TY - JOUR

T1 - A Tale of Two Vectors

T2 - A Lanczos Algorithm For Calculating RPA Mean Excitation Energies

AU - Zamok, Luna

AU - Coriani, Sonia

AU - Sauer, Stephan P. A.

PY - 2022/1/3

Y1 - 2022/1/3

N2 - 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 andmaterial 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.

AB - 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 andmaterial 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.

KW - Faculty of Science

KW - Mean excitation energy

KW - stopping power

KW - RPA

KW - Lanczos

KW - random phase approximation

KW - time-dependent Hartree Fock

U2 - 10.1063/5.0071144

DO - 10.1063/5.0071144

M3 - Journal article

C2 - 34998356

VL - 156

JO - The Journal of Chemical Physics

JF - The Journal of Chemical Physics

SN - 0021-9606

IS - 1

M1 - 014102

ER -