General polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method applied to small atoms, ions, and molecules at finite temperatures

Abstract

The nonlinear optical properties of matter have a broad relevance and many methods have been invented to compute them from first principles. However, the effects of electronic correlation, finite temperature, and breakdown of the Born-Oppenheimer approximation have turned out to be challenging and tedious to model. Here we propose a straightforward approach and derive general field-free polarizability and hyperpolarizability estimators for the path-integral Monte Carlo method. The estimators are applied to small atoms, ions, and molecules with one or two electrons. With the adiabatic, i.e., Born-Oppenheimer, approximation we obtain accurate tensorial ground state polarizabilities, while the nonadiabatic simulation adds in considerable rovibrational effects and thermal coupling. In both cases, the 0 K, or ground-state, limit is in excellent agreement with the literature. Furthermore, we report here the internal dipole moment of PsH molecule, the temperature dependence of the polarizabilities of ${\mathrm{H}}^{\ensuremath{-}}$, and the average dipole polarizabilities and the ground-state hyperpolarizabilities of ${\mathrm{HeH}}^{+}$ and $\mathrm{H}{{}_{3}}^{+}$.