In Situ Measure of Intrinsic Bond Strength in Crystalline Structures: Local Vibrational Mode Theory for Periodic Systems.

The local vibrational mode analysis developed by Konkoli and Cremer has been successfully applied to characterize the intrinsic bond strength via local bond stretching force constants in molecular systems. A wealth of new insights into covalent bonding and weak chemical interactions ranging from hydrogen, halogen, pnicogen, and chalcogen to tetrel bonding has been obtained. In this work we extend the local vibrational mode analysis to periodic systems, i.e. crystals, allowing for the first time a quantitative in situ measure of bond strength in the extended systems of one, two, and three dimensions. We present the study of one-dimensional polyacetylene and hydrogen fluoride chains and two-dimensional layers of graphene, water, and melamine-cyanurate as well as three-dimensional ice I h and crystalline acetone. Besides serving as a new powerful tool for the analysis of bonding in crystals, a systematic comparison of the intrinsic bond strength in periodic systems and that in isolated molecules becomes possible, providing new details into structure and bonding changes upon crystallization. The potential application for the analysis of solid-state vibrational spectra will be discussed.

From strong to weak NF bonds: on the design of a new class of fluorinating agents.

A set of 50 molecules with NF bonds was investigated to determine the factors that influence the strength of a NF bond, with the aim of designing a new class of fluorinating agents. The intrinsic bond strength of the NF bonds was used as bond strength measure, derived from local stretching NF force constants obtained at the CCSD(T)/aug-cc-pVTZ and ωB97XD/aug-cc-pVTZ levels of theory. The investigation showed that the NF bond is a tunable covalent bond, with bond strength orders ranging from 2.5 (very strong) to 0.1 (very weak). NF bond strengthening is caused by a combination of different factors and can be achieved by e.g. ionization. Whereas, the NF bond weakening can be achieved by hypervalency on the N atom, using a N→Ch (Ch: O, S, Se) donor-acceptor type bond with different electron-withdrawing groups. These new insights into the nature of the NF bond were used to propose and design a new class of fluorinating agents. Hypervalent amine-chalcogenides turned out as most promising candidates for efficient electrophilic fluorinating agents.

Recovering Intrinsic Fragmental Vibrations Using the Generalized Subsystem Vibrational Analysis.

Normal vibrational modes are generally delocalized over the molecular system, which makes it difficult to assign certain vibrations to specific fragments or functional groups. We introduce a new approach, the Generalized Subsystem Vibrational Analysis (GSVA), to extract the intrinsic fragmental vibrations of any fragment/subsystem from the whole system via the evaluation of the corresponding effective Hessian matrix. The retention of the curvature information with regard to the potential energy surface for the effective Hessian matrix endows our approach with a concrete physical basis and enables the normal vibrational modes of different molecular systems to be legitimately comparable. Furthermore, the intrinsic fragmental vibrations act as a new link between the Konkoli-Cremer local vibrational modes and the normal vibrational modes.

Correlating the vibrational spectra of structurally related molecules: A spectroscopic measure of similarity.

Using catastrophe theory and the concept of a mutation path, an algorithm is developed that leads to the direct correlation of the normal vibrational modes of two structurally related molecules. The mutation path is defined by weighted incremental changes in mass and geometry of the molecules in question, which are successively applied to mutate a molecule into a structurally related molecule and thus continuously converting their normal vibrational spectra from one into the other. Correlation diagrams are generated that accurately relate the normal vibrational modes to each other by utilizing mode-mode overlap criteria and resolving allowed and avoided crossings of vibrational eigenstates. The limitations of normal mode correlation, however, foster the correlation of local vibrational modes, which offer a novel vibrational measure of similarity. It will be shown how this will open new avenues for chemical studies. © 2017 Wiley Periodicals, Inc.

Characterizing Chemical Similarity with Vibrational Spectroscopy: New Insights into the Substituent Effects in Monosubstituted Benzenes.

A novel approach is presented to assess chemical similarity based the local vibrational mode analysis developed by Konkoli and Cremer. The local mode frequency shifts are introduced as similarity descriptors that are sensitive to any electronic structure change. In this work, 59 different monosubstituted benzenes are compared. For a subset of 43 compounds, for which experimental data was available, the ortho-/para- and meta-directing effect in electrophilic aromatic substitution reactions could be correctly reproduced, proving the robustness of the new similarity index. For the remaining 16 compounds, the directing effect was predicted. The new approach is broadly applicable to all compounds for which either experimental or calculated vibrational frequency information is available.

The Many Facets of Chalcogen Bonding: Described by Vibrational Spectroscopy.

A diverse set of 100 chalcogen-bonded complexes comprising neutral, cationic, anionic, divalent, and double bonded chalcogens has been investigated using ωB97X-D/aug-cc-pVTZ to determine geometries, binding energies, electron and energy density distributions, difference density distributions, vibrational frequencies, local stretching force constants, and associated bond strength orders. The accuracy of ωB97X-D was accessed by CCSD(T)/aug-cc-pVTZ calculations of a subset of 12 complexes and by the CCSD(T)/aug-cc-pVTZ //ωB97X-D binding energies of 95 complexes. Most of the weak chalcogen bonds can be rationalized on the basis of electrostatic contributions, but as the bond becomes stronger, covalent contributions can assume a primary role in the strength and geometry of the complexes. Covalency in chalcogen bonds involves the charge transfer from a lone pair orbital of a Lewis base into the σ* orbital of a divalent chalcogen or a π* orbital of a double bonded chalcogen. We describe for the first time a symmetric chalcogen-bonded homodimer stabilized by a charge transfer from a lone pair orbital into a π* orbital. New polymeric materials based on chalcogen bonds should take advantage of the extra stabilization granted by multiple chalcogen bonds, as is shown for 1,2,5-telluradiazole dimers.

Calculations of atomic magnetic nuclear shielding constants based on the two-component normalized elimination of the small component method.

A new method for calculating nuclear magnetic resonance shielding constants of relativistic atoms based on the two-component (2c), spin-orbit coupling including Dirac-exact NESC (Normalized Elimination of the Small Component) approach is developed where each term of the diamagnetic and paramagnetic contribution to the isotropic shielding constant σiso is expressed in terms of analytical energy derivatives with regard to the magnetic field B and the nuclear magnetic moment 𝝁. The picture change caused by renormalization of the wave function is correctly described. 2c-NESC/HF (Hartree-Fock) results for the σiso values of 13 atoms with a closed shell ground state reveal a deviation from 4c-DHF (Dirac-HF) values by 0.01%-0.76%. Since the 2-electron part is effectively calculated using a modified screened nuclear shielding approach, the calculation is efficient and based on a series of matrix manipulations scaling with (2M)3 (M: number of basis functions).

The Peculiar Role of the Au3 Unit in Aum Clusters: σ-Aromaticity of the Au5Zn+ Ion.

The stability of small Aum (m = 4-7) clusters is investigated by analyzing their energetic, geometric, vibrational, magnetic, and electron density properties. Gold clusters can be constructed from stable cyclic 3-center-2-electron (3c-2e) Au3+ units (3-rings) with σ-aromaticity. The stabilization requires a flow of negative charge from internal 3-rings with electron-deficient bonding to peripheral 3-ring units with stronger Au-Au bonds. The valence-isoelectronic clusters Au6 and Au5Zn+ have similar electronic properties: Au5Zn+ is a strongly σ-aromatic molecule. An understanding of the structure of Aum clusters is obtained by deriving a Clar's Rule equivalent for polycyclic gold clusters: The structure with the larger number of rings with dominant 3c-2e character and a smaller degree of 3c-3e character occupies the global minimum of the Aum potential energy surface.

Generalization of the Tolman electronic parameter: the metal-ligand electronic parameter and the intrinsic strength of the metal-ligand bond.

The catalytic activity of transition metal complexes (R)nM-L can be predicted utilizing the metal-ligand electronic parameter (MLEP) that is based on the local stretching force constant of the M-L bond. Vibrational spectroscopy is an excellent tool to accurately determine vibrational mode properties such as stretching frequencies. These correspond, because of mode-mode coupling, to delocalized vibrational modes, which have to be first converted into local vibrational modes, and their properties. Each bond of a molecule can be uniquely characterized by the local stretching force constant and frequency. The former is ideally suited to set up a scale of bond strength orders, which identifies weak M-L bonds with promising catalytic activity. It is shown how the MLEP replaces the TEP (Tolman Electronic Parameter), which is based on the CO stretching frequencies of a (CO)nM-L complex and which is now exclusively used in hundreds of investigations. However, the TEP is at best a qualitative parameter that suffers from relatively large mode-mode coupling errors and the basic deficiency of most indirect descriptors: They cannot correctly describe the intrinsic M-L bond strength via the CO stretching frequencies.

Different Ways of Hydrogen Bonding in Water - Why Does Warm Water Freeze Faster than Cold Water?

The properties of liquid water are intimately related to the H-bond network among the individual water molecules. Utilizing vibrational spectroscopy and modeling water with DFT-optimized water clusters (6-mers and 50-mers), 16 out of a possible 36 different types of H-bonds are identified and ordered according to their intrinsic strength. The strongest H-bonds are obtained as a result of a concerted push-pull effect of four peripheral water molecules, which polarize the electron density in a way that supports charge transfer and partial covalent character of the targeted H-bond. For water molecules with tetra- and pentacoordinated O atoms, H-bonding is often associated with a geometrically unfavorable positioning of the acceptor lone pair and donor σ*(OH) orbitals so that electrostatic rather than covalent interactions increasingly dominate H-bonding. There is a striking linear dependence between the intrinsic strength of H-bonding as measured by the local H-bond stretching force constant and the delocalization energy associated with charge transfer. Molecular dynamics simulations for 1000-mers reveal that with increasing temperature weak, preferentially electrostatic H-bonds are broken, whereas the number of strong H-bonds increases. An explanation for the question why warm water freezes faster than cold water is given on a molecular basis.

Quantitative Assessment of Halogen Bonding Utilizing Vibrational Spectroscopy.

A total of 202 halogen-bonded complexes have been studied using a dual-level approach: ωB97XD/aug-cc-pVTZ was used to determine geometries, natural bond order charges, charge transfer, dipole moments, electron and energy density distributions, vibrational frequencies, local stretching force constants, and relative bond strength orders n. The accuracy of these calculations was checked for a subset of complexes at the CCSD(T)/aug-cc-pVTZ level of theory. Apart from this, all binding energies were verified at the CCSD(T) level. A total of 10 different electronic effects have been identified that contribute to halogen bonding and explain the variation in its intrinsic strength. Strong halogen bonds are found for systems with three-center-four-electron (3c-4e) bonding such as chlorine donors in interaction with substituted phosphines. If halogen bonding is supported by hydrogen bonding, genuine 3c-4e bonding can be realized. Perfluorinated diiodobenzenes form relatively strong halogen bonds with alkylamines as they gain stability due to increased electrostatic interactions.

The intrinsic strength of the halogen bond: electrostatic and covalent contributions described by coupled cluster theory.

36 halogen-bonded complexes YXARm (X: F, Cl, Br; Y: donor group; ARm acceptor group) have been investigated at the CCSD(T)/aug-cc-pVTZ level of theory. Binding energies, geometries, NBO charges, charge transfer, dipole moments, electrostatic potential, electron and energy density distributions, difference density distributions, vibrational frequencies, local stretching and bending force constants, and relative bond strength orders n have been calculated and used to order the halogen bonds according to their intrinsic strength. Halogen bonding is found to arise from electrostatic and strong covalent contributions. It can be strengthened by H-bonding or lone pair delocalization. The covalent character of a halogen bond increases in the way 3c-4e (three-center-four-electron) bonding becomes possible. One can characterize halogen bonds by their percentage of 3c-4e bonding. FCl-phosphine complexes can form relatively strong halogen bonds provided electronegative substituents increase the covalent contributions in form of 3c-4e halogen bonding. Binding energies between 1 and 45 kcal mol-1 are calculated, which reflects the large variety in halogen bonding.

Calculations of electric dipole moments and static dipole polarizabilities based on the two-component normalized elimination of the small component method.

The analytical energy gradient and Hessian of the two-component Normalized Elimination of the Small Component (2c-NESC) method with regard to the components of the electric field are derived and used to calculate spin-orbit coupling (SOC) corrected dipole moments and dipole polarizabilities of molecules, which contain elements with high atomic number. Calculated 2c-NESC dipole moments and isotropic polarizabilities agree well with the corresponding four-component-Dirac Hartree-Fock or density functional theory values. SOC corrections for the electrical properties are in general small, but become relevant for the accurate prediction of these properties when the molecules in question contain sixth and/or seventh period elements (e.g., the SO effect for At2 is about 10% of the 2c-NESC polarizability). The 2c-NESC changes in the electric molecular properties are rationalized in terms of spin-orbit splitting and SOC-induced mixing of frontier orbitals with the same j = l + s quantum numbers.

A Reaction Valley Investigation of the Cycloaddition of 1,3-Dipoles with the Dipolarophiles Ethene and Acetylene: Solution of a Mechanistic Puzzle.

The reaction mechanism of the cycloaddition of 10 1,3-dipoles with the two dipolarphiles ethene and acetylene is investigated and compared using the Unified Reaction Valley Approach in a new form, which is based on a dual-level strategy, an accurate description of the reaction valley far out into the van der Waals region, and a comparative analysis of the electronic properties of the reaction complex. A detailed one-to-one comparison of 20 different 1,3-dipolar cycloadditions is performed, and unknown mechanistic features are revealed. There are significant differences in the reaction mechanisms for the two dipolarophiles that result from the van der Waals complex formation in the entrance channel of the cycloadditions. Hydrogen bonding between the 1,3-dipoles and acetylene is generally stronger, which leads to higher reaction barriers in the acetylene case, but which also facilitates to overcome the problem of a reduced charge transfer from 1,3-dipole to acetylene. Mechanistic differences are found in the prechemical and chemical reaction regions with regard to reactant orientation, preparation for the reaction, charge transfer, charge polarization, rehybridization, and bond formation. It is shown that similarities in the reaction barriers as determined by CCSD(T)-F12/aug-cc-pVTZ calculations result from a fortuitous cancellation of different electronic effects. In general, a caveat must be made with regard to oversimplified descriptions of the reaction mechanism based on orbital theory or energy decomposition schemes.

Quantitative Assessment of Aromaticity and Antiaromaticity Utilizing Vibrational Spectroscopy.

Vibrational frequencies can be measured and calculated with high precision. Therefore, they are excellent tools for analyzing the electronic structure of a molecule. In this connection, the properties of the local vibrational modes of a molecule are best suited. A new procedure is described, which utilizes local CC stretching force constants to derive an aromaticity index (AI) that quantitatively determines the degree of π-delocalization in a cyclic conjugated system. Using Kekulé benzene as a suitable reference, the AIs of 30 mono- and polycyclic conjugated hydrocarbons are calculated. The AI turns out to describe π-delocalization in a balanced way by correctly describing local aromatic units, peripheral, and all-bond delocalization. When comparing the AI with the harmonic oscillator model of AI, the latter is found to exaggerate the antiaromaticity of true and potential 4n π-systems or to wrongly describe local aromaticity. This is a result of a failure of the Badger relationship (the shorter bond is always the stronger bond), which is only a rule and therefore cannot be expected to lead to an accurate description of the bond strength via the bond length. The AI confirms Clar's rule of disjoint benzene units in many cases, but corrects it in those cases where peripheral π-delocalization leads to higher stability. [5]-, [6]-, [7]-Circulene and Kekulene are found to be aromatic systems with varying degree of delocalization. Properties of the local vibrational modes provide an accurate description of π-delocalization and an accurate AI.

Rational Design in Catalysis: A Mechanistic Study of ß-Hydride Eliminations in Gold(I) and Gold(III) Complexes Based on Features of the Reaction Valley.

ß-Hydride eliminations for ethylgold(III) dichloride complexes are identified as reactions with an unusually long prechemical stage corresponding to the conformational preparation of the reaction complex and spanning six phases. The prechemical process is characterized by a geared rotation of the L-Au-L group (L = Cl) driving methyl group rotation and causing a repositioning of the ligands. This requires more than 28 kcal/mol of the total barrier of 34.0 kcal/mol, according to the unified reaction valley approach, which also determines that the energy requirements of the actual chemical process leading to the ß-elimination product are only about 5.5 kcal/mol. A detailed mechanistic analysis was used as a basis for a rational design of substrates (via substituents on the ethyl group) and/or ligands, which can significantly reduce the reaction barrier. This strategy takes advantage of either a higher trans activity of the ligands or a tuned electronic demand of the ethyl group. The ß-hydride elimination of gold(I) was found to suffer from strong Coulomb and exchange repulsion when a positively charged hydrogen atom enforces a coordination position in a d(10)-configured gold atom, thus triggering an unassisted σ-π Au(I)-C conversion.

B-H···π Interaction: A New Type of Nonclassical Hydrogen Bonding.

For the first time, nonclassical hydrogen (H)-bonding involving a B-H···π interaction is described utilizing both quantum chemical predictions and experimental realization. In the gas phase, a B-H···π H-bond is observed in either B2H6···benzene (ΔE = -5.07 kcal/mol) or carborane···benzene (ΔE = -3.94 kcal/mol) complex at reduced temperatures. Ir-dimercapto-carborane complexes [Cp*Ir(S2C2B10H10)] are designed to react with phosphines PR3 (R = C6H4X, X = H, F, OMe) to give [Cp*Ir(PR3)S2C2B10H10] for an investigation of B-H···π interactions at ambient temperatures. X-ray diffraction studies reveal that the interaction between the carborane BH bonds and the phosphine aryl substituents involves a BH···π H-bond (H···π distance: 2.40-2.76 Å). (1)H NMR experiments reveal that B-H···π interactions exist in solution according to measured (1)H{(11)B} signals at ambient temperatures in the range 0.0 ≤ δ ≤ 0.3 ppm. These are high-field shifted by more than 1.5 ppm relative to the (1)H{(11)B} signals obtained for the PMe3 analog without B-H···π bonding. Quantum chemical calculations suggest that the interaction is electrostatic and the local (B)H···ring stretching force constant is as large as the H-bond stretching force constant in the water dimer.

Direct Measure of Metal-Ligand Bonding Replacing the Tolman Electronic Parameter.

The Tolman electronic parameter (TEP) derived from the A1-symmetrical CO stretching frequency of nickel-tricarbonyl complexes L-Ni(CO)3 with varying ligands L is misleading as (i) it is not based on a mode decoupled CO stretching frequency and (ii) a generally applicable and quantitatively correct or at least qualitatively reasonable relationship between the TEP and the metal-ligand bond strength does not exist. This is shown for a set of 181 nickel-tricarbonyl complexes using both experimental and calculated TEP values. Even the use of mode-mode decoupled CO stretching frequencies (L(ocal)TEPs) does not lead to a reliable description of the metal-ligand bond strength. This is obtained by introducing a new electronic parameter that is directly based on the metal-ligand local stretching force constant. For the test set of 181 nickel complexes, a direct metal-ligand electronic parameter (MLEP) in the form of a bond strength order is derived, which reveals that phosphines and related ligands (amines, arsines, stibines, bismuthines) are bonded to Ni both by σ-donation and π-back-donation. The strongest Ni-L bonds are identified for carbenes and cationic ligands. The new MLEP quantitatively assesses electronic and steric factors.

Extraordinary Mechanism of the Diels-Alder Reaction: Investigation of Stereochemistry, Charge Transfer, Charge Polarization, and Biradicaloid Formation.

The Diels-Alder reaction between 1,3-butadiene and ethene is investigated from far-out in the entrance channel to the very last step in the exit channel thus passing two bifurcation points and extending the range of the reaction valley studied with URVA (Unified Reaction Valley Approach) by 300% compared to previous studies. For the first time, the pre- and postchemical steps of the reaction are analyzed at the same level of theory as the actual chemical processes utilizing the path curvature and its decomposition into internal coordinate or curvilinear coordinate components. A first smaller charge transfer to the dienophile facilitates the rotation of gauche butadiene into its cis form. The actual chemical processes are initiated by a second larger charge transfer to the dienophile that facilitates pyramidalization of the reacting carbon centers, bond equalization, and biradicaloid formation of the reactants. The transition state is aromatically stabilized and moved by five path units into the entrance channel in line with the Hammond-Leffler postulate. The pseudorotation of the boat form into the halfchair of cyclohexene is analyzed. Predictions are made for the Diels-Alder reaction based on a 11-phase mechanism obtained by the URVA analysis.