Electric quadrupole moment of the 27Al nucleus: Converging results from the AlF and AlCl molecules and the Al atom

Nuclear quadrupole moments for Al27 and Ga69 derived from four-component molecular coupled cluster calculations

“…Based on the spread of values at the highest level of theory ͓CCSD͑T͔͒ and the experimental error bars in the NQCCs we therefore suggest an 27 Al NQM value of 146.0Ϯ0.4 mb. This value falls within the error bars of the value suggested by Kellö et al 8 There exist two 69 Ga reference values: A molecular value of 165 mb determined in GaF by Pernpointner and Schwerdtfeger 35 and an atomic value of 173͑3͒ mb obtained from an atomic MCHF wave function in combination with relativistic corrections by Tokman et al 36 In addition one can calculate DFT molecular values ranging from 165.3 mb ͑GaBr͒ to 168.1 mb ͑GaF͒ from the results of van Lenthe and Baerends. 7 This means that the spread in NQM values is considerably larger than the one for Al which is mostly due to the precision of the EFG calculations.…”

“…7 Their best results should be the ZORA-4 values that range from 141.9 mb ͑AlBr͒ to 145.0 mb ͑AlF͒. A recent value of the 27 Al NQM ͑146.6Ϯ1.0 mb͒ was suggested by Kellö et al 8 on basis of Douglas-Kroll CCSD͑T͒ calculations on AlF and AlCl and an atomic MCHF calculation. The discrepancy between their separate calculations is only 1.0 mb.…”

“…This has been the method of choice for many recent calculations of EFGs. [7][8][9] Although both methods give an accurate description of relativistic effects it is of utmost importance that the so-called picture change is taken into account. [10][11][12][13] This can either be done by applying the Douglas-Kroll 14 or ZORA transformation explicitly to the EFG operator, or by modelling the nuclear charge distribution with an array of point charges that is implicitly included in the standard transformation of the nuclear attraction integrals.…”

Density functional calculations of nuclear quadrupole coupling constants in the zero-order regular approximation for relativistic effects

“…It has been applied with standard quantum chemical methods for total energy calculations, such as CCSD͑T͒, but also with the two-component Douglas-Kroll relativistic method. [9][10][11][12]25 Avoiding the erroneous direct use of the density of the two-component wave function by taking the derivative with respect to the energy is commonly denoted as taking into account the picture change that has occurred in going from the four-component Dirac to a twocomponent formalism. However, such a picture change correction does, to order c Ϫ2 , not only consist of introduction of small components, which is what we find taking the derivative amounts to, but also entails correction of the large component, see Ref.…”

Theoretical study of the hyperfine-interaction constants and the isotope-shift factors for the 3s21S0–3s3pZhang1, Xie2, Li3 et al. 2017Phys. Rev. A

“…In the chain of aluminum isotopes, the proton-rich isotope 23 Al has the proton-halo structure [2,3], the neutron-rich isotopes 31−33 Al are in the vicinity of the "island of inversion", and the 26 Al is a self-conjugate nucleus [4]. Up to date, the Q and r 2 values are only available for a few isotopes of aluminum, and the accuracies are not high enough except for 27 Al [5][6][7]. For example, the Q value of 26 Al, with an uncertainty about 12%, was deduced from the experimental hyperfine structures measured by using the atomic laser spectroscopy [8] in assistance of the relation 26 Q/ 27 Q = 26 B/ 27 B (B is the electric quadrupole hyperfine interaction constants).…”