  Eigenlevel correlation diagrams has proven to be a very useful tool to
understand eigenstate characteristics of classically chaotic systems. In
particular, we showed in a previous publication [Phys. Rev. Lett. 80, 944
(1998)] how to unveil the scarring mechanism, a cornerstone in the theory of
quantum chaos, using the Planck constant as the correlation parameter. By
increasing Planck constant, we induced a transition from order to chaos, in
which scarred wavefunctions appeared as the interaction of pairs of eigenstates
in broad avoided crossings, forming a well defined frontier in the correlation
diagram. In this paper, we demonstrate that this frontier can be obtained by
means of the semiclassical quantization of the involved scarring periodic
orbits. Additionally, in order to calculate the Maslov index of each scarring
periodic orbit, which is necessary for the semiclassical quantization
procedure, we introduce a novel straightforward method based on Lagrangian
descriptors. We illustrate the theory using the vibrational eigenstates of the
LiCN molecular system.
