Final Defense Announcement

Luca Murg

Candidate for Doctor of Philosophy

The Grainger College of Engineering

Department of Nuclear, Plasma, and Radiological Engineering

Advisor and Doctoral Committee Chair: Jianqi Xi, Assistant Professor 

Date: April 30, 2026

Time: 1:00 pm - 3:00 pm Central Time

Location: Talbot Laboratory 101A

Zoom information: https://illinois.zoom.us/my/final.defense.lmurg2

Meeting ID: 218 757 9726 | Password: 100111

     

The Dirac-Coulomb-Breit Hamiltonian for Relativistic and Strongly Correlated Electrons

Materials utilized by novel energy systems (e.g. Generation IV Nuclear Reactors) are often studied using weakly correlated mean-field theories. However, if these systems incorporate heavy elements or strongly correlated topological materials, relativistic effects must be included. Therefore, a Kramers unrestricted coupled-cluster (CC) with single and double (SD) excitation formalism using a molecular mean-field exact-two component (X2Cₘₘ) transformation applied to the four component Dirac-Hartree-Fock (DHF) reference state is presented. The mean-field transformations incorporate all one-electron and two-electron contributions from, Dirac-Coulomb, Dirac-Coulomb-Gaunt (DCG) and Dirac-Coulomb-Breit (DCB) Hamiltonian and is used with the Equation of Motion (EOM) method to calculate the excitation energies of the alkali group of elements. Using this framework, the effects of two-electron Gaunt and Breit integrals on the generated relativistic mean-fields and on fine structure splitting is studied. Results show growing discrepancy in positive eigenvalue spectrum in non-exact X2Cₘₘ transformation with increasing Z number and that the gauge term in the Breit operator plays a non-trivial role in fine structure calculations with increasing Z number.  

Furthermore, an algorithmic enhancement to the CCSD algorithm is developed using a conditional variance and a minimal amplitude suppression mechanism. This modified algorithm especially aims to remedy calculations where a single reference determinant is still sufficient to obtain useful an electronic structure, but multi-reference effects begin to plague convergence of the excitation amplitudes.  It is demonstrated that this algorithm gives the same results as a classical algorithm but with a superior minimization technique. Additionally, through use of a dynamic threshold, the modified algorithm is designed to revert to a classical CC convergence algorithm near convergence tolerance. Although the algorithm is general, the efficacy of this modified algorithm is demonstrated in the context of a Kramers unrestricted CCSD framework using a X2Cₘₘ transformation and a four-component Kramers unrestricted DHF reference state using the DC Hamiltonian.

Finally, a generalization of the nonperiodic DHF-DCB formalism to the periodic case is explored by deriving working equations for the periodic four-component Kramers unrestricted DHF-DCB Hamiltonian within the maximally component- and spin-separated Pauli spinor representation in the restricted kinetic balance condition. Using polymeric Carbon, Silicon, Germanium, and Graphene, it is demonstrated that band structure and topological information can be successfully calculated from within this framework. Overall, this work allows outlines new methods for study of relativistic processes within exact two-component mean-field approaches and lays the foundation for future theoretical development of relativistic calculations for solid-state systems.

Luca Murg is a Ph.D. candidate in Nuclear, Plasma, and Radiological Engineering at the University of Illinois at Urbana-Champaign. His research focuses on strongly correlated, relativistic electronic structure theory for modeling heavy elements and strongly correlated topological materials. At Illinois, he worked on collaborative projects with Los Alamos National Laboratory and has served as a teaching assistant for undergraduate and graduate courses covering foundational topics in nuclear engineering and energy systems, including materials, heat transfer, and fluid flow, with emphasis on the mathematical similarities between heat transfer, fluid dynamics, and neutron diffusion.