Local vibrational force constants – From the assessment of empirical force constants to the description of bonding in large systems

Deciphering the direct heterometallic interaction in κ3-bis(donor)ferrocenyl-transition-metal complexes

Ligands featuring a 1,1'-bis(donor)ferrocene motif can adopt various binding modes. Among them, the κ3 binding mode, which involves interaction between the iron center of the ferrocene unit and the transition metal is the most unique. Although various examples highlight the interaction itself, the exact quantification of its strength remains uncertain. In our computational study, we systematically investigate the nature of this unique heterometallic bond, demonstrating that the electron density at the transition metal primarily governs the heterobimetallic interaction. On the other hand, the contribution of the ipso-carbon atoms of the cyclopentadiene ring is not negligible. We demonstrated that isodesmic reactions provide the most quantifiable data regarding the interaction. If the transition metal center is complexed with good electron-donor ligands or its positive charge is compensated by the negative charge of the ligands, the interaction with the electron-rich iron center recedes into the background. Finally, we highlighted the importance of the accurate computational description of these systems.

Cleavage of an Aromatic C-C Bond in Ferrocene by Insertion of an Iridium Nitrido Nitrogen Atom

The intermolecular cleavage of C-C bonds is a rare event. Herein, we report on a late transition-metal terminal nitrido complex, which upon oxidation undergoes insertion of the nitrido nitrogen atom into the aromatic C-C bond of ferrocene. This reaction path was confirmed through ¹⁵N and deuterium isotope labeling experiments of the nitrido complex and ferrocenium, respectively. Cyclic voltammetry and UV/vis spectroscopy monitoring of the reaction revealed that oxidation is the initial step, yielding the tentative radical cationic nitrido complex, which is experimentally supported by extended X and Q-band electron paramagnetic resonance (EPR) and ENDOR, UV/vis, vT ¹H NMR, and vibrational spectroscopic data. Density functional theory (DFT) and multireference calculations of this highly reactive intermediate revealed an S = 1/2 ground state. The high reactivity can be traced to the increased electrophilicity in the oxidized complex. Based on high-level PNO-UCCSD(T) calculations and UV/vis kinetic measurements, it is proposed that the reaction proceeds by initial electrophilic exo attack of the nitrido nitrogen atom at the cyclopentadienyl ring and consecutive ring expansion to a pyridine ring.

Selectivity Rule of Cryptands for Anions: Molecular Rigidity and Bonding Site

Cryptands utilize inside CH or NH groups as hydrogen bond (H-bond) donors to capture anions such as halides. In this work, the nature and selectivity of confined hydrogen bonds inside cryptands were computationally analyzed with the energy decomposition scheme based on the block-localized wavefunction method (BLW-ED), aiming at an elucidation of governing factors in the binding between cryptands and anions. It was revealed that the intrinsic strengths of inward hydrogen bonds are dominated by the electrostatic attraction, while the anion preferences (selectivity) of inner CH and NH hydrogen bonds are governed by the Pauli exchange repulsion and electrostatic interaction, respectively. Typical conformers of cages are classified into two groups, including the C_3(h) -symmetrical conformers, in which all halide anions are located near the centroids of cages, and the "semi-open" conformers, which exhibit shifted bonding sites for different halide anions. Accordingly, the difference in governing factors of selectivity is attributed to either the rigidity of cages or the binding site of anions for these two groups. In details, the C₃ conformers of NH cryptands can be enlarged more remarkably than the C_3(h) -symmetrical conformers of CH cryptands as the size of anion (ionic radius) increases, resulting in the relaxation of the Pauli repulsion and a dramatic reduction in electrostatic attraction, which eventually rules the selectivity of NH cryptands for halide anions. By contrary, the CH cryptands are more rigid and cannot effectively reduce the Pauli repulsion, which subsequently governs the anion preference. Unlike C₃ conformers whose rigidity determines the selectivity, semi-open conformers exhibit different binding sites for different anions. From F^- to I^- , the bonding site shifts toward the outside end of the pocket inside the semi-open NH cryptand, leading to the significant reduction of the electrostatic interaction that dominates the anion preference. Differently, binding sites are much less affected by the size of anion inside the semi-open CH cryptand, in which the Pauli exchange repulsion remains the key factor for the selectivity of inner hydrogen bonds.

Pas de Deux of an NO Couple: Synchronous Photoswitching from a Double-Linear to a Double-Bent Ru(NO)2 Core under Nitrosyl Charge Conservation

The {Ru(NO)₂ }¹⁰ dinitrosylruthenium complex [Ru(NO)₂ (PPh₃ )₂ ] (1) shows photo-induced linkage isomerism (PLI) of a special kind: the two NO ligands switch, on photo-excitation, synchronously from the ground state (GS) with two almost linear RuNO functions to a metastable state (MS) which persists up to 230 K and can be populated to ≈50 %. The MS was experimentally characterised by photo-crystallography, IR spectroscopy and DS-calorimetry as a double-bent variant of the double-linear GS. The experimental results are confirmed by computation which unravels the GS/MS transition as a disrotatory synchronous 50° turn of the two nitrosyl ligands. Although 1 shows the usual redshift of the N-O stretch on bending the MNO unit, there is no increased charge transfer from Ru to NO along the GS-to-MS path. In terms of the effective-oxidation-state (EOS) method, both isomers of 1 and the transition state are Ru^-II (NO⁺ )₂ species.

Synthesis and reactivity of dinuclear copper(I) pyridine diimine complexes

The reaction of a tethered pyridine diimine (PDI) ligand with copper(I) chloride yielded a μ-chlorido bridged cationic dicopper(I) PDI complex, which is a rare structural motif. The geometric constraint of the ligand is fostering attractive van der Waals interactions between the coplanar pyridine units. This is supported by an Atoms in Molecules (AIM) and NCI (non-covalent interaction) analysis. Reaction with carbon monoxide yields the corresponding mono- and dicarbonyl complexes, which display reversible binding of carbon monoxide. This equilibrium was studied by ¹³C-NMR exchange spectroscopy and complemented by DFT and LNO-CCSD(T) calculations.

Mechanistic Details of the Sharpless Epoxidation of Allylic Alcohols—A Combined URVA and Local Mode Study

In this work, we investigated the catalytic effects of a Sharpless dimeric titanium (IV)–tartrate–diester catalyst on the epoxidation of allylalcohol with methyl–hydroperoxide considering four different orientations of the reacting species coordinated at the titanium atom (reactions R1–R4) as well as a model for the non-catalyzed reaction (reaction R0). As major analysis tools, we applied the URVA (Unified Reaction Valley Approach) and LMA (Local Mode Analysis), both being based on vibrational spectroscopy and complemented by a QTAIM analysis of the electron density calculated at the DFT level of theory. The energetics of each reaction were recalculated at the DLPNO-CCSD(T) level of theory. The URVA curvature profiles identified the important chemical events of all five reactions as peroxide OO bond cleavage taking place before the TS (i.e., accounting for the energy barrier) and epoxide CO bond formation together with rehybridization of the carbon atoms of the targeted CC double bond after the TS. The energy decomposition into reaction phase contribution phases showed that the major effect of the catalyst is the weakening of the OO bond to be broken and replacement of OH bond breakage in the non-catalyzed reaction by an energetically more favorable TiO bond breakage. LMA performed at all stationary points rounded up the investigation (i) quantifying OO bond weakening of the oxidizing peroxide upon coordination at the metal atom, (ii) showing that a more synchronous formation of the new CO epoxide bonds correlates with smaller bond strength differences between these bonds, and (iii) elucidating the different roles of the three TiO bonds formed between catalyst and reactants and their interplay as orchestrated by the Sharpless catalyst. We hope that this article will inspire the computational community to use URVA complemented with LMA in the future as an efficient mechanistic tool for the optimization and fine-tuning of current Sharpless catalysts and for the design new of catalysts for epoxidation reactions.

LModeA-nano: A PyMOL Plugin for Calculating Bond Strength in Solids, Surfaces, and Molecules via Local Vibrational Mode Analysis

The analysis of chemical bonding in crystal structures and surfaces is an important research topic in theoretical chemistry. In this work, we present a PyMOL plugin, named LModeA-nano, as implementation of the local vibrational mode theory for periodic systems (Tao et al. J. Chem. Theory Comput. 2019, 15, 1761) assessing bond strength in terms of local stretching force constants in extended systems of one, two, and three dimensions. LModeA-nano can also analyze chemical bonds in isolated molecular systems thus enabling a head-to-head comparison of bond strength across systems with different dimensions in periodicity (0-3D). The new code is interfaced to the output generated by various solid-state modeling packages including VASP, CP2K, Quantum ESPRESSO, CASTEP, and CRYSTAL. LModeA-nano is cross-platform, open-source and freely available on GitHub: https://github.com/smutao/LModeA-nano.

Forces from Stochastic Density Functional Theory under Nonorthogonal Atom-Centered Basis Sets

We develop a formalism for calculating forces on the nuclei within the linear-scaling stochastic density functional theory (sDFT) in a nonorthogonal atom-centered basis set representation (Fabian et al. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 2019, 9, e1412, 10.1002/wcms.1412) and apply it to the Tryptophan Zipper 2 (Trp-zip2) peptide solvated in water. We use an embedded-fragment approach to reduce the statistical errors (fluctuation and systematic bias), where the entire peptide is the main fragment and the remaining 425 water molecules are grouped into small fragments. We analyze the magnitude of the statistical errors in the forces and find that the systematic bias is of the order of 0.065 eV/Å (∼1.2 × 10-3Eh/a0) when 120 stochastic orbitals are used, independently of system size. This magnitude of bias is sufficiently small to ensure that the bond lengths estimated by stochastic DFT (within a Langevin molecular dynamics simulation) will deviate by less than 1% from those predicted by a deterministic calculation.

The "silent CO": a new technique for calculating transition metal carbonyl force fields

The notion of a "silent CO group" (effectively an infinitely heavy CO group) is introduced to enable energy-factored force fields to be estimated accurately for molecules where there are fewer ν(CO) frequencies than force constants in the force field (viz. underdetermined force fields). The symmetry classes of molecules covered are the C_s tricarbonyls (e.g. Fe(CO)₃(diene) and fac-Re(CO)₃(L-L)X), C_2v tricarbonyls (e.g. mer-M(CO)₃(L)₃ M = Cr, Mo, W), C_3v tetracarbonyls (e.g. Fe(CO)₄(L)), C_2v tetracarbonyls (e.g. cis-M(CO)₄(L)₂ and Fe(CO)₄(L)) and C_4v pentacarbonyls (e.g. M(CO)₅(L) M = Cr, Mo, W and M(CO)₅(X) M = Mn, Re). It is a relatively simple matter to extend the method to types of molecules not directly considered in this paper.

Capturing Individual Hydrogen Bond Strengths in Ices via Periodic Local Vibrational Mode Theory: Beyond the Lattice Energy Picture

Local stretching force constants derived from periodic local vibrational modes at the vdW-DF2 density functional level have been employed to quantify the intrinsic hydrogen bond strength of 16 ice polymorphs, ices Ih, II, III, IV, V, VI, VII, VIII, IX, XI, XII, XIII, XIV, XV, XVII, and XIX, that are stable under ambient to elevated pressures. Based on this characterization on 1820 hydrogen bonds, relationships between local stretching force constants and structural parameters such as hydrogen bond length and angle were identified. Moreover, different bond strength distributions, from uniform to inhomogeneous, were observed for the 16 ices and could be explained in relation to different local structural elements within ices, that is, rings, that consist of different hydrogen bond types. In addition, criteria for the classification of hydrogen bonds as strong, intermediate, and weak were introduced. The latter was used to explore a different dimension of the water-ice phase diagram. These findings will provide important guidelines for assessing the credibility of new ice structures.

The effect of hydrogen-bonding on flavin's infrared absorption spectrum

Cluster and continuum solvation computational models are employed to model the effect of hydrogen bonding interactions on the vibrational modes of lumiflavin. Calculated spectra were compared to experimental Fourier-transform infrared (FTIR) spectra in the diagnostic 1450-1800 cm^-1 range, where intense ν_C=C, ν_C=N, [Formula: see text] , and [Formula: see text] stretching modes of flavin's isoalloxazine ring are found. Local mode analysis is used to describe the strength of hydrogen-bonding in cluster models. The computations indicate that ν_C=C and ν_C=N mode frequencies are relatively insensitive to intermolecular interactions while the [Formula: see text] and [Formula: see text] modes are sensitive to direct (and also indirect for [Formula: see text] ) hydrogen-bonding interactions. Although flavin is neutral, basis sets without the diffuse functions provide incorrect relative frequencies and intensities. The 6-31+G* basis set is found to be adequate for this system, and there is limited benefit to considering larger basis sets. Calculated vibrational mode frequencies agree with experimentally determined frequencies in solution when cluster models with multiple water molecules are used. Accurate simulation of relative FTIR band intensities, on the other hand, requires a continuum (or possibly quantum mechanical/molecular mechanical) model that accounts for long-range electrostatic effects. Finally, an experimental peak at ca. 1624 cm^-1 that is typically assigned to the [Formula: see text] vibrational stretching mode has a complicated shape that suggests multiple underlying contributions. Our calculations show that this band has contributions from both the C₆-C₇ and C₂ = O stretching vibrations.

Theoretical Insights into [NHC]Au(I) Catalyzed Hydroalkoxylation of Allenes: A Unified Reaction Valley Approach Study

Hydroxylation is an effective approach for the synthesis of carbon-oxygen bonds and allylic ethers. The [NHC]Au(I) catalyzed intermolecular hydroalkoxylation of allene was studied at the DFT and Coupled Cluster level of theory. Using the Unified Reaction Valley Approach (URVA), we carry out a comprehensive mechanistic analysis of [NHC]Au(I)-catalyzed and noncatalyzed reactions. The URVA study of several possible reaction pathways reveal that the [NHC]Au(I) catalyst enables the hydroalkoxylation reaction to occur via a two step mechanism based upon the Au ability to switch between π- and σ-complexation. The first step of the mechanism involves the formation of a CO bond after the transition state with no energy penalty. Following the CO bond breakage, the OH bond breaks and CH bond forms during the second step of the mechanism, as the catalyst transforms into the more stable π-Au complex. The URVA results were complemented with local vibrational mode analysis to provide measures of intrinsic bond strength for Au(I)-allene interactions of all stationary points, and NBO analysis was applied in order to observe charge transfer events along the reaction pathway. Overall, the π-Au C═C interactions of the products are stronger than those of the reactants adding to their exothermicity. Our work on the hydroxylation of allene provides new insights for the design of effective reaction pathways to produce allylic ethers and also unravels new strategies to form C-O bonds by activation of C═C bonds.

Modeling Hydrogen Release from Water with Borane and Alane Catalysts: A Unified Reaction Valley Approach

The unified reaction valley approach combined with the local vibrational mode and ring puckering analysis is applied to investigate the hydrogen evolution from water in the presence of small hydrides such as BH₃, metal hydrides as AlH₃, and their derivatives. We studied a series of reactions involving BH₃, AlH₃, B₂H₆, Al₂H₆, and AlH₃BH₃ with one- and two-water molecules, considering multiple reaction paths. In addition, the influence of the aqueous medium was examined. A general reaction mechanism was identified for most of the reactions. Those that deviate could be associated with unusually high reaction barriers with no hydrogen release. The charge transfer along the reaction path suggests that a viable hydrogen release is achieved when the catalyst adopts the role of a charge donor during the chemical processes. The puckering analysis showed that twistboat and boat forms are the predominant configurations in the case of an intermediate six-membered ring formation, which influences the activation barrier. The local mode analysis was used as a tool to detect the H-H bond formation as well as to probe catalyst regenerability. Based on the correlation between the activation energy and the change in the charge separation for cleaving O-H and B(Al)-H bonds, two promising subsets of reactions could be identified along with prescriptions for lowering the reaction barrier individually with electron-donating/withdrawing substituents.