Electronic structure of square planar bis(benzene-1,2-dithiolato)metal complexes [M(L)(2)](z) (z = 2-, 1-, 0; M = Ni, Pd, Pt, Cu, Au): an experimental, density functional, and correlated ab initio study

The three diamagnetic square planar complexes of nickel(II), palladium(II), and platinum(II) containing two S,S-coordinated 3,5-di-tert-butylbenzene-1,2-dithiolate ligands, (L(Bu))(2-), namely [M(II)(L(Bu))(2)](2-), have been synthesized. The corresponding paramagnetic monoanions [M(II)(L(Bu))(L(Bu)(*))](-) (S = (1)/(2)) and the neutral diamagnetic species [M(II)(L(Bu)(*))(2)] (M = Ni, Pd, Pt) have also been generated in solution or in the solid state as [N(n-Bu)(4)][M(II)(L(Bu))(L(Bu)(*))] salts. The corresponding complex [Cu(III)(L(Bu))(2)](-) has also been investigated. The complexes have been studied by UV-vis, IR, and EPR spectroscopy and by X-ray crystallography; their electro- and magnetochemistry is reported. The electron-transfer series [M(L(Bu))(2)](2-,-,0) is shown to be ligand based involving formally one (L(Bu)(*))(-) pi radical in the monoanion or two in the neutral species [M(II)(L(Bu)(*))(2)] (M = Ni, Pd, Pt). Geometry optimizations using all-electron density functional theory with scalar relativistic corrections at the second-order Douglas-Kroll-Hess (DKH2) and zeroth-order regular approximation (ZORA) levels result in excellent agreement with the experimentally determined structures and electronic spectra. For the three neutral species a detailed analysis of the orbital structures reveals that the species may best be described as containing two strongly antiferromagnetically interacting ligand radicals. Furthermore, multiconfigurational ab initio calculations using the spectroscopy oriented configuration interaction (SORCI) approach including the ZORA correction were carried out. The calculations predict the position of the intervalence charge-transfer band well. Chemical trends in the diradical characters deduced from the multiconfigurational singlet ground-state wave function along a series of metals and ligands were discussed.     

An improvement of the resolution of the identity approximation for the formation of the Coulomb matrix

A straightforward modification of the resolution of the identity (RI) approximation to the Coulomb interaction is described. In the limit of basis sets that are dominated by high angular momentum functions the observed speedups in realistic test systems reach a factor of 2 compared to the standard RI algorithm, and a factor of up to 300 compared to the standard algorithm to form the Coulomb matrix. More moderate savings on the order of 0-20% are obtained for the more commonly used smaller basis sets. A series of test calculations is reported to illustrate the efficiency of the algorithm.     

Spectroscopic and electronic structure studies of protocatechuate 3,4-dioxygenase: nature of tyrosinate-Fe(III) bonds and their contribution to reactivity.

The geometric and electronic structure of the high-spin ferric active site of protocatechuate 3,4-dioxygenase (3,4-PCD) has been examined by absorption (Abs), circular dichroism (CD), magnetic CD (MCD), and variable-temperature-variable-field (VTVH) MCD spectroscopies. Density functional (DFT) and INDO/S-CI molecular orbital calculations provide complementary insight into the electronic structure of 3,4-PCD and allow an experimentally calibrated bonding scheme to be developed. Abs, CD, and MCD indicate that there are at least seven transitions below 35 000 cm(-1) which arise from tyrosinate ligand-to-metal-charge transfer (LMCT) transitions. VTVH MCD spectroscopy gives the polarizations of these LMCT bands in the principal axis system of the D-tensor, which is oriented relative to the molecular structure from the INDO/S-CI calculations. Three transitions are associated with the equatorial tyrosinate and four with the axial tyrosinate. This large number of transitions per tyrosinate is due to the pi and importantly the sigma overlap of the two tyrosinate valence orbitals with the metal d orbitals and is governed by the Fe-O-C angle and the Fe-O-C-C dihedral angles. The previously reported crystal structure indicates that the Fe-O-C angles are 133 degrees and 148 degrees for the equatorial and axial tyrosinate, respectively. Each tyrosinate has transitions at different energies with different intensities, which correlate with differences in geometry that reflect pseudo-sigma bonding to the Fe(III) and relate to reactivity. These factors reflect the metal-ligand bond strength and indicate that the axial tyrosinate-Fe(III) bond is weaker than the equatorial tyrosinate-Fe(III) bond. Furthermore, it is found that the differences in geometry, and hence electronic structure, are imposed by the protein. The consequences to catalysis are significant because the axial tyrosinate has been shown to dissociate upon substrate binding and the equatorial tyrosinate in the enzyme-substrate complex is thought to influence asymmetric binding of the chelated substrate moiety via a strong trans influence which activates the substrate for reaction with O2.     

Efficient implementation of the analytical second derivatives of hartree–fock and hybrid DFT energies within the framework of the conductor-like polarizable continuum model

Calculation of vibrational frequencies for solvated systems is essential to study reactions in complex environments. In this paper, we report the implementation of the analytical self-consistent field Hessian at the Hartree–Fock and density functional theory levels in the framework of the conductor-like polarizable continuum model (C-PCM) into the ORCA quantum chemistry suite. The calculated vibrational frequencies agree very well with those computed through numerical differentiation of the analytical gradients. The deviation between both sets of data is smaller than 3 cm⁻¹ for frequencies larger than 200 cm⁻¹ and smaller than 5 cm⁻¹ for the low-frequency regime (100 cm⁻¹ < ω < 200 cm⁻¹). The accuracy of the frequencies is not significantly affected by the size of the density functional theory (DFT) integration grid, with a deviation lower than 0.5 cm⁻¹ between data computed with the smallest and that with the largest DFT grid size. The calculation of the analytical Hessian is between 3 and 12 times faster than its numerical counterpart. The C-PCM terms only add an overhead of 10–30% relative to the gas phase calculations. Finally, for acetone, the (B3LYP) values for the frequency shifts obtained in going from the gas phase to liquid acetone are in agreement with experiment. © 2019 Wiley Periodicals, Inc.     

Magnetic circular dichroism spectroscopy on the Cr₈ antiferromagnetic ring

A Magnetic Circular Dichroism (MCD) spectroscopic study of the antiferromagnetic ring [Cr?F?Piv??] (Piv = pivalate) is reported. From the splitting of the MCD bands, the single ion anisotropy parameters in the cluster spin ground state at different fields were determined to be d(Cr) = -0.33 ± 0.02 cm?1, e(Cr) = 0.11 ± 0.01 cm?1. Analysis of the MCD intensity as a function of field and temperature revealed the influence of spin mixing effects and yielded independent estimates of the single ion anisotropies (d(Cr) = -0.19 cm?1, e(Cr) = 4.3 × 10-4 cm?1), as well as yielding the isotropic exchange interaction strength (J = -6.00 cm?1). Thus it is shown that MCD is a powerful method to unravel the relation between single-ion and cluster anisotropy, furthering the design of molecular magnets with desired properties.     

Electronic structure of binuclear mixed valence copper azacryptates derived from integrated advanced EPR and DFT calculations

Binuclear, mixed valence copper complexes with a [Cu(+1)(.5), Cu(+1)(.5)] redox state and S = (1)/(2) can be stabilized with rigid azacryptand ligands. In this system the unpaired electron is delocalized equally over the two copper ions, and it is one of the very few synthetic models for the electron mediating Cu(A) site of nitrous oxide reductase and cytochrome c oxidase. The spatial and electronic structures of the copper complex in frozen solution were obtained from the magnetic interactions, namely the g-tensor and the (63,65)Cu, (14)N, (2)H, and (1)H hyperfine couplings, in combination with density functional theory (DFT) calculations. The magnetic interactions were determined from continuous wave (CW) electron paramagnetic resonance (EPR), pulsed electron nuclear double resonance (ENDOR), two-dimensional TRIPLE, and hyperfine sublevel correlation spectroscopy (HYSCORE) carried out at W-band or/and X-band frequencies. The DFT calculated g and Cu hyperfine values were in good agreement with the experimental values showing that the structure in solution is indeed close to that of the optimized structure. Then, the DFT calculated hyperfine parameters were used as guidelines and starting points in the simulations of the various experimental ENDOR spectra. A satisfactory agreement with the experimental results was obtained for the (14)N hyperfine and quadrupole interactions. For (1)H the DFT calculations gave good predictions for the hyperfine tensor orientations and signs, and they were also successful in reproducing trends in the magnitude of the various proton hyperfine couplings. These, in turn, were very useful for ENDOR signals assignments and served as constraints on the simulation parameters.     

First-principles calculations of zero-field splitting parameters

In this work, an implementation of an approach to calculate the zero-field splitting (ZFS) constants in the framework of ab initio methods such as complete active space self-consistent field, multireference configuration interaction, or spectroscopy oriented configuration interaction is reported. The spin-orbit coupling (SOC) contribution to ZFSs is computed using an accurate multicenter mean-field approximation for the Breit-Pauli Hamiltonian. The SOC parts of ZFS constants are obtained directly after diagonalization of the SOC operator in the basis of a preselected number of roots of the spin-free Hamiltonian. This corresponds to an infinite order treatment of the SOC in terms of perturbation theory. The spin-spin (SS) part is presently estimated in a mean-field fashion and appears to yield results close to the more complete treatments available in the literature. Test calculations for the first- and second-row atoms as well as first-row transition metal atoms and a set of diatomic molecules show accurate results for the SOC part of ZFSs. SS contributions have been found to be relatively small but not negligible (exceeding 1 cm(-1) for oxygen molecule). At least for the systems studied in this work, it is demonstrated that the presented method provides much more accurate estimations for the SOC part of ZFS constants than the emerging density functional theory approaches.