# Diagnosis of two evaluation paths to density-based descriptors of molecular electronic transitions

## TL;DR

This paper evaluates the reliability of two computational methods for analyzing electronic transitions in molecules, comparing their accuracy and convergence across various molecules, basis sets, and functionals.

## Contribution

It introduces a diagnostic framework to assess the accuracy of population analysis relative to numerical integration for density-based descriptors.

## Key findings

- Population analysis can deviate from numerical integration results.
- Eight diagnostic tests effectively identify when population analysis is unreliable.
- The reliability varies with basis sets and exchange-correlation functionals.

## Abstract

In this paper we discuss the reliability of two computational methods (numerical integration on Cartesian grids, and population analysis) used for evaluating scalar quantities related to the nature of electronic transitions. These descriptors are integrals of charge density functions built from the detachment and attachment density matrices projected in the Euclidean space using a finite basis of orbitals. While the numerical integration on Cartesian grids is easily considered to be converged for medium-sized density grids, the population analysis approximation to the numerical integration values is diagnosed using eight diagnostic tests performed on fifty-nine molecules with a combination of fifteen Gaussian basis sets and six exchange-correlation functionals.