Visualisation of Electronic Excited‐State Correlation in Real Space

Abstract

A method for the visualisation of excited-state electron correlation is introduced and shown to address two notorious problems in excited-state electronic structure theory, the analysis of excitonic correlation and the distinction between covalent and ionic wavefunction character. The method operates by representing the excited state in terms of electron and hole quasiparticles, fixing the hole on a fragment of the system and observing the resulting conditional electron density in real space. The application of this approach to oligothiophene, an exemplary conjugated polymer, illuminates excitonic correlation effects of its excited states in unprecedented clarity and detail. 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. More generally, the method is relevant for any excited state that cannot be described by a single electronic configuration.Electronically excited states of molecules form the underpinnings of a wide range of processes of utmost scientific interest, such as light-driven natural processes [1,2] photochemical reactions, [3] signalling and sensing, [4] and the operation of organoelectronic materials. [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. Indeed, the predictive power of computational photochemistry has steadily increased over the recent years due to the tremendous effort spent in the development of new methods as well as rapid progress in computer technology. [7][8][9][10][11][12] However, the interpretation of this wealth of computational data can act as a significant impediment in practical work. Therefore, a number of analysis tools have been developed to quantify excited-state properties [13][14][15][16][17] and to visualise the molecular orbitals (MOs) involved and their location in space in a compact and rigorous way. [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. Such cases are widespread and two notorious failures of the MO picture relate to excitons in extended systems [24][25][26] and to ionic/ covalent wavefunction character in alternant hydrocarbons. [27,28] The first case is related to the emergence of band structure in large systems, which leads to excited states formed as a superposition of many different electronic configurations whose description requires moving from the MO picture to a representation in terms of correlated electron and hole quasiparticles. [26,[29][30][31] Previous attempts of visualising the ensuing correlated electron-hole distribution ha...

TheoDORE: A toolbox for a detailed and automated analysis of electronic excited state computations

“…49,50 Whereas the Ω-matrices provide a very compact representation of the correlated exciton, this representation may be too abstract in many cases. Therefore, a different representation has been developed, 27 which formally proceeds by modifying Eq. (2) in the sense that only one of the integrations is carried out leaving the one-body function…”

“…[17][18][19][20] A particular effort has been devoted to the task of visualising excited-state correlations using correlation plots [21][22][23][24][25][26] and conditional densities. 27 The TheoDORE toolbox 28 has been designed with the goal of providing rigorous and detailed excited-state analysis methods in a lightweight and modular framework that is amenable to a variety of electronic structure methods and codes. At the moment interfaces to ten quantum chemistry codes exist encompassing Columbus, 29 OpenMolcas, 30 a) Electronic mail: f.plasser@lboro.ac.uk; https://fplasser.scipublic.lboro.ac.uk Q-Chem, 31 ADF, 32 DFTB+, 33 Firefly, 34 Gaussian, 35 Orca, 36 Terachem, 37 and Turbomole, 38 and we will use three of these (Turbomole, Q-Chem, and Orca) in the present work.…”

“…42,43 More strikingly, the implemented analysis methods allow to understand correlation effects, which are not apparent at all in the standard MO picture with two prominent examples being excitonic correlation in conjugated polymers 44 and the ionic and covalent states in alternating hydrocarbons. 27 The purpose of this work is to highlight some of the prominent features implemented and to give a compact introduction to new users of the code while a more comprehensive discussion of the available functionalities and the more technical details is given in the literature. 8,25,44 We will focus on three methods, as summarised in Sec.…”

“…Third, exciton correlation occurring in a ladder polymer is illustrated using abstract matrix plots 44 along with a newly developed real-space representation of conditional densities. 27 The more technical details are given in Sec. IV providing an overview of the structure of the code, the computational details, and a step-by-step instruction for performing the analyses and creating the graphics shown here.…”

Following the evolution of excited states along photochemical reaction pathways

“…It is worth mentioning that in few particular molecular systems some states may be described by more than one hole-particle pair with almost equally dominant contributions. [47,48] In such systems, different ESs may be characterized by similar NTOs. For instance, in the case of the naphthalene molecule there are several pairs of ESs described by almost equivalent orbital transitions (see ref.…”