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 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.

Quantum plasmonic nanoantennas

“…Also, the presence of deexcitations (described by the Y eigenvector) complicates calculating the transition density matrix. (Within the TammDancoff approximation, where there is no coupling between the hole-particle and hole-particle correlations, it is possible to simply identify that T ia = X ia [72].) In Appendix B, the necessary postanalysis of typical TDDFT results is shown.…”

“…There has been some work on uniquely determining the transition density matrix, including ph-hp correlation [32,72,78]. Given that the different methods return similar values, we use the simplest method from [32], where two pseudotransition matrices are defined, and then we use the following equation for the collectivity:…”

Visualisation of Electronic Excited‐State Correlation in Real Space

“…A study of naphthalene shows that the distinction between the ionic and covalent states of this molecule, which has so far only been achieved using elaborate valence-bond theory protocols, arises naturally in terms of electron-hole avoidance and enhanced overlap, respectively. [18][19][20][21][22][23] However, the above-mentioned visualisation tools -and the MO picture itself -break down if the information of interest does not lie in the MOs themselves but in the interaction of different quasidegenerate electronic configurations. [5,6] Computational photochemistry has become an indispensable part of scientific investigations in these areas through two main tasks, the interpretation of experimental results and the prediction of unknown photophysical properties.…”

“…[7][8][9][10][11][12] However, the interpretation of this wealth of computational data can act as a significant impediment in practical work. [18][19][20][21][22][23] However, the above-mentioned visualisation tools -and the MO picture itself -break down if the information of interest does not lie in the MOs themselves but in the interaction of different quasidegenerate electronic configurations. [18][19][20][21][22][23] However, the above-mentioned visualisation tools -and the MO picture itself -break down if the information of interest does not lie in the MOs themselves but in the interaction of different quasidegenerate electronic configurations.…”

A comprehensive, self‐contained derivation of the one‐body density matrices from single‐reference excited‐state calculation methods using the equation‐of‐motion formalism

“…Depending on the method used for computing the electronic transitions, the objects derived from these calculations will not have the same structure and the same properties . As the analysis of the nature of the excited states generally relies on the use of these objects (in particular the transition and difference density matrices, that will both be at the center of this contribution), either from a qualitative point of view using exciton analysis or one‐particle charge density functions and their corresponding density matrices, or under a quantitative perspective using descriptors, a proper knowledge of their structure is required for selecting the right post‐processing strategy. Unfortunately, while the structure of the objects derived from the calculations are often known for the most common calculation methods, in most of the cases this structure is given without a demonstration.…”