On the characterization of regions of avoided surface crossings using an analytic gradient based method

The characterization of regions of avoided surface crossings in polyatomic systems using multiconfiguration self-consistent field/configuration interaction(CI) wave functions is considered. It is shown that when the difference density matrices ΔγIJ =γI−γJ and ΔΓIJ =ΓI−ΓJ are introduced construction of the energy difference gradient ∂/∂Rα [EI(R)−EJ(R) ] becomes formally equivalent to the construction of the energy gradient (∂/∂Rα)EI(R). Here EI(R) is electronic potential energy surface at the CI level and γI and ΓI are the standard one- and two-particle density matrices. The formalism presented here provides a unified approach for the evaluation of three important classes of derivatives, energy gradients (using standard density matrices γI and ΓI ), energy difference gradients (using difference density matrices ΔγIJ and ΔΓIJ) and intersurface nonadiabatic derivative couplings (using transition density matrices γIJ and ΓIJ). The algorithms for the evaluation of the energy difference gradient permit efficient exploitation of the formal similarities which exist between the Newton–Raphson procedure for the minimization of EI(R) and that for ΔEIJ(R)2 =[EI(R)−EJ(R) ]2. These similarities can be used to advantage in the characterization of ΔEIJ(R)2 surfaces. The use of this formalism to analyze regions of avoided surface crossings is considered. In particular the methodology introduced here is used to locate an energetically accessible portion of a seam of avoided crossings for the two lowest potential energy surfaces of the Na–HCl system. These surfaces describe the electronic quenching reaction Na(2P)+HCl→NaCl+H. This avoided crossing seam is the analog of a (C2v) allowed crossing seam in the Na(2P)+H2→Na(2S)+H2 nonreactive quenching problem.