Description du sujet de thèse

Towards Systematically Improvable and Broadly Applicable Green's Function Methods in Quantum Chemistry and Condensed Matter Physics

PhD Project Summary:
Green's function-based methods offer a promising framework for the ab initio description of electronic properties in molecular and condensed systems. However, their full potential remains untapped due to the lack of systematic improvement schemes and the technical challenges involved in going beyond standard approximations such as GW. The primary objective of this PhD project is to contribute to the development of new Green's function-based approaches that are both systematically improvable, more predictive, and applicable to a broad range of electronic phenomena.

Scientific Background and Research Problem:
Hedin's equations and the parquet formalism provide a theoretical basis for improving upon standard approximations through the inclusion of vertex corrections. Nevertheless, their algorithmic complexity has hindered practical implementations, especially in quantum chemistry and molecular spectroscopy. To date, the parquet approximation has never been implemented for molecular systems using Gaussian-type orbital bases, although it is well established in condensed matter physics for simplified model systems.

Moreover, while the Bethe-Salpeter Equation (BSE) method combined with GW is currently a leading approach for describing excited states, it still suffers from significant limitations. These include difficulties in describing specific types of excited states (e.g., triplets, double excitations), the absence of analytical gradients, and high computational cost. These drawbacks limit its adoption in dynamical and photochemical studies, despite its excellent performance for complex excitations such as charge-transfer and Rydberg states.

Thesis Objectives:
1. Implement the parquet approximation in a Gaussian basis for molecular systems and evaluate its performance on benchmark cases.
2. Develop full analytical gradients for GW and BSE methods, leveraging structural analogies with coupled-cluster theory.
3. Extend these methods to the ab initio description of unconventional superconductivity, using formalisms based on particle-number non-conserving reference states (e.g., Hartree-Fock-Bogoliubov).
4. Integrate these developments into efficient computational codes and disseminate the results within the theoretical chemistry and computational physics communities.

Methodology:
The project will combine rigorous analytical derivations with high-performance numerical implementations. It will involve the development of theoretical frameworks, efficient coding, and validation on both model and realistic systems. The work will take place in a collaborative environment involving experts in parquet formalism and excitation theory.

Expected Scientific Impact:
This PhD project aims to push the current boundaries of Green's function-based methods by enabling their systematic improvement and extending their applicability to complex systems of fundamental or technological interest. The expected outcomes will open new avenues for the accurate description of correlated electronic phenomena in chemistry, materials science, and quantum data science.

Contexte de travail

The Laboratoire de Chimie et Physique Quantiques (LCPQ) UMR5626 in Toulouse (Universite Paul Sabatier) is part of the IRSAMC (physics) institute and is located on the campus og the Universite Paul Sabatier.
The LCPQ gathers more than 20 permanent researchers working on various areas of computational and theoretical chemsitry.

Contraintes et risques

N/A