Towards automated calculations of stationary solutions in the complex plane via Padé approximant

Physical and Analytical Chemistry Seminar

Lecturer: Idan Haritan, Schulich Faculty of Chemistry, group of Prof. Nimrod Moiseyev

14-14 Mar 2021 @ 12:30

Location: Join Zoom Meeting at

Resonances are metastable states with a finite lifetime. They play an important role in a large variety of fields in physics and chemistry.  Such as unimolecular and cold molecular reactions, electron scattering from molecules, molecular auto-ionization, photo-induced reactions, surface chemistry, nuclear physics and optics. Non-hermitian quantum mechanics is a formalism that excels in describing these metastable states. It does so by time independent computational algorithms originally developed for the calculations of bound states. Under this formalism, the resonances are described as complex eigenvalues of the Hamiltonian. The real part of the eigenvalue stands for the energy value, whereas the imaginary part is inversely proportional to the lifetime of the state. Nevertheless, calculating complex eigenvalues is not a trivial task.

In this talk, I will present a method that enables calculating these complex eigenvalues from real data of any system. This method, termed RVP – Resonances Via Padé, was implemented on various physical systems, and even helped give birth to two new research fields. The first, calculation of complex energy surfaces and transition dipoles of molecules, highly contributed to the understanding of cold chemistry processes. The second, threshold energies and poles identification for hadron physical problems, was a consequence of a collaboration with an elementary particle physicist.

As a final note, I will present how we were able to take this method further by writing an automated “black-box” code, linked to standard quantum chemistry packages, for the use of chemists in their studies of chemical reactions.