# Inferring crystal electronic properties from experimental data sets through Semidefinite Programming

## TL;DR

This paper introduces a semidefinite programming approach to infer the one-electron reduced density matrix of crystals from experimental data, minimizing assumptions and overcoming previous constraints, with successful application to dry ice.

## Contribution

The paper presents a novel semidefinite programming framework for inferring the 1-RDM from experimental data with minimal assumptions, improving upon existing methods.

## Key findings

- Successfully applied to dry ice crystal data
- Provides results comparable to ab-initio calculations
- Addresses constraints that limited previous models

## Abstract

Constructing a quantum description of crystals from scattering experiments is of paramount importance to explain their macroscopic properties and to evaluate the pertinence of theoretical ab-initio models. While reconstruction methods of the one-electron reduced density matrix have already been proposed, they are usually tied to strong assumptions that limit and may introduce bias in the model. The goal of this paper is to infer a one-electron reduced density matrix (1-RDM) with minimal assumptions. We have found that the mathematical framework of Semidefinite Programming can achieve this goal. Additionally, it conveniently addresses the nontrivial constraints on the 1-RDM which were major hindrances for the existing models. The framework established in this work can be used as a reference to interpret experimental results. This method has been applied to the crystal of dry ice and provides very satisfactory results when compared with periodic ab-initio calculations.