A Tale of Two Vectors: A Lanczos Algorithm For Calculating RPA Mean Excitation Energies
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A Tale of Two Vectors : A Lanczos Algorithm For Calculating RPA Mean Excitation Energies. / Zamok, Luna; Coriani, Sonia; Sauer, Stephan P. A.
In: The Journal of Chemical Physics, Vol. 156, No. 1, 014102, 03.01.2022.Research output: Contribution to journal › Journal article › Research › peer-review
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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 -
ID: 286431719