Statistical analysis of electronic excitation processes: Spatial location, compactness, charge transfer, and electron-hole correlation

Abstract

We report the development of a set of excited-state analysis tools that are based on the construction of an effective exciton wavefunction and its statistical analysis in terms of spatial multipole moments. This construction does not only enable the quantification of the spatial location and compactness of the individual hole and electron densities but also correlation phenomena can be analyzed, which makes this procedure particularly useful when excitonic or charge-resonance effects are of interest. The methods are first applied to bianthryl with a focus on elucidating charge-resonance interactions. It is shown how these derive from anticorrelations between the electron and hole quasiparticles, and it is discussed how the resulting variations in state characters affect the excited-state absorption spectrum. As a second example, cytosine is chosen. It is illustrated how the various descriptors vary for valence, Rydberg, and core-excited states, and the possibility of using this information for an automatic characterization of state characters is discussed.

Describing excited states of [n]cycloparaphenylenes by hybrid and double-hybrid density functionals: from isolated to weakly interacting molecules

“…In order to better rationalize the assignments of UV-vis absorption energies, we consider next the Natural Transition Orbitals (NTO) [75,76]. In this way, the transition density matrix coupling the ground-state |Ψ and the excited-state |Ψ ⋆ wavefunctions is made diagonal, and then each hole in the occupied space is associated to a single particle in the virtual space, without changing the corresponding excitation energies obtained here.…”

Communication: Exciton analysis in time-dependent density functional theory: How functionals shape excited-state characters

“…In recent work, [24][25][26][27] we established a series of excitedstate descriptors based on the physical picture of an exciton wavefunction, which is constructed from the one-particle transition density matrix (1TDM) (see also Refs. [28][29][30].…”

“…The properties and relation of these expectation values to natural transition orbital analysis 35 have been discussed in detail recently. 27 The main focus of this study is the description of spatial distributions and correlation effects of exciton wavefunctions, a task which can be achieved by computing multipole moments of the electron and hole position operators. 27 Two measures of charge transfer are investigated: the mean…”

“…The methodology presented should not only be suitable for diagnosing methodological shortcomings but should, ultimately, also provide a new viewpoint for generating improved functionals. Due to the general formulation used, the quantities are also accessible in an ab-initio context 26,27 offering new ways for benchmarking. Finally, the computed excited-state properties open a new route for property-based diabatization schemes.…”

Communication: Unambiguous comparison of many-electron wavefunctions through their overlaps

“…[1][2][3] However, the assignment of state characters based on orbitals alone is challenging in many cases, e.g., when the orbital character is not clearly visible, when the orbitals are delocalized, when many configurations are involved, or when partial double excitation character is present. To overcome some of these problems, different phenomenological descriptors have been introduced that monitor diverse specific properties, such as the number of unpaired electrons, 4-6 double excitation character, 3,7 charge transfer, [8][9][10][11][12] excitonic effects, [13][14][15] collectivity, 16 entanglement, 17,18 and orbital relaxation. 19 While these certainly provide important insight, the sheer number of such descriptors shows how challenging it is to grasp many-electron wavefunctions in their full complexity.…”