On the origin of Baeyer strain in molecules – an ab initio and DFT analysis

Open shell versus closed shell bonding interaction in cyclopropane derivatives: EDA-NOCV analyses

Cyclopropane ring is a very common motif in organic/bio-organic compounds. The chemical bonding of this strained ring is taught to all chemistry students. This three-membered cyclic, C3 ring is quite reactive which has attracted both, synthetic and theoretical chemists to rationalize/correlate its stability and bonding with its reactivity and physical properties over a century. There are a few bonding models (mainly the Bent-Bond model and Walsh model) of this C3 ring that are debated to date. Herein, we have carried out energy decomposition analysis coupled with natural orbital for chemical valence (EDA-NOCV) to study the two most reactive bonds of cyclopropane rings of 49 different organic compounds containing different functional groups to obtain a much deeper bonding insight toward a more general bonding model of this class of compounds. The EDA-NOCV analyses of fragment orbitals and susequent bond formation revealed that the nature of the CC bond of the cyclopropane (splitting two bonds at a time out of three CC bonds) ring is preferred to form two dative covalent CC bonds (between a singlet olefin-fragment and an excited singlet carbene-fragment with a vacant sp2 orbital and a filled p-orbital) for the majority (37/49) of compounds over two covalent electron sharing bonds in some (7/49) compounds (between an excited triplet olefin and triplet carbene), while a few (5/49) compounds show flexibility to adopt either the electron sharing or dative covalent bond as both are equally possible. The effects of functional groups on the nature of chemical bond in cyclopropane rings have been studied in detail. Our bonding analyses are in line with the QTAIM analyses which produce small negative values of the Laplacian, significantly positive values of bond ellipticity, and accumulation of electron densities around the ring critical point of C3 -rings. These corresponding QTAIM parameters of C3 -rings are quite different for CC single bonds of normal hydrocarbons as expected. The chemical bonding in the majority of cyclopropane rings can be very similar to those of metal-olefin systems.

Synthesis and Applications of Bicyclo[1.1.0]butyl and Azabicyclo[1.1.0]butyl Organometallics

The use of metalated (aza)bicyclo[1.1.0]butanes in synthesis is currently experiencing a renaissance, as evidenced by the numerous reports in the last 5 years that have relied on such intermediates to undergo unique transformations or generate novel fragments. Since their discovery, these species have been demonstrated to participate in a wide range of reactions with carbon and heteroatom electrophiles, as well as metal complexes, to facilitate the rapid diversification of (aza)bicyclo[1.1.0]butane-containing compounds. Key to this is the relative acidity of the bridgehead C-H bonds which promotes facile deprotonation and subsequent functionalization of an unsubstituted position on the carbon framework via the intermediacy of a metalated (aza)bicyclo[1.1.0]butane. Additionally, the late-stage incorporation of deuterium atoms in strained fragments has led to the elucidation of numerous reaction mechanisms that involve strained bicycles. The continued investigation into the inimitable reactivity of metalated bicycles will cement their importance within the field of organometallic chemistry.

Bicyclobutanes: from curiosities to versatile reagents and covalent warheads

The unique chemistry of small, strained carbocyclic systems has long captivated organic chemists from a theoretical and fundamental standpoint. A resurgence of interest in strained carbocyclic species has been prompted by their potential as bioisosteres, high fraction of sp3 carbons, and limited appearance in the patent literature. Among strained ring systems, bicyclo[1.1.0]butane (BCB) stands apart as the smallest bicyclic carbocycle and is amongst the most strained carbocycles known. Despite the fact that BCBs have been synthesized and studied for well over 50 years, they have long been regarded as laboratory curiosities. However, new approaches for preparing, functionalizing, and using BCBs in "strain-release" transformations have positioned BCBs to be powerful synthetic workhorses. Further, the olefinic character of the bridgehead bond enables BCBs to be elaborated into various other ring systems and function as covalent warheads for bioconjugation. This review will discuss the recent developments in the synthesis and functionalization of BCBs as well as the applications of these strained rings in synthesis and drug discovery. An overview of the properties and the historical context of this interesting structure will be provided.

Fullerenes Pose a Strain on Hybrid Density Functional Theory

The computational modeling of fullerenes plays a fundamental role in designing low-dimension carbon nanostructures. Nevertheless, the relative energies of fullerenes larger than C20 and C24 have not been comprehensively examined by means of highly accurate ab initio methods, for example, the CCSD(T) method. Here we report such an investigation for a diverse set of 29 C40 isomers. We calculate the energies of the C40 fullerenes using the G4(MP2) composite ab initio method, which approximates the CCSD(T) energy in conjunction with a triple-ζ-quality basis set (CCSD(T)/TZ). The CCSD(T)/TZ isomerization energies span 43.1-763.3 kJ mol-1. We find a linear correlation (R2 = 0.96) between the CCSD(T)/TZ isomerization energies and the fullerene pentagon signatures (P1 index), which reflect the strain associated with fused pentagon-pentagon rings. Using the reference CCSD(T)/TZ isomerization energies, we examine the relationship between the percentage of exact Hartree-Fock (HF) exchange in hybrid density functional theory (DFT) methods and the pentagon-pentagon strain energies. We find that the performance of hybrid DFT methods deteriorates with the pentagon-pentagon strain energy. This deterioration in performance becomes more pronounced with the inclusion of high amounts of HF exchange. For example, for B3LYP (20% HF exchange), the root-mean-square deviation (RMSD) relative to G4(MP2) increases from 8.9 kJ mol-1 for the low-strain isomers (P1 = 11) to 18.0 kJ mol-1 for the high-strain isomers (P1 > 13). However, for BH&HLYP (50% HF exchange) the RMSD increases from 23.0 (P1 = 11) to 113.2 (P1 > 13) kJ mol-1. A similar trend is observed for the M06/M06-2X pair of functionals. Namely, for M06 (27% HF exchange) the RMSD increases from 0.8 (P1 = 11) to 21.0 (P1 > 13) kJ mol-1, whereas for M06-2X (54% HF exchange) the RMSD increases from 16.7 (P1 = 11) to 77.7 (P1 > 13) kJ mol-1. Overall, we find that the strain associated with pentagon adjacency is an inherently challenging problem for hybrid DFT methods involving high amounts of HF exchange and that there is an inverse relationship between the optimal percentage of HF exchange and the pentagon-pentagon strain energy. For example, for BLYP the optimal percentages of HF exchange are 13% (P1 = 11), 10% (P1 = 12), 7.5% (P1 = 13), and 6% (P1 > 13).

A more effective catalysis of the CO2 fixation with aziridines: computational screening of metal-substituted HKUST-1

A vital issue for the fixation and conversion of CO₂ into useful chemical products is to find effective catalysts. In this work, in order to develop more effective and diverse catalysts, we implemented the first computational screening study (at M06-2X//B3LYP level) on the cycloaddition of CO₂ with aziridines under eighteen metal-substituted HKUST-1 MOFs and tetrabutylammonium bromide (TBAB) as a co-catalyst. For all considered catalytic systems, the ring-opening of aziridine is calculated to be the rate-determining step. Up to 11 M-HKUST-1 systems, i.e., Rh (31.87 kcal mol^-1), Y (31.02), Sc (30.50), V (30.02), Tc (29.90), Cd (29.80), Ti (29.32), Mn (29.05), Zn (28.29), Fe (27.85) and Zr (25.09), possess lower ring-opening barrier heights than the original Cu-HKUST-1 (32.90), indicative of their superior catalytic ability to the original Cu-HKUST-1 in theory. With the lowest ring-opening barrier, Zr-HKUST-1 is strongly advocated for future synthetic and catalytic studies.

Recent advances in the chemistry of bicyclo- and 1-azabicyclo[1.1.0]butanes

Bicyclo[1.1.0]- and 1-azabicyclo[1.1.0]butanes are structurally unique compounds that exhibit diverse chemistry. Bicyclo[1.1.0]butane is a four-membered carbocycle with a bridging C(1)-C(3) bond and 1-azabicyclo[1.1.0]butane is an analog of bicyclo[1.1.0]butane featuring a nitrogen atom at one bridgehead. These structures are highly strained, allowing them to participate in a range of strain-releasing reactions which typically cleave the central, strained bond to deliver cyclobutanes or azetidines. However, despite these molecules being discovered in the 1950s and 1960s, and possessing a myriad of alluring chemical features, the chemistry and applications of bicyclo[1.1.0]- and 1-azabicyclo[1.1.0]butanes remain underexplored. In the past 5 years, there has been a resurgent interest in their chemistry driven by the pharmaceutical industry’s increasing desire for new methods to access cyclobutanes and azetidines. This short review intends to provide a timely summary of the most recent developments in the chemistry of bicyclo[1.1.0]- and 1-azabicyclo[1.1.0]butane to highlight the diverse chemistry they can access, their value as synthetic precursors to cyclobutanes and azetidines, and to identify areas for future research.

Strain release – an old tool for new transformations

This Feature Article provides an overview of research advances in the chemistry of spring-loaded molecules, focusing mainly on strain-release transformations.

Intramolecular multi-bond strain: the unrecognized side of the dichotomy of conjugated systems

Apart from the more familiar π-conjugation, there is also significant π–π repulsion which is a kind of unrecognized intramolecular strain and can be quantified with the linear B₄H₂ model system.

Electron conjugation stabilizes unsaturated systems and diminishes the differences among bond distances. Experimentally, Kistiakowsky and coworkers first measured and noticed the difference between the hydrogenation heats of carbon–carbon double bonds in conjugated systems. For instance, the hydrogenation heat of butadiene is 57.1 kcal mol^–1, which is less than two times that of the hydrogenation heat of 1-butene (30.3 kcal mol^–1), and the difference (3.5 kcal mol^–1) is the extra stabilization due to the resonance between two double bonds in the former, and is referred to as the experimental resonance energy. Following Kistiakowsky's definition, Rogers et al. studied the stepwise hydrogenation of 1,3-butadiyne and concluded that there is no conjugation stabilization in this molecule. This claim received objections instantly, but Rogers and coworkers further showed the destabilizing conjugation in 2,3-butanedione and cyanogen. Within resonance theory, the conjugation energy is derived “by subtracting the actual energy of the molecule in question from that of the most stable contributing structure.” The notable difference between the experimental and theoretical resonance energies lies in that the former needs other real reference molecules while the latter does not. Here we propose and validate a new concept, intramolecular multi-bond strain, which refers to the repulsion among π bonds. The π–π repulsion, which is contributed to by both Pauli exchange and electrostatic interaction, is quantified with the B₄H₂ model system (16.9 kcal mol^–1), and is compared with the σ–σ repulsion in B₂H₄ (7.7 kcal mol^–1). The significance of the π–π repulsion can be demonstrated by the much longer carbon–nitrogen bond in nitrobenzene (1.486 Å) than in aniline (1.407 Å), the very long and weak nitrogen–nitrogen bond (1.756 Å) in dinitrogen tetroxide, and the instability of long polyynes. This new concept successfully reconciles the discrepancy between experimental and theoretical conjugation energies. However, we maintain that by definition, electron conjugation must be stabilizing.

Ring-strain-enabled reaction discovery: new heterocycles from bicyclo[1.1.0]butanes

Mechanistically as well as synthetically, bicyclo[1.1.0]butanes represent one of the most fascinating classes of organic compounds. They offer a unique blend of compact size (four carbon atoms), high reactivity (strain energy of 66 kcal/mol), and mechanistic pathway diversity that can be harvested for the rapid assembly of complex scaffolds. The C(1)-C(3) bond combines the electronic features of both σ and π bonds with facile homolytic and heterolytic bond dissociation properties and thereby readily engages pericyclic, transition-metal-mediated, nucleophilic, and electrophilic pathways as well as radical acceptor and donor substrates. Despite this multifaceted reaction profile and recent advances in the preparation of bicylo[1.1.0]butanes, the current portfolio of synthetic applications is still limited compared with those of cyclopropanes and cyclobutanes. In this Account, we describe our work over the past decade on the exploration of substituent effects on the ring strain and the reactivity of bicyclo[1.1.0]butanes, particularly in the context of metal-mediated processes. We first describe Rh(I)-catalyzed cycloisomerization reactions of N-allyl amines to give pyrrolidine and azepine heterocycles. The regioselectivity of the C,C-bond insertion/ring-opening step in these reactions is controlled by the phosphine ligand. After metal carbene formation, an intramolecular cyclopropanation adds a second fused ring system. A proposed mechanism rationalizes why rhodium(I) complexes with monodentate ligands favor five-membered heterocycles, as opposed to Rh(I)-bidentate ligand catalysts, which rearrange N-allyl amines to seven-membered heterocycles. The scope of Rh(I)-catalyzed cycloisomerization reactions was extended to allyl ethers, which provide a mixture of five- and seven-membered cyclic ethers regardless of the nature of the phosphine additive and Rh(I) precatalyst. The chemical diversity of these cycloisomerization products was further expanded by a consecutive one-pot metathesis reaction. Rh(I)-catalyzed cycloisomerizations of propargyl amides, ethers, and electron-deficient bicyclo[1.1.0]butanes diverged mechanistically and often led to a significant number of decomposition products. In these cases, Pt(II) emerged as a superior, more alkynophilic late transition metal with its own mechanistic peculiarities. While monosubstituted bicyclo[1.1.0]butanes led to the formation of tetrahydropyridines, 1,3-disubstituted and electron-deficient bicyclo[1.1.0]butanes reacted distinctly differently with Pt(II) and ultimately provided a complementary set of nitrogen- and oxygen-containing cyclic scaffolds. The metal-catalyzed ring transformations of bicyclo[1.1.0]butanes presented herein suggest additional strategies for new reaction discoveries that can access a wide variety of novel cyclic frameworks from relatively simple starting materials. In addition, these case studies highlight the considerable potential for future applications in natural products, medicinal, and diversity-oriented synthesis based on the wealth of mechanistic pathways available to these strained small-ring carbocycles.

A hierarchy of homodesmotic reactions for thermochemistry

Chemical equations that balance bond types and atom hybridization to different degrees are often used in computational thermochemistry, for example, to increase accuracy when lower levels of theory are employed. We expose the widespread confusion over such classes of equations and demonstrate that the two most widely used definitions of "homodesmotic" reactions are not equivalent. New definitions are introduced, and a consistent hierarchy of reaction classes (RC1-RC5) for hydrocarbons is constructed: isogyric (RC1) superset of isodesmic (RC2) superset of hypohomodesmotic (RC3) superset of homodesmotic (RC4) superset of hyperhomodesmotic (RC5). Each of these successively conserves larger molecular fragments. The concept of isodesmic bond separation reactions is generalized to all classes in this hierarchy, providing a unique sectioning of a given molecule for each reaction type. Several ab initio and density functional methods are applied to the bond separation reactions of 38 hydrocarbons containing five or six carbon atoms. RC4 and RC5 reactions provide bond separation enthalpies with errors consistently less than 0.4 kcal mol(-1) across a wide range of theoretical levels, performing significantly better than the other reaction types and far superior to atomization routes. Our recommended bond separation reactions are demonstrated by determining the enthalpies of formation (at 298 K) of 1,3,5-hexatriyne (163.7 +/- 0.4 kcal mol(-1)), 1,3,5,7-octatetrayne (217.5 +/- 0.6 kcal mol(-1)), the larger polyynes C(10)H(2) through C(26)H(2), and an infinite acetylenic carbon chain.

Interplay of pi-electron delocalization and strain in [n](2,7)pyrenophanes

The geometries of a series of [n](2,7)pyrenophanes (n = 6-12) were optimized at the B3LYP/6-311G** DFT level. The X-ray crystal structures determined for the [9](2,7)- and [10](2,7)pyrenophanes agreed excellently with the computed structures. The degree of nonplanarity of the pyrene moiety depends on the number of CH2 groups in the aliphatic bridge and, as analyzed theoretically, influences the strain energy and the extent of pi-electron delocalization in the pyrene fragment. Various indices, e.g., the relative aromatic stabilization energies (DeltaASE), magnetic susceptibility exaltations (Lambda), nucleus-independent chemical shifts (NICS), and the harmonic oscillator model of aromaticity (HOMA) were used to quantify the change in aromatic character of the pyrene fragment. DeltaASE and relative Lambda values (with respect to planar pyrene) were evaluated by homodesmotic equations comparing the bent pyrene unit with its bent quinoid dimethylene-substituted analog. The bend angle, alpha, DeltaASE, and Lambda were linearly related. The aromaticity decreases smoothly and regularly over a wide range of bending, but the magnitude of the change is not large. The differences between planar pyrene (alpha = 0 degrees) and the most distorted pyrene unit (alpha = 39.7 degrees in [6](2,7)pyrenophane) are only 15.8 kcal/mol (DeltaASE) and 18.8 cgs-ppm (Lambda). Also, the geometry-based HOMA descriptor changes by only 0.07 unit. The local NICS descriptors of aromatic character also correlate very well with the global indices of aromaticity. In line with the known reactivity of pyrenophanes, the variations of NICS(1), a measure of pi-electron delocalization, were largest for the outer, biphenyl-type rings. The strain energies of the pyrene fragments were much larger and varied more than those evaluated for the bridge. Both strain energies were interrelated (correlation coefficient R = 0.979) and depend on the bend angle, alpha.