Comparison ofab initioand density functional calculations of electric field gradients: The 57Fe nuclear quadrupole moment from Mössbauer data

Multinuclear Residual Quadrupolar Couplings for Structure and Assignment

Most stable isotopes have a nuclear spin >1/2, but the quadrupole interaction poses challenge on their detection by nuclear magnetic resonance (NMR). On the other hand, the quadrupole interaction is a rich source of structural information that may be exploited for solution NMR in the form of residual quadrupolar couplings (RQCs) of weakly oriented samples. While 2H RQCs are now well established for structure verification and enantiomeric discrimination of organic molecules, we will in this article highlight some recent work on RQCs of other nuclei (especially 7Li and 11B).

57Fe Mössbauer parameters from domain based local pair-natural orbital coupled-cluster theory

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.

Polymorphous Indium Metal-Organic Frameworks Based on a Ferrocene Linker: Redox Activity, Porosity, and Structural Diversity

The metallocene-based linker molecule 1,1'-ferrocenedicarboxylic acid (H₂FcDC) was used to synthesize four different polymorphs of composition [In(OH)(FeC₁₂H₈O₄)]. Using conventional solvent-based synthesis methods and varying the synthetic parameters such as metal source, reaction temperature, and solvent, two different MOFs and one 1D-coordination polymer denoted as CAU-43 (1), In-MIL-53-FcDC_a (2), and In-FcDC (3) were obtained. Furthermore, thermal treatment of CAU-43 (1) at 190 °C under vacuum yielded a new polymorph of 2, In-MIL-53-FcDC_b (4). Both MOFs 2 and 4 crystallize in a MIL-53 type structure, but in different space groups C2/m for 2 and P1̅ for 4. The structures of the four title compounds were determined by single-crystal X-ray diffraction (SCXRD), powder X-ray diffraction (PXRD), or a combination of three-dimensional electron diffraction measurements (3D ED) and PXRD. N₂ sorption experiments of 1, 2, and 4 showed specific surface areas of 355 m² g^-1, 110 m² g^-1, and 140 m² g^-1, respectively. Furthermore, the electronic properties of the title compounds were characterized via Mössbauer and EPR spectroscopy. All Mössbauer spectra showed the characteristic doublet, proving the persistence of the ferrocene moiety. In the cases of 1, 3, and 4, appreciable impurities of ferrocenium ions could be detected by electron paramagnetic resonance spectroscopy. Cyclovoltammetric experiments were performed to demonstrate the accessible redox activity of the linker molecule of the title compounds. A redox process of FcDC^2- with oxidation (between 0.86 and 0.97 V) and reduction wave (between 0.69 and 0.80 V) was observed.

Observation of three different linker conformers in a scandium ferrocenedicarboxylate coordination polymer

In the coordination polymer CAU-50 based on 1,1′-ferrocenedicarboxylate and scandium, three different conformers of the same linker molecule are observed.

A porous and redox active ferrocenedicarboxylic acid based aluminium MOF with a MIL-53 architecture

A new redox active MOF Al-MIL-53-FcDC based on 1,1′-ferrocenedicarboxylate exhibits reversible electrochemical activity and permanent porosity.

The nuclear electric quadrupole moment of copper

The nuclear electric quadrupole moment (NQM) of the (63)Cu nucleus was determined from an indirect approach by combining accurate experimental nuclear quadrupole coupling constants (NQCCs) with relativistic Dirac-Coulomb coupled cluster calculations of the electric field gradient (EFG). The data obtained at the highest level of calculation, DC-CCSD-T, from 14 linear molecules containing the copper atom give rise to an indicated NQM of -198(10) mbarn. Such result slightly deviates from the previously accepted standard value given by the muonic method, -220(15) mbarn, although the error bars are superimposed.

Theoretical 57Fe Mössbauer spectroscopy: isomer shifts of [Fe]-hydrogenase intermediates

A computational protocol for ⁵⁷Fe isomer shifts, based on the relativistic eXact 2-Component Hamiltonian (X2C), is applied to discriminate between proposed intermediates of [Fe]-hydrogenase. Detailed analysis reveals that the difference in isomer shifts between two intermediates is due to an overlap effect.

CRYSTAL: a computational tool for the ab initio study of the electronic properties of crystals

CRYSTAL [1] computes the electronic structure and properties of periodic systems (crystals, surfaces, polymers) within Hartree-Fock [2], Density Functional and various hybrid approximations.

CRYSTAL was developed during nearly 30 years (since 1976) [3] by researchers of the Theoretical Chemistry Group in Torino (Italy), and the Computational Materials Science group in CLRC (Daresbury, UK), with important contributions from visiting researchers, as documented by the main authors list and the bibliography.

The basic features of the program CRYSTAL are presented, with two examples of application in the field of crystallography [4, 5].

On the calculation of Mössbauer isomer shift

A quantum chemical computational scheme for the calculation of isomer shift in Mossbauer spectroscopy is suggested. Within the described scheme, the isomer shift is treated as a derivative of the total electronic energy with respect to the radius of a finite nucleus. The explicit use of a finite nucleus model in the calculations enables one to incorporate straightforwardly the effects of relativity and electron correlation. The results of benchmark calculations carried out for several iron complexes as well as for a number of atoms and atomic ions are presented and compared with the available experimental and theoretical data.

The quadrupole moment of the 3∕2+ nuclear ground state of Au197 from electric field gradient relativistic coupled cluster and density-functional theory of small molecules and the solid state

An attempt is made to improve the currently accepted muonic value for the 197Au nuclear quadrupole moment [+0.547(16)x10(-28) m2] for the 3/2+ nuclear ground state obtained by Powers et al. [Nucl. Phys. A230, 413 (1974)]. From both measured Mossbauer electric quadrupole splittings and solid-state density-functional calculations for a large number of gold compounds a nuclear quadrupole moment of +0.60x10(-28) m2 is obtained. Recent Fourier transform microwave measurements for gas-phase AuF, AuCl, AuBr, and AuI give accurate bond distances and nuclear quadrupole coupling constants for the 197Au isotope. However, four-component relativistic density-functional calculations for these molecules yield unreliable results for the 197Au nuclear quadrupole moment. Relativistic singles-doubles coupled cluster calculations including perturbative triples [CCSD(T) level of theory] for these diatomic systems are also inaccurate because of large cancellation effects between different field gradient contributions subsequently leading to very small field gradients. Here one needs very large basis sets and has to go beyond the standard CCSD(T) procedure to obtain any reliable field gradients for gold. From recent microwave experiments by Gerry and co-workers [Inorg. Chem. 40, 6123 (2001)] a significantly enhanced (197)Au nuclear quadrupole coupling constant in (CO)AuF compared to free AuF is observed. Here, these cancellation effects are less important, and relativistic CCSD(T) calculations finally give a nuclear quadrupole moment of +0.64x10(-28) m2 for 197Au. It is argued that it is currently very difficult to improve on the already published muonic value for the 197Au nuclear quadrupole moment.

Anisotropic NMR interaction tensors in the decamethylaluminocenium cation

Solid-state NMR experiments, analytical and numerical simulations of solid NMR powder patterns, ab initio self-consistent field and hybrid density functional theory calculations, and single-crystal X-ray diffraction are used to characterize the molecular structure and anisotropic NMR interaction tensors in the bis(pentamethylcyclopentadienyl)aluminum cation, [Cp(2)Al](+). This highly symmetric main group metallocene has a structure analogous to that of ferrocene and the cobaltocenium cation. The single-crystal X-ray diffraction structure is reported for [Cp(2)Al][AlCl(4)]. Solid-state (27)Al[(1)H] magic-angle spinning and static NMR experiments are used to study the aluminum chemical shielding and electric field gradient tensors, revealing axial symmetry in both cases with a large chemical shielding span of Omega = 83(3) ppm and a small nuclear quadrupole coupling constant, C(Q)((27)Al) = 0.86(10) MHz. Carbon-13 CPMAS NMR experiments in combination with ab initio calculations and simulations of the effects of chemical exchange on (13)C static powder patterns reveal dynamic rotation of rings and suggest a low internal rotational barrier for this process. Theoretical computations of interaction tensors using the Gaussian 98 and Amsterdam Density Functional software packages are in good agreement with experiment and lend insight into the molecular origin of these NMR interactions. Orientations of the NMR tensors determined from theory, the large chemical shielding span, and the very small value of C(Q)((27)Al) can all be rationalized in terms of the high molecular symmetry.