Sigma Hole Potentials as Tools: Quantifying and Partitioning Substituent Effects.

Empirical substituent constants, such as the Hammett parameters, have found important utility in organic and other areas of chemistry. They are useful both in predicting the impact of substitutions on chemical processes and in rationalizing after-the-fact observations on chemical bonding and reactivity. We assess the impact of substitutions on monoiodinated benzene rings and find that the modifications that substituents induce on the electrostatic potentials at the sigma hole on the terminal I center correlate strongly with established trends of common substituents. As an alternative to the experimental procedures involved in obtaining empirically based substituent constants, the computationally determined constants based on induced electrostatic potentials offer a model for quantifying the influence of mono- and polyatomic, neutral, and ionic substituents on their compounds. A partitioning scheme is proposed that allows us to discretely separate σ and π contributions to generate quantitative measures of substituent effects.

On Neutral Unsaturated Ouroboric Borylenes.

The search is on for stable isolated borylenes. Potential roles in modern synthetic chemistry for boron analogues of carbenes continue to motivate interest in locating them. Using density functional and ab initio methods, we posit and examine the thermochemistry, and chemical bonding, including aromaticity, of several classes of 5- and 6-membered borylenic rings. In these systems, cyclization relies on dative bonding (ouroboric coordination) and π donation to a monovalent boron center from an adjacent O center. Certain neutral five-membered rings (heterocyclic cyclopentadienyl analogues) in particular are found to exhibit exceptionally strong preferences for the singlet multiplicity, each with singlet-triplet (S-T) gaps in excess of 40 kcal·mol-1. The singlet five-membered rings with the largest S-T gaps and some of the six-membered rings show evidence of weak aromaticity. Relationships of the form N = A·r-b, in line with Gordy's and other functions linking bond order, N, and covalent bond length, are identified for dative B←O contacts, r, reinforced in rings by π-delocalization.

Substituent Effects and the Energetics of Noncatalyzed Aryl Halide Aminations: A Theoretical Investigation.

We report the influence of substituents and physical conditions on activation energies for the noncatalyzed amination (C-N cross-coupling reactions) of aryl halides. We uncover a significant correlation between the barrier heights of the C-N bond formation and Hammett σ parameters-a formal measure of the electron-withdrawing or -donating ability of substituents on the aryl halides. Our results indicate that such correlations are useful predictive tools for the amination of aryl halides over a wide range of substituent types. From 54 cases studied (six substituents occupying specific positions relative to halogen atoms), the 2-COOHPhI + NH2 n Pr amination reaction is predicted to possess the lowest noncatalyzed activation free energy (135.6 kJ mol-1) using the B3LYP method. The lower barriers for the 2-COOHPhX (for X = Cl, Br, and I) compounds are shown to originate from collusion between steric and electronic effects-specifically, the momentary formation of a hydrogen bond between an oxygen site on the ortho-COOH and the lone pair of the entering amine. Internal reaction coordinate (IRC) path calculations afforded us these and other key insights into the nature of the reactions. The control exerted by substituents on the arrangement of the transition state structure, as well as the sensitivity of the reaction barriers to temperature and solvent polarity, are discussed. These results offer new perspectives from which to assess the nature of the C-N bond formation and suggest new avenues for future exploration, especially in progress toward the metal-free amination of aryl compounds.

Group 14 Central Atoms and Halogen Bonding in Different Dielectric Environments: How Germanium Outperforms Silicon.

The nature of halogen bonding under different dielectric conditions remains underexplored, especially for inorganic systems. The structural and energetic properties of model halogen bonded complexes (R3 M-I-NH3 for R=H and F, and M=C, Si, and Ge) are examined computationally for relative permittivities between 1 and 109 using an implicit solvent model. We confirm and assess the exceptionally high maximum potentials at the sigma hole on I (Vs,max ) in F3 Ge-I relative to cases where M=C or Si. In particular, Ge far outperforms Si in mediating inductive effects. Linear relationships, typically with R2 >0.97, are identified between Vs,max , the full point charge on I in R3 M-I, and the interaction energy, and optimized I-N distance in the complexes. An anomalous trend is identified in which, for each M, F3 M-I-NH3 becomes less stable as the optimized I-N distance gets shorter in different dielectric environments; it is explained using the F-I-NH3 complex as a reference.

A comparison of the chemical bonding and reactivity of Si8H8O12 and Ge8H8O12: A theoretical study.

We have analyzed the chemical bonding and reactivity in the cubic molecule octahydridosilsesquioxane, Si8H8O12, and its counterpart Ge8H8O12 by means of ab initio quantum chemical methods and group theory. Density functional theory and MP2 methods combined with the basis sets 6-311+G(d) and 6-311++G(2d,p) were used for geometry optimization and vibrational frequency analysis. The geometries of Si8H8O12 and Ge8H8O12 are unstable under Oh symmetry and distort to the rare Th molecular symmetry. The energy gained from this pseudo-Jahn-Teller distortion ranges from 0.78 to 6.14 kcal mol-1 depending on methodological treatment. The Fukui functions and the molecular electrostatic potential were both used as DFT-based reactivity descriptors. Our study shows that Si8H8O12 and Ge8H8O12 are both hard amphoteric molecules. The cavity within each cage is acidic and able to encapsulate hard small bases such as F-. The exterior of the cages is basic and can form stable exohedral complexes with hard acids, as in the case of H+. The insertion of F- in Si8H8O12 and Ge8H8O12 cages gives the most stable endohedral complexes of the series studied, characterized by formation energies of -3.50 and -3.45 eV at CAM-B3LYP/6-311+G(d) and -3.61 and -3.68 eV at the MP2/6-311++G(d,p) level, respectively. The calculated formation energies of the exohedral and endohedral complexes align with the DFT reactivity descriptor analysis.

From Molecules to Solids: A vdW-DF-C09 Case Study of the Mercury Dihalides.

The mercury dihalides show a remarkable diversity in the structural preferences in their minimum energy structure types, spanning molecular to strongly bound ionic solids. A challenge in the development of density functional methods for extended systems is to arrive at strategies that serve equally well such a broad range of bonding modes or structural preferences. The chemical bonding and the stabilities of mercury dihalides and the general utility and reliability of the van der Waals density functional with C09 exchange (vdW-DF-C09) in predicting or describing the energetics and structural preferences in these metal dihalides is examined. We show that, in contrast with the uncorrected generalized gradient approximation of the Perdew-Burke-Erzenhoff (PBE) exchange-correlation functional, qualitative and quantitative patterns in the bonding of the mercury dihalide solids are well reproduced with vdW-DF-C09 for the full series of HgX2 systems for X = F, Cl, Br, and I. The possible existence of a low-temperature cotunnite polymorph for HgF2 and PbF2 is posited.

Aromatic ouroboroi: heterocycles involving a σ-donor-acceptor bond and 4n + 2 π-electrons.

The aromaticity and dynamics of a set of recently proposed neutral 5- and 6-membered heterocycles that are closed by dative (donor-acceptor) or multi-center σ bonds, and have resonance forms with a Hückel number of π-electrons, are examined. The donors and acceptors in the rings include N, O, and F, and B, Be, and Mg, respectively. The planar geometry of the rings, coupled with evidence from different measures of aromaticity, namely the NICSzz, and NICSπzz components of the conventional nucleus independent chemical shifts (NICS), and ring current strengths (RCS), indicate non-trivial degrees of aromaticity in certain cases, including the cyclic C3B2OH6 and C3BOH5 isomers, both with three bonds to the O site in the ring. The former is lower in energy by at least 17.6 kcal mol-1 relative to linear alternatives obtained from molecular dynamics simulations in this work. Some of the other systems examined are best described as non-aromatic. Ring opening, closing, and isomerization are observed in molecular dynamics simulations for some of the systems studied. In a few cases, the ring indeed persists.

On Transannulation in Azaphosphatranes: Synthesis and Theoretical Analysis.

A combined synthetic-theoretical study has been undertaken to determine the factors that influence transannulation in azaphosphatranes. The commonly used proazaphosphatrane P(i-BuNCH2CH2)3N and several of its oxidized congeners are used as model systems. The haloazaphosphatranes of P(i-BuNCH2CH2)3N were synthesized, including a rare fluoroazaphopshatrane, and used as references for computational investigations. Comparisons of the experimental and theoretical observations highlight the flexibility observed in transannulated atranes and the potential for multiple local energetic minima depending on the identity of the equatorial substituents for a given azaphosphatrane. Theoretical calculations also identify the role of the ethylene linker in azaphosphatrane bonding, the influence of transannulation on P-electrophile interactions, and the contribution of electrostatic interactions to transannulation.

Bending Ternary Dihalides.

The bonding preferences in the mixed dihalides (MXY) of groups 2 and 12 metals, including the extent of any anomalous bending, are assessed and established. The deviation from linearity in group 2 metal binary dihalides is well-known, runs contrary to simple bonding models, and is believed to be decisive for structural preferences in the extended solids. Yet the bonding in the ternary, MXY, molecules has not been investigated systematically until now. The structure and bonding in these ternary systems (and, for completeness, the binary cases as well) are determined herein at high levels of theory. A softness criterion formulated by Szentpály and Schwerdtfeger, and tested initially on binary dihalides with predictions for mixed systems, is confirmed to apply broadly for binary and ternary species of the group 2 and 12 metals. For each M, a function of the form E(Θ) = Ae- kΘ is shown to predict the barriers to linearization for all of the bent molecules. The extended solids of some of the ternary dihalides are of interest for their optical properties. The bonding in the molecular (MXY) units may offer we think some new perspectives from which to rationalize the bonding preferences in those crystal structures.

Coordination and Insertion: Competitive Channels for Borylene Reactions.

Monovalent boron, free borylene species of the form B-R are notoriously unstable. Consequently, there are substantial gaps in the literature concerning the potential utility of those species in organic and inorganic synthesis either as ligands or as critical intermediates in reactions. We show that the relative stability of borylene complexes varies widely, depending on the electron donating ability of the R group. We find that borylenes can form, in the gas phase, weak sigma hole type interactions to saturated carbon centers and stronger dative bonds to tetravalent silicon and germanium. An insertion reaction of the form FH3M + BR → FH2MBHR competes against dative bonding, however, and the reaction is barrierless in several cases when M = Si and in a few cases when M = Ge. For M = C, the barriers are high enough to stabilize monovalent boron complexes. In each case, the barrier heights to M-H bond activation and BR insertion are very sensitive to the nucleophilicity of BR. We confirm, at the MP2(full) and CCSD(T) levels, a substantial preference in borylenes for the singlet over the triplet state. An account is provided at the B3LYP-D3 and MP2(full) levels for the facile insertion reaction on the singlet surface when M = Si and for the stability of FH3M·BR type complexes and the higher barriers to insertion when M = C and Ge.

Dynamical behavior of boron clusters.

Several of the lowest energy structures of small and medium sized boron clusters are two-dimensional systems made up of a pair of concentric rings. In some cases, the barriers to the rotation of one of those rings relative to the other are remarkably low. We find that a combination of electronic and geometrical factors, including apparently the relative sizes and symmetries of the inner and outer rings, are decisive for the diminished barriers to in-plane rotation in these two dimensional clusters. A sufficiently large outer ring is important; for instance, expansion of the outer ring by a single atom may reduce the barrier significantly. A crucial factor for an apparent rotation is that the σ-skeleton of the individual rings remains essentially intact during the rotation. Finally, the transition state for the rotation of the inner ring comprises the transformation of a square into a diamond, which may be linked to a mechanism suggested decades ago for the isomerization of carboranes and boranes.

Turn: Weak Interactions and Rotational Barriers in Molecules-Insights from Substituted Butynes.

The nature of the bonding and a definite preference for an eclipsed geometry in several substituted but-2-ynes, including certain novel derivatives are uncovered and examined. In particular, we consider the molecular species R3C-C≡C-CR3 (where R= H, F, Cl, Br, I, and CN), their R3C-B≡N-CR3 analogues, and a few novel exo-bridge systems with intramolecular hydrogen bonds running parallel to the C-C≡C-C chain. In some cases, the potential energy surfaces are remarkably flat-so flat, in fact, that free rotation is predicted for those molecules at very low temperatures. A systematic investigation of the bonding in the halogenated butynes demonstrates that the eclipsed conformation actually becomes more stable relative to the staggered form as R becomes larger and less electron-withdrawing. The rotational barriers (the differences in energy between the eclipsed and staggered geometries) are magnified significantly, however, in a special case where selected R groups at the ends of the R3C-C≡C-CR'3 molecule form hydrogen bonds parallel to the C-C≡C-C core. In those systems, the hydrogen bonds serve as a weak locking mechanism that favors the eclipsed conformation. A comparison of HF and uncorrected DFT methods versus the MP2(full), CCSD(T), and other dispersion-corrected methods confirms that correlation accounts to a significant extent for barriers in substituted butyne compounds. In the hydrogen-bonded systems, the barriers are comparable to and larger in some cases than the barriers observed for the more extensively studied ethane molecule.

The HgF2 Ionic Switch: A Triumph of Electrostatics against Relativistic Odds.

A remarkable transition in the chemical bonding in (HgF2)n clusters as a function of n is identified and characterized. HgF2 is a fascinating material. Certain significant consequences of relativistic effects on the structure of the HgF2 molecule, dimer, and trimer disappear in the extended solid. Relativistic effects in Hg ensure that HgX2 molecules (X≡F, Cl, Br, and I) are linear, rigid, and form weakly bound dimers and trimers held together by weak electrostatic and van der Waals-type forces (unlike ZnX2 and CdX2 systems in which the intermonomer contacts are strong polar covalent bonds). For HgF2, the location and nature of an apparent transition from weak interactions in the smallest (HgF2)n clusters to ionic bonding in the (fluorite) HgF2 extended solid has remained a mystery. Computational evidence obtained at the M06-2X, B97D3, and MP2 levels of theory and reported herein indicate that polar covalent bonding in (HgF2)n begins as early as n=5. For n=2 through to n=13, the transition or switch from weak (primarily dipole-dipole-type) intermonomer interactions to a preference for polar covalent bonding occurs within the range 5

Weak interactions as diagnostic tools for inductive effects.

No broadly applicable and well-defined measure for the inductive effects of substituents (outside of the context of substituted benzenes) exists. We assess the viability of two different forms of weak interactions as tools for this purpose. The responses of interatomic (I···N and Ge···N) separations in the halogen-bonded and dative covalent complexes F3CI···Y and FH3Ge···Y, where Y = NH2R, afford a direct ordering of a diverse set of substituents, R, according to their influence on the availability of the N lone pair in the base (NH2R) for bonding. Despite their structural and electronic differences, the two bonding modes that we consider show good qualitative agreement on the electron-withdrawing inductive tendencies of substituents because of their sensitivity to the electronic environment at the donor site (the N center, in this case) on the base. The choice of the monosubstituted (NH2R) base minimizes steric interactions, resonance, and other electronic effects that could interfere with the bonding between N and the I or Ge centers in the complexes. We find, moreover, that the inductive tendencies for substituents in these complexes are, in general, not additive. Depending on the identity of R, the trisubstituted base (NR3) may actually reverse rather than enhance changes in the acid-base interactions that are achieved going from NH3 to NH2R. These outcomes are observed at the MP2(full) and the M06-2X levels of theory, for both halogen and dative bonding interactions. A conservative ordering of substituents according to the observed inductive tendencies is presented.

Halogen bonding: unifying perspectives on organic and inorganic cases.

We find for distinct classes of halogen bonded complexes (MF3-X···Y) that the ab initio BSSE-corrected binding energies (ΔE) and enthalpies (ΔH) are predicted by functions of the form y = A/r(n) + C. Here X is a halogen atom, Y is a base, r is the X···Y separation, and A, n, and C are constants. The actual value of n (5.5 < n < 7.0 for ΔE) for each class is determined evidently by the availability of the lone pairs on the base and is insensitive to M such that all of the complexes of a given base fall on the same curve for y versus r. Remarkably, several bases show the same behavior in some cases such that just three curves account for 55 MF3I···Y complexes of 11 bases, where M = C, Si, Ge, Sn, and Pb. Two additional bases, THF and NF3, which form especially strong and weak complexes, respectively, are in classes by themselves. Anomalous modes of halogen bonding are identified; in particular, furan forms sigma-hole complexes via carbons 2 and 3 (through the π system) in the ring in preference to the oxygen site. These results are in line with experimental observations for furan-dihalogen complexes, and several other small MF3I···Y pairs are proposed in this work for experimental interrogation. Instead of halogen bonding, CF4 tends to form weak sigma-hole bonds to bases via the polarized central carbon atom, and new examples of such pro-dative interactions to carbon in CF4 are identified in this work. We find that GeF3I and SnF3I form I···Y halogen bonds of comparable energies to those formed by the smaller and better studied CF3I. PbF3I forms the strongest halogen bond regardless of the identity of the base; SiF3I consistently forms the weakest link.

Stop rotating! One substitution halts the B1919⁻ motor.

The B19(-) anion and other boron species have been dubbed 'Wankel motors' for the almost barrierless rotation of inner and outer concentric rings relative to each other in these compounds. A single substitution in B19(-) is shown to shut down the well-established fluxionality in the anion. A carbon atom substituted in the structure to give a neutral CB18 species is shown computationally to enforce bond localization.

cluster: Searching for Unique Low Energy Minima of Structures Using a Novel Implementation of a Genetic Algorithm.

A new flexible implementation of a genetic algorithm for locating unique low energy minima of isomers of clusters is described and tested. The strategy employed can be applied to molecular or atomic clusters and has a flexible input structure so that a system with several different elements can be built up from a set of individual atoms or from fragments made up of groups of atoms. This cluster program is tested on several systems, and the results are compared to computational and experimental data from previous studies. The quality of the algorithm for locating reliably the most competitive low energy structures of an assembly of atoms is examined for strongly bound Si-Li clusters, and ZnF2 clusters, and the more weakly interacting water trimers. The use of the nuclear repulsion energy as a duplication criterion, an increasing population size, and avoiding mutation steps without loss of efficacy are distinguishing features of the program. For the Si-Li clusters, a few new low energy minima are identified in the testing of the algorithm, and our results for the metal fluorides and water show very good agreement with the literature.

The weak helps the strong: sigma-holes and the stability of MF(4)·base complexes.

Bonding interactions between an electron-deficient region (a sigma-hole) on M and electron donors in MF4-Base complexes, where M = C, Si, Ge, Sn, and Pb, are examined and rationalized. These interactions are seen to transition from weak primarily noncovalent interactions for all bases when M = C to stronger primarily covalent bonds in adducts as the valence shell expands for the heavier M atoms. For M = Ge, Sn, and Pb, the complexes are particularly stable. The consistent axial preference in these systems is anticipated by previous studies and is readily explained from the vantage point of sigma-hole interactions. A series of bound complexes of common bases such as pyridine, tetrahydrofuran, and water are identified, some of which are even more stable than the SiF4·NH3 and SiF4·N(CH3)3 complexes that have already been identified experimentally. Sigma-hole bonding to di- and poly-substituted central atoms, perhaps on par with halogen bonding, is expected to become increasingly important as an ordering interaction in materials science and engineering. Group 14 compounds have distinct advantages in this respect.

Isomerization energy decomposition analysis for highly ionic systems: case study of starlike E5Li7(+) clusters.

The most stable forms of E(5)Li(7)(+) (E = Ge, Sn, and Pb) have been explored by means of a stochastic search of their potential-energy surfaces by using the gradient embedded genetic algorithm (GEGA). The preferred isomer of the Ge(5)Li(7)(+) ion is a slightly distorted analogue of the D(5h) three-dimensional seven-pointed starlike structure adopted by the lighter C(5)Li(7)(+) and Si(5)Li(7)(+) clusters. In contrast, the preferred structures for Sn(5)Li(7)(+) and Pb(5)Li(7)(+) are quite different. By starting from the starlike arrangement, corresponding lowest-energy structures are generated by migration of one of the E atoms out of the plane with the a corresponding rearrangement of the Li atoms. To understand these structural preferences, we propose a new energy decomposition analysis based on isomerizations (isomerization energy decomposition analysis (IEDA)), which enable us to extract energetic information from isomerization between structures, mainly from highly charged fragments.