Physical Properties, Exciton Analysis, and Visualization of Core-Excited States: An Intermediate State Representation Approach

Abstract

The theoretical simulation of X-ray absorption spectra is in general a challenging task. However, for small and medium-sized organic molecules, the algebraic diagrammatic construction scheme (ADC) for the polarization operator in combination with the core-valence separation approximation (CVS) has proven to yield core-excitation energies and transition moments with almost quantitative accuracy allowing for reliable construction of X-ray absorption spectra. Still, to understand core-excitation processes in detail, it is not sufficient to only compute energies, but also properties like static dipole moments and state densities are important as they provide deeper insight into the nature of core-excited states. Here, we present for the first time an implementation of the intermediate state representation (ISR) approach in combination with the CVS approximation (CVS-ISR), which gives, in combination with the CVS-ADC method, direct access to core-excited state properties. The performance of the CVS-ADC/CVS-ISR approach is demonstrated by means of small- and medium-sized organic molecules. Besides the calculation of core-excited state dipole moments, advanced analyses of core-excited state densities are performed using descriptors like exciton sizes and distances. Plotting electron and hole densities helps to determine the character of the state, and in particular, the investigation of detachment/attachment densities provides information about orbital relaxation effects that are crucial for understanding core excitations.

Benchmarking Excited-State Calculations Using Exciton Properties

“…2(c). These quantities are particularly useful for distinguishing between different types of excited states, e.g., Rydberg states, core-excited states, 55 etc.…”

Simulation of X-ray transient absorption for following vibrations in coherently ionized F2 molecules

“…30 ADC has a long history of being applied to highly energetic electronic states and resonances. In particular, we employ the recently implemented core-valence separated approximation of ADC2x (CVS-ADC2x), 49,50,53 in which excitations that do not have one index referring to the annihilation of one of the target core orbitals are neglected entirely, this being justified by the large energetic separation of this group of resonances from other states (at least, from those to which there are nonzero Hamiltonian couplings). As with coupled-cluster theory, ADC may be applied on top of a spin-restricted reference (RADC) or an unrestricted reference (UADC).…”

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.…”

“…density functions and their corresponding density matrices, [4,5,20,[36][37][38][39][40] or under a quantitative perspective using descriptors, [6][7][8][26][27][28][29][30][31][32][33][39][40][41][42][43][44][45][46][47][48][49] 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.…”

“…These methods will be discussed in this paper. Note also that the algebraic diagrammatic construction [28,85,[110][111][112] (ADC) involves matrices with similar interpretation.…”