SYSTEMATIC DETERMINATION OF INTERSECTIONS OF POTENTIAL-ENERGY SURFACES USING A LAGRANGE MULTIPLIER CONSTRAINED PROCEDURE

Two nonrelativistic Born-Oppenheimer potential energy surfaces of distinct space-spin symmetry intersect on a surface of dimension N - 1 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 which avoids the determination of the full N - 1 dimensional surface, while directly locating portions of the crossing surface that are energetically important. The algorithm is based on the minimization of the Lagrangian function L(IJ)(R,lambda0,lambda) = E(I)(R) + lambda0[E(I)(R) - E(J)(R)] + SIGMA(k=1)(M)lambda(k)C(k)(R) where Ck(R) is any geometrical equality constraint such as R(KL)2 - a(KL)2 = 0 or R(KL)2 - R(MN)2 = 0, R(KL) = \R(K) - R(L)\, and lambda0 and lambda are Lagrange multipliers. The efficacy of this algorithm is demonstrated using a simple MCSCF/first-order CI description of the spin-forbidden reaction CH(X2PI) + N2(X1SIGMA(g+)) - HCN(X1SIGMA+) + N(4S). Sections of the crossing surface and the interstate spin-orbit couplings for the 4A'' and 2A'' potential energy surfaces are reported in the vicinity of a minimum energy crossing point.