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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--dipole--quadrupole polarizability $B$ and quadrupole--quadrupole polarizability $C$ are computed for several up to two-electron systems: H, H$^-$, He, Li$^+$, Be$^{2+}$, Ps$_2$, PsH, H$_2^+$, H$_2$, 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., Comment: 6 pages, 2 figures, 2 supplementary pages

We present a new approach based on real time domain Feynman path integrals (RTPI) for electronic structure calculations and quantum dynamics, which includes correlations between particles exactly but within the numerical accuracy. We demonstrate that incoherent propagation by keeping the wave function real is a novel method for finding and simulation of the ground state, similar to Diffusion Monte Carlo (DMC) method, but introducing new useful tools lacking in DMC. We use 1D Hooke's atom, a two-electron system with very strong correlation, as our test case, which we solve with incoherent RTPI (iRTPI) and compare against DMC. This system provides an excellent test case due to exact solutions for some confinements and because in 1D the Coulomb singularity is stronger than in two or three dimensional space. The use of Monte Carlo grid is shown to be efficient for which we determine useful numerical parameters. Furthermore, we discuss another novel approach achieved by combining the strengths of iRTPI and DMC. We also show usefulness of the perturbation theory for analytical approximates in case of strong confinements.

Excitons, trions, biexcitons, and exciton-trion complexes in two-dimensional transition metal dichalcogenide sheets of MoS$_2$, MoSe$_2$, MoTe$_2$, WS$_2$ and WSe$_2$ are studied by means of density functional theory and path integral Monte Carlo method in order to accurately account for the particle-particle correlations. In addition, the effect of dielectric environment on the properties of these exciton complexes is studied by modifying the effective interaction potential between particles. Calculated exciton and trion binding energies are consistent with previous experimental and computational studies, and larger systems such as biexciton and exciton-trion complex are found highly stable. Binding energies of biexcitons are similar or higher than those of trions, but the binding energy of the trion depends significantly stronger on the dielectric environment than that of biexciton. Therefore, as a function of an increasing dielectric constant of the environment the exciton-trion complex "dissociates" to a biexciton rather than to an exciton and a trion., Comment: 5 pages, 4 figures

We present a technique to efficiently compute long-range interactions in systems with periodic boundary conditions. We extend the well-known Ewald method by using a linear combination of screening Gaussian charge distributions instead of only one as in the standard Ewald scheme. The combined simplicity and efficiency of our method is demonstrated, and the scheme is readily applicable to large-scale periodic simulations, classical as well as quantum.

In this work we develop tools that enable the study of non-adiabatic effects with variational and diffusion Monte Carlo methods. We introduce a highly accurate wave function ansatz for electron-ion systems that can involve a combination of both fixed and quantum ions. We explicitly calculate the ground state energies of H$_{2}$, LiH, H$_{2}$O and FHF$^{-}$ using fixed-node quantum Monte Carlo with wave function nodes that explicitly depend on the ion positions. The obtained energies implicitly include the effects arising from quantum nuclei and electron-nucleus coupling. We compare our results to the best theoretical and experimental results available and find excellent agreement., Comment: 6 Pages

We present full quantum statistical energetics of some electron-light nuclei systems. This is accomplished with the path integral Monte Carlo method. The effects on energetics arising from the change in the nuclear mass are studied. The obtained results may serve as reference data for the multicomponent density functional theory calculations of light nuclei system. In addition, the results reported here will enable better fitting of todays electron-nuclear energy functionals, for which the description of light nuclei is most challenging, in particular.

Full $NVT$ quantum statistics of the H$_3^+$ ion is simulated at low densities using the path integral Monte Carlo approach. For the first time, the molecular total energy, partition function, free energy, entropy and heat capacity are evaluated in temperatures relevant for planetary atmospheric physics. Temperature and density dependent dissociation recombination reaction balance of the molecule and its fragments above 4000 K is described, and also, the density dependence of thermal ionization above $10 000$ K is demonstrated. We introduce a new well-behaving analytical model for the molecular partition function of the H$_3^+$ ion for the temperature range below dissociation and fit the parameters to the energetics from our simulations. The approach presented here can be regarded as an extension of the traditional {\it ab initio} quantum chemistry beyond the Born--Oppenheimer approximation to description of nonadiabatic phenomena, and even further, account of nuclear quantum dynamics., Comment: submitted to The Astrophysical Journal

Full quantum statistical $NVT$ simulation of the five-particle system H$_3^+$ has been carried out using the path integral Monte Carlo method. Structure and energetics is evaluated as a function of temperature up to the thermal dissociation limit. The weakly density dependent dissociation temperature is found to be around $4000$ K. Contributions from the quantum dynamics and thermal motion are sorted out by comparing differences between simulations with quantum and classical nuclei. The essential role of the quantum description of the protons is established., Comment: submitted to the Journal of Chemical Physics

Path integral Monte Carlo simulation of the dipositronium "molecule" Ps$_2$ reveals its surprising thermal instability. Although, the binding energy is $\sim 0.4$ eV, due to the strong temperature dependence of its free energy Ps$_2$ dissociates, or does not form, above $\sim 1000$ K, except for high densities where a small fraction of molecules are in equilibrium with Ps atoms. This prediction is consistent with the recently reported first observation of stable Ps$_2$ molecules by Cassidy & Mills Jr., Nature {\bf 449}, 195 (07), and Phys.Rev.Lett. {\bf 100}, 013401 (08); at temperatures below 1000 K. The relatively sharp transition from molecular to atomic equilibrium, that we find, remains to be experimentally verified. To shed light on the origin of the large entropy factor in free energy we analyze the nature of interatomic interactions of these strongly correlated quantum particles. The conventional diatomic potential curve is given by the van der Waals interaction at large distances, but due to the correlations and high delocalization of constituent particles the concept of potential curve becomes ambiguous at short atomic distances., Comment: Submitted to the Physical Review Letters