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Title: Transition matrices and orbitals from reduced density matrix theory

Abstract

In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transitionmore » density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.« less

Authors:
 [1];  [2];  [3]
  1. Université de Lorraine – Nancy, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy (France)
  2. (France)
  3. (Belgium)
Publication Date:
OSTI Identifier:
22490823
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 24; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; 97 MATHEMATICAL METHODS AND COMPUTING; CONFIGURATION INTERACTION; DECOMPOSITION; DENSITY FUNCTIONAL METHOD; DENSITY MATRIX; ELECTRONIC STRUCTURE; EXCITATION; EXCITED STATES; HARTREE-FOCK METHOD; POLARIZATION; TIME DEPENDENCE; VECTORS

Citation Formats

Etienne, Thibaud, CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, and Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur. Transition matrices and orbitals from reduced density matrix theory. United States: N. p., 2015. Web. doi:10.1063/1.4922780.
Etienne, Thibaud, CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, & Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur. Transition matrices and orbitals from reduced density matrix theory. United States. doi:10.1063/1.4922780.
Etienne, Thibaud, CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy, and Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur. Sun . "Transition matrices and orbitals from reduced density matrix theory". United States. doi:10.1063/1.4922780.
@article{osti_22490823,
title = {Transition matrices and orbitals from reduced density matrix theory},
author = {Etienne, Thibaud and CNRS, Théorie-Modélisation-Simulation, SRSMC, Boulevard des Aiguillettes 54506, Vandoeuvre-lès-Nancy and Unité de Chimie Physique Théorique et Structurale, Université de Namur, Rue de Bruxelles 61, 5000 Namur},
abstractNote = {In this contribution, we report two different methodologies for characterizing the electronic structure reorganization occurring when a chromophore undergoes an electronic transition. For the first method, we start by setting the theoretical background necessary to the reinterpretation through simple tensor analysis of (i) the transition density matrix and (ii) the natural transition orbitals in the scope of reduced density matrix theory. This novel interpretation is made more clear thanks to a short compendium of the one-particle reduced density matrix theory in a Fock space. The formalism is further applied to two different classes of excited states calculation methods, both requiring a single-determinant reference, that express an excited state as a hole-particle mono-excited configurations expansion, to which particle-hole correlation is coupled (time-dependent Hartree-Fock/time-dependent density functional theory) or not (configuration interaction single/Tamm-Dancoff approximation). For the second methodology presented in this paper, we introduce a novel and complementary concept related to electronic transitions with the canonical transition density matrix and the canonical transition orbitals. Their expression actually reflects the electronic cloud polarisation in the orbital space with a decomposition based on the actual contribution of one-particle excitations from occupied canonical orbitals to virtual ones. This approach validates our novel interpretation of the transition density matrix elements in terms of the Euclidean norm of elementary transition vectors in a linear tensor space. A proper use of these new concepts leads to the conclusion that despite the different principles underlying their construction, they provide two equivalent excited states topological analyses. This connexion is evidenced through simple illustrations of (in)organic dyes electronic transitions analysis.},
doi = {10.1063/1.4922780},
journal = {Journal of Chemical Physics},
number = 24,
volume = 142,
place = {United States},
year = {Sun Jun 28 00:00:00 EDT 2015},
month = {Sun Jun 28 00:00:00 EDT 2015}
}
  • The density operator (density matrix) of a quantum mechenical system can be decomposed into operators which transform as irreducible representations of the symmetry group in coordinate and spin space. Each of these components has a physical meaning connected with the expectation values of certain operators. The reduced density matrices can be decomposed in a completely analogous way. The symmetry properties of the total wave function give rise to degeneracies of the eigenvalues of the reduced density matrices. These degeneracies can be removed by requiring that the natural spin orbitals (NSO, defined as the eigenfunctions of the first-order density matrix), asmore » well as the natural spin geminals (NSG, the eigenfunctions of the second-order density matrix) and their spinless counterparts transform as irreducible representations of the symmetry group and are eigenfunctions of S/sup 2/ and S/sub z/. In many cases this requirement is compatible with the original definition of the NSO, the NSG, etc., e.g., when there is no spatial degeneracy of the total wave function and when the Z- component of the total spin vanishes. When these conditions are not fulfilled an alternative definition of the NSO and the NSG is proposed. (auth)« less
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  • Understanding the roles of the temporary and spatial structures of quantum functional noise in open multilevel quantum molecular systems attracts a lot of theoretical interests. I want to establish a rigorous and general framework for functional quantum noises from the constructive and computational perspectives, i.e., how to generate the random trajectories to reproduce the kernel and path ordering of the influence functional with effective Monte Carlo methods for arbitrary spectral densities. This construction approach aims to unify the existing stochastic models to rigorously describe the temporary and spatial structure of Gaussian quantum noises. In this paper, I review the Euclideanmore » imaginary time influence functional and propose the stochastic matrix multiplication scheme to calculate reduced equilibrium density matrices (REDM). In addition, I review and discuss the Feynman-Vernon influence functional according to the Gaussian quadratic integral, particularly its imaginary part which is critical to the rigorous description of the quantum detailed balance. As a result, I establish the conditions under which the influence functional can be interpreted as the average of exponential functional operator over real-valued Gaussian processes for open multilevel quantum systems. I also show the difference between the local and nonlocal phonons within this framework. With the stochastic matrix multiplication scheme, I compare the normalized REDM with the Boltzmann equilibrium distribution for open multilevel quantum systems.« less