A Story of Three Levels of Sophistication in SCF/KS-DFT Orbital Optimization Procedures.

In this work, three versions of self-consistent field/Kohn-Sham density functional theory (SCF/KS-DFT) orbital optimization are described and benchmarked. The methods are a modified version of the geometry version of the direct inversion in the iterative subspace approach (which we call r-GDIIS), the modified restricted step rational function optimization method (RS-RFO), and the novel subspace gradient-enhanced Kriging method combined with restricted variance optimization (S-GEK/RVO). The modifications introduced are aimed at improving the robustness and computational scaling of the procedures. In particular, the subspace approach in S-GEK/RVO allows the application to SCF/KS-DFT optimization of a machine learning technique that has proven to be successful in geometry optimizations. The performance of the three methods is benchmarked for a large number of small- to medium-sized organic molecules, at equilibrium structures and close to a transition state, and a second set of molecules containing closed- and open-shell transition metals. The results indicate the importance of the resetting technique in boosting the performance of the r-GDIIS procedure. Moreover, it is demonstrated that already at the inception of the subspace version of GEK to optimize SCF wave functions, it displays superior and robust convergence properties as compared to those of the standard state-of-the-art SCF/KS-DFT optimization methods.

Simulation Reveals the Chameleonic Behavior of Macrocycles.

Conformational analysis is central to the design of bioactive molecules. It is particularly challenging for macrocycles due to noncovalent transannular interactions, steric interactions, and ring strain that are often coupled. Herein, we simulated the conformations of five macrocycles designed to express a progression of increasing complexity in environment-dependent intramolecular interactions and verified the results against NMR measurements in chloroform and dimethyl sulfoxide. Molecular dynamics using an explicit solvent model, but not the Monte Carlo method with implicit solvation, handled both solvents correctly. Refinement of conformations at the ab initio level was fundamental to reproducing the experimental observations─standard state-of-the-art molecular mechanics force fields were insufficient. Our simulations correctly predicted the intramolecular interactions between side chains and the macrocycle and revealed an unprecedented solvent-induced conformational switch of the macrocyclic ring. Our results provide a platform for the rational, prospective design of molecular chameleons that adapt to the properties of the environment.

Water on ceria{111}: Comparison between 23 experimental vibrational studies in the literature and new modeling.

Theoretical and experimental vibrational signatures of H2O and OH- (dissociated water) adsorbed on stoichiometric ceria{111} surfaces are compared. The experimental ones were collected from low-coverage experiments in the literature, and the theoretical anharmonic frequencies were generated using density functional theory calculations employing the optPBE-vdW functional for coverages from 0.5 to a few monolayers. It is found that (i) the experiments and our calculations overall agree well, lending credibility to both; (ii) the calculations manage to resolve the large class of H-bonded motifs into frequency classes that can guide experimental assignments; (iii) it is possible to find a geometrical H-bond definition that also captures the OH vibrational frequency downshifts well: R(H⋯O) ≤2.5 Å and the O-H⋯O angle θ ≥ 100°; and (iv) the frequency vs electric field relations for water and hydroxides (i.e., dissociated water) follow different and well-separated curves.

Probing Halogen Bonds by Scalar Couplings.

As halogen bonding is a weak, transient interaction, its description in solution is challenging. We demonstrate that scalar coupling constants (J) are modulated by halogen bonding. The binding-induced magnitude change of one-bond couplings, even up to five bonds from the interaction site, correlates to the interaction strength. We demonstrate this using the NMR data of 42 halogen-bonded complexes in dichloromethane solution and by quantum chemical calculations. Our observation puts scalar couplings into the toolbox of methods for characterization of halogen bond complexes in solution and paves the way for their applicability for other types of weak σ-hole interactions.

Are bis(pyridine)iodine(I) complexes applicable for asymmetric halogenation?

Enantiopure halogenated molecules are of tremendous importance as synthetic intermediates in the construction of pharmaceuticals, fragrances, flavours, natural products, pesticides, and functional materials. Enantioselective halofunctionalizations remain poorly understood and generally applicable procedures are lacking. The applicability of chiral trans-chelating bis(pyridine)iodine(I) complexes in the development of substrate independent, catalytic enantioselective halofunctionalization has been explored herein. Six novel chiral bidentate pyridine donor ligands have been designed, routes for their synthesis developed and their [N-I-N]+-type halogen bond complexes studied by 15N NMR and DFT. The chiral complexes encompassing a halogen bond stabilized iodenium ion are shown to be capable of efficient iodenium transfer to alkenes; however, without enantioselectivity. The lack of stereoselectivity is shown to originate from the availability of multiple ligand conformations of comparable energies and an insufficient steric influence by the chiral ligand. Substrate preorganization by the chiral catalyst appears a necessity for enantioselective halofunctionalization.

Modified Density Functional Dispersion Correction for Inorganic Layered MFX Compounds (M = Ca, Sr, Ba, Pb and X = Cl, Br, I).

MFX (M = Ca, Ba, Sr, Pb and X = Cl, Br, I) compounds have received considerable attention due to their technological application as X-ray detectors, pressure sensors, and optical data storage materials, when doped with rare-earth ions. MFX compounds belong to the class of layered materials with a tetragonal Matlockite crystal structure, characterized by weakly stacked double-halide layers along the crystallographic c-axis. These layers predominantly determine phase transitions, elastic, and mechanical properties. However, the correct description of the lattice parameter c is a challenge for most standard DFT functionals, which tend to overestimate the lattice parameter c. Because of the weak interactions between the halide layers, dispersion-corrected functionals seem to be a better choice. We investigated 11 different inorganic layered MFX compounds for which experimental data are available, with standard and dispersion-corrected functionals to assess their performance in reproducing the lattice parameter c, structural, and vibrational properties of the MFX compounds. Our results revealed that these functionals do not describe the weak interactions between the halide layers in a balanced way. Therefore, we modified Grimme's popular DFT-D2 dispersion correction scheme in two different ways by (i) replacing the dispersion coefficients and van der Waals radii with those of noble gas atoms or (ii) increasing the van der Waals radii of the MFX atoms up to 40%. Comparison with the available experimental data revealed that the latter approach applied to the PBE (Perdew-Burke-Ernzerhof)-D2 functional with 30% increased van der Waals radii, which we coined PBE-D2* (Srvdw 1.30) is best suited to fine-tune the description of the weak interlayer interactions in MFX compounds, thus significantly improving the description of their structural, vibrational, and mechanical properties. Work is in progress applying this new, computationally inexpensive scheme to other inorganic layered compounds and periodic systems with weakly stacked layers.

Local vibrational mode analysis of ion-solvent and solvent-solvent interactions for hydrated Ca2+ clusters.

Hydrated calcium ion clusters have received considerable attention due to their essential role in biological processes such as bone development, hormone regulation, blood coagulation, and neuronal signaling. To better understand the biological role of the cation, the interactions between the Ca2+ ions and water molecules have been frequently investigated. However, a quantitative measure for the intrinsic Ca-O (ion-solvent) and intermolecular hydrogen bond (solvent-solvent) interactions has been missing so far. Here, we report a topological electron density analysis and a natural population analysis to analyze the nature of these interactions for a set of 14 hydrated calcium clusters via local mode stretching force constants obtained at the ωB97X-D/6-311++G(d,p) level of theory. The results revealed that the strength of inner Ca-O interactions for Ca(H2O)n 2+ (n = 1-8) clusters correlates with the electron density. The application of a second hydration shell to Ca(H2O)n 2+ (n = 6-8) clusters resulted in stronger Ca-O interactions where a larger electron charge transfer between lp(O) of the first hydration shell and the lower valence of Ca prevailed. The strength of the intermolecular hydrogen bonds, formed between the first and second hydration shells, became stronger when the charge transfers between hydrogen bond (HB) donors and HB acceptors were enhanced. From the local mode stretching force constants of implicitly and explicitly solvated Ca2+, we found the six-coordinated cluster to possess the strongest stabilizations, and these results prove that the intrinsic bond strength measures for Ca-O and hydrogen bond interactions form new effective tools to predict the coordination number for the hydrated calcium ion clusters.

Quantitative Assessment of B-B-B, B-Hb -B, and B-Ht Bonds: From BH3 to B12 H122.

We report the thermodynamic stabilities and the intrinsic strengths of three-center-two-electron B-B-B and B-Hb -B bonds ( Hb : bridging hydrogen), and two-center-two-electron B-Ht bonds ( Ht : terminal hydrogen) which can be served as a new, effective tool to determine the decisive role of the intermediates of hydrogenation/dehydrogenation reactions of borohydride. The calculated heats of formation were obtained with the G4 composite method and the intrinsic strengths of B-B-B, B-Hb -B, and B-Ht bonds were derived from local stretching force constants obtained at the B3LYP-D2/cc-pVTZ level of theory for 21 boron-hydrogen compounds, including 19 intermediates. The Quantum Theory of Atoms in Molecules (QTAIM) was used to deepen the inside into the nature of B-B-B, B-Hb -B, and B-Ht bonds. We found that all of the experimentally identified intermediates hindering the reversibility of the decomposition reactions are thermodynamically stable and possess strong B-B-B, B-Hb -B, and B-Ht bonds. This proves that thermodynamic data and intrinsic B-B-B, B-Hb -B, and B-Ht bond strengths form a new, effective tool to characterize new (potential) intermediates and to predict their role for the reversibility of the hydrogenation/dehydrogenation reactions.

Theoretical Study of Halogenated B12H nX(12- n)2- (X = F, Cl, Br).

The closoborane and their derivatives have attracted high interest due to their superionic conductivity. Very recently, high ionic conductivities have been reported for compounds containing the closoborane ion B12H122-. In this work, we address halogen-substituted ions B12H nX(12- n)2- ( n = 0-3, 6, 9-12 and X = F, Cl, Br) using DFT calculations to probe the structures, the chemical stability, and the electrochemical stability, as well as spectroscopic properties in view of potential future applications. Considering the theoretical reaction n/12 B12H122- + (12- n)/12 B12X122- → B12H nX(12- n)2-, it appears that for X = Cl and Br the compounds with n = 6 are stabilized by about 100 kJ/mol. The calculation of the vertical detachment energy (which is indirectly related to the electrochemical stability) shows an increasing stability with increasing halogen content. These results suggest that, for practical applications, it is likely that a partially halogenated ion offers the best compromise. The calculations of vibrational properties and NMR chemical shifts also reveal several systematic trends, which are discussed and compared to available literature values.

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.

Quantitative Assessment of Tetrel Bonding Utilizing Vibrational Spectroscopy.

A set of 35 representative neutral and charged tetrel complexes was investigated with the objective of finding the factors that influence the strength of tetrel bonding involving single bonded C, Si, and Ge donors and double bonded C or Si donors. For the first time, we introduced an intrinsic bond strength measure for tetrel bonding, derived from calculated vibrational spectroscopy data obtained at the CCSD(T)/aug-cc-pVTZ level of theory and used this measure to rationalize and order the tetrel bonds. Our study revealed that the strength of tetrel bonds is affected by several factors, such as the magnitude of the σ-hole in the tetrel atom, the negative electrostatic potential at the lone pair of the tetrel-acceptor, the positive charge at the peripheral hydrogen of the tetrel-donor, the exchange-repulsion between the lone pair orbitals of the peripheral atoms of the tetrel-donor and the heteroatom of the tetrel-acceptor, and the stabilization brought about by electron delocalization. Thus, focusing on just one or two of these factors, in particular, the σ-hole description can only lead to an incomplete picture. Tetrel bonding covers a range of -1.4 to -26 kcal/mol, which can be strengthened by substituting the peripheral ligands with electron-withdrawing substituents and by positively charged tetrel-donors or negatively charged tetrel-acceptors.

Do 2-coordinate iodine(I) and silver(I) complexes form nucleophilic iodonium interactions (NIIs) in solution?

The interaction of a [bis(pyridine)iodine(I)]+ cation with a [bis(pyridine)silver(I)]+ cation, in which an iodonium ion acts as a nucleophile by transferring electron density to the silver(I) cation, is reinvestigated herein. No measurable interaction is observed between the cationic species in solution by NMR; DFT reveals that if there is an attractive interaction between these complexes in solution, it is dominantly the π-π interaction of pyridines.

Modulating photoswitch performance with halogen, coordinative and hydrogen bonding: a comparison of relative bond strengths.

The behavior of an enediyne photoswitch is modulated with halogen bonding, coordinative bonding and hydrogen bonding. Through NMR and computational studies we demonstrate that the relative strength of the secondary bonding directly influences the rate of photoisomerization and the photostationary state.

Halogen Bond of Halonium Ions: Benchmarking DFT Methods for the Description of NMR Chemical Shifts.

Because of their anisotropic electron distribution and electron deficiency, halonium ions are unusually strong halogen-bond donors that form strong and directional three-center, four-electron halogen bonds. These halogen bonds have received considerable attention owing to their applicability in supramolecular and synthetic chemistry and have been intensely studied using spectroscopic and crystallographic techniques over the past decade. Their computational treatment faces different challenges to those of conventional weak and neutral halogen bonds. Literature studies have used a variety of wave functions and DFT functionals for prediction of their geometries and NMR chemical shifts, however, without any systematic evaluation of the accuracy of these methods being available. In order to provide guidance for future studies, we present the assessment of the accuracy of 12 common DFT functionals along with the Hartree-Fock (HF) and the second-order Møller-Plesset perturbation theory (MP2) methods, selected from an initial set of 36 prescreened functionals, for the prediction of 1H, 13C, and 15N NMR chemical shifts of [N-X-N]+ halogen-bond complexes, where X = F, Cl, Br, and I. Using a benchmark set of 14 complexes, providing 170 high-quality experimental chemical shifts, we show that the choice of the DFT functional is more important than that of the basis set. The M06 functional in combination with the aug-cc-pVTZ basis set is demonstrated to provide the overall most accurate NMR chemical shifts, whereas LC-ωPBE, ωB97X-D, LC-TPSS, CAM-B3LYP, and B3LYP to show acceptable performance. Our results are expected to provide a guideline to facilitate future developments and applications of the [N-X-N]+ halogen bond.

Computational analysis of vibrational frequencies and rovibrational spectroscopic constants of hydrogen sulfide dimer using MP2 and CCSD(T).

Previous studies have shown that the weakly bonded H2S dimer demands high level quantum chemical calculations to reproduce experimental values. We investigated the hydrogen bonding of H2S dimer using MP2 and CCSD(T) levels of theory in combination with aug-cc-pV(D,T,Q)Z basis sets. More precisely, the binding energies, potential energy curves, rovibrational spectroscopic constants, decomposition lifetime, and normal vibrational frequencies were calculated. In addition, we introduced the local mode analysis of Konkoli-Cremer to quantify the hydrogen bonding in the H2S dimer as well as providing for the first time the comprehensive decomposition of normal vibrational modes into local modes contributions, and a decomposition lifetime based on rate constant. The local mode force constant of the H2S dimer hydrogen bond is smaller than that of the water dimer, in accordance with the weaker hydrogen bonding in the H2S dimer.

Accurate Computational Thermodynamics Using Anharmonic Density Functional Theory Calculations: The Case Study of B-H Species.

The thermal decomposition of boron-hydrogen compounds is complex and multistep and involves the formation of various intermediates. An accurate description of the thermodynamics of the reactants, products, and intermediates is required for an in-depth understanding of their reactivity. In this respect, we have proceeded to the accurate determination of the key thermodynamic functions (ΔH(T), S(T), and C P (T)) of 44 isolated B-H molecular species involved in the decomposition of B-H solids, with the inclusion of anharmonic effects. An excellent agreement is observed with available experimental data. We report the analytic expressions of these functions obtained by fitting them with NASA functions in the 200-900 K temperature range. Because the vibrational spectra of these species are their fingerprints, we also report the predicted IR and Raman spectra. The calculated anharmonic spectra show an excellent agreement with experiments and allow for a clear-cut identification of fundamentals, combinations, and overtones.

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.