Highly Accurate Molecular Properties using High-Order Relativistic Coupled Cluster Theory. – (Gabriele FABBRO / LCPQ / Thèse). – 5/12/2025, 14H

PhD Defence

Gabriele FABBRO, LCPQ, Seminar room, Bat. 3R4

Abstract :
Heavy atoms present formidable theoretical challenges, arising from the interplay of relativistic motion of inner electrons, quantum electrodynamics (QED) effects, and strong electron correlation. The HAMP-vQED (Highly Accurate Molecular Properties using variational Quantum Electrodynamics) project tackles these challenges by providing a unified computational framework that simultaneously incorporates relativistic, QED, and correlation effects, enabling highly accurate predictions of molecular properties. Among these effects, this thesis focuses on the accurate treatment of electron correlation. To achieve this, the Coupled-Cluster (CC) method has been adopted as the primary computational approach, due to its high accuracy and systematic improvability. However, extending CC methods to higher excitation levels, such as triple, quadruple, or beyond, makes the derivation of the corresponding working equations extremely complex and prone to errors. These challenges can be effectively addressed through the development of automated equation generators, such as the tenpi toolchain, developed within the HAMP-vQED project. The primary goal of this thesis has therefore been the implementation of analytical first derivatives of the CC energy at arbitrary excitation levels using the tenpi toolchain. To do that, following the Lagrangian formalism, we derived and implemented the Λ-equations and the corresponding one-body density matrices for high-level order of theory. This enabled the calculation of molecular properties at the CCSDT and CCSDTQ levels within the DIRAC program package.
The molecular property that we have primarily investigated in this thesis is the electric field gradient (EFG) evaluated at the nuclear positions. For nuclei possessing a nuclear quadrupole moment (NQM), the latter couples to the EFG, and their interaction is quantified by the nuclear quadrupole coupling constant (NQCC). Accurate values of NQM can be extracted from experimentally determined NQCCs combined with high-level quantum-chemical calculations of the EFG. For heavy atoms, the EFG is highly sensitive to both electron correlation and relativistic effects, making it a particularly appealing property in the context of this thesis. In addition to these electronic-structure contributions, the accurate prediction of molecular properties also requires the inclusion of rovibrational corrections, which arise from the fact that molecules rotate and vibrate around their equilibrium geometry. Within this thesis, these contributions have been derived and implemented for diatomic molecules in order to enhance the agreement between theory and experiment. Beyond its connection to the nuclear quadrupole moment, the EFG also encodes chemically relevant information, particularly regarding the nature of chemical bonding. This aspect is emphasized in the Dailey-Townes model, which assumes that the dominant contribution to the EFG arises from valence p shells. However, this model neglects the role of partially occupied d and f shells, relativistic effects, and core-polarization contributions. Part of this thesis has been devoted to critically assessing and refining this model in order to provide a more complete and accurate description of the chemical factors influencing the EFG..

Supervisor :
Trond SAUE

Committee :
• Mr Robert BERGER, Reviewer, Philipps-Universität Marburg
• Ms Stella STOPKOWICZ, Reviewer, Universität des Saarlandes
• Ms Pina ROMANIELLO, Examiner, Université de Toulouse
• Mr Andre Severo Pereira GOMES, Examiner, Institut Universitaire de Technologie de Lille
• Mr Trond SAUE, Thesis Director, Université de Toulouse