Thermal Effects in Atomic and Molecular Polarizabilities with Path Integral Monte Carlo

This Thesis is a review of polarizability and different means to estimate it from pathintegral Monte Carlo (PIMC) simulations. Polarizability is the quantum mechanical equivalent of electric susceptibility: it describes the electric field response of atoms and molecules. The static and dynamic multipole polarizabilies are, arguably, the most important electronic response properties and multipurpose parameters for physical modeling. Computing them from first principles is challenging in many ways, and in this Thesis we focus on a few particular aspects: exact many-body correlations, nonadiabatic effects and thermal coupling.

The Thesis contains an introduction to polarizability in the framework of nonrelativistic Feynman path integrals and thermal density matrices. The electric field interactions due to electric multipoles is associated with causal time-correlation functions and nonlinear response theory. The original scientific contribution manifests in various strategies to obtain the polarizabilities from PIMC simulations: we demonstrate finite-field simulations, static field-derivative estimators, and analytic continuation of imaginarytime correlation functions. The required analytic continuation of Matsubara frequencies is a common but ill-posed numerical challenge, which we approach with the Maximum Entropy method.

For data, we provide the most important polarizabilities and hyperpolarizabilities of several one- or two-electron systems: H, H₂⁺, H₂, H₃⁺, HD⁺, He, He⁺, HeH⁺, Li⁺, Be₂⁺, Ps, PsH, and Ps₂. Our benchmark simulations within the Born–Oppenheimer approximation (BO) agree with the available literature and complement it in many cases. Beyond BO, we are able to demonstrate weak and strong thermal effects due to, e.g., rovibrational coupling. We also estimate the first-order multipole spectra, dynamic polarizabilities and van der Waals coefficients. The simulations show unprecedented accuracy in terms of exact many-body correlations and fully nonadiabatic coupling of the electronic and nuclear quantum effects.