Complex Scaling in Quantum Chemistry

In theoretical chemistry, we are interested in the calculation of all kinds of spectra, with the goal of understanding and describing the properties of molecules.

This piece of work is especially interested in resonance states. Electronic resonances are bound-like states with a finite lifetime above the ionization or detachment energy of a system. Such states decay into the continuum. For describing those resonance states, Hermitian quantum mechanics and conventional computational chemistry reach their limits. The method of complex scaling of the Schrödinger equation provides access to resonances in molecular systems that belong to non-Hermitian quantum mechanics.

This work’s focus will be on the application of the complex scaling on the basis set method and the investigation of the basis set dependence. The most theoretical considerations and all practical implementations are in one dimension to reduce the complexity, which is useful for a better understanding and for increased visibility of arising problems. One sticking point is the special behaviour of the resonance wave function with its exponentially diverging behaviour in non-Hermitian quantum mechanics and a suitable definition of a basis. Furthermore, the complex scaling method is analytically and numerically applied to the harmonic oscillator. Moreover, the complex scaling method is numerically applied to a model system capable of resonances.