Conical intersections in H₂Cl⁺(¹A′) Available to Purchase

A 10×10 model Hamiltonian matrix for the ¹A′ states of the H₂Cl⁺ molecule in a valence‐bond basis is shown to exhibit conical intersections between states 2 and 3 along a line in configuration space (linea diaboli). The points of intersection are located by finding the minimum in the square of the difference of the two eigenvalues and then confirming the nature of the intersection by calculation of the geometrical phase associated with transporting an eigenvector about the point. The locus of the linea diaboli does not correspond to any obvious special geometrical symmetry but rather appears to be related to the charge distributions in the molecular states correlating with the H+HCl⁺ (A ²Σ⁺ ) and H⁺ +HCl(X ¹Σ⁺) asymptotic channels. Some properties of the degenerate eigenstates at the intersections are presented and it is shown how the approximate geometric configurations of the intersection can be found from the eigenvectors of the two appropriate states.