Ionization of molecules using a Gaussian representation of the continuum states

We are interested in investigating single ionization of small molecules by photon or electron impact. The focus of our work is on the description of the electron ejected into the continuum.

The theoretical study of molecular ionization processes requires accurate multicentric wavefunctions. Because of their very interesting mathematical properties, Gaussian basis sets are widely exploited for bound states calculations, while their use is far less developed in the context of fragmentation processes where continuum states play a leading role. Nodeless real Gaussian-type orbitals (rGTO) are not suited to represent oscillating and non-decreasing continuum wavefunctions. On the other hand, complex GTO (cGTO) --i.e. Gaussians with a complex exponent-- intrinsically oscillate and should be more adapted for this task.

Recently [1], we have explored this lead and developed an efficient non-linear optimization method to provide sets of cGTOs able to reproduce accurately --within a large radial box-- continuum-type functions, on an energy range suitable for a number of physical applications. Using such a tool, we could provide an analytical formulation to obtain molecular photoionization observables within a one-active-electron model and a single-center approach. The reliability and efficiency of the method was shown by studying the photoionization of several neon-like molecules (NH3, H2O and CH4) [2].

Here we present also an application to the ionization of such molecules but by electron impact [3]. All the necessary transition integrals are again expressed in closed form. Differential cross sections calculated for methane compare well with other theoretical calculations and with available experimental data in asymmetric coplanar geometry.

Further exploiting the mathematical advantages of cGTO, our strategy for the continuum state can be equally applied together with a multicentric initial state description [4] and opens up for several applications, for example for ionization processes involving large molecules.

[1] Ammar A et al, 2020 J. Comput. Chem., 41, 2365.

[2] Ammar A et al, 2021 J. Comput. Chem., 42, 2294.

[3] Ammar A et al, submitted.

[4] Ammar A et al, 2021 Adv. Quantum Chem., 83, 287.