# Graph-theoretical evaluation of the inelastic propensity rules for molecules with destructive quantum interference

## TL;DR

This paper introduces a graph-theoretical method to evaluate inelastic propensity rules in molecules with destructive quantum interference, enabling automated analysis and visualization of interference effects and inelastic signals.

## Contribution

It develops an automated graph-based approach using an extended adjacency matrix to determine inelastic signals in molecules with quantum interference, with a publicly accessible computational tool.

## Key findings

- Method accurately predicts inelastic signals in interference molecules
- Provides a visual tool for understanding quantum interference configurations
- Automates the analysis process for complex molecular structures

## Abstract

We present a method based on graph theory for evaluation of the inelastic propensity rules for molecules exhibiting complete destructive quantum interference in their elastic transmission. The method uses an extended adjacency matrix corresponding to the structural graph of the molecule for calculating the Green function between the sites with attached electrodes and consequently states the corresponding conditions the electron-vibration coupling matrix must meet for the observation of an inelastic signal between the terminals. The method can be fully automated and we provide a functional website running a code using Wolfram Mathematica, which returns a graphical depiction of destructive quantum interference configurations together with the associated inelastic propensity rules for a wide class of molecules.