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Journal of Physics B Atomic Molecular and Optical Physics

Quantum dynamical calculation of rovibrational bound states of Ne2Ar

Benhui Yang, Bill Poirier

Published Jun 1, 2012• 10 citations
Publisher

Abstract

The eigenstate energy levels and wavefunctions for the bound rovibrational states of the Ne2Ar complex, up to the maximum J value for which bound states exist (J = 0–30), have been calculated using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space-optimized discrete variable representation, optimal separable basis and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The rovibrational (J > 0) Ne2Ar energy levels and wavefunctions were computed using a pairwise Tang–Tonnies potential with three-body contribution in Jacobi coordinates. For the vibrational (J = 0) energy levels, a comparison, using different potentials was performed; the effect of three-body interaction is discussed. Selected wavefunction plots are also provided. From the plots, ‘horseshoe’ states may be observed; the horseshoe localization effect is found to be stronger than in Ne3. Corrections were made to this article on 18 July 2012. The grant number in the acknowledgments section was amended.

DOI
10.1088/0953-4075/45/13/135102

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The eigenstate energy levels and wavefunctions for the bound rovibrational states of the Ne2Ar complex, up to the maximum J value for which bound states exist (J = 0–30), have been calculated using the ScalIT suite of parallel codes. These codes employ a combination of highly efficient methods, including phase-space-optimized discrete variable representation, optimal separable basis and preconditioned inexact spectral transform methods, together with an effective massive parallelization scheme. The rovibrational (J > 0) Ne2Ar energy levels and wavefunctions were computed using a pairwise Tang–Tonnies potential with three-body contribution in Jacobi coordinates. For the vibrational (J = 0) energy levels, a comparison, using different potentials was performed; the effect of three-body interaction is discussed. Selected wavefunction plots are also provided. From the plots, ‘horseshoe’ states may be observed; the horseshoe localization effect is found to be stronger than in Ne3. Corrections were made to this article on 18 July 2012. The grant number in the acknowledgments section was amended.
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Rovibrational energy levels of H2_22​O by quantum computing
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We study theoretically the ground and excited bound states of the bosonic rare gas van der Waals trimer Ne(3). A slow variable discretization approach is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved using basis splines at a series of fixed finite-element methods discrete variable representation hyper-radii. We consider not only zero total nuclear orbital angular momentum, J = 0, states but also J > 0 states. By using the best empirical neon dimer interaction potentials, all the bound state energy levels of Ne(3) will be calculated for total angular momenta up to J = 6, as well as their average root-mean-square radii. We also analyze the wave functions in hyperspherical coordinates for several selected bound states.
This dissertation describes methods and results of spectroscopic studies of the NaCs molecule. NaCs is of particular interest in many labs where experimental studies of ultra-cold molecules are being conducted. Data obtained in the present work will also be useful as benchmarks for various theoretical calculations. Our goals in studying this molecule were to map out high lying electronic states and to understand how these states interact with one another. Sodium and cesium metal were heated in a heat-pipe oven to form a vapor of NaCs molecules. These molecules were excited using narrow band, continuous wave (cw), tunable lasers. We employed the optical-optical double resonance (OODR) technique to obtain Doppler-free spectra of transitions to rotational and vibrational levels of high lying electronic states. One state of particular interest was the 12(0+) electronic state. Rovibrational level energies corresponding to this state were measured and used to generate a potential energy curve using computer programs to implement both the Rydberg-Klein-Rees (RKR) method and the inverted perturbation approach (IPA). By observing fluorescence from the 12(0+) state resolved as a function of wavelength, we determined that this state interacts with the nearby 11(0+) electronic state, which was previously mapped out by Ashman et al. A two-stage coupling model was devised to describe the resolved fluorescence originating from these two interacting states. The electronic states interact via spin-orbit coupling, while the individual rovibrational levels interact via a second mechanism, likely nonadiabatic coupling. This two-stage coupling between the levels of these states causes quantum interference between fluorescence pathways associated with different components of the wavefunctions describing these levels. This interference results in more complicated resolved fluorescence spectra. The model was used to fit parameters describing these interactions so that the resolved fluorescence spectra could be reproduced. The NaCs 43 π electronic state was also studied in this work. Energies of many rovibrational levels belonging to the 43 π electronic state were measured. This state is interesting because it likely has a potential energy curve with a double minimum, which results in a different type of quantum interference, directly observed in resolved spectra. The state also very likely has interactions with the 11(0+) and 12(0+) states. Energies of many rovibrational levels lying above the energy of the barrier between the two minima were measured, and it appears that we also observed a few levels lying below the barrier. Since the laser wavelengths necessary to excite the lowest vibrational levels were not available, an experimental potential curve could not be produced. Therefore, rovibrational level energies and spectroscopic constants are tabulated.
We develop a computationally and numerically efficient approach to determine binding energies and corresponding wave functions of a quantum-mechanical three-body problem in low dimensions. Our approach exploits the tensor structure intrinsic to the multidimensional stationary Schr\odinger equation, which we express as a discretized eigenvalue problem. In order to obtain numerical solutions of the three-body system in one spatial dimension, we represent the Hamiltonian operator as a series of dense matrix-matrix products and propose an efficient preconditioned Jacobi-Davidson QR iteration for the resulting algebraic eigenvalue problem. This implementation allows a significantly faster computation of three-body bound states with a higher accuracy than in previous works. To investigate the feasibility of solving higher dimensional problems, we also consider the two-dimensional case where we make use of an efficient shared-memory parallel implementation. Our novel approach is of high relevance for investigating the universal behavior of few-body problems governed only by the particle masses, overall symmetries, and the dimensionality of space. Moreover, our results have straightforward applications in the physics of ultracold atomic gases that are nowadays widely utilized as quantum sensors.
Convergent hierarchies of theories for calculating many-body vibrational ground and excited-state wave functions, such as M{o}ller-Plesset perturbation theory or coupled cluster theory, tend to rely on matrix-algebraic manipulations of large, high-dimensional arrays of anharmonic force constants, tasks which require large amounts of computer storage space and which are very difficult to implement in a parallel-scalable fashion. On the other hand, existing quantum Monte Carlo (QMC) methods for vibrational wave functions tend to lack robust techniques for obtaining excited-state energies, especially for large systems. By exploiting analytical identities for matrix elements of position operators in a harmonic oscillator basis, we have developed stochastic implementations of the size-extensive vibrational self-consistent field (MC-XVSCF) and size-extensive vibrational M{o}ller-Plesset second-order perturbation (MC-XVMP2) theories which do not require storing the potential energy surface (PES). The programmable equations of MC-XVSCF and MC-XVMP2 take the form of a small number of high-dimensional integrals evaluated using Metropolis Monte Carlo techniques. The associated integrands require independent evaluations of only the value, not the derivatives, of the PES at many points, a task which is trivial to parallelize. However, unlike existing vibrational QMC methods, MC-XVSCF and MC-XVMP2 can calculate anharmonic frequencies directly, rather than as a small difference between two noisy total energies, and do not require user-selected coordinates or nodal surfaces. MC-XVSCF and MC-XVMP2 can also directly sample the PES in a given approximation without analytical or grid-based approximations, enabling us to quantify the errors induced by such approximations.