Separation of variables in multi-Hamiltonian systems: an application to the Lagrange top

Starting from the tri-Hamiltonian formulation of the Lagrange top in a six-dimensional phase space, we discuss the reduction of the vector field and of the Poisson tensors. We show explicitly that, after the reduction on each one of the symplectic leaves, the vector field of the Lagrange top is separable in the sense of Hamilton-Jacobi.Comment: report to XVI NEEDS (Cadiz 2002): 15 pages, no figures, LaTeX. To appear in Theor. Math. Phy

On the Treves theorem for the AKNS equation

According to a theorem of Treves, the conserved functionals of the AKNS equation vanish on all pairs of formal Laurent series of a specified form, both of them with a pole of the first order. We propose a new and very simple proof for this statement, based on the theory of B\"acklund transformations; using the same method, we prove that the AKNS conserved functionals vanish on other pairs of Laurent series. The spirit is the same of our previous paper on the Treves theorem for the KdV, with some non trivial technical differences.Comment: LaTeX, 16 page

Quantum Monte Carlo study of the H- impurity in small helium clusters

We report ground state energies and structural properties for small helium clusters (4He) containing an H- impurity computed by means of variational and diffusion Monte Carlo methods. Except for 4He_2H- that has a noticeable contribution from collinear geometries where the H- impurity lies between the two 4He atoms, our results show that our 4He_NH- clusters have a compact 4He_N subsystem that binds the H- impurity on its surface. The results for $N\geq 3$ can be interpreted invoking the different features of the minima of the He-He and He-H- interaction potentials.Comment: 12 pages, 7 Ps figure

On a class of dynamical systems both quasi-bi-Hamiltonian and bi-Hamiltonian

It is shown that a class of dynamical systems (encompassing the one recently considered by F. Calogero [J. Math. Phys. 37 (1996) 1735]) is both quasi-bi-Hamiltonian and bi-Hamiltonian. The first formulation entails the separability of these systems; the second one is obtained trough a non canonical map whose form is directly suggested by the associated Nijenhuis tensor.Comment: 11 pages, AMS-LaTex 1.

On the nodal structure of single-particle approximation based atomic wave functions

The nodal structures of atomic wave functions based on a product of spatial orbitals, namely, restricted, unrestricted, and generalized valence bond wave functions, are shown to be equivalent. This result is verified by fixed node-diffusion Monte Carlo simulations for atoms up to Ne. Also for a molecular system, Li2 at the equilibrium geometry, a multideterminantal generalized valence bond wave function does not improve the nodal surfaces of a restricted Hartree-Fock wave function

Stability and production of positron-diatomic molecule complexes

The energies at geometries close to the equilibrium for the e(+)LiF and e(+)BeO 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. Moreover, low-energy positron scattering on LiF and BeO targets may show vibrational Feshbach resonances as fingerprints of the existence of stable ground states of e(+)LiF and e(+)BeO

Quantum Monte Carlo calculations of the dimerization energy of borane

Accurate thermodynamic data are required to improve the performance of chemical hydrides that are potential hydrogen storage materials. Boron compounds are among the most interesting candidates. However, different experimental measurements of the borane dimerization energy resulted in a rather wide range ( 1234.3 to 1239.1) \ub1 2 kcal/mol. Diffusion Monte Carlo (DMC) simulations usually recover more than 95% of the correlation energy, so energy differences rely less on error cancellation than other methods. DMC energies of BH3, B2H6, BH3 CO, CO, and BH2+ allowed us to predict the borane dimerization energy, both via the direct process and indirect processes such as the dissociation of BH3CO. Our De = 1243.12(8) kcal/mol, corrected for the zero point energy evaluated by considering the anharmonic contributions, results in a borane dimerization energy of 1236.59(8) kcal/mol. The process via the dissociation of BH3CO gives 1234.5(2) kcal/mol. Overall, our values suggest a slightly less De than the most recent W4 estimate De = 1244.47 kcal/mol [A. Karton and J. M. L. Martin, J. Phys. Chem. A 111, 5936 2007)]. Our results show that reliable thermochemical data for boranes can be predicted by fixed node (FN)-DMC calculations

An investigation of nodal structures and the construction of trial wave functions

The factors influencing the quality of the nodal surfaces, namely, the atomic basis set, the single-particle orbitals, and the configurations included in the wave-function expansion, are examined for a few atomic and molecular systems. The following empirical rules are found: the atomic basis set must be fairly large, complete active space and natural orbitals are usually better than Hartree-Fock orbitals, multiconfiguration expansions perform better than single-determinant wave functions, but only few configurations are effective and their choice is suggested by symmetry considerations, while too long determinantal expansions spoil the nodal surfaces. These rules allow us to reduce the nodal error and to compute the best fixed node-diffusion Monte Carlo energies for a series of dimers of first-row atoms