Interdimensional degeneracies in van der Waals clusters and quantum Monte Carlo computation of rovibrational states

Abstract

Quantum Monte Carlo estimates of the spectrum of rotationally invariant states of noble gas clusters suggest inter-dimensional degeneracy in N − 1 and N + 1 spacial dimensions. We derive this property by mapping the Schrödinger eigenvalue problem onto an eigenvalue equation in which D appears as a continuous variable. We discuss implications for quantum Monte Carlo and dimensional scaling methods.

Vibrational Levels of Ar4: New Odd-Parity Bosonic States

“…The ground-state energy we compute agrees well with the result (−5.11881) of ref . For excited states, the new numbers reported in ref agree with our results; see Table . The energy levels 35 obtained using the adiabatic hyperspherical approach have larger errors because it is an approximate method.…”

Excited States of Weakly Bound Bosonic Clusters: Discrete Variable Representation and Quantum Monte Carlo

“…This system will have a higher zero-point energy than the previously studied neon trimer and is expected to provide a more stringent test of the performance of the DVR and CFMC techniques. The present excited-state results also complement a recent study that addressed the issue of interdimensional degeneracies for the ground state of the half-neon trimer . We also stress that we present for the first time, a comparison of the DVR and CFMC methods for all the J = 0 bound states below the dissociation threshold.…”

“…This is because the underlying basis functions of the CFMC method are highly correlated multidimensional functions generated by quantum Monte Carlo. Indeed, excited state energies of seven and five particle systems respectively in three and six spacial dimensions have been obtained with this method. , …”

Discrete spectra for confined and unconfined −a/r + br2 potentials in d-dimensions

“…Following the introduction of 'interdimensional degeneracies' [9,10] there have been several reports involving arbitrary d-dimensional analyses covering many branches of chemical physics which have been briefly reviewed in Refs. [11][12][13][14]. It is interesting to note here that the information-theoretical uncertainty-like relationships in terms of the Shannon entropy [15,16] and the Fisher measure [17,18] are also stated in d-dimensional form.…”