Charge transfer in collisions of H⁺with Li (1s²2s, 2p_z): TD-MADNESS approach

Abstract

In this work we carry out a study of the single-electron charge transfer process for H+ collisions with atomic neutral lithium, in its ground and first excited state, at 1−25 keV amu−1. For this, we solve numerically the time dependent Schrödinger equation to the defined accuracy by using a multi-resolution adaptive approach, thus removing the uncertainties connected to a basis size and spatial and temporal numeric mesh size. We approximate the atomic lithium target by a single electron model in a frozen-core pseudo-potential while the projectile follows a straight line trajectory. Within these approximations we report new benchmark data for charge transfer cross sections to n = 2, and 3 states of hydrogen from 1s22s and 1s22pz of Li. Available theoretical and experimental data in the literature are in reasonable agreement with our results.

Coupled-Cluster in Real Space. 1. CC2 Ground State Energies Using Multiresolution Analysis

“…The working equations are solved by inverting the shifted kinetic energy operator (instead of diagonalizing a Hamilton matrix as in LCAO), by applying the bound-state Helmholtz operator on the wave function guess, and iterating until convergence . MRA has successfully been applied in quantum chemistry for computing SCF energies and gradients, − CIS and TD-DFT excitation energies, ,, MP2 energies, , magnetic properties, and also explicit time-dependent problems. , Its unique features include the computation of molecular properties at the limit of the complete basis, and, despite having a high computational prefactor, MRA exhibits naturally low-scaling algorithms, as e.g. CC2 formally scales as N occ 3 , similar to MP2 .…”

Coupled-Cluster in Real Space. 2. CC2 Excited States Using Multiresolution Analysis

“…MRA based approaches have been used for Hartree–Fock and density functional theory for a variety of molecular properties like total energies, , atomization energies, first and second order ground state properties, , magnetic properties, static polarizabilities, and excitation energies obtained with the CIS and TDHF/TDDFT , models. Also correlated methods like MP2 , and ground state CC2, as well as explicitly time dependent approaches which are not based on linear response were developed using MRA. − …”