Saddle point localization of molecular wavefunctions

The [H,C,N] molecular system is an important prototypical double well system of molecular physics. The bending states at the H-CN and CN-H sides of the isomerization barrier merge into the bond breaking internal rotation states of the hydrogen atom around the CN core as the excitation is increased above the isomerization barrier. This internal rotation is very different from other well known internal rotations in molecules as in the time domain picture chemical bonds are broken and newly formed. An important still unanswered question of molecular physics is the one of the connection between the internal dynamics above and below the isomerization barrier for double well systems with chemically relevant barrier heights. To answer this question I am using the spectroscopically assigned eigenenergy spectrum [1] extended up to 23000 cm-1 above the HCN minimum with stored wavefunctions.

The quantum mechanical description of isomerization is based on bound eigenstates of the molecular potential energy surface. For the near-minimum regions there is a textbook-based relationship between the potential and eigenenergies. Here we show how the saddle point region that connects the two minima is encoded in the eigenstates of the model quartic potential and in the energy levels of the [H, C, N] potential energy surface. We model the spacing of the eigenenergies with the energy dependent classical oscillation frequency decreasing to zero at the saddle point. The eigenstates with the smallest spacing are localized at the saddle point. The analysis of the HCN ↔ HNC isomerization states shows that the eigenstates with small energy spacing relative to the effective (v₁, v₃, ℓ) bending potentials are highly localized in the bending coordinate at the transition state. These spectroscopically detectable states represent a chemical marker of the transition state in the eigenenergy spectrum. The method developed here provides a basis for modeling characteristic patterns in the eigenenergy spectrum of bound states.

[1] G. C. Mellau

Complete experimental rovibrational eigenenergies of HCN up to 6880 cm-1 above the ground state

J. Chem. Phys. 134, 234303 (2011).

[2] G. Ch. Mellau, A. A. Kyuberis, O. L. Polyansky, N. Zobov,  R. W. Field

Saddle point localization of molecular wavefunctions

Scientific Reports 6, Article number: 33068 (2016) http://www.nature.com/articles/srep33068