Two-state versus three-state quantization: An ab initio study of the three lower states of the { N , H 2 ∣ A ′ } system

In this article we present the first ab initio study of the conical intersections (cis) and their electronic nonadiabatic coupling terms (NACTs) for the { N , H 2 } system. Efforts were made to reveal the location of cis between the two lower, 1 A ′ 2 and 2 A ′ 2 states-to be designated as (1,2) cis-and the cis between the two upper, 2 A ′ 2 and 3 A ′ 2 states-to be designated as the (2,3) cis-of this system. We found that these cis are located along the collinear {NHH) arrangement. The study is carried out by analyzing two-state magnitudes such as the (1,2) and (2,3) adiabatic-to-diabatic transformation angles (known also as the mixing angles) and the corresponding topological phases (known also as the Berry phases or the Longuet-Higgins phases). In addition, a detailed three-state study is carried out. Here the emphasis is on driving the diagonal elements of the topological D matrix and analyzing situations for which the corresponding nonadiabatic coupling matrix is quantized . The reliability of two-state results is carefully examined by comparing them with corresponding outcomes derived for the three-state study. In addition we also calculated the potential-energy surfaces related to the two lower states and studied to what extent they are affected by the (1,2) ci. The results obtained in this treatment were found to be in full agreement with the NACT's calculations.