The Adventures of Siegert Eigenvalues
Prateek Goel1, Bryan P. Changala2 , John F. Stanton1
1University of Florida, Quantum Theory Project, Gainesville, FL, 32611-8435
2JILA, University of Colorado, Boulder, CO, 80309
Siegert eigenvalues are explored and investigated in context of passage through a barrier. Often referred to as transition state resonances, they provide insight into the validity of a semiclassical approximation to computing the cumulative reaction probability (CRP), a central quantity in chemical kinetics. With the help of two-dimensional model system, Siegert eigenvalues are computed using different levels of theory – numerically exact (using DVR schemes), second and fourth order vibrational perturbation theory (VPT2 and VPT4 respectively) and vibrational self-consistent field theory (VSCF). If the VPT Siegert eigenvalues are in good agreement with the exact Siegert eigenvalues, one can confidently use the Semiclassical Transition State Theory (SCTST) in conjunction with VPT in order to compute the CRP. Application to molecules will also be discussed briefly.