On the intersection of two potential energy surfaces of the same symmetry. Systematic characterization using a Lagrange multiplier constrained procedure

Two nonrelativistic Born–Oppenheimer potential energy surfaces of the same space-spin symmetry may intersect on a surface of dimension N−2, where N is the number of internal nuclear degrees of freedom. Characterization of this entire surface can be quite costly. An algorithm, employing multiconfiguration self-consistent-field (MCSCF)/configuration interaction(CI) wave functions and analytic gradient techniques, is presented that avoids the determination of the full N−2 dimensional surface, while directly locating portions of the crossing surface that are energetically important. The algorithm determines extrema of the Lagrangian function LIJ(R,ξ,λ) = EI(R) + ξ1EI(R) − EJ(R) + ξ2HIJ(R)/2+ ∑Mk=1λkCk(R), where Ck(R) is any geometric equality constraint such as RKL2−αKL2=0, or RKL2−RMN2=0, RKL=‖RK−RL‖ and the ξ and λ are Lagrange multipliers. The efficacy of this algorithm is demonstrated using a MCSCF/first order CI description of 1,22A′ states of HCO.