Comparison of ab initio and density functional calculations of electric field gradients: The Fe57 nuclear quadrupole moment from Mössbauer data

Abstract

The difficulty in accurate determination of the nuclear quadrupole moment of the first I=3/2 excited nuclear state of Fe57 from electronic structure calculations of the iron electric field gradient combined with Mössbauer measurements of the nuclear quadrupole splitting in the isomer shift is addressed by comparing ab initio with density functional calculations for iron pentacarbonyl, Fe(CO)5, ferrocene, Fe(C5H5)2, and the Δg5 electronic ground states of FeCl2 and FeBr2. While the ligand field gradient tensor components change relatively little with the method applied, the iron electric field gradient is sensitive to the specific density functional used. Single reference many-body perturbation theory for electron correlation also performs poorly for the iron electric field gradient and shows extreme oscillatory behavior with a change in the order of the perturbation series. Even with larger basis sets and coupled cluster techniques a precise value for the iron electric field gradient could not be determined from electronic structure calculations due to limitations in the theoretical procedures. In order to avoid uncertainties in the measured isomer shift which enters into the nuclear quadrupole coupling constant we determined the Mössbauer spectrum of Fe(C5H5)2 between temperatures of 4.2 and 295 K. In this range two phase transitions are observed, but the quadrupole splitting is not very dependent on the solid state structure in each phase. Solid state effects for the Fe(CO)5 are determined by comparing the iron electric field gradient of the isolated molecule with the value obtained from first principle solid state calculations at various levels of theory. These calculations show that the influence of near neighboring effects to the iron electric field gradient is small. Fully relativistic Dirac–Hartree–Fock calculations for Fe(CO)5 reveal that relativistic effects for the iron electric field gradient are small as well. Fe(CO)5 is therefore an ideal test molecule for the determination of an accurate nuclear quadrupole moment from electronic structure calculations if combined with an experimental nuclear quadrupole coupling constant. Our best estimate for the Fe57 nuclear quadropole moment is 0.14(2) barn in reasonable agreement with recent nuclear structure calculations.