Static field-gradient polarizabilities of small atoms and molecules at finite temperature

In this work, we propose new field-free estimators of static field-gradient polarizabilities for finite temperature path-integral Monte Carlo method. Namely, dipole–quadrupole polarizability A, dipole–dipole–quadrupole polarizability B, and quadrupole–quadrupole polarizability C are computed for several up to two-electron systems: H, H⁻, He, Li⁺, Be²⁺, Ps₂, PsH, $H2+$⁠, H₂, $H3+$⁠, and HeH⁺. We provide complementary data for ground state electronic properties within the adiabatic approximation and demonstrate good agreement with available values in the literature. More importantly, we present fully non-adiabatic results from 50 K to 1600 K, which allow us to analyze and discuss strong thermal coupling and rovibrational effects in total field-gradient polarizabilities. These phenomena are most relevant but clearly overlooked, e.g., in the construction of modern polarizable force field models. However, our main purpose is demonstrating the accuracy and simplicity of our approach in a problem that is generally challenging.