Thermal dissociation of dipositronium: path integral Monte Carlo approach

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 Letter

Finite temperature quantum statistics of H3+_3^+ molecular ion

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 Physic

Few-body reference data for multicomponent formalisms: Light nuclei molecules

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

First-principles finite temperature electronic structure of some small molecules

The work presented in this thesis is based on the Feynman path integral formalism for quantum statistics. This brings forth a novel approach to solve quantum many-body systems giving complementary knowledge to more conventional approaches. In practice, the multidimensional path integrals are evaluated with Monte Carlo methods, and hence, the approach is called path integral Monte Carlo (PIMC). The PIMC method has not gained the deserved popularity, yet, even though this finite temperature approach yields exact quantum statistics. In practice, the PIMC method faces challenges deriving from its computational labour and the proper treatment of antisymmetric density matrix in case of identical fermions, that is,the fermi statistics. Also, the singularity of the Coulomb potential sets challenges for the most direct application of the path integrals. In this thesis we concentrate on the finite temperature quantum chemistry of some small molecules using the path integral Monte Carlo method. First, we give a brief introduction to the basics of the path integral formalism and its application using the Metropolis Monte Carlo algorithm. Second, we show how to overcome the problems related to the Coulomb singularity. Third, a brief survey on path integrals for fermions is carried out. Finally, we present the results from the four papers, which are included in this thesis and have been published in the refereed journals of the American Institute of Physics and the American Physical Society. In Paper I, a three-body quantum system, hydrogen molecule ion H2+, is revisited, once again. There we aim at tracing the electron-nuclei coupling effects in the three-body all-quantum, i.e. nonadiabatic, molecule. Among others we have evaluated spectroscopic constants and molecular deformation, also considering the isotope effects. Distinct features of coupling are found for the nuclei. In Paper II, we have found and explained the surprising thermal instability of the dipositronium molecule, Ps2. A proper nonadiabatic treatment is necessary for the dipositronium, thus making it challenging for conventional methods of quantum chemistry. In addition, with the PIMC method the present strong correlations are described properly. In Paper III, the quantum statistics of the five-particle molecule, H3+ ion, is examined. There we show how contributions from quantum and thermal dynamics to the particle distributions and correlation functions can be sorted out, and furthermore, how the quantum to classical dynamics transition can be monitored. At low temperatures the necessity of the fully quantum mechanical approach for all five particles is established. In Paper IV, the nonadiabatic simulations of Paper III are extended to higher temperatures, also, where the molecular dissociation-recombination equilibrium is studied. The temperature dependent mixed state description of the H3+ ion, the density dependent equilibrium dissociation-recombination balance and the energetics has been evaluated for the first time. At about 4000 K the fragments of the molecule, H2 + H+, H2+ +H and 2H + H+, start contributing. Paper IV gives major additions to the earlier published studies in the literature, where the dissociation-recombination reaction of H3+ has been neglected

First-principles finite temperature electronic structure of some small molecules

The work presented in this thesis is based on the Feynman path integral formalism for quantum statistics. This brings forth a novel approach to solve quantum many-body systems giving complementary knowledge to more conventional approaches. In practice, the multidimensional path integrals are evaluated with Monte Carlo methods, and hence, the approach is called path integral Monte Carlo (PIMC). The PIMC method has not gained the deserved popularity, yet, even though this finite temperature approach yields exact quantum statistics. In practice, the PIMC method faces challenges deriving from its computational labour and the proper treatment of antisymmetric density matrix in case of identical fermions, that is,the fermi statistics. Also, the singularity of the Coulomb potential sets challenges for the most direct application of the path integrals. In this thesis we concentrate on the finite temperature quantum chemistry of some small molecules using the path integral Monte Carlo method. First, we give a brief introduction to the basics of the path integral formalism and its application using the Metropolis Monte Carlo algorithm. Second, we show how to overcome the problems related to the Coulomb singularity. Third, a brief survey on path integrals for fermions is carried out. Finally, we present the results from the four papers, which are included in this thesis and have been published in the refereed journals of the American Institute of Physics and the American Physical Society. In Paper I, a three-body quantum system, hydrogen molecule ion H2+, is revisited, once again. There we aim at tracing the electron-nuclei coupling effects in the three-body all-quantum, i.e. nonadiabatic, molecule. Among others we have evaluated spectroscopic constants and molecular deformation, also considering the isotope effects. Distinct features of coupling are found for the nuclei. In Paper II, we have found and explained the surprising thermal instability of the dipositronium molecule, Ps2. A proper nonadiabatic treatment is necessary for the dipositronium, thus making it challenging for conventional methods of quantum chemistry. In addition, with the PIMC method the present strong correlations are described properly. In Paper III, the quantum statistics of the five-particle molecule, H3+ ion, is examined. There we show how contributions from quantum and thermal dynamics to the particle distributions and correlation functions can be sorted out, and furthermore, how the quantum to classical dynamics transition can be monitored. At low temperatures the necessity of the fully quantum mechanical approach for all five particles is established. In Paper IV, the nonadiabatic simulations of Paper III are extended to higher temperatures, also, where the molecular dissociation-recombination equilibrium is studied. The temperature dependent mixed state description of the H3+ ion, the density dependent equilibrium dissociation-recombination balance and the energetics has been evaluated for the first time. At about 4000 K the fragments of the molecule, H2 + H+, H2+ +H and 2H + H+, start contributing. Paper IV gives major additions to the earlier published studies in the literature, where the dissociation-recombination reaction of H3+ has been neglected

Path integral Monte Carlo benchmarks for two-dimensional quantum dots

We report numerically accurate path integral Monte Carlo results for harmonically confined two-dimensional quantum dots containing up to N=60 interacting electrons. The finite-temperature values are extrapolated to 0 K and zero time step in order to provide precise upper-bound energies. The ground-state energies are compared against coupled-cluster and diffusion Monte Carlo results available in the literature for N≤20. We also provide Padé fits for the energies as a function of N for different strengths of the confining potential. The fits deviate less than 0.25% from the path integral Monte Carlo data. Overall, our upper-bound estimates for the ground-state energies have lower values than previous diffusion Monte Carlo benchmarks due to the accurate nodal surface in our simulations. Hence, our results set a new numerical benchmark for two-dimensional (spin-unpolarized) quantum dots up to a large number of electrons.acceptedVersionPeer reviewe