Chemical Physics 179 ( 1994) 469-478 North-Holland On the role of potential features in fine-structure transitions with application to H++F(2P1,2)-+H++F(2P3,2) D.A. Padmavatbi, Manoj K. Mishra Department of Chemistry, Indian Institute of Technology, Powai, Bombay 400 076, India and Herschel Rabitz Department of Chemistry, Princeton University, Princeton, NJ 08544, USA Received 19 August 1992; in tinal form 22 September 1993 The firs order functional sensitivity densities 8 In u 1,2_s,2(E)/81n W,,,,(R) are employed to assess the role of structure in potential energy curves W,(R) and W,(R) involved in the fine-structuretransition H++F(2PI,z)+H+ +F(rPr,r). The results reveal that the fmc&ructure transition cross-section draws on the Wt,(rE) and W, (*II) potentials in a highly correlated fashion and a measurement of u,,~_~,~(E) for H+ +F will primarily allow information to be extracted only on the potential function difference W,(R) - W,(R) for moderate to large internuclear distances (RZ 3 a,,). While there is a marginal preference for the A alignment in the region where splitting between the ‘II and ‘2 curves is equal to the tine-structuretransition energy, the oscillatory nature of the sensitivity densities with respect to R indicates that the alignment effects may disappear upon averaging over many impact parameters. The results from both functional sensitivity and adiabatic analysis isolate the region of potential energy curves centered at R= 7.8 a0 where the potential function difference W,(R) - W,(R) is equal to the fine-structure splitting, to be of maximum significance to the collisional fine-structure transition in this system. 1. Introduction Fine-structure transitions play an important role in diverse chemical phenomena [ 1,2] and have re- ceived extensive experimental and theoretical atten- tion [ l-7 1. It is well known that the fine-structure transition cross-sections are extremely sensitive to the features in underlying potential energy curves but be- cause of inherent difficulties in performing accurate ab initio calculations of potential energy curves (hy- persurfaces) and the corresponding nonadiabatic coupling matrix elements [ 8 1, most calculations of fine-structure transition cross-sections utilize physi- cally motivated approximate curves. Understanding of the role of different features in these curves is typ- ically attempted by performing a set of calculations with different potentials and at different energies to correlate with the cross-section profiles [ 6,7,9- 131. While much valuable insight into the role of poten- tial features in fine-structure transitions has been ob- tained from this approach, the conclusions drawn from such an analysis, per force, can only be qualita- tive and quite often, inconclusive [ 2,3,9]. The need to repeat cross-section calculations for many differ- ent curves at different energies makes this approach ineffkient and nonexhaustive in its goal. The adiabatic analysis technique [ 5-7,12- 19 ] is a physically motivated and easily performed compu- tation for isolation of the critical regions of potential energy curves and has offered interesting mechanis- tic insights in this area. While the coupled scattering equations are routinely formulated in the asymptotic diabatic basis, the coupling matrix elements in this basis are typically exponentially decaying functions spanning all zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQ R values [ 5 ] and an analysis of the cou- pling structure in this basis is therefore not useful for isolating the regions of potential curves critical to the outcome of collisional fine-structure transitions. 0301-0104/94/$07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDZ 0301-0104(93)E0344-U