Potential Energy Surfaces for F-H 2 and Cl-H 2 : Long-Range Interactions and Nonadiabatic Couplings ² Vincenzo Aquilanti, Simonetta Cavalli, Fernando Pirani, and Alessandro Volpi Dipartimento di Chimica and INFM, UniVersita ` di Perugia, 06123 Perugia, Italy David Cappelletti* Dipartimento di Ingegneria CiVile ed Ambientale and INFM, UniVersita ` di Perugia, 06125 Perugia, Italy ReceiVed: October 16, 2000; In Final Form: January 3, 2001 The intermediate and long-range behavior of the three lowest doublet potential energy surfaces for the F( 2 P j )- H 2 and Cl( 2 P j )-H 2 systems has been studied, using a harmonic expansion of the potential, where the dependence on the relative orientation of the half-filled orbital of the open-shell atom and the molecular axis has been given in terms of bipolar spherical harmonics, whereas the coefficients modulate the effect of the variation of the intermolecular distance. The contribution of van der Waals, electrostatic, and charge-transfer interactions to the strength and the intermolecular distance dependence of each radial term are derived from previous molecular beam scattering experiments and from correlation formulas. The latter provide the link of these quantities to basic properties of the interacting partners. Besides describing elastic and inelastic channels, these surfaces also provide accurate information on the entrance channel for reactions. I. Introduction Chemical reactions and many inelastic processes typically involve open-shell species, which play a crucial role in the chemistry of atmospheres, plasmas, and lasers; 1 their interactions are described by a manifold of potential energy surfaces, among which nonadiabatic transitions occur and spin-orbit coupling may be operative. This is also of increasing modern relevance in view of the interest of ultracold collisions for astrophysical and Bose-Einstein condensation studies. 2 Typical open-shell species can be atoms, free radicals, molecules such as NO, or atomic and molecular ions. Their interactions with closed shell molecules are weak (of the order of magnitude of 1 kcal/mol) and manifest from large (tens of Å) down to intermediate (a few Å) intermolecular distances. In this range, both the attractive interaction (due to dispersion, induction and charge transfer contributions) and the tail of the repulsion (determined by the size of the two partners) are operative. Electrostatic effects arise when permanent multipoles are present on both interacting partners; they often vanish when averaged over the spatial orientations of particles, but crucially affect the anisotropic part of the interaction. Because of the small overlap of the electronic clouds, such interactions are unable to induce an appreciable modification in the internal structure of the involved species but can strongly affect the collision dynamics at thermal energies (e10 kcal/ mol), defining the nature of steric effects which control the selectivity of chemical and physical elementary phenomena and determining transport and energy transfer processes which occur in various environments. These interactions depend on the relative orientation of the two partners, on the intermolecular distance and on coordinates defining the internal structure of the system: they are elusive to quantum chemistry and are known to an accuracy level often insufficient to adequately assess their influence on collision dynamics. In this work, we consider the interactions of F( 2 P j ) and Cl( 2 P j ) atoms with the H 2 molecule, which are prototypes of open- shell atom-homonuclear diatomic molecule cases. These systems have been the object of many experimental (reaction rate constants, 3-5 elastic, inelastic, and reactive cross sections 6-18 and photoelectronic spectroscopy measurements 19-23 ) and theo- retical studies (ab initio potential energy surfaces 24-34 and reaction dynamics). 14,35-44 Despite this long (and admittedly partial) list of references, the available results on the interaction from ab initio, semiem- pirical and empirical methods, are still unable to simultaneously reproduce all the existing experimental data. Three potential energy surfaces, two of A′ and one of A′′ symmetry, must be considered to describe the evolution of the chemical reaction or of the energy exchange in the case of inelastic collisions. Theoretical information is especially precious for the description of the features of the ground potential energy surface in the neighborhood of the reaction transition state: this region mostly affects reactive scattering. The role of excited surfaces has been often neglected, and the intermediate and long-range behavior of the potential energy is known to a level of accuracy insufficient to satisfactorily account for experimental data such as elastic 8,10 and inelastic cross sections. 11,15,17 The most recent ab initio potential energy surface for F + H 2 32 appears to accurately reproduce many details of the reaction dynamics but a realistic entrance valley with possible refinements of the strong interaction region is required by new experiments. 17 For this system, some relevant attempts have been made in the past in combining ab initio and experimental information, 29,30 but they have been insufficient to adequately represent the long and intermediate range of the interaction. 15,17 Also, for the Cl + H 2 system, the importance of shallow wells located at intermediate intermolecular distance in the reactant and product valleys has been recently pointed out. 44 The investigation and the application of a suitable representa- tion for the asymptotic and intermediate behavior of the ² Part of the special issue “Aron Kuppermann Festschrift”. 2401 J. Phys. Chem. A 2001, 105, 2401-2409 10.1021/jp003782r CCC: $20.00 © 2001 American Chemical Society Published on Web 02/24/2001