A Tale of Two Vectors: A Lanczos Algorithm For Calculating RPA Mean Excitation Energies

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The experimental and theoretical determination of the mean excitation energy,
I(0), and the stopping power, S(v), of a material is of great interest in particle and
material physics, as well as radiation therapy. For calculations of I(0), the complete set of electronic transitions in a given basis set is required, effectively limiting such calculations to systems with a small number of electrons, even at the random-phase approximation (RPA)/time-dependent Hartree-Fock (TDHF) or time-dependent density functional theory (TDDFT) level. To overcome such limitations, we present here the implementation of a Lanczos algorithm adapted for the paired RPA/TDHF eigenvalue problem in the Dalton program and show that it provides good approximations of the entire RPA eigenspectra in a reduced space. We observe rapid convergence of I(0) with the number of Lanczos vectors as the algorithm favors the transitions with large contributions. In most cases, the algorithm recovers RPA I(0) values of up to 0.5 % accuracy at less than a quarter of the full space size. The algorithm not only exploits the RPA paired structure to save computational resources, but it is also preserves certain sum-over-states properties, as first demonstrated by Johnson et al. [Comput. Phys. Commun. 1999, 120, 155]. The block Lanczos RPA solver, as presented here, thus shows promise for computing mean excitation energies for systems larger than what was computationally feasible before.
Original languageEnglish
Article number014102
JournalThe Journal of Chemical Physics
Issue number1
Number of pages16
Publication statusPublished - 3 Jan 2022

    Research areas

  • Faculty of Science - Mean excitation energy, stopping power, RPA, Lanczos, random phase approximation, time-dependent Hartree Fock

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