Rare Gas Trimers Research Articles

Study of the van der Waals Rare Gas Trimers $$\hbox {Ne}_3$$ Ne 3 , $$\hbox {Ar}_3$$ Ar 3 , $$\hbox {Kr}_3$$ Kr 3 , and $$\hbox {Xe}_3$$ Xe 3 Using Hyperspherical Coordinates

We study the bosonic van der Waals rare gas trimers $$\hbox {Ne}_3$$ , $$\hbox {Ar}_3$$ , $$\hbox {Kr}_3$$ , and $$\hbox {Xe}_3$$ in zero total angular momentum, $$J=0$$ , states. The three-body Schrodinger equation in hyperspherical coordinates is solved using the slow variable discretization approach. We calculate the $$J=0$$ trimer bound state energy levels as well as their average root-mean-square radii. The adiabatic hyperspherical potential curves converging near the three-body dissociation threshold are also studied.

Assessment of DFT and DFT-D for Potential Energy Surfaces of Rare Gas Trimers-Implementation and Analysis of Functionals and Extrapolation Procedures.

Given the recent developments in methodology associated with the accurate computation of molecular systems with weak interactions, it is of particular interest to revisit systems that are notoriously challenging for determining reliable potential energy surface (PES) descriptions. Additionally, challenges associated with carrying out complete basis set extrapolation procedures and treatment of basis set superposition error (BSSE) are of importance in these descriptions. In this work, investigation into the ability to accurately predict the potential energy surfaces of the main Rg3 molecules (Rg = He, Ne, Ar) is made across a range of wave function types and large basis sets, including the use of several established extrapolation procedures and counterpoise corrections. Wave function types span most classes of density functional types, including the newest DFT-D schemes, and are benchmarked against high accuracy CCSD(T)/CBS methodology. Study of such systems is valuable, as they serve as simple models for many complex properties, most importantly n-body weak interaction energies.

Postionization fragmentation of rare-gas trimers revisited with new theoretical approaches

A new theoretical approach is presented for the general treatment of nonadiabatic hybrid dynamics (mixing classical and quantum approach) and applied to the postionization of rare-gas trimers. There was an important disagreement between trajectory surface hopping (TSH) or mean field (MF) approaches and the experimental results; noteworthy, with the new method qualitative and almost quantitative agreement is found for the fragmentation ratios of ionic monomers and dimers. For the first time in the theory as in the experiment, the dimers prevail for argon while monomers strongly dominate for the heavier rare gases, krypton and xenon. A new compromise between MF and TSH approaches is proposed and the new method is found quite robust with results not too sensitive to various possible implementations.

Hyperspherical coupled channel calculations for the spectra and structure parameters of rare gas trimers NeAr2 and Ne2Ar

We calculate the L=0 vibration energies and rotational constants for the van der Waals trimers 20NeAr2, 20Ne2Ar, and their corresponding isotopologues within the framework of hyperspherical coordinates. The Schrodinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B-splines and the resulting coupled hyper-radial equation is solved using the slow variable discretization method developed by Tolstikhin et al. [J. Phys. B 29, L389 (1996)]. Using the special properties of B-splines, we make the knot distributions more precisely, characterizing the behavior of channel functions. Our method improves the convergence greatly. It turns out that our numerical tool works quite well in study of rare gas trimers. Calculations are performed on two kinds of pair potentials, the HFD-B and Tang-Toennies (TT) potentials, and the resultant rotational constants and their isotope shifts are compared with the experimental results obtained from high-resolution spectroscopy. The TT pair potentials give much better agreement with the experimental values for 20Ne2Ar and 22Ne2Ar trimers, while the HFD-B pair potentials give much better agreement with the experimental values for 20NeAr2 and 22NeAr2 trimers.

Theoretical modeling of postionization fragmentation of rare-gas trimer cations

The dynamics of ionic rare-gas trimers (Ar(3) (+), Kr(3) (+), and Xe(3) (+)) produced by a sudden ionization of neutral precursors is investigated theoretically with a hybrid classical-quantum method for solving the equations of motion governed by a Hamiltonian obtained from a previously tested diatomics-in-molecules model. Initial conditions are selected with Monte Carlo sampling. Two possibilities for generating the initial electronic state are considered: diabatic (local) and adiabatic (delocalized). The dynamics generally leads to fragmentation, producing either monomer ions or dimer ions in a relatively short time; however, a large number of long-lived metastable trimer ions are also seen in some cases. We have analyzed the dynamics with respect to the fraction of monomer ions produced, the distribution of the kinetic energy of the products, and the distribution of fragmentation times of the trimers. Initial diabatic ionization is associated with much faster fragmentation than adiabatic ionization. Spin-orbit coupling plays an important role in the fragmentation dynamics.

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.

Design and application of a multicoefficient correlation method for dispersion interactions.

A new multicoefficient correlation method (MCCM) is presented for the determination of accurate van der Waals interactions. The method utilizes a novel parametrization strategy that simultaneously fits to very high-level binding, Hartree-Fock and correlation energies of homo- and heteronuclear rare gas dimers of He, Ne, and Ar. The decomposition of the energy into Hartree-Fock and correlation components leads to a more transferable model. The method is applied to the krypton dimer system, rare gas-water interactions, and three-body interactions of rare gas trimers He3, Ne3, and Ar3. For the latter, a very high-level method that corrects the rare-gas two-body interactions to the total binding energy is introduced. A comparison with high-level CCSD(T) calculations using large basis sets demonstrates the MCCM method is transferable to a variety of systems not considered in the parametrization. The method allows dispersion interactions of larger systems to be studied reliably at a fraction of the computational cost, and offers a new tool for applications to rare-gas clusters, and the development of dispersion parameters for molecular simulation force fields and new semiempirical quantum models.

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

An approach is presented for the accurate calculation of the energy levels of weakly bound bosonic rare gas trimers. A Pekeris coordinate system is used in order to avoid the interdependent range problem associated with internuclear distance coordinates. The present choice of coordinates also permits a straightforward treatment of boson symmetry and allows one to assess the importance of linear configurations through the calculation of one-body reduced distribution functions. The discrete variable representation is used and the eigenvalue problem is solved using a Lanczos recursion combined with projection operator techniques in order to extract totally symmetric states. Lennard-Jones systems corresponding to Argon and Neon are studied in order to assess the accuracy of the method by comparing them with those of recent benchmark calculations. The approach allows the accurate calculation of several bound states. Calculations are also performed for the case of a Morse interaction potential and the results are compared to those studies based on the commonly used internuclear distance coordinates. The present approach is found to be more accurate.

Comparative study of He3, Ne3, and Ar3 using hyperspherical coordinates

We calculate the L=0 ground and excited state energies for the rare gas trimers He3, Ne3, and Ar3. An adiabatic representation is adopted to solve the nuclear Schrödinger equation, in which the Schrödinger equation in hyperangular coordinates is solved at a series of fixed hyper-radii using B splines. We compare results obtained in a strict adiabatic approximation with nonperturbative coupled-adiabatic-channel calculations. Structural properties such as the pair and angle distributions are monitored as functions of the hyper-radius. These structural studies pinpoint the locus of configurational changes that occur as the trimer fragments into a diatom plus an atom. Analysis of the angular channel functions and their associated radial components permits an approximate classification of the vibrational spectrum.

Turning point surfaces and their enclosed volumes for rotating Lennard-Jones rare-gas trimers ArxNe3-x, x = 0–3

An earlier study (Lohr, L. L., 1997, Molec. Phys., 91, 1097) of classical turning point surfaces of homonuclear rare-gas clusters Ar3 and Ar4 has been extended to include the clusters Ne3, ArNe2 and Ar2Ne, with emphasis on the two mixed trimers. A new procedure, applied here both to homonuclear and heteronuclear clusters, is the calculation by Monte Carlo integrations of the hypervolumes enclosed by the classical turning point surfaces as functions of the total energy and the rotational angular momentum. These hypervolumes provide an informative characterization of the potential energy surfaces of the clusters. For a given vibrational energy it is found that the hypervolumes decrease as Ne atoms are replaced by Ar atoms, reflecting the more steeply rising pair potentials for Ar-Ne and Ar-Ar interactions compared with Ne-Ne interactions. A new result is the observation that the classically allowed configuration space for rotating rare-gas trimers is disconnected for certain ranges of total energy and rotational angular momentum; within these ranges, classical trajectories which conserve rotational angular momentum are confined either to the neighbourhood of triangular structures or to that of linear structures.

Turning point surfaces and their enclosed volumes for rotating Lennard-Jones rare-gas trimers Ar x Ne 3- x , x = 0-3

Turning point surfaces and their enclosed volumes for rotating Lennard-Jones rare-gas trimers Ar x Ne 3- x , x = 0-3

Comparative configurational study for He, Ne, and Ar trimers

Helium trimer bound states are calculated by means of a variational method described in terms of atom pair coordinates and distributed Gaussian basis functions for zero total angular momentum. To show the feasibility of this method, we also apply it to the calculation of the first vibrational levels of the Ar3 and Ne3 clusters. Special emphasis is made on the study of the possible Efimov behavior of the first excited state found in the He34 trimer. Geometrical configurations of the ground and first excited states of these rare gas trimers have been exhaustively studied owing to the proper symmetry of the coordinates chosen.

Regular and irregular vibrational states: Localized anharmonic modes in Ar3

We present a method for calculating the energy levels and wave functions of floppy triatomic molecules such as the rare gas trimers. It is based upon a potential-optimized discrete variable representation and takes into account the wide-amplitude vibrations that occur in such systems. We have investigated the energy levels and wave functions for Ar3. The wave functions for the low-lying states show very regular behavior. Above the barrier to linearity, most of the wave functions are irregular but some have simple nodal patterns that suggest localization along periodic orbits. In addition to the “horseshoe” states previously described for H3+, we have identified localized features corresponding to symmetric and antisymmetric stretching vibrations around a linear configuration. The different localized modes can be combined to form more complex states in a manner analogous to normal modes.

Effects of three-body (Axilrod-Teller) forces on the classical and quantum behavior of rare-gas trimers

We have studied the structure and dynamics of nonrotating rare-gas trimers bound by a potential that combines two-body Lennard-Jones interactions and three-body Axilrod-Teller (triple dipole) interactions. Both classical and quantum trimers are examined. We investigate the onset and development of chaotic dynamics in the classical clusters by computing the Liapunov exponents associated with various phase space trajectories. In our studies of the quantum clusters, we examine the structure of the vibrational eigenstates, the statistical properties of the distribution of energy levels, and the average cluster structure at finite temperatures. Both avenues of research are principally aimed at understanding the effect of the three-body term on the clusters' behavior. We find that the three-body term gives rise to an integrable or nearly integrable component of phase space that is associated with the clusters' linear configuration and that manifests itself in both the classical and quantum properties of the trimers. The finite temperature structures predicted for quantum Ne${}_{3}$ clusters suggest that over the range of parameters considered here, these clusters are sufficiently delocalized that properties associated with the linear configuration should be readily observable, even at very low temperatures.

Spin–orbit effects in the photodissociation of ionized rare gas trimers: Comparison of He+3, Ar+3, and Xe+3

The velocities of neutral and charged photofragments of the rare gas trimers He+3, Ar+3, and Xe+3 have been examined in a comprehensive study for photon energies ranging from 1.5 to 6 eV. For this purpose, a novel time-of-flight technique has been applied which allows the simultaneous examination of both neutral and charged fragments. The general fragmentation pattern of all three species was that of a linear trimer with a parallel transition moment and a totally repulsive excited state: In the course of the dissociation, two of the particles gain high velocities in opposite directions, while the third particle (the middle particle of the linear trimer) only obtains a small velocity. The positive charge generally localizes on one of the fast outer particles, as can be expected from the symmetry properties of the excited state. For Ar+3 and Xe+3, however, also localization of the charge on the slow particle can be observed. This effect strongly depends on the energy of the absorbed photon, and can be quenched by decreasing the vibrational excitation of the trimer. Comparison of the results with new potential energy surface calculations indicate that mainly spin–orbit coupling induced conical intersections are responsible for this charge redistribution phenomenon.

Nodal configurations and many-body energies in Li 33+, F 33−, Li 22+ F − and Li +F 22− ions at crystal and cluster geometries

An attempt is made to investigate the properties of nodal configurations and analyse many-body energies in Li 3 3+, F 3 3−, Li 2 2+ F − and Li +F 2 2− ions at the lithium fluoride crystal geometries both in the short- and long-range regions of interacti Cluster geometries in the short-range regions were also investigated and the effect of introducing diffuse and polarization functions to the 6-311G basis set was considered. For three ions of the same type, nodal configurations were detected at the apex angles 126.5° and 135.0° using the 6-311G basis and at the apex angles 127.0° and 129.35° using the 6-311 + +G** basis. For three ions of different types, the occurrence of nodal configurations depends on the basis set size used in the calculations. While at the 6-311G level no nodal configurations were detected for Li 2 2+ F − and Li +F 2 2− ions, at the 6-311 + +G** level a nodal configu was detected for Li 2 2+ F − at 83.0°. The conjecture of a symmetric compensation between the SCF regimes is discussed and correlated with reported results on rare-gas trimers.

Heavy rare-gas trimers and tetramers: Testing ground for few-body techniques in chemical physics

The ground-state energies of systems of three and four identical heavy rare-gas atoms, treated as spinless bosons and assumed to interact via pairwise Morse potentials, are calculated using five different methods. Self-bound trimers and tetramers are found in every case with upper and lower bound formulas yielding energies which are extremely close. For these near-classical and massive systems, the Faddeev–UPE method is decidedly poor. On the other hand, the simple generalization of Bruch–Sawada’s upper bound is particularly effective. The plight of Faddeev–UPE here implies that great caution must be exercised in using the unitary pole expansion in chemical physics. ATMS is excellent and appears the method of choice for bound-state problems.

Nodal structure of the three-body nonadditive interaction

A discussion of qualitative aspects of the three-body non-pairwise-additive interaction V3 for three identical closed shell atoms and especially of its nodal structure is given. The rare-gas trimers He3, Ne3, and Ar3 and also the Be3 system are analyzed reviewing information coming from perturbation theory results for triatomic dispersion energies V3d, and of the three-body exchange–overlap energies coming from SCF and modified-effective-electron model studies. New SCF results, especially for the Be3 system, are also reported.