There is not much correct in this article: 
 * The sentence  
 "The eigenvalues of a Hermitian matrix depending on N continuous real parameters cannot cross except at a manifold of N-2 dimensions. In the case of a diatomic molecule (one parameter, which describes the bond length), this means that the eigenvalues do not cross." 

 is wrong (take the diagonal 2x2 matrix  Diag(1,A) with eigenvalues one and A, where A is our real parameter. When changing A from zero to two we see a crossing in contradiction to the sentence (N=1). 

 * Also "In the case of a triatomic molecule, this means that the eigenvalues can intersect at a point only (see conical intersection)." 

 is at least missleading - in 3 dimensions conical intersections are not points but lines (one dimensional). 
 Hope someone takes the time to improve it soon. Ciao.