On the representation of coupled adiabatic potential energy surfaces using quasi-diabatic Hamiltonians: description of accidental seams of conical intersection

The ability to describe seams of conical intersection that couple adiabatic potential energy surfaces is a key issue in describing nonadiabatic processes. This work considers the description of these seams provided by a recently introduced description of coupled adiabatic states using a coupled quasi-diabatic state Hamiltonian, Hd, whose matrix elements are polynomials in the internal coordinates. The conical intersection seam is represented in intersection adapted coordinates. Using the seam of accidental conical intersection of the 1,21A states of NH3 as an example the ability of the proposed algorithm to describe a seam of conical intersection in its full dimensionality is demonstrated. The success of this description is attributable to the use of orthogonal intersection adapted coordinates and to the Lagrange multiplier constraints in our algorithm which enables us to require the locus, energies and local topography of selected points on the Hd determined seam of intersection to agree exactly with the ab initio results.