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E. K. U. Gross - One of the best experts on this subject based on the ideXlab platform.
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Reduced Density Matrix functional theory at finite temperature theoretical foundations
Physical Review A, 2015Co-Authors: Tim Baldsiefen, Attila Cangi, E. K. U. GrossAbstract:We present an ab initio approach for grand-canonical ensembles in thermal equilibrium (eq) with local or nonlocal external potentials based on the one-Reduced Density Matrix (1RDM). We show that equilibrium properties of a grand-canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its 1RDM. We further prove the existence of a Kohn-Sham system capable of reproducing the 1RDM of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Doping induced metal-insulator phase transition in NiO—a Reduced Density Matrix functional theory perspective
New Journal of Physics, 2015Co-Authors: Yasushi Shinohara, Nektarios N. Lathiotakis, S. Sharma, J. K. Dewhurst, Sam Shallcross, E. K. U. GrossAbstract:The insulator to metal phase transition in NiO is studied within the framework of Reduced Density Matrix functional theory (RDMFT) and Density functional theory (DFT). We find that the spectral Density obtained using RDMFT is in good agreement with experiments both for undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition qualitatively differs depending on whether NiO is calculated within DFT or Reduced Density Matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.
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doping induced metal insulator phase transition in nio a Reduced Density Matrix functional theory perspective
New Journal of Physics, 2015Co-Authors: Yasushi Shinohara, Nektarios N. Lathiotakis, J. K. Dewhurst, Sam Shallcross, S Sharma, E. K. U. GrossAbstract:The insulator to metal phase transition in NiO is studied within the framework of Reduced Density Matrix functional theory (RDMFT) and Density functional theory (DFT). We find that the spectral Density obtained using RDMFT is in good agreement with experiments both for undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition qualitatively differs depending on whether NiO is calculated within DFT or Reduced Density Matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.
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Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, Attila Cangi, E. K. U. GrossAbstract:We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-Reduced Density Matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-Reduced Density Matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-Reduced Density Matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Minimization procedure in Reduced Density Matrix functional theory by means of an effective noninteracting system
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, E. K. U. GrossAbstract:In this work, we propose a self-consistent minimization procedure for functionals in Reduced Density Matrix functional theory. We introduce an effective noninteracting system at finite temperature which is capable of reproducing the groundstate one-Reduced Density Matrix of an interacting system at zero temperature. By introducing the concept of a temperature tensor the minimization with respect to the occupation numbers is shown to be greatly improved.
Tim Baldsiefen - One of the best experts on this subject based on the ideXlab platform.
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Reduced Density Matrix functional theory at finite temperature theoretical foundations
Physical Review A, 2015Co-Authors: Tim Baldsiefen, Attila Cangi, E. K. U. GrossAbstract:We present an ab initio approach for grand-canonical ensembles in thermal equilibrium (eq) with local or nonlocal external potentials based on the one-Reduced Density Matrix (1RDM). We show that equilibrium properties of a grand-canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its 1RDM. We further prove the existence of a Kohn-Sham system capable of reproducing the 1RDM of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Reduced Density Matrix Functional Theory at Finite Temperature: Theoretical Foundations
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, Attila Cangi, E. K. U. GrossAbstract:We present an ab-initio approach for grand canonical ensembles in thermal equilibrium with local or nonlocal external potentials based on the one-Reduced Density Matrix. We show that equilibrium properties of a grand canonical ensemble are determined uniquely by the eq-1RDM and establish a variational principle for the grand potential with respect to its one-Reduced Density Matrix. We further prove the existence of a Kohn-Sham system capable of reproducing the one-Reduced Density Matrix of an interacting system at finite temperature. Utilizing this Kohn-Sham system as an unperturbed system, we deduce a many-body approach to iteratively construct approximations to the correlation contribution of the grand potential.
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Minimization procedure in Reduced Density Matrix functional theory by means of an effective noninteracting system
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, E. K. U. GrossAbstract:In this work, we propose a self-consistent minimization procedure for functionals in Reduced Density Matrix functional theory. We introduce an effective noninteracting system at finite temperature which is capable of reproducing the groundstate one-Reduced Density Matrix of an interacting system at zero temperature. By introducing the concept of a temperature tensor the minimization with respect to the occupation numbers is shown to be greatly improved.
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Reduced Density Matrix functional theory at finite temperature. II. Application to the electron gas: Exchange only
arXiv: Strongly Correlated Electrons, 2012Co-Authors: Tim Baldsiefen, F. G. Eich, E. K. U. GrossAbstract:Using the newly introduced theory of finite-temperature Reduced Density Matrix functional theory, we apply the first-order approximation to the homogeneous electron gas. We consider both collinear spin states as well as symmetry broken states describing planar spin spirals and investigate the magnetic phase diagram as well as the temperature-dependence of the single particle spectra.
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Reduced Density Matrix functional theory at finite temperature. III. Application to the electron gas: Correlation effects
arXiv: Other Condensed Matter, 2012Co-Authors: Tim Baldsiefen, E. K. U. GrossAbstract:Based on our derivation of finite temperature Reduced Density Matrix functional theory and the discussion of the performance of its first-order functional this work presents several different correlation-energy functionals and applies them to the homogeneous electron gas. The zero temperature limits of the correlation-energy and the momentum distributions are investigated and the magnetic phase diagrams in collinear spin configuration are discussed.
David A. Mazziotti - One of the best experts on this subject based on the ideXlab platform.
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Active-Space Pair Two-Electron Reduced Density Matrix Theory for Strong Correlation.
The Journal of Physical Chemistry A, 2020Co-Authors: Kade Head-marsden, David A. MazziottiAbstract:An active-space variational calculation of the two-electron Reduced Density Matrix (2-RDM) is derived and implemented where the active orbitals are correlated within the pair approximation. The pai...
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Current-constrained one-electron Reduced Density-Matrix theory for non-equilibrium steady-state molecular conductivity
Physical Chemistry Chemical Physics, 2019Co-Authors: Alexandra E. Raeber, David A. MazziottiAbstract:In the effort to create ever smaller electronic devices, the idea of single molecule circuit elements has sparked the imagination of scientists for nearly fifty years. While traditional theories for non-equilibrium steady-state molecular conductivity like the non-equilibrium Green's function Density functional theory determine the current from an applied voltage, the recently proposed current-constrained Density-Matrix theory computes the voltage from a current constraint on the molecule. In the present paper we extend the current-constrained Density-Matrix theory from its two-electron Reduced Density-Matrix (2-RDM) formulation to a one-electron Reduced Density Matrix (1-RDM) formulation that is applicable to Hartree–Fock, Density functional, and tight-binding theories. We demonstrate the current-constrained 1-RDM method through the computation of the theoretical, intrinsic resistance of acenes and phenacenes.
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excited state spectra of strongly correlated molecules from a Reduced Density Matrix approach
Journal of Physical Chemistry Letters, 2018Co-Authors: Shayan Hemmatiyan, Manas Sajjan, Anthony W Schlimgen, David A. MazziottiAbstract:Excited-state energies are computed in the space of single-electron transitions from the ground state from only a knowledge of the two-electron Reduced Density Matrix (2-RDM). Previous work develop...
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pair 2 electron Reduced Density Matrix theory using localized orbitals
Journal of Chemical Physics, 2017Co-Authors: Kade Headmarsden, David A. MazziottiAbstract:Full configuration interaction (FCI) restricted to a pairing space yields size-extensive correlation energies but its cost scales exponentially with molecular size. Restricting the variational two-electron Reduced-Density-Matrix (2-RDM) method to represent the same pairing space yields an accurate lower bound to the pair FCI energy at a mean-field-like computational scaling of O(r3) where r is the number of orbitals. In this paper, we show that localized molecular orbitals can be employed to generate an efficient, approximately size-extensive pair 2-RDM method. The use of localized orbitals eliminates the substantial cost of optimizing iteratively the orbitals defining the pairing space without compromising accuracy. In contrast to the localized orbitals, the use of canonical Hartree-Fock molecular orbitals is shown to be both inaccurate and non-size-extensive. The pair 2-RDM has the flexibility to describe the spectra of one-electron RDM occupation numbers from all quantum states that are invariant to ti...
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Computation of quantum phase transitions by Reduced-Density-Matrix mechanics
Physical Review A, 2006Co-Authors: Gergely Gidofalvi, David A. MazziottiAbstract:Quantum phase transitions are explored with Reduced-Density-Matrix (RDM) mechanics. While in wave mechanics the quantum phase transition is identified by a crossing or avoided crossing between ground- and excited-state energies, in RDM mechanics the transition is characterized by movement of the ground-state two-electron RDM (2-RDM) along the boundary of the convex set of 2-RDMs between regions with dramatically different expectation values (order parameters) of one or more operators. With recent advances the ground-state 2-RDM can be directly computed without the many-particle wave function by variational optimization of the energy with the 2-RDM [D. A. Mazziotti, Phys. Rev. Lett. 93, 213001 (2004)]. Because the variational calculation of the 2-RDM does not depend on a reference wave function, it can accurately predict the energies and properties of a system both near and far from the quantum phase transition.
Jean-michel Gillet - One of the best experts on this subject based on the ideXlab platform.
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Inferring the one-electron Reduced Density Matrix of molecular crystals from experimental data sets through semidefinite programming.
Acta crystallographica. Section A Foundations and advances, 2020Co-Authors: Benjamin De Bruyne, Jean-michel GilletAbstract:Constructing a quantum description of crystals from scattering experiments is of great significance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab initio models. While reconstruction methods of the one-electron Reduced Density Matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron Reduced Density Matrix (1-RDM) with minimal assumptions. It has been found that the mathematical framework of semidefinite programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab initio calculations.
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Inferring the one‐electron Reduced Density Matrix of molecular crystals from experimental data sets through semidefinite programming
Acta Crystallographica Section A Foundations and Advances, 2020Co-Authors: Benjamin De Bruyne, Jean-michel GilletAbstract:Constructing a quantum description of crystals from scattering experiments is of great significance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab initio models. While reconstruction methods of the one-electron Reduced Density Matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron Reduced Density Matrix (1-RDM) with minimal assumptions. It has been found that the mathematical framework of semidefinite programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab initio calculations.
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Inferring the one-electron Reduced Density Matrix of molecular crystals from experimental data sets through semidefinite programming
Acta Crystallographica Section A Foundations and Advances, 2020Co-Authors: Benjamin De Bruyne, Jean-michel GilletAbstract:Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of the one-electron Reduced Density Matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron Reduced Density Matrix (1-RDM) with minimal assumptions. We have found that the mathematical framework of Semidefinite Programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab-initio calculations.
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Development of a joint refinement model for the spin-resolved one-electron Reduced Density Matrix using different data sets
Acta Crystallographica Section A Foundations and Advances, 2018Co-Authors: Saber Gueddida, Zeyin Yan, Jean-michel GilletAbstract:The paper describes a joint refinement model of the spin-resolved one-electron Reduced Density Matrix using simultaneously magnetic structure factors and magnetic directional Compton profiles. The model is guided by two strategies: (i) variation of basis functions and (ii) variation of the spin population Matrix. The implementation for a finite system is based on an expansion of the natural orbitals on basis sets. To show the potential benefits brought by the joint refinement model, the paper also presents the refinement results using magnetic structure factors only. The joint refinement model provides very satisfactory results reproducing the pseudo-data. In particular, magnetic Compton profiles have a strong effect not only on the off-diagonal elements of the spin-resolved one-electron Reduced Density Matrix but also on its diagonal elements.
Nektarios N. Lathiotakis - One of the best experts on this subject based on the ideXlab platform.
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Structure of the first order Reduced Density Matrix in three electron systems: A generalized Pauli constraints assisted study.
The Journal of Chemical Physics, 2018Co-Authors: Iris Theophilou, Nektarios N. Lathiotakis, N. HelbigAbstract:We investigate the structure of the one-body Reduced Density Matrix of three electron systems, i.e., doublet and quadruplet spin configurations, corresponding to the smallest interacting system with an open-shell ground state. To this end, we use configuration interaction (CI) expansions of the exact wave function in Slater determinants built from natural orbitals in a finite dimensional Hilbert space. With the exception of maximally polarized systems, the natural orbitals of spin eigenstates are generally spin dependent, i.e., the spatial parts of the up and down natural orbitals form two different sets. A measure to quantify this spin dependence is introduced and it is shown that it varies by several orders of magnitude depending on the system. We also study the ordering issue of the spin-dependent occupation numbers which has practical implications in Reduced Density Matrix functional theory minimization schemes, when generalized Pauli constraints (GPCs) are imposed and in the form of the CI expansion ...
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Conditions for Describing Triplet States in Reduced Density Matrix Functional Theory
Journal of Chemical Theory and Computation, 2016Co-Authors: Iris Theophilou, Nektarios N. Lathiotakis, N. HelbigAbstract:We consider necessary conditions for the one-body Reduced Density Matrix (1RDM) to correspond to a triplet wave function of a two-electron system. The conditions concern the occupation numbers and are different for the high spin projections, Sz = ±1, and the Sz = 0 projection. Hence, they can be used to test if an approximate 1RDM functional yields the same energies for both projections. We employ these conditions in Reduced Density Matrix functional theory calculations for the triplet excitations of two-electron systems. In addition, we propose that these conditions can be used in the calculation of triplet states of systems with more than two electrons by restricting the active space. We assess this procedure in calculations for a few atomic and molecular systems. We show that the quality of the optimal 1RDMs improves by applying the conditions in all the cases we studied.
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doping induced metal insulator phase transition in nio a Reduced Density Matrix functional theory perspective
New Journal of Physics, 2015Co-Authors: Yasushi Shinohara, Nektarios N. Lathiotakis, J. K. Dewhurst, Sam Shallcross, S Sharma, E. K. U. GrossAbstract:The insulator to metal phase transition in NiO is studied within the framework of Reduced Density Matrix functional theory (RDMFT) and Density functional theory (DFT). We find that the spectral Density obtained using RDMFT is in good agreement with experiments both for undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition qualitatively differs depending on whether NiO is calculated within DFT or Reduced Density Matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.
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Doping induced metal-insulator phase transition in NiO—a Reduced Density Matrix functional theory perspective
New Journal of Physics, 2015Co-Authors: Yasushi Shinohara, Nektarios N. Lathiotakis, S. Sharma, J. K. Dewhurst, Sam Shallcross, E. K. U. GrossAbstract:The insulator to metal phase transition in NiO is studied within the framework of Reduced Density Matrix functional theory (RDMFT) and Density functional theory (DFT). We find that the spectral Density obtained using RDMFT is in good agreement with experiments both for undoped as well as doped NiO. We find that the physical description of the hole-doping induced phase transition qualitatively differs depending on whether NiO is calculated within DFT or Reduced Density Matrix functional. In the former case the underlying mechanism of the phase transition is identified to be a rigid shift of chemical potential, while in the latter case a redistribution of the spectral weight drives the transition. These latter results are found to be in good agreement with both experiments and previous many-body calculations.
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Generalized Pauli constraints in Reduced Density Matrix functional theory
The Journal of Chemical Physics, 2015Co-Authors: Iris Theophilou, Miguel A. L. Marques, Nektarios N. Lathiotakis, N. HelbigAbstract:Functionals of the one-body Reduced Density Matrix (1-RDM) are routinely minimized under Coleman’s ensemble N-representability conditions. Recently, the topic of pure-state N-representability conditions, also known as generalized Pauli constraints, received increased attention following the discovery of a systematic way to derive them for any number of electrons and any finite dimensionality of the Hilbert space. The target of this work is to assess the potential impact of the enforcement of the pure-state conditions on the results of Reduced Density-Matrix functional theory calculations. In particular, we examine whether the standard minimization of typical 1-RDM functionals under the ensemble N-representability conditions violates the pure-state conditions for prototype 3-electron systems. We also enforce the pure-state conditions, in addition to the ensemble ones, for the same systems and functionals and compare the correlation energies and optimal occupation numbers with those obtained by the enforcement of the ensemble conditions alone.
