Abstract. The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued decision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation algorithms can be developed to exploit the structure of particular constraints, much as is done for domain filtering algorithms. We propose specialized propagation algorithms for alldiff and inequality constraints. Preliminary experiments show that MDD propagation solves multiple alldiff problems an order of magnitude more rapidly than traditional domain propagation. It also significantly reduces the search tree for inequality problems, but additional research is needed to reduce the computation time.

The reactions of (I) Li+HF→LiF+H and (II) Li+HCl→LiCl+H have been studied by the crossed molecular beams method. Angular distributions [N(Θ)] of product molecules have been measured at 4 collision energies (Ec) ranging from about 2 to 9 kcal/mole and time-of-flight (TOF) measurements of product velocity distributions were made at approximately Ec=3 and 9 kcal/mole for both reactions (I) and (II). The combined N(Θ) and TOF results were used to generate contour maps of lithium–halide product flux in angle and recoil velocity in the center-of-mass (c.m.) frame. For reaction (I) at Ec=3 kcal/mole the c.m. angular distribution [T(ϑ)] shows evidence of complex formation with near forward–backward symmetry; slightly favored backward peaking is observed. The shape of this T(ϑ) indicates there is significant parallel or antiparallel spatial orientation of initial and final orbital angular momentum L and L′, even though with H departing L′ must be rather small and L?J′, where J′ is the final rotational angular momentum vector. It is deduced that coplanar reaction geometries are strongly favored. At Ec=8.7 kcal/mole the T(ϑ) of reaction (I) becomes strongly forward peaked. The product translational energy distributions P(ET′) at both these collision energies give an average ET′of ∼55% of the total available energy; this appears consistent with a theoretically calculated late exit barrier to reaction. The T(ϑ) at Ec=2.9 and 9.2 kcal/mole for reaction (II) are forward–sideways peaked. Most of the available energy (∼70%) goes into recoil velocity at both Ec for LiCl formation. This suggests a late energy release for this 11 kcal/mole exoergic reaction. Both reactions (I) and (II) show evidence of no more than a minor partitioning of energy into product vibrational excitation. Integral reactive cross sections (σR) are evaluated by integrating the product distributions in the c.m. frame and using small angle nonreactive scattering of Li as an absolute calibrant. Values of σR are: for LiF formation σR?0.8 Å2 and 0.94 Å2 at Ec=3 and 8.7 kcal/mole, while for LiCl formation σR= 27 Å2 and 42 Å2 at Ec=2.9 and 9.2 kcal/mole, with estimated absolute and relative uncertainties of a factor of 2, and 30%, respectively. Average opacities for reaction have been estimated from the reaction cross sections and the extent of rotational excitation of products to be about 0.1 for reaction (I) and 1 for reaction (II), for L values allowed to react. These results are discussed in some detail with regard to the kinematic constraints, reaction dynamics, and potential energy surfaces for these two reactions, and related experimental and theoretical works are noted. In addition, angular distributions of nonreactive scattering of Li off HF and HCl are measured at 4 different Ec each. Rainbow structure is observed at low Ec and the angular distributions are fit by a spherically symmetric piecewise analytic potential. The resulting values of the potential’s well depth (ε) and minimum position (rm) are: for Li+HF ε=0.46 kcal/mole and rm=4.34 Å and for Li+HCl ε=0.32 kcal/mole and rm=4.7 Å. These results differ significantly from some earlier estimates based on the measurements of integral scattering cross sections.

The absolute proton affinity of NH3 (203.6±1.3 kcal/mole at 298 K) and the proton solvation energies by more than one NH3 have been determined by the molecular beam–photoionization method. In addition, the NH3+–NH3 interaction energy (0.79±0.05 eV) has been measured by photoionization of the neutral van der Waals dimer. These experiments have shown that photoionization of van der Waals clusters is a very powerful method for determining the energetics of gas phase proton solvation.