No abstract

No abstract

No abstract

d i s tr i b u ti o n o f t h i s d o c u m e n t i s u n lim ite d An AHirmative Action/Equal Opportunity Employer rf-1 ' This work was supported by the US Department o f Energy and the Naval Surface Weapons Center under project order number N6092I-80-W R-W 0165. Edited by Katherine H. Harper Photocom position by Alice Creek D IS C IJ tlM E R This report was prepared as an account o f w ork sponsored by an agency o f the U nited States Ckrvemment. N either the U nited States G overnm ent nor any agency th ereo f, nor any o f their em ployees, makes any w arranty, express or im plied, or assumes any legal liability or responsibility for the accuracy, com pleteness, or usefulness o f any inform ation, apparatus, p roduct, or process disclosed, or represents th a t its use w ould not infringe privately ow ned rights. References herein to any specific com m ercial p ro d u c t, process, or service by trade name, tradem ark, m anufacturer, or otherw ise, does not necessarily c o nstitute or im ply its endorsem ent, recom m endation, or favoring by the U nited States G overnm ent or any agency thereof. The views and opinions o f authors expressed herein do not necessarily state or reflect those o f the U nited Slates G overnm ent o r any agency thereof.

It is found that within the two (electronic) -state approximation, the multidimensional surface intersection problem may be reduced to an equivalent local one-dimensional curve crossing problem. The unique direction along which the adiabatic surfaces avoid a crossing is found to be normal to the ’’surface of avoided intersection.’’ One may apply this result to the surface hopping trajectory method of Tully and Preston without having to define the surfaces of avoided intersection beforehand. Furthermore, the Landau–Zener transition probability at such an avoided intersection may be calculated from information obtained along the trajectory. These results are applied to trajectory calculations of H+2+H2 collisions.