Calculation of argon trimer rovibrational spectrum

Abstract

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.

Accurate calculations of bound rovibrational states for argon trimer

“…Further improvements can be made via the introduction of three-body corrections, such as the Axilrod-Teller correction (AT3) 17 used by Lepetit and co-workers. 18 The differences between these various PESs are not relevant for the present studyalthough a comprehensive study of the quantum dynamical ramifications has already been presented in Ref. 11, which may be consulted for further details (see also The two parameters that define the LJ PES are: , the dimer well depth; σ , the length scale parameter, related to the dimer equilibrium bond distance via r m = 6 √ 2σ .…”

“…Most previous work is limited to the vibrational lines only, with few researchers venturing into the strenuous and costly realm of rovibrational calculations. Of the papers that have investigated the rovibrational spectra, only two 10,18 were able to accurately go beyond J = 1, with both of these previous studies confined to J ≤ 6. The errors reported in said works were ≈10 −2 cm −1 and ≈0.1-0.3 cm −1 , respectively.…”

“…In this paper, we provide a modest discussion of two other PES's used for rare gas clusters, i.e., the Aziz PES 12-14 and the Patkowski PES. 15,16 Although both of these exist in pairwise form, they are usually used in conjunction with the Axilrod-Teller 17,18 three-body (AT3) correction term. Each PES has its benefits for dynamical and other purposes.…”

Vibrational spectrum of Ar3+ and relative importance of linear and perpendicular isomers in its photodissociation

“…As this method has already been described in Ref. [22][23][24][25], we recall here only its most important features. The 6 degrees of freedom of the system in the center of mass frame are parametrized by a hyperradius ρ, which defines the global size of the system, and five angles collectively labeled by Ω.…”

“…This formalism can be used for any value of the total angular momentum, J, to compute high accuracy rovibrational spectra, as was done for instance in Ref. 23 for the neutral Ar 3 system. The present paper focuses on the vibrational spectrum for the case J = 0 (even parity Π) and incorporates rotational corrections in a subsequent step.…”