Nodal surfaces and interdimensional degeneracies

The aim of this paper is to shed light on the topology and properties of the nodes (i.e. the zeros of the wave function) in electronic systems. Using the "electrons on a sphere" model, we study the nodes of two-, three- and four-electron systems in various ferromagnetic configurations ($sp$, $p^2$, $sd$, $pd$, $p^3$, $sp^2$ and $sp^3$). In some particular cases ($sp$, $p^2$, $sd$, $pd$ and $p^3$), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the $sp^3$ configuration are exact.Comment: 7 pages, 3 figures, accepted for publication in the Journal of Chemical Physic

Stability and production of positron-diatomic molecule complexes

The energies at geometries close to the equilibrium for the e$^+$BeO and e$^+$LiF ground states were computed by means of diffusion Monte Carlo simulations. These results allow us to predict the equilibrium geometries and the vibrational frequencies for these exotic systems,and to discuss their stability with respect to the various dissociation channels. Since the adiabatic positron affinities were found to be smaller than the dissociation energies for both complexes, we propose these two molecules as possible candidates in the challenge to produce and detect stable positron-molecule systems.Comment: submitted to Phys. Rev. Let

Variance reduction in MCMC

We propose a general purpose variance reduction technique for MCMC estimators. The idea is obtained by combining standard variance reduction principles known for regular Monte Carlo simulations (Ripley, 1987) and the Zero-Variance principle introduced in the physics literature (Assaraf and Caffarel, 1999). The potential of the new idea is illustrated with some toy examples and an application to Bayesian estimationMarkov chain Monte carlo, Metropolis-Hastings algorithm, Variance reduction, Zero-Variance principle

Unexpected symmetry in the nodal structure of the he atom

The nodes of even simple wave functions are largely unexplored. Motivated by their importance to quantum simulations of fermionic systems, we have found unexpected symmetries in the nodes of several atoms and molecules. Here, we report on helium. We find that in both ground and excited states the nodes have simple forms. In particular, they have higher symmetry than the wave functions they come from. It is of great interest to understand the source of these new symmetries. For the quantum simulations that motivated the study, these symmetries may help circumvent the fermion sign problem

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. Core electrons usually require smaller time steps than valence electrons. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so moves of both valence and core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.

On the nature of the two-positron bond: Evidence for a novel bond type

The nature of the newly proposed two-positron bond in (PsH)2, which is composed of two protons, four electrons and two positrons, is considered in this contribution. The study is done at the multi-component-Hartree-Fock (MC-HF) and the Diffusion Monte Carlo (DMC) levels of theory by comparing ab initio data, analyzing the spatial structure of the DMC wavefunction, and applying the multi-component quantum theory of atoms in molecules and the two-component interacting quantum atoms energy partitioning schemes to the MC-HF wavefunction. The analysis demonstrates that (PsH)2 to a good approximation may be conceived of two slightly perturbed PsH atoms, bonded through a two-positron bond. In contrast to the usual two-electron bonds, the positron exchange phenomenon is marginal in the considered two-positron bond. The main stabilizing mechanism of bonding is a novel type of classical electrostatic interaction between the positrons, which are mainly localized between nuclei, and the surrounding electrons. To emphasize its uniqueness, this mechanism of bonding is proposed to be called gluonic which has also been previously identified as the main deriving mechanism behind formation of the one-positron bond in [H-, e+, H-] . We conclude that the studied two-positron bond should not be classified as a covalent bond and it must be seen as a brand-new type of bond, foreign to the electronic bonding modes discovered so far in the purely electronic systems.Comment: main text plus supporting informatio

Nodal surfaces and interdimensional degeneracies

The aim of this paper is to shed light on the topology and properties of the nodes (i.e., the zeros of the wave function) in electronic systems. Using the "electrons on a sphere" model, we study the nodes of two-, three-, and four-electron systems in various ferromagnetic configurations (sp, p2, sd, pd, p3, sp2, and sp3). In some particular cases (sp, p2, sd, pd, and p3), we rigorously prove that the non-interacting wave function has the same nodes as the exact (yet unknown) wave function. The number of atomic and molecular systems for which the exact nodes are known analytically is very limited and we show here that this peculiar feature can be attributed to interdimensional degeneracies. Although we have not been able to prove it rigorously, we conjecture that the nodes of the non-interacting wave function for the sp3 configuration are exact

Quantum Monte Carlo investigation of small He-4 clusters with a He-3 impurity

Small helium (He-4) clusters containing the lighter isotope He-3 are studied by means of quantum Monte Carlo methods. Accurate ground state energies and structural properties are obtained using accurate trial wave functions and the Tang-Tonnies-Yiu (TTY) helium-helium pair potential. The dimer He-4-He-3 is not bound; as well as the trimer (HeHe2)-He-4-He-3. The smallest cluster containing He-3 is He-4(2) He-3 with a nonrigid structure having a marked linear contribution. Interestingly, this weakly bound system, with an energy one order of magnitude less than the He-4(3) trimer, is able to bind another He-3 atom, forming the tetramer He-4(2) He-3(2), which shows the odd feature of having five out of six unbound pairs. In general, the substitution of a single He-4 atom in a pure cluster with a He-3 atom leads to an energetic destabilization, as the pair He-4-He-3 is not bound. The isotopic impurity is found to perturb only weakly the distributions of the remaining He-4 atoms, which retain the high floppiness already found in the pure clusters. As the number of atoms increases the isotopic impurity has the marked tendency to stay on the surface of the cluster. This behavior is consistent with the formation of the so-called "Andreev states" of a single He-3 in liquid He-4 helium and droplets, where the impurity tends to form single-particle states on the surface of the pure He-4

Delayed Rejection Variational Monte Carlo

A new acceleration algorithm to address the problem of multiple time scales in variational Monte Carlo simulations is presented. After a first attempted move has been rejected, the delayed rejection algorithm attempts a second move with a smaller time step, so that even moves of the core electrons can be accepted. Results on Be and Ne atoms as test cases are presented. Correlation time and both average accepted displacement and acceptance ratio as a function of the distance from the nucleus evidence the efficiency of the proposed algorithm in dealing with the multiple time scales problem.Comment: To be published on the Journal of Chemical Physic