Complex eigenvalues, resonances, play an important role in large variety of fields in physics and chemistry. For example, in cold molecular collision experiments and electron scattering experiments, autoionizing and pre-dissociative metastable resonances are generated. However, the computation of complex resonance eigenvalues is difficult, since it requires severe modifications of standard electronic structure codes and methods. Here we show how resonance eigenvalues, positions and widths, can be calculated using the standard, widely used, electronic-structure packages. Our method enables the calculations of the complex resonance eigenvalues by using analytical continuation procedures (such as Padé). The key point in our approach is the existence of narrow analytical passages from the real axis to the complex energy plane. In fact, the existence of these analytical passages relies on using finite basis sets. These passages become narrower as the basis set becomes more complete, whereas in the exact limit, these passages to the complex plane are closed.

A consistent method for optimizing Gaussian primitives for Rydberg and multiply excited helium states is designed. A novel series for the "exponentially tempered Gaussians" is introduced, which is markedly more efficient than the commonly used series of even tempered Gaussians. The optimization is made computationally feasible due to an approximate calculation of excited states using the effective one-electron Hamiltonian that is defined as Fockian from which the redundant Coulomb and exchange terms are dropped. Finally, ExTG5G and ExTG7F Gaussian basis sets are proposed. They enable calculations of the helium spectrum all the way from the ground state up to the (5, 4)(5) (1)S(e) and (6, 5)(7) (1)S(e) doubly excited resonances, respectively, mostly in the spectroscopic accuracy of 1 cm(-1).

We present an ab-initio approach for computing the photoionization spectrum near autoionization resonances in multielectron systems. While traditional (Hermitian) theories typically require computing the continuum states, which are difficult to obtain with high accuracy, our non-Hermitian approach requires only discrete bound and metastable states, which can be accurately computed with available quantum chemistry tools. We derive a simple formula for the absorption lineshape near Fano resonances, which relates the asymmetry of the spectral peaks to the phase of the complex transition dipole moment. Additionally, we present a formula for the ionization spectrum of laser-driven targets and relate the "Autler-Townes" splitting of spectral lines to the existence of exceptional points in the Hamiltonian. We apply our formulas to compute the autoionization spectrum of helium, but our theory is also applicable for non-trivial multi-electron atoms and molecules.We present an ab-initio approach for computing the photoionization spectrum near autoionization (AI) resonances in multi-electron systems. Recent developments in attosecondlaser technology enable probing and controlling photoionization processes, and lead to a renewed interest in ionization and related phenomena, such as high-harmonic generation and strong-field electronic dynamics 1-5 . These experimental capabilities call for ab-initio theories, which can relate the electronic structure of the sampled medium to the measured ionization spectrum. However, most existing theories require the calculation of the continuum states 6,7 (above the ionization threshold), which are difficult to obtain with high accuracy with traditional methods 8,9 . In this work, we use non-Hermitian quantum mechanics (NHQM) 10 in order to avoid the need of computing continuum states. Our theory produces a simple formula for the "Fano asymmetry parameter" [Eq. (8)], which expresses the asymmetry of the peaks in the ionization spectrum near AI resonances 11 , and a formula for the photoionization spectrum of laser-driven systems [Eq. (10)]. We relate the Autler-Townes 12 splitting of ionization spectral peaks to the existence of exceptional points 13 (EPs)-special degenerate resonances where multiple AI states share the same energy and wavefunction. We demonstrate the predictions of our theory for helium using ab-initio electronic-structure data from Ref. 14,15. By using advanced non-Hermitian quantum-chemistry algorithms 16,17 , our theory can also be applied for larger atoms and molecules.In NHQM, the time-independent Schrödinger equation is solved with outgoing boundary conditions and the resulting energy spectrum is discrete, containing real-energy bound states and complex-energy metastable states 10 . This situation is very different from traditional Hermitian quantum mechanics (HQM), where metastable (autoionizing) states are described as real-energy bound states embedded in a continuum of free states 11 . Moreover, in HQM, the transition dipole moment is real, while in NHQM, it is ge...