Energy levels and wave functions of weakly bound bosonic trimers using Pekeris coordinates and a symmetry-adapted Lanczos approach

ROVIBRATIONAL BOUND STATES OF THE Ar2Ne COMPLEX

We report exact quantum dynamics calculations of the eigenstate energy levels for the bound rovibrational states of the Ar2Ne complex, across the range of J values for which such states are observed (J = 0–35). All calculations have been carried out 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 (PIST) methods, together with an effective massive parallelization scheme. The Ar2Ne energy levels were computed using a pair-wise Aziz potential plus a three-body correction, in Jacobi co-ordinates. Effective potentials for the radial co-ordinates are constructed, which reveal important physical insight into the two distinct dissociation pathways, Ar2Ne → NeAr + Ar and Ar2Ne → Ar2 + Ne . A calculation of the bound vibrational (J = 0) levels, computed using the Tang–Toennies potential, is also performed for comparison with results from the previous literature.

What is the shape of the helium trimer? A comparison with the neon and argon trimers

Despite its apparent simplicity and extensive theoretical investigations, the issue of what is the shape of the helium trimer is still debated in the literature. After reviewing previous conflicting interpretations of computational studies, we introduce the angle-angle distribution function as a tool to discuss in a simple way the shape of any trimer. We compute this function along with many different geometrical distributions using variational and diffusion Monte Carlo methods. We compare them with the corresponding ones for the neon and argon trimers. Our analysis shows that while Ne(3) and Ar(3) fluctuate around an equilibrium structure that is an equilateral triangle, (4)He(3) shows an extremely broad angle-angle distribution function, and all kinds of three-atom configurations must be taken into account in its description. Classifying (4)He(3) as either equilateral or linear or any other particular shape, as was done in the past, is not sensible, because in this case the intuitive notion of equilibrium structure is ill defined. Our results could help the interpretation of future experiments aimed at measuring the geometrical properties of the helium trimer.

Theoretical and experimental study of weakly bound CO2-(pH2)2 trimers

The infrared spectrum of CO(2)-(pH(2))(2) trimers is predicted by performing exact basis-set calculations on a global potential energy surface defined as the sum of accurately known two-body pH(2)-CO(2) (J. Chem. Phys. 2010, 132, 214309) and pH(2)-pH(2) potentials (J. Chem. Phys. 2008, 129, 094304). These results are compared with new spectroscopic measurements for this species, for which 13 transitions are now assigned. A reduced-dimension treatment of the pH(2) rotation has been employed by applying the hindered-rotor averaging technique of Li, Roy, and Le Roy (J. Chem. Phys. 2010, 133, 104305). Three-body effects and the quality of the potential are discussed. A new technique for displaying the three-dimensional pH(2) density in the body-fixed frame is used, and shows that in the ground state the two pH(2) molecules are localized much more closely together than is the case for the two He atoms in the analogous CO(2)-(He)(2) species. A clear tunneling splitting is evident for the torsional motion of the two pH(2) molecules on a ring about the CO(2) molecular axis, in contrast to the case of CO(2)-(He)(2) where a more regular progression of vibrational levels reflects the much lower torsional barrier.

Theoretical study of the microwave spectrum of isotopologues of OCS–(He)2

The rovibrational energy levels (J = 0–3) and rotational spectra of seven isotopologues of the OCS–(He)2 complex have been determined by numerically exact basis set calculations. The interaction energy is represented as a sum of two-body terms consisting of the OCS–He potential, which Howson and Hutson (J. Chem. Phys. 2001, 115, 5059) obtained at the CCSD(T)/aug-cc-pVTZ level of theory, and the He–He potential that Jeziorska et al. (J. Chem. Phys. 2007, 127,124303) obtained with SAPT theory. Three-body effects and the quality of the potential are discussed. Comparison with experiment shows that microwave transitions can be predicted by this additive approach with an accuracy equal or better than 0.7% for all the observed spectral lines. A method for the three-dimensional representation of the helium density in the body-fixed frame is presented that highlights the highly delocalized nature of the helium subsystem.

Eigen energies and the statistical distributions of the rovibrational levels of the bosonic van der Waals argon trimer

The eigen energies and the statistical distributions of the rovibrational levels (J = 0-2) of the bosonic van der Waals argon trimer were calculated using a full angular momentum three-dimensional finite element method. The influence of interatomic potentials on the vibrational levels and statistical properties of the trimer was discussed.

A theoretical study of the rovibrational levels of the bosonic van der Waals neon trimer

The eigenenergies and root mean square radii of the rovibrational levels (J = 0-3) of the weakly bound bosonic van der Waals neon trimer were calculated using a full angular momentum three-dimensional finite element method. The differing results of three previous studies for zero angular momentum are discussed, explained, and compared with the results presented here.

Calculation of argon trimer rovibrational spectrum

Rovibrational spectra of Ar3 are computed for total angular momenta up to J=6 using row-orthonormal hyperspherical coordinates and an expansion of the wave function on hyperspherical harmonics. The sensitivity of the spectra to the two-body potential and to the three-body corrections is analyzed. First, the best available semiempirical pair potential (HFDID1) is compared with our recent ab initio two-body potential. The ab initio vibrational energies are typically 1-2 cm-1 higher than the semiempirical ones, which is related to the slightly larger dissociation energy of the semiempirical potential. Then, the Axilrod-Teller asymptotic expansion of the three-body correction is compared with our newly developed ab initio three-body potential. The difference is found smaller than 0.3 cm-1. In addition, we define approximate quantum numbers to describe the vibration and rotation of the system. The vibration is represented by a hyper-radial mode and a two-degree-of-freedom hyperangular mode, including a vibrational angular momentum defined in an Eckart frame. The rotation is described by the total angular momentum quantum number, its projection on the axis perpendicular to the molecular plane, and a hyperangular internal momentum quantum number, related to the vibrational angular momentum by a transformation between Eckart and principal-axes-of-inertia frames. These quantum numbers provide a qualitative understanding of the spectra and, in particular, of the impact of the nuclear permutational symmetry of the system (bosonic with zero nuclear spin). Rotational constants are extracted from the spectra and are shown to be accurate only for the ground hyperangular mode.

Vibrational Levels of Ar4: New Odd-Parity Bosonic States

Vibrational levels of Ar4 are computed using the Lanczos algorithm and a large basis set. We find both even- and odd-parity states with wave functions that are invariant with respect to permutations of the Ar atoms. The odd-parity bosonic levels have not been computed previously. The even-parity levels are close to those obtained using the correlation-function Monte Carlo method (CFMC).

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: Excited states

The authors show that a recently proposed approach [J. Chem. Phys. 123, 084103 (2005)] for the inclusion of geometric constraints in semiclassical initial value representation calculations can be used to obtain excited states of weakly bound complexes. Sample calculations are performed for free and constrained rare gas clusters. The results show that the proposed approach allows the evaluation of excited states with reasonable accuracy when compared to exact basis set calculations.

Path integral ground state study of finite-size systems: Application to small (parahydrogen)N (N=2–20) clusters

We use the path integral ground state method to study the energetic and structural properties of small para-H2 clusters of sizes ranging from 2 to 20 molecules. A fourth order formula is used to approximate the short imaginary-time propagator and two interaction potentials are considered. Our results are compared to those of exact basis set calculations and other quantum Monte Carlo methods when available. We find that for all cluster sizes considered, our results show a lower ground state energy than literature values obtained by diffusion Monte Carlo and variational Monte Carlo. For the dimer and trimer, ground state energies are in good agreement with exact results obtained using the discrete variable representation. Structural properties are found to be insensitive to the choice of interaction potential. We explore the use of Pekeris coordinates to analyze the importance of linear arrangement in trimers and for trimers within clusters of larger size.

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

We compare two approaches for the accurate calculation of the energy levels of weakly bound boson trimers. The first approach is based on correlation function Monte Carlo employing optimized trial functions, while the second approach is based on the discrete variable representation. A trimer with atoms of half the mass of neon is used as a test problem for benchmark calculations. The two approaches yield identical results, within error bars, for all the J = 0 energy levels below the dissociation threshold. The relative merits of the two techniques are discussed, and a perspective is given for extension to larger clusters.

Geometric constraints in semiclassical initial value representation calculations in Cartesian coordinates: Accurate reduction in zero-point energy

An approach for the inclusion of geometric constraints in semiclassical initial value representation calculations is introduced. An important aspect of the approach is that Cartesian coordinates are used throughout. We devised an algorithm for the constrained sampling of initial conditions through the use of multivariate Gaussian distribution based on a projected Hessian. We also propose an approach for the constrained evaluation of the so-called Herman-Kluk prefactor in its exact log-derivative form. Sample calculations are performed for free and constrained rare-gas trimers. The results show that the proposed approach provides an accurate evaluation of the reduction in zero-point energy. Exact basis set calculations are used to assess the accuracy of the semiclassical results. Since Cartesian coordinates are used, the approach is general and applicable to a variety of molecular and atomic systems.

Bound-state energies in argon trimers via a variational expansion: The effects from many-body corrections

In this paper we study the bound-state energies and geometries of Ar(3) for J=0, using the distributed Gaussian functions method that provides a configurational description of the different structures contributing to these states. Atom-atom potentials are employed and three-body long-range effects are also included in the computational treatment by adding to the sum of potentials the Axilrod-Teller triple-dipole correction for the whole rotationless energy spectrum. An estimate of the total number of bound states for the Ar trimer is given. With respect to previous calculations, limited to the lower-lying states, our results show slightly larger nonadditive effects and are further able to predict the full range of the bound spectrum. Changes on the geometries of a large part of the vibrationally excited states of Ar(3) when the Axilrod-Teller term is included in the molecular potential are found by the present study.

Accurate quantum calculation of the bound and resonant rovibrational states of Li−(H2)

In a recent paper [B. Poirier, Chem. Phys. 308, 305 (2005)] a full-dimensional quantum method for computing the rovibrational dynamics of triatomic systems was presented, incorporating three key features: (1) exact analytical treatment of Coriolis coupling, (2) three-body "effective potential," and (3) a single bend angle basis for all rotational states. In this paper, these ideas are applied to the Li-(H2) electrostatic complex, to compute all of the rovibrational bound state energies, and a number of resonance energies and widths, to very high accuracy (thousandths of a wave number). This application is very challenging, owing to the long-range nature of the interaction and to narrow level spacings near dissociation. Nevertheless, by combining the present method with a G4 symmetry-adapted phase-space-optimized representation, only modest basis sizes are required for which the matrices are amenable to direct diagonalization. Several new bound levels are reported, as compared with a previous calculation [D. T. Chang, G. Surratt, G. Ristroff, and G. I. Gellene, J. Chem. Phys. 116, 9188 (2002)]. The resonances exhibit a clear-cut separation into shape and Feshbach varieties, with the latter characterized by extremely long lifetimes (microseconds or longer).

A complete configurational study for the bound states of Ne trimers

The structural properties and the energetics of the ground and the excited bound states of Ne(3) for zero total angular momentum are examined using different modelings for the two-body interactions. We employ a method consisting of a variational approach with a distributed Gaussian functions (DGF) basis set expansion. We discuss at length the advantages and possible limitations of such an approach, comparing it to other methods which have been applied in the literature to the same system. The DGF method turns out to be very accurate in giving us the bound states energetics and also provides in a natural way a convincing pictorial description of all the states, including those with dominant linear configurations. Additional bound states are found for the Ne(3) system with respect to those indicated in previous works and we suggest a "stabilization" procedure that can be used to assess the truly bound nature of a state. Some considerations on the relative reliability of the examined two-body interactions are also reported.

Energy levels and wave functions of weakly-bound 4Hex 20NeyH (x+y=2) systems using Pekeris coordinates and a symmetry-adapted Lanczos approach

Energy levels and wave functions of floppy triatomic rare gas hydrides are calculated using a Pekeris coordinate system and the importance of various triangular configurations is assessed through the calculation of reduced distribution functions and relative weights. The calculations are performed using a symmetry-adapted Lanczos recursion within the discrete variable representation. For the 4He2H- anion, the present results are compared with those obtained from calculations based on other methods, and the accuracy of the present method is discussed. Calculations are also performed for the case of 4He2H and 20Ne2H, as well as for the mixed 4He 20NeH neutrals. Our results show that no bound states are found for 4He2H while only one bound state is found for both the 20Ne2H and 4He 20NeH complexes. Interestingly, a very important and common property of these systems is that there is a significant contribution from linear configurations to their bound states.