238 research outputs found
Entanglement Measures for Single- and Multi-Reference Correlation Effects
Electron correlation effects are essential for an accurate ab initio
description of molecules. A quantitative a priori knowledge of the single- or
multi-reference nature of electronic structures as well as of the dominant
contributions to the correlation energy can facilitate the decision regarding
the optimum quantum chemical method of choice. We propose concepts from quantum
information theory as orbital entanglement measures that allow us to evaluate
the single- and multi-reference character of any molecular structure in a given
orbital basis set. By studying these measures we can detect possible artifacts
of small active spaces.Comment: 14 pages, 4 figure
ON VOLUME DATA REDUCTION FOR LIDAR DATASETS
This paper discusses a current issue for several experimental science disciplines, which is the Big Data Problem (BDP). This research study focused on light intensity and ranging (LiDAR) datasets, which are collected for modelling spatial features found on the surface of the earth. Currently, LiDAR datasets are known to be extremely redundant for many applications. Using a formula that allows for calculating the variance of the target-induced error (so-called T-error) caused by the discretisation and quantisation of a 3D surface as a criterion for the quantitative assessment of the fidelity of a model, the use of a Q-tree-based split of the surface is proposed for cells of various sizes depending on the fidelity requirements. A LiDAR dataset representing a 1 km x 1 km terrain surface tile using approximately 12 x 106 points was used during the experiments. The initial LiDAR dataset was used to produce a digital terrain model (DTM) at a 0.5 m x 0.5 m resolution, which was used as a reference model. Subsequently, the initial LiDAR dataset was decimated at various rates, and the resulting DTMs were compared with the reference model. The Q-tree based data structure was utilised to illustrate that the Q-tree approach allows for the production of DTMs at a ‘controlled’ fidelity with a considerable reduction in data volume
Analysis of two-orbital correlations in wave functions restricted to electron-pair states
Wavefunctions constructed from electron-pair states can accurately model strong electron corre- lation effects and are promising approaches especially for larger many-body systems. In this article, we analyze the nature and the type of electron correlation effects that can be captured by wave- functions restricted to electron-pair states. We focus on the Antisymmetric Product of 1-reference orbital Geminal (AP1roG) method combined with an orbital optimization protocol presented in [Phys. Rev. B, 89, 201106(R), 2014] whose performance is assessed against electronic structures obtained form DMRG reference data. Our numerical analysis covers model systems for strong cor- relation: the one-dimensional Hubbard model with periodic boundary condition as well as metallic and molecular hydrogen rings. Specifically, the accuracy of AP1roG is benchmarked using the single-orbital entropy, the orbital-pair mutual information as well as the eigenvalue spectrum of the one-orbital and two-orbital reduced density matrices. Our study indicates that contributions from singly occupied states become important in the strong correlation regime which highlights the limitations of the AP1roG method. Furthermore, we examine the effect of orbital rotations within the AP1roG model on correlations between orbital pairs
Tensor Product Approximation (DMRG) and Coupled Cluster method in Quantum Chemistry
We present the Copupled Cluster (CC) method and the Density matrix
Renormalization Grooup (DMRG) method in a unified way, from the perspective of
recent developments in tensor product approximation. We present an introduction
into recently developed hierarchical tensor representations, in particular
tensor trains which are matrix product states in physics language. The discrete
equations of full CI approximation applied to the electronic Schr\"odinger
equation is casted into a tensorial framework in form of the second
quantization. A further approximation is performed afterwards by tensor
approximation within a hierarchical format or equivalently a tree tensor
network. We establish the (differential) geometry of low rank hierarchical
tensors and apply the Driac Frenkel principle to reduce the original
high-dimensional problem to low dimensions. The DMRG algorithm is established
as an optimization method in this format with alternating directional search.
We briefly introduce the CC method and refer to our theoretical results. We
compare this approach in the present discrete formulation with the CC method
and its underlying exponential parametrization.Comment: 15 pages, 3 figure
Elucidating cation-cation interactions in neptunyl dications using multi-reference ab initio theory
Accurate ab initio spin densities
We present an approach for the calculation of spin density distributions for
molecules that require very large active spaces for a qualitatively correct
description of their electronic structure. Our approach is based on the
density-matrix renormalization group (DMRG) algorithm to calculate the spin
density matrix elements as basic quantity for the spatially resolved spin
density distribution. The spin density matrix elements are directly determined
from the second-quantized elementary operators optimized by the DMRG algorithm.
As an analytic convergence criterion for the spin density distribution, we
employ our recently developed sampling-reconstruction scheme [J. Chem. Phys.
2011, 134, 224101] to build an accurate complete-active-space
configuration-interaction (CASCI) wave function from the optimized matrix
product states. The spin density matrix elements can then also be determined as
an expectation value employing the reconstructed wave function expansion.
Furthermore, the explicit reconstruction of a CASCI-type wave function provides
insights into chemically interesting features of the molecule under study such
as the distribution of - and -electrons in terms of Slater
determinants, CI coefficients, and natural orbitals. The methodology is applied
to an iron nitrosyl complex which we have identified as a challenging system
for standard approaches [J. Chem. Theory Comput. 2011, 7, 2740].Comment: 37 pages, 13 figure
A quantum informational approach for dissecting chemical reactions
The focal-plane detector system for the KArlsruhe TRItium Neutrino (KATRIN) experiment consists of a multi-pixel silicon p-i-n-diode array, custom readout electronics, two superconducting solenoid magnets, an ultra high-vacuum system, a high-vacuum system, calibration and monitoring devices, a scintillating veto, and a custom data-acquisition system. It is designed to detect the low-energy electrons selected by the KATRIN main spectrometer. We describe the system and summarize its performance after its final installation
New Strategies in Modeling Electronic Structures and Properties with Applications to Actinides
This chapter discusses contemporary quantum chemical methods and provides
general insights into modern electronic structure theory with a focus on
heavy-element-containing compounds. We first give a short overview of
relativistic Hamiltonians that are frequently applied to account for
relativistic effects. Then, we scrutinize various quantum chemistry methods
that approximate the -electron wave function. In this respect, we will
review the most popular single- and multi-reference approaches that have been
developed to model the multi-reference nature of heavy element compounds and
their ground- and excited-state electronic structures. Specifically, we
introduce various flavors of post-Hartree--Fock methods and optimization
schemes like the complete active space self-consistent field method, the
configuration interaction approach, the Fock-space coupled cluster model, the
pair-coupled cluster doubles ansatz, also known as the antisymmetric product of
1 reference orbital geminal, and the density matrix renormalization group
algorithm. Furthermore, we will illustrate how concepts of quantum information
theory provide us with a qualitative understanding of complex electronic
structures using the picture of interacting orbitals. While modern quantum
chemistry facilitates a quantitative description of atoms and molecules as well
as their properties, concepts of quantum information theory offer new
strategies for a qualitative interpretation that can shed new light onto the
chemistry of complex molecular compounds.Comment: 43 pages, 3 figures, Version of Recor
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