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

Abstract

In this work, we propose new field-free estimators for static field-gradient polarizabilities in finite temperature PIMC simulation. Namely, dipole-quadrupole polarizability A, dipole-dipolequadrupole polarizability B and quadrupole-quadrupole polarizability C are computed for several up to two-electron systems: H, H − , He, Li + , Be 2+ , Ps2, PsH, H + 2 , H2, H + 3 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.

Computation of Dynamic Polarizabilities and van der Waals Coefficients from Path-Integral Monte Carlo

“…41 High rotational ensemble interferes with the orientation, and hence, the rotational effect fades off as the temperature increases. 42,43,46 In higher orders, this effect is reproduced between nonzero anisotropy of tensorial polarizability and an associated hyperpolarizability. 42,43,46 Here, permanent moments are present in α 2 of H 2 and each α l of HD + , whose figures also have insets showing the strong decay of the rotational polarizability as T increases.…”

“…42,43,46 In higher orders, this effect is reproduced between nonzero anisotropy of tensorial polarizability and an associated hyperpolarizability. 42,43,46 Here, permanent moments are present in α 2 of H 2 and each α l of HD + , whose figures also have insets showing the strong decay of the rotational polarizability as T increases. At the lowtemperature limit, all rotational motion is deactivated and the static polarizability saturates to a finite value.…”

Path Integrals: From Quantum Mechanics to Photonics

“…There, however, only very simple systems were studied, such as the hydrogen (H) and hydrogen-like (Li + and Be + 2 ) atoms, the helium atoms He and He + , the hydrogen molecule H 2 and H + 2 , hydrogenhelium (HeH + ) and hydrogen-deuterium (HD + ) molecules, and the positronium atom. These systems have been studied employing different methods, including finite-field simulations for static polarisabilities 64 , polarisability estimators for simulation without the external field 73 , static field-gradient polarisabilities 65 , and finally, dynamic polarisabilities and van der Waals coefficients 72 . The last one, in particular, is of great interest, as the macroscopic electric susceptibility is constructed starting from the dynamic frequency dependent polarisabilities.…”

“…In recent years, one of the authors of this tutorial (TTR) has significantly contributed to taking PIMC simulations to new though simple quantum particle systems, such as small atoms 60,61 , molecules [62][63][64][65] , a chemical reaction 66 and quantum dots [67][68][69] , with the ultimate goal of providing a more accurate description of their electronic structure and related properties including many-body effects, and how they change with temperature 61,70,71 . In this context, PIMC has proven to be a very reliable and excellent method to calculate the electric polarisabilities of atomic and molecular systems, leading therefore to an accurate estimation of the optical properties of both individual small quantum systems and collections of them, in the form of dilute gases 65,72,73 .…”

Shell-confined atom and plasma: incidental degeneracy, metallic character and information entropy

“…A host of macroscopic properties like refractive index, dielectric constant can be estimated via dipole polarizability [10]. The latter plays an important role in the determination of physicochemical properties, like optical response, as well as atomic and molecular interactions [11].…”