data of the 110 kV prototype, the SCFCL modules, the general design of the whole system and the most important high voltage design aspects. The calculations and estimations show that the conceptual design presented in this paper seems feasible and that a major technical challenge is to ensure a reliable electrical insulation system.
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