# An Open-Source Framework for Analyzing $N$-Electron Dynamics: I. Multi-Determinantal Wave Functions

## TL;DR

This paper introduces an open-source Python framework for analyzing and visualizing correlated many-electron dynamics in molecules, focusing on electronic flux density derived from multi-determinant wave functions, applicable to charge migration studies.

## Contribution

It provides a novel post-processing tool that extracts electronic flux data directly from standard quantum chemistry outputs, enabling detailed analysis of ultrafast electron dynamics.

## Key findings

- Demonstrates broad applicability to charge migration in various molecules.
- Assesses convergence of dynamics with respect to theory level and basis set.
- Shows robustness of dynamical features across different computational parameters.

## Abstract

The aim of the present contribution is to provide a framework for analyzing and visualizing the correlated many-electron dynamics of molecular systems, where an explicitly time-dependent electronic wave packet is represented as a linear combination of $N$-electron wave functions. The central quantity of interest is the electronic flux density, which contains all information about the transient electronic density, the associated phase, and their temporal evolution. It is computed from the associated one-electron operator by reducing the multi-determinantal, many-electron wave packet using the Slater-Condon rules. Here, we introduce a general tool for post-processing multi-determinant configuration-interaction wave functions obtained at various levels of theory. It is tailored to extract directly the data from the output of standard quantum chemistry packages using atom-centered Gaussian-type basis functions. The procedure is implemented in the open-source Python program detCI@ORBKIT, which shares and builds upon the modular design of our recently published post-processing toolbox [J. Comput. Chem. 37 (2016) 1511]. The new procedure is applied to ultrafast charge migration processes in different molecular systems, demonstrating its broad applicability. Convergence of the $N$-electron dynamics with respect to the electronic structure theory level and basis set size is investigated. This provides an assessment of the robustness of qualitative and quantitative statements that can be made concerning dynamical features observed in charge migration simulations.