Abstract
We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CCSD) to the calculation of 57Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states. The electron densities and electric field gradients needed for these calculations were obtained within the recently implemented analytic derivative scheme. A method for the direct treatment of scalar relativistic effects in the calculation of effective electron densities is described by using the first-order Douglas-Kroll-Hess Hamiltonian and a Gaussian charge distribution model for the nucleus. The performance of DLPNO-CCSD is compared with four modern-day density functionals, namely, RPBE, TPSS, B3LYP, and B2PLYP, as well as with the second-order Møller-Plesset perturbation theory. An excellent correlation between the calculated electron densities and the experimental isomer shifts is attained with the DLPNO-CCSD method. The correlation constant a obtained from the slope of the linear correlation plot is found to be ≈-0.31 a.u.3 mm s-1, which agrees very well with the experimental calibration constant α = -0.31 ± 0.04 a.u.3 mm s-1. This value of a is obtained consistently using both nonrelativistic and scalar relativistic DLPNO-CCSD electron densities. While the B3LYP and B2PLYP functionals achieve equally good correlation between theory and experiment, the correlation constant a is found to deviate from the experimental value. Similar trends are observed also for quadrupole splittings. The value of the nuclear quadrupole moment for 57Fe is estimated to be 0.15 b at the DLPNO-CCSD level. This is consistent with previous results and is here supported by a higher level of theory. The DLPNO-CCSD results are found to be insensitive to the intrinsic approximations in the method, in particular the PNO occupation number truncation error, while the results obtained with density functional theory (DFT) are found to depend on the choice of the functional. In a statistical sense, i.e., on the basis of the linear regression analysis, however, the accuracies of the DFT and DLPNO-CCSD results can be considered comparable.
Highlights
Following the discovery of the Mössbauer effect,1–3 Mössbauer spectroscopy has emerged as a powerful analytic tool in chemistry and solid-state physics.4 Mössbauer spectroscopy is based on the phenomenon of recoilless resonant absorption of gamma-ray photons by atomic nuclei situated in a solid.1–3 Since the gamma-ray absorption occurs at a very precise energy, Mössbauer spectroscopy allows probing minute changes in the nuclear energy levels arising from hyperfine interactions of the active nuclei with surrounding electrons, in this way providing valuable information about chemical environments of the active nuclei
We report on applications of the domain based local pair-natural orbital (PNO) coupled-cluster method within the singles and doubles approximation (DLPNO-CC singles and doubles (CCSD)) to the calculation of 57Fe isomer shifts and quadrupole splittings in a small training set of iron complexes consisting of large molecular ligands and iron atoms in varying charge, spin, and oxidation states
The quality of the linear fit, which is expressed in terms of the R2 value, is the most important parameter in the linear regression analysis, it is encouraging to note the excellent agreement between the correlation constant a (≈−0.31 a.u.3 mm s−1) and the experimental value of −0.31 ± 0.04 a.u.3 mm s−1 for the calibration constant α
Summary
Following the discovery of the Mössbauer effect, Mössbauer spectroscopy has emerged as a powerful analytic tool in chemistry and solid-state physics. Mössbauer spectroscopy is based on the phenomenon of recoilless resonant absorption of gamma-ray photons by atomic nuclei situated in a solid. Since the gamma-ray absorption occurs at a very precise energy, Mössbauer spectroscopy allows probing minute changes in the nuclear energy levels arising from hyperfine interactions of the active nuclei with surrounding electrons, in this way providing valuable information about chemical environments of the active nuclei. The two important parameters obtained from a Mössbauer spectrum are the isomer shift (IS) and the quadrupole splitting (QS) at a metal center The former is proportional to the electron density at the nucleus under consideration, while the latter is proportional to the electric field gradient (EFG). Two factors determine the isomer shift, viz., the change in nuclear radius attendant on gamma transition and the differential electronic environments of the active nucleus in the source and in the absorber.. Two factors determine the isomer shift, viz., the change in nuclear radius attendant on gamma transition and the differential electronic environments of the active nucleus in the source and in the absorber.10 None of these two factors can be individually determined from a Mössbauer experiment. Accurate quantum-chemical calculations are indispensable for determining the chemical species that are compatible with an observed Mössbauer spectrum (see, for example, Ref. 11)
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