The HeH2 energy surface

Abstract

A composite ab initio energy surface is obtained for the HeH2 triatomic molecular system by combining earlier calculations that covered parts of the surface. The extended surface covers the full angular range of He relative to the H–H axis as well as the full range of He–H2 separations. As with all calculations thus far, the extended ab initio energy surface covers only a narrow range of H–H separations in the vicinity of 1.4 a.u., the equilibrium separation of ground state H2. In addition, a new parametric representation of the ab initio energy surface is developed in terms of simple analytic functions based on the physics underlying the three principal interaction mechanisms responsible for the energy surface, and collisional applications are discussed briefly. All of the interaction mechanisms give rise to three-body interaction terms, an understanding of which is crucial to interpreting the behavior of the energy surface. This parametric representation reproduces the ab initio calculated values with an average [root-mean-square (rms)] percentage error under 7%, and because the parametric form is based on the physics, it can be extrapolated into the hitherto unexplored region of large H–H separations. A very interesting double inversion of the force between the two H atoms caused by proximity of He is explained. The H–H force is repulsive for large distances of He from H2, weakly attractive for intermediate He distances, and strongly repulsive for small He distances.

Isotope effects in complex scattering lengths for He collisions with molecular hydrogen

“…The potential energy surface (PES) adopted here was that of Muchnick and Russek (MR) [23]; this surface, along with that of Boothroyd et al (BMP) [24], was discussed previously by Lee et al [25] who performed state-to-state rovibrational scattering calculations for He-H 2 and found that the MR surface gave the best agreement with available experimental data at thermal energies.…”

Quasiresonance

“…Figures (16) and (17) display the quasiresonance domain associated with the nonlinear resonance N : M = 1 : 1 for different number m of coupling terms. As was expected, the resonance zone presents a chain composed of mM islands, two in figure (16) and three in figure (17), associated with the mM elliptic and mM hyperbolic fixed points located at the resonance action J 1:1 2,E . The thick lines on the Poincare surface of sections represent the curves of the separatrices Υ N :M k (τ p , φ 1 ) (k = 1, ...m) (61) when the transient interaction reachs its maximum amplitude at τ = τ p .…”

Quenching ofH2Vibrations in Ultracold3HeandBalakrishnan1, Forrey2, Dalgarno3 1998Phys. Rev. Lett.

“…We obtained the diatomic vibrational wave functions used in generating the coupled equations as expansions in Hermite polynomials with the diatomic H 2 potential of [17]. Close-coupling calculations for collisions of 4 He with H 2 have been carried out using various potential energy surfaces and scattering formulations [18][19][20][21][22], and rate coefficients have been reported for temperatures above 50 K. We have adopted the more recent potential energy surface (PES) of Muchnick and Russek [23]. In Fig.…”