Internal dynamics of the 3-Pyrroline-N-Oxide ring in spin-labeled proteins

Site-directed spin labeling is a versatile tool to study structure as well as dynamics of proteins using EPR spectroscopy. Methanethiosulfonate (MTS) spin labels tethered through a disulfide linkage to an engineered cysteine residue were used in a large number of studies to extract structural as well as dynamic information on the protein from the rotational dynamics of the nitroxide moiety. The ring itself was always considered to be a rigid body. In this contribution, we present a combination of high-resolution X-ray crystallography and EPR spectroscopy of spin-labeled protein single crystals demonstrating that the nitroxide ring inverts fast at ambient temperature while exhibiting nonplanar conformations at low temperature. We have used quantum chemical calculations to explore the potential energy that determines the ring dynamics as well as the impact of the geometry on the magnetic parameters probed by EPR spectroscopy

Redox-Dependent Structural Transformations of the [4Fe-3S] Proximal Cluster in O₂‑Tolerant Membrane-Bound [NiFe]-Hydrogenase: A DFT Study

Broken-symmetry density functional theory (BS-DFT) has been used to address the redox-dependent structural changes of the proximal [4Fe-3S] cluster, implicated in the O₂-tolerance of membrane-bound [NiFe]-hydrogenase (MBH). The recently determined structures of the [4Fe-3S] cluster together with its protein ligands were studied at the reduced [4Fe-3S]³⁺, oxidized [4Fe-3S]⁴⁺, and superoxidized [4Fe-3S]⁵⁺ levels in context of their relative energies and protonation states. The observed proximal cluster conformational switch, concomitant with the proton transfer from the cysteine Cys20 backbone amide to the nearby glutamate Glu76 carboxylate, is found to be a single-step process requiring ∼12–17 kcal/mol activation energy at the superoxidized [4Fe-3S]⁵⁺ level. At the more reduced [4Fe-3S]^4+/3+ oxidation levels, this rearrangement has at least 5 kcal/mol higher activation barriers and prohibitively unfavorable product energies. The reverse transformation of the proximal cluster is a fast unidirectional process with ∼8 kcal/mol activation energy, triggered by one-electron reduction of the superoxidized species. A previously discussed ambiguity of the Glu76 carboxylate and ‘special’ Fe4 iron positions in the superoxidized cluster is now rationalized as a superposition of two local minima, where Glu76-Fe4 coordination is either present or absent. The calculated 12.3–17.9 MHz ¹⁴N hyperfine coupling (HFC) for the Fe4-bound Cys20 backbone nitrogen is in good agreement with the large 13.0/14.6 MHz ¹⁴N couplings from the latest HYSCORE/ENDOR studies

Local Hybrid Functional Applicable to Weakly and Strongly Correlated Systems

The recent idea (Wodyński, A.; Arbuznikov, A. V.; Kaupp M. J. Chem. Phys.2021,155, 144101) to augment local hybrid functionals by a strong-correlation (sc) factor obtained from the adiabatic connection in the spirit of the KP16 model has been extended and applied to generate the accurate sc-corrected local hybrid functional scLH22t. By damping small values of the ratio between nondynamical and dynamical correlation entering the correction factor, it has become possible to avoid double counting of nondynamical correlation for weakly correlated situations and thereby preserve the excellent accuracy of the underlying LH20t local hybrid for such cases almost perfectly. On the other hand, scLH22t improves substantially over LH20t in reducing fractional-spin errors (FSEs), in providing improved spin-restricted bond dissociation curves, and in treating some typical systems with multireference character. The obtained FSEs are similar to those of the KP16/B13 model and slightly larger than for B13, but performance for weakly correlated systems is better than for these two related methods, which are also difficult to use self-consistently. The recent DM21 functional based on the training of a deep neural network still performs somewhat better than scLH22t but allows no physical insights into the origins of reduced FSEs. Examination of local mixing functions (LMFs) for the corrected scLH22t and uncorrected LH20t functionals provides further insights: in weakly correlated situations, the LMF remains essentially unchanged. Strong-correlation effects manifest in a reduction of the LMF values in certain regions of space, even to the extent of producing negative LMF values. It is suggested that this is the mechanism by which also DM21, which may be viewed as a range-separated local hybrid, is able to reduce FSEs

Quantum-Chemical Approach to NMR Chemical Shifts in Paramagnetic Solids Applied to LiFePO₄ and LiCoPO₄

A novel protocol to compute and analyze NMR chemical shifts for extended paramagnetic solids, accounting comprehensively for Fermi-contact (FC), pseudocontact (PC), and orbital shifts, is reported and applied to the important lithium ion battery cathode materials LiFePO₄ and LiCoPO₄. Using an EPR-parameter-based ansatz, the approach combines periodic (hybrid) DFT computation of hyperfine and orbital-shielding tensors with an incremental cluster model for g- and zero-field-splitting (ZFS) D-tensors. The cluster model allows the use of advanced multireference wave function methods (such as CASSCF or NEVPT2). Application of this protocol shows that the ⁷Li shifts in the high-voltage cathode material LiCoPO₄ are dominated by spin–orbit-induced PC contributions, in contrast with previous assumptions, fundamentally changing interpretations of the shifts in terms of covalency. PC contributions are smaller for the ⁷Li shifts of the related LiFePO₄, where FC and orbital shifts dominate. The ³¹P shifts of both materials finally are almost pure FC shifts. Nevertheless, large ZFS contributions can give rise to non-Curie temperature dependences for both ⁷Li and ³¹P shifts

Noncollinear Two-Component Quasirelativistic Description of Spin Interactions in Exchange-Coupled Systems. Mapping Generalized Broken-Symmetry States to Effective Spin Hamiltonians

We provide a consistent mapping of noncollinear two-component quasirelativistic DFT energies with appropriate orientations of localized spinor quantization axes for multinuclear exchange-coupled transition-metal complexes onto an uncoupled anisotropic effective spin Hamiltonian. This provides access to the full exchange interaction tensor between the centers of spin-coupled systems in a consistent way. The proposed methodology may be best viewed as a generalized broken-symmetry density functional theory approach (gBS-DFT). While the calculations provided are limited to trinuclear systems ([M₃O­(OOCH)₆(H₂O)₃]⁺, where M = Cr­(III), Mn­(III), Fe­(III)) with <i>C</i>₃ symmetry, the method provides a general framework that is extendable to arbitrary systems. It offers an alternative to previous approaches to single-ion zero-field splittings, and it provides access to the less often examined antisymmetric Dzyaloshinskii–Moriya exchange interaction. Spin–orbit coupling is included self-consistently. This will be of particular importance for complexes involving 4d or 5d transition metal centers or possibly also for f-block elements, where a perturbational treatment of spin–orbit coupling may not be valid anymore. While a comparison with experimental data was indirect due to simplifications in the chosen model structures, the agreement obtained indicates the essential soundness of the presented approach

Four-Component Relativistic Density Functional Calculations of EPR Parameters for Model Complexes of Tungstoenzymes

For a closer validation of four-component relativistic DFT methods within the matrix Dirac–Kohn–Sham (mDKS) framework with global hybrid functionals for EPR parameter calculations to be applied in the modeling of tungsten enzymes, we refine a previously suggested protocol for computations on 5d systems. This is done for a series of larger, unsymmetrical W­(V) complexes thought to closely resemble enzyme active sites in this oxidation state. Particular focus is placed on complexes with thiolate and dithiolene ligands, along with an evaluation of the influence of different amounts of exact-exchange incorporated in hybrid PBE0-<i>x</i>HF functionals, an implicit solvent model, and structural changes on the computed EPR parameters. Compared to previous work, a slightly modified protocol with different optimal exact-exchange admixtures for electronic <i>g</i>- and hyperfine <i>A</i>-tensors is found to provide the best agreement with experimental EPR data. It will provide the basis for our subsequent tungsten enzyme modeling efforts

Validation of the Direct-COSMO-RS Solvent Model for Diels–Alder Reactions in Aqueous Solution

The modeling of chemical reactions in protic solvents tends to be far more computationally demanding than in most aprotic solvents, where bulk solvent effects are well described by dielectric continuum solvent models. In the presence of hydrogen bonds from a protic solvent to reactants, transition states or intermediates, a faithful modeling of the solvent effects usually requires some kind of molecular dynamics treatment. In contrast, the COSMO-RS (conductor-like screening model for real solvents) approach has been known for about a decade to describe protic solvent effects much better than continuum solvents, in spite of being an implicit solvent model without explicit molecular dynamics. More recently, the self-consistent use of its potential in electronic-structure methods has led to the Direct-COSMO-RS approach. It allows, for example, structure optimization in the presence of a protic solvent, of solvent mixtures, as well as self-consistent property calculations. In view of recent successful tests for electron transfer in organic mixed-valence systems, in this work the wider applicability of D-COSMO-RS for organic reactivity is evaluated by computation of activation and reaction free energies, as well as transition-state structures of two prototypical Diels–Alder reactions, with an emphasis on aqueous solution. D-COSMO-RS indeed provides substantial improvements over the COSMO continuum model and in judicious testing compares well with embedded supermolecular model cluster treatments, without prior knowledge about the average numbers of hydrogen-bonding interactions present

Gauge effects in local hybrid functionals evaluated for weak interactions and the GMTKN30 test set

<p>The so-called ‘gauge problem’, due to the non-uniqueness of exchange-energy densities, is a fundamental challenge for density functionals depending on these energy densities, such as local hybrid functionals. We have recently demonstrated how gauge effects influence the potential-energy curves of the argon dimer, and other quantities depending on ‘non-physical’ Pauli repulsions introduced by incompatible gauges of (semi-)local and exact-exchange energy densities . Introduction of suitable calibration functions depending only on semi-local quantities allowed to correct for these deficiencies and suggested ways to obtain more accurate local hybrid functionals beyond the local spin density approximation (LSDA) exchange-energy density. Here we extend the study of the gauge problem by comparing a number of uncalibrated and calibrated local hybrids for (1) the potential-energy curves of further noble-gas dimers and (2) for the entire GMTKN30 test set and its individual subsets. We find that DFT-D3 dispersion corrections fitted to be compatible with uncalibrated local hybrids have to correct not only for missing London dispersion but also for gauge artefacts that make weak interactions too repulsive. This burden is taken away when using properly calibrated local hybrids, which perform much better for dispersion-sensitive quantities already without D3 corrections, and which require only the physically relevant dispersion to be corrected for. The present results suggest directions for further improvement of calibration functions for local hybrids.</p

MVO-10: A Gas-Phase Oxide Benchmark for Localization/Delocalization in Mixed-Valence Systems

Ten simple gas-phase, main-group as well as transition-metal, mixed-valence (MV) oxo complexes are suggested for the screening of electronic-structure methods for the computational study of localization vs delocalization of charge and spin density in MV systems, without the usual added complication of environmental effects. Benchmark coupled-cluster energies up to CCSDT­(Q)/CBS (for Al₂O₄^–, Si₂O₄⁺, Si₂O₄^–, ScO₂, TiO₂⁺) and CCSD­(T)/CBS (for Ti₂O₄^–, Ti₂O₄^–, V₂O₄⁺, Cr₂O₆^–) quality are provided as a basis for screening a variety of density-functional methods, ranging from a generalized gradient approximation via global and range-separated to local hybrid functionals. Additionally, experimental evidence for a delocalized D_2d structure of the somewhat larger V₄O₁₀^– is used. None of the functionals is fully satisfactory when tasked with describing simultaneously the most extreme cases, the localized Al₂O₄^– and the delocalized V₄O₁₀^–. While relatively large exact-exchange admixtures are required for the former, and for related localized cases, lower ones are preferable for the latter, as well for other delocalized d¹d⁰ systems. The overall best combined performance is provided by a Lh-SVWN (g­(<b>r</b>) = 0.670 τ_W/τ) local hybrid, the MN15 global hybrid, and the ωB97X-D range-separated hybrid. We also provide vibrational data for comparison with experiment

Can Zinc Really Exist in Its Oxidation State +III?

Very recently, a thermochemically stable Zn^III complex has been predicted by Samanta and Jena (J. Am. Chem. Soc. 2012, 134, 8400−8403). In contrast to their conclusions we show here by quantum chemical calculations that (a) Zn­(AuF₆)₃ is not a thermochemically feasible compound, and (b) even if it could be made, it would not represent a Zn^III oxidation state by any valid definition