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Abstract Metal–ligand bonding and noncovalent interactions (NCIs), such as hydrogen bonding orπ–πinteractions, play a crucial role in determining the structure, function, and selectivity of both biological and artificial metalloproteins. In this study, we employed a hybrid quantum mechanics/molecular mechanics (QM/MM) approach to investigate the ligation of water or cyanide in a mutated myoglobin system, in which the native heme scaffold was replaced with M-salophen or M-salen Schiff base complexes (M = Cr, Mn, Fe). Using our local vibrational mode analysis, particularly local vibrational mode force constants as intrinsic bond strength parameters, complemented with electron density and natural orbital analyses we explored the role of metal–ligand bonding and NCIs in different environments within the myoglobin pocket. Our analysis revealed that metal–ligand bonding, for both water and cyanide ligands, is strongest in the delta form of distal histidine and favors salophen prosthetic groups, as indicated by an overall increase in metal–ligand bond strength. Hydrogen bonding between the distal histidine and ligand also exhibited greater strength in the delta form; however, this effect was more pronounced with salen prosthetic groups. Additionally, the NCIs within the active pocket of the protein were found to be variable, highlighting the adaptability of local force constants. In summary, our data underscore the potential of computational methodologies in guiding the rational design of artificial metalloproteins for tailored applications, with local vibrational mode analysis serving as a powerful tool for bond strength assessment. 

Abstract ContextThe efficient extraction of uranyl from spent nuclear fuel wastewater for subsequent reprocessing and reuse is an essential effort toward minimization of long-lived radioactive waste. N-substituted amides and Schiff base ligands are propitious candidates, where extraction occurs via complexation with the uranyl moiety. In this study, we extensively probed chemical bonding in various uranyl complexes, utilizing the local vibrational modes theory alongside QTAIM and NBO analyses. We focused on (i) the assessment of the equatorial O-U and N-U bonding, including the question of chelation, and (ii) how the strength of the axial U$$=$$ $=$O bonds of the uranyl moiety changes upon complexation. Our results reveal that the strength of the equatorial uranium-ligand interactions correlates with their covalent character and with charge donation from O and N lone pairs into the vacant uranium orbitals. We also found an inverse relationship between the covalent character of the equatorial ligand bonds and the strength of the axial uranium-oxygen bond. In summary, our study provides valuable data for a strategic modulation of N-substituted amide and Schiff base ligands towards the maximization of uranyl extraction. MethodQuantum chemistry calculations were performed under the PBE0 level of theory, paired with the relativistic NESCau Hamiltonian, currently implemented in Cologne2020 (interfaced with Gaussian16). Wave functions were expanded in the cc-pwCVTZ-X2C basis set for uranium and Dunning’s cc-pVTZ for the remaining atoms. For the bonding properties, we utilized the package LModeA in the local modes analyses, AIMALL in the QTAIM calculations, and NBO 7.0 for the NBO analyses. Graphical abstract 

ABSTRACT Using the QM/MM methodology and a local mode analysis, we investigated a character and a strength of FeS bonds of heme groups in oxidized and reduced forms of Bacterioferritin fromAzotobacter vinelandii. The strength of the FeS bonds was correlated with a bond length, an energy density at a bond critical point, and a charge difference of the F and S atoms. Changing the oxidation state from ferrous to ferric generally makes the FeS bonds weaker, longer, more covalent, and more polar. We also investigated the SFeS bond bending and found that the stronger FeS bond, generally makes the SFeS bond bending stiffer, which could play a key role in the balance between ferric and ferrous oxidation states and related biological activities. 

Abstract For a series of cytochrome b5 proteins isolated from various species, including bacteria, animals, and humans, we analyzed the intrinsic strength of their distal/proximal FeN bonds and the intrinsic stiffness of their axial NFeN bond angles. To assess intrinsic bond strength and bond angle stiffness, we employed local vibrational stretching force constants k^a(FeN) and bending force constants k^a(NFeN) derived from the local mode theory developed by our group; the ferric and ferrous oxidation states of the heme Fe were considered. All calculations were conducted with the QM/MM methodology. We found that the reduction of the heme Fe from the ferric to the ferrous state makes the FeN axial bonds weaker, longer, less covalent, and less polar. Additionally, the axial NFeN bond angle becomes stiffer and less flexible. Local mode force constants turned out to be far more sensitive to the protein environment than geometries; evaluating force constant trends across diverse protein groups and monitoring changes in the axial heme‐framework revealed redox‐induced changes to the primary coordination sphere of the protein. These results indicate that local mode force constants can serve as useful feature data for training machine learning models that predict cytochrome b5 redox potentials, which currently rely more on geometric data and qualitative descriptors of the protein environment. The insights gained through our investigation also offer valuable guidance for strategically fine‐tuning artificial cytochrome b5 proteins and designing new, versatile variants. 

ABSTRACT The chemical bond is a fundamental concept in chemistry, and various models and descriptors have evolved since the advent of quantum mechanics. This study extends the overlap density and its topological descriptors (OP/TOP) to multiconfigurational wavefunctions. We discuss a comparative analysis of OP/TOP descriptors using CASSCF and DCD‐CAS(2) wavefunctions for a diverse range of molecular systems, including X–O bonds in X–OH (XH, Li, Na, H₂B, H₃C, H₂N, HO, F) and Li–X′ (XF, Cl, and Br). Results show that OP/TOP aligns with bonding models like the quantum theory of atoms in molecules (QTAIM) and local vibrational modes theory, revealing insights such as overlap densities shifting towards the more electronegative atom in polar bonds. The Li–F dissociation profile using OP/TOP descriptors demonstrated sensitivity to ionic/neutral inversion during Li–F dissociation, highlighting their potential for elucidating complex bond phenomena and offering new avenues for understanding multiconfigurational chemical bond dynamics. 

Abstract The Local Vibrational Mode Analysis, initially applied to diverse molecular systems, was extended to periodic systems in 2019. This work introduces an enhanced version of the LModeA software, specifically designed for the comprehensive analysis of two and three‐dimensional periodic structures. Notably, a novel interface with theCrystalpackage was established, enabling a seamless transition from molecules to periodic systems using a unified methodology. Two distinct sets of uranium‐based systems were investigated: (i) the evolution of the Uranyl ion (UO) traced from its molecular configurations to the solid state, exemplified by CsUOCl and (ii) Uranium tetrachloride (UCl) in both its molecular and crystalline forms. The primary focus was on exploring the impact of crystal packing on key properties, including IR and Raman spectra, structural parameters, and an in‐depth assessment of bond strength utilizing local mode perspectives. This work not only demonstrates the adaptability and versatility of LModeA for periodic systems but also highlights its potential for gaining insights into complex materials and aiding in the design of new materials through fine‐tuning. 

Abstract We investigated the intrinsic strength of distal and proximal FeN bonds for both ferric and ferrous oxidation states of bishistidyl hemoproteins from bacteria, animals, human, and plants, including two cytoglobins, ten hemoglobins, two myoglobins, six neuroglobins, and six phytoglobins. As a qualified measure of bond strength, we used local vibrational force constants k(FeN) based on local mode theory developed in our group. All calculations were performed with a hybrid QM/MM ansatz. Starting geometries were taken from available x‐ray structures. k(FeN) values were correlated with FeN bond lengths and covalent bond character. We also investigated the stiffness of the axial NFeN bond angle. Our results highlight that protein effects are sensitively reflected in k(FeN), allowing one to compare trends in diverse protein groups. Moreover, k(NFeN) is a perfect tool to monitor changes in the axial heme framework caused by different protein environments as well as different Fe oxidation states. 

Abstract Atomistic simulation has a broad range of applications from drug design to materials discovery. Machine learning interatomic potentials (MLIPs) have become an efficient alternative to computationally expensive ab initio simulations. For this reason, chemistry and materials science would greatly benefit from a general reactive MLIP, that is, an MLIP that is applicable to a broad range of reactive chemistry without the need for refitting. Here we develop a general reactive MLIP (ANI-1xnr) through automated sampling of condensed-phase reactions. ANI-1xnr is then applied to study five distinct systems: carbon solid-phase nucleation, graphene ring formation from acetylene, biofuel additives, combustion of methane and the spontaneous formation of glycine from early earth small molecules. In all studies, ANI-1xnr closely matches experiment (when available) and/or previous studies using traditional model chemistry methods. As such, ANI-1xnr proves to be a highly general reactive MLIP for C, H, N and O elements in the condensed phase, enabling high-throughput in silico reactive chemistry experimentation. 

AbstractThe characterization of normal mode (CNM) procedure coupled with an adiabatic connection scheme (ACS) between local and normal vibrational modes, both being a part of the Local Vibrational Mode theory developed in our group, can identify spectral changes as structural fingerprints that monitor symmetry alterations, such as those caused by Jahn-Teller (JT) distortions. Employing the PBE0/Def2-TZVP level of theory, we investigated in this proof-of-concept study the hexaaquachromium cation case,$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$/$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$, as a commonly known example for a JT distortion, followed by the more difficult ferrous and ferric hexacyanide anion case,$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$/$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$. We found that in both cases CNM of the characteristic normal vibrational modes reflects delocalization consistent with high symmetry and ACS confirms symmetry breaking, as evidenced by the separation of axial and equatorial group frequencies. As underlined by the Cremer-Kraka criterion for covalent bonding, from$$\mathrm {[Cr{(OH_2)}_6]^{3+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{3+}$to$$\mathrm {[Cr{(OH_2)}_6]^{2+}}$$ ${\left[\mathrm{Cr}{\left({\mathrm{OH}}_2\right)}_6\right]}^{2+}$there is an increase in axial covalency whereas the equatorial bonds shift toward electrostatic character. From$$\mathrm {[Fe{(CN)}_6]^{4-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{4-}$to$$\mathrm {[Fe{(CN)}_6]^{3-}}$$ ${\left[\mathrm{Fe}{\left(\mathrm{CN}\right)}_6\right]}^{3-}$we observed an increase in covalency without altering the bond nature. Distinct$$\pi $$ $\pi$back-donation disparity could be confirmed by comparison with the isolated CN$$^-$$ ${}^{-}$system. In summary, our study positions the CNM/ACS protocol as a robust tool for investigating less-explored JT distortions, paving the way for future applications. Graphical abstractThe adiabatic connection scheme relates local to normal modes, with symmetry breaking giving rise to axial and equatorial group local frequencies 

Abstract The photophysical properties of a series of recently synthesized single benzene fluorophores were investigated using ensemble density functional theory calculations. The energetic stability of the ground and excited state species were counterposed against the aromaticity index derived from local vibrational modes. It was found that the large Stokes shift of the fluorophores (up toca.5800 cm) originates from the effect of electron donating and electron withdrawing substituents rather than ‐delocalization and related (anti‐)aromaticity. On the basis of nonadiabatic molecular dynamics simulations, the absence of fluorescence from one of the regioisomers was explained by the occurrence of easily accessible S/S conical intersections below the vertical excitation energy level. It is demonstrated in the manuscript that the analysis of local mode force constants and the related aromaticity index represent a useful tool for the characterization of ‐delocalization effects in ‐conjugated compounds.