Energies and structures of rotating argon clusters: Analytic descriptions and numerical simulations

Abstract

The dependence of the rotational energy of small argon clusters on the magnitude and direction of their rotational angular momenta is obtained by two different methods, namely, by analytic descriptions parametric in structural variables (centrifugal displacements) and by classical simulations carried out in rotating frames so that rotational angular momenta are conserved. Potential energies are taken as additive Ar, pair potentials [R. A. Aziz, J. Chem. Phys. 99,4518 (199311, augmented in some cases by three-body Axilrod-Teller interactions, thus complementing our earlier studies of rare-gas clusters modeled by additive Lennard-Jones oscillator (LJO) pair potentials [L. L. Lohr and C. H. Huben, J. Chem. Phys. 99, 6369 (199311. Quartic and sextic spectroscopic constants are found to be approximately 10% smaller when the Aziz pair potential is used, reflecting its greater stiffness as compared to the LJO potential. The sign of the sextic tensor coefficient for both tetrahedral Ar, and octahedral Ar, is such that for sufficiently high J the C,,, (or D 2 h ) structures with I parallel to a pseudo-C, (or true C,) axis (saddle points on the rotational energy surface at low J ) become local energy maxima, the D2d (or D4\,) structures with J parallel to an S, (or C,) axis representing the energy minima. The trigonal bipyramidal cluster Ar, resembles both Ar, and Ar, in its rotational characteristics but with reduced manifestations of nonrigidity. As found with an LJO with J parallel to a C, axis are saddle points on the rotational energy surface. The scalar quartic spectroscopic coefficient for Arl, is found to be 2.15 X times that for the reference diatomic Ar,. A variety of structural instabilities are described for Ar,, clusters with very high rotational energies.

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

“…In this sense, the effect of the AT term on the analytical expression of the centrifugal displacements for a rotating Ar 3 was considered not large enough to be taken into account when dealing with bigger Ar clusters. 25 Interestingly enough, an artificial increase of the AT term has been associated with an earlier appearance of the Ar 3 lowest-energy linear bound state. 26 An analysis of the possible influence of the AT term on the geometries associated with a broader number of vibrational bound states beyond just simply the ground state therefore constitutes an interesting task.…”

Symmetry and structure of rotating H3+

“…The approach described here resembles in many respects the works of Lohr on argon clusters. 13,14 It also lies behind the general formalism of Jellinek and Li 15 for the separation of rotational energy, and in particular their analysis of J-dependent normal vibrational modes. Miller and Wales 16 also classify RE ͑there called stationary points͒ by Hessian indices, but the latter are different from the ones used here.…”

Relative equilibria of D2H+and H2D+

“…They typically take the form of steady rotations about stationary axes during which the 'shape' of the system does not change. In applications to molecular spectroscopy they have previously been referred to as 'stationary points' [ 1, 21 or J-dependent reference points [3]. Unstable relative equilibria have also been studied in the guise of 'rotational' or 'centrifugal barriers' [4,51 and 'transition states' [6].…”