tokens: = 6.50 a 0 and along R and φ for θ = 75° is given. These cuts show that the R stretch coordinate is strongly coupled with θ and φ . Finally, it is worth noting that this interaction potential is strongly anisotropic especially along the R , θ and φ coordinates. This strong anisotropy is expected to lead to significant values for the collisional rates of the HNS rotational (de)-excitation by He. Figure 2. Two-dimensional contour plots of the 3D HNS–He PES along the R and θ coordinates for fixed φ = 0°, 90° and 180°. We give also the cuts along the angular coordinates and along R and φ for θ = 75°. Energies are in cm −1 . Black (red) contour lines represent repulsive (attractive) interaction energies. Table 1. Equilibrium geometries and energies of the minimal structures of HNS–He 3D-PES for φ = 0°, φ = 90° and φ = 180°. 3 DYNAMICAL CALCULATION DETAILS We consider the collision between an asymmetric top molecule (HNS) with He atom. The rotational Hamiltonian of the HNS molecule is given by where I α (α = x , y , z ) are the principal moments of inertia with respect to the principal axes of inertia (Gx), (Gy) and (Gz) of HNS. (G,x,y,z) is the body-fixed reference related to the space-fixed reference (G,X,Y,Z) by the Euler angles. I x , I y and I z are related to the rotational constants according to , and . The total angular momentum of the molecule is such that . D J , D JK and D K are first-order centrifugal distortion corrections. The rotational wave function | j τ m 〉 of an asymmetric top can be defined by three quantum numbers j , τ , m and can be expressed as a linear combination of the rotational wave functions | j τ m 〉 of a symmetric top molecule such as (Townes Schawlow 1955 ): where, j, k and m denote the rotational quantum number, its projection along the molecular z -axis and its projection along the space-fixed Z -axis, respectively. τ is the pseudo-quantum number that varies between − j and j . The rotational levels of an asymmetric top molecule are conventionally labelled (adopted hereafter) where K a and K c are the projection of the rotational angular momentum along the axis of symmetry in case of prolate and oblate symmetric tops limits being related to τ through τ = K a − K c . The rotational energy levels, of HNS, are deduced from the ab initio rotational and distortional constants calculated by Ben Yaghlane et al. ( 2014 ) at the CCSD(T)-F12/cc-pVQZ-F12 level of theory which are A e = 0.63583, B e = 0.61585, C e = 19.59885, D J = 9.11 × 10 −7 , D K = 4.68 × 10 −5 , D JK = 5.30 × 10 −3 (all values are in cm −1 ). The precision of these rotational parameters should be better than ∼0.3% according to theoretical benchmarks and their comparison to experimental data dealing with sulphur compounds (see for instance Cazzoli, Puzzarini Gauss 2014 ). All data represent predictions that can help for the identification of this molecule. For scattering calculations, only the first 29 levels of HNS molecule are considered. This corresponds
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