Multifractal analysis for the eigencoefficients of the eigenstates of highly excited vibration

The multifractal nature of the eigencoefficients of the eigenstates of the highly excited vibration of H2O, D2O and H2S is probed. The Hamiltonian includes the two stretches and the bend with anharmonic interaction and multiple resonances. It is shown that there are eigenstates possessing multifractal structure but not all. As the polyad number increases, larger percentages of eigenstates become multifractal. The self-similar structure that exists in the distribution of the eigencoefficients of the eigenstates as displayed on the zero-order state energy axis is also demonstrated.