“Localized” perturbation theory for projected states for a two-element group

B. Atalay, D.M. Brink, A. Mann

F. A. Matsen

The unitary group formulation of many-body theory is based on particle-hole Gel'fand states, states labeled only by the excitation process: h(hole orbitals)-p(particle orbitals). The particle-hole Gel'fand states are constructed from generator states, states obtained by applying weight-lowering products of generators to the highest weight state and then evaluating the matrix elements Lie algebraically. We make application to spin-projected, quasidegenerate perturbation theory.

David Atkinson

Jeff Robert Keyes

Localized methods for more efficient quantum chemical calculations, December 12, 2025, https://doi.org/10.14418/8qbns2ce, Keyes, Jeff Robert (creator), Jiménez-Hoyos, Carlos Alberto, dissertations, Doctor of Philosophy, Chemistry, This thesis will discuss two projects aimed at improving the computational cost of electronic structure methods using the local approximation. These are methods that take advantage of the local nature of the Hamiltonian in real space to provide low cost approximations to solutions of the Schrodinger equation. The first project is a modification of local correlation methods where a set of Hartree-Fock orbitals are produced to be compact in real space, then correlations are restricted to orbitals that are nearby, typically using perturbation theory or coupled cluster. These orbitals are usually constructed using a projection after variation approach where the canonical orbitals are produced, then localized through unitary transformation and orthogonalization tails are projected out. We instead consider a variation after projection approach, where we construct a set of localized constraints on the orbitals, then optimize them in those constraints. We will show that this approach produces local orbitals that are closer to the canonical orbitals and are very well-suited to local correlation techniques. The second project is a method for calculating the correlation energy of strongly correlated systems. The main idea is to construct local orbitals, then divide them into groups called clusters typically chosen by proximity. The orbitals in each cluster are then used to construct a local Fock space with which we use as a basis of matrix product states. First as a single product state called the cluster mean field(cMF) wavefunction, which can then be improved with the cluster versions of perturbation theory and coupled cluster. We will show that this method scales substantially better than other available methods and provides a high quality result that is systematically improvable. , d2026-keyes, Wesleyan University Library, Wesleyan University, Middletown, CT, USA, Quantum chemistry, Electronic structure theory, Local correlation, Matrix product states, Perturbation theory, Coupled cluster theory, Cluster mean field, Text, English, In Copyright, born digital, University Archives

Carl G. Adler, Ollie James Rose

Péter R. Śurján, Ágnes Szabados

We argue that the so-called localization diagrams, originating from off-diagonal Fockian elements, do not have to be dealt with explicitly in the Davidson-Kapuy many-body perturbation theory with localized orbitals but can be accounted for by dressed two-electron integrals.