# Algorithm for distance list extraction from pair distribution functions

## TL;DR

This paper introduces an automated algorithm that accurately extracts atomic distance lists from pair distribution functions using curve fitting and innovative initialization techniques, applicable to nanostructured samples and similar spectral data.

## Contribution

The paper presents a novel, automated algorithm for extracting distance lists from PDFs, incorporating a new initialization approach to handle non-convex optimization challenges.

## Key findings

- Effective initial guess improves extraction accuracy
- Algorithm performs well on nanostructured samples
- Potential extension to Gaussian-sum spectra

## Abstract

We present an algorithm to extract the distance list from atomic pair distribution functions (PDFs) in a highly automated way. The algorithm is constructed via curve fitting based on a Debye scattering equation model. Due to the non-convex nature of the resulting optimization problem, a number of techniques are developed to overcome various computational difficulties. A key ingredient is a new approach to obtain a reasonable initial guess based on the theoretical properties of the mathematical model. Tests on various nanostructured samples show the effectiveness of the initial guess and the accuracy and overall good performance of the extraction algorithm. This approach could be extended to any spectrum that is approximated as a sum of Gaussian functions.