Bayesian Inference for Model Analyses of Supramolecular Complexes: A Case Study with Nanocarbon Hosts

A 126 π-electron nanobowl molecule, phenine tridehydrosumanene, was synthesized in 12 steps through the development of a polygon cyclization strategy that assembled the polygonal precursors by Ni-mediated macrocyclization. The bowl-shaped structure accommodated C70 as a guest at the concave site, and the ball-in-bowl structure was determined by X-ray crystallography. The host-guest equilibrium in solution was studied with titration experiments using isothermal calorimetry, which provided an interesting test case for studying the host-guest stoichiometry. Bayesian inference was introduced for stoichiometric analyses of the equilibrium, and a procedure to estimate the volume of prior probability in the parameter space was developed. The Bayesian procedure functioned as Occam's razor and provided quantitative support for a specific stoichiometry. The method was examined with five host-guest examples comprising nanocarbon hosts, which suggested the versatility of Bayesian inference for studies of supramolecular complexes.

Ligand- and metal-exchange reactions of robust nickel complexes with pentagonal bipyramidal structures

The coordination chemistries of transition metal complexes with pentagonal bipyramidal geometries were investigated, and the highly stable nature of a cyclic pentapyridyl ligand was disclosed. A NiCl2 complex with the pentapyridyl ligand was found to be stable toward water and acidic conditions. The stable complex underwent ligand-exchange reactions with nucleophilic reagents, and a series of pentagonal bipyramidal complexes with different apical ligands was prepared. Crystallographic analyses with the aid of theoretical calculations revealed that the complexes were constructed by electrostatic threading of a divalent linear nickel complex into the ring of the neutral, cyclic pentapyridyl, which resulted in robust water- and acid-resistant complexes with unique pentagonal bipyramidal structures. A reductive metal exchange reaction was then discovered, which enabled "linear divalent metal + electrostatic ring" formulations with different metal atoms.

Stoichiometry validation of supramolecular complexes with a hydrocarbon cage host by van 't Hoff analyses

Defining chemical processes with equations is the first important step in characterizing equilibria for the assembly of supramolecular complexes, and the stoichiometry of the assembled components must be defined to generate the equation. Recently, this subject has attracted renewed interest, and statistical and/or information-theoretic measures were introduced to examine the validities of the equilibrium models used during curve fitting analyses of titration. The present study shows that these measures may not always be appropriate for credibility examinations and that further reformation of the protocols used to determine the overall stoichiometry is necessary. Hydrocarbon cage hosts and their chloroform complexes formed via weak CH-π hydrogen bonds were studied, which allowed us to introduce van 't Hoff analyses for effective validation of the stoichiometries of supramolecular complexes. This study shows that the stoichiometries of supramolecular complexes should be carefully examined by adopting multiple measures with different origins.

Akaike's Information Criterion for Stoichiometry Inference of Supramolecular Complexes

"How do we decide the stoichiometry of host-guest complexes?" This question has long been answered by the Job plot since its first report in 1928. However, as the Job plot was claimed to be misleading in 2016, the question became an open question again and called for renewed investigations. An information-theoretic approach, called Akaike's information criterion, is introduced in this study to select the best model of host-guest complexes, which can rank the models with weight of evidence. A few test cases with unique cylindrical hosts were examined to demonstrate the applicability of the information-theoretic method. Consequently, reasonable views over the thermodynamic behaviors of dumbbell-and-cylinder complexes were obtained. Akaike's information criterion can be a useful and superior alternative to statistical null hypothesis testing, which was proposed as a remedy in place of the Job plot.

Concise Synthesis of Molecular Hyperboloids by Oligomeric Macrocyclization of Octagonal Molecules

Molecular hyperboloids were designed and synthesized. The synthesis was achieved by development of oligomeric macrocyclization of an octagonal molecule with a saddle shape. The saddle-shaped molecule, that is, [8]cyclo-meta-phenylene ([8]CMP), was decorated with two linkers for the oligomeric macrocyclization and was synthetically assembled by Ni-mediated Yamamoto coupling. Three congeners of the molecular hyperboloids (2mer-4mer) were obtained, and 2mer and 3mer were subjected to X-ray crystallographic analysis. Crystal structures revealed nanometer-sized hyperboloidal structures with 96π and 144π electrons, which also possessed nanopores on the curved molecular structures. Structures of [8]CMP cores of the molecular hyperboloids were compared with those of saddle-shaped phenine [8]circulene with a negative Gauss curvature to confirm their structural resemblance, which suggests further explorations of expanded networks of molecular hyperboloids.

Facile Synthesis and Chiral Resolution of Expanded Helicenes with up to 35 cata-Fused Benzene Rings

Expanded helicenes are expected to show enhanced chiroptical properties as compared to the classical helicenes but the synthesis is very challenging. Herein, we report the facile synthesis of a series of expanded helicenes Hn (n=1-4) containing 11, 19, 27 and 35 cata-fused benzene rings through Suzuki coupling-based oligomerization followed by Bi(OTf)₃ -mediated regioselective cyclization of vinyl ethers. Their structures were determined by X-ray crystallographic analysis. Enantiopure H2, H3, and H4 can be isolated by chiral HPLC and they all exhibit strong chiroptical responses with high absorption dissymmetry factor (|g_abs |) values (0.020 for H2, 0.021 for H3, and 0.021-0.024 for H4).

Target-oriented design of helical nanotube molecules for rolled incommensurate bilayers

Incommensurate double-wall carbon nanotubes give rise to unique stereochemistry originating from twisted stacks of hexagon arrays. However, atomic-level studies on such unique systems have rarely been performed, even though syntheses of molecular segments of carbon nanotubes have been extensively explored. The design of cylindrical molecules with chirality, particularly, in pairs provides synthetic challenges, because relationships between diameters specified with chiral indices and structures of arylene panels have not been investigated in a systematic manner. Here we show that a molecular version of incommensurate double-wall carbon nanotubes can be designed through the development of an atlas for the top-down design of cylindrical molecules. A large-bore cylindrical molecule with a diameter of 1.77 nm was synthesized using a readily available pigment and encapsulated a small-bore cylindrical molecule with a diameter of 1.04 nm. The large- and small-bore molecules possessed helicity in atomic arrangements, and their coaxial assembly proceeded in nonstereoselective manner to give both heterohelical and homohelical combinations.

Synthesis of a Negatively Curved Nanocarbon Molecule with an Octagonal Omphalos via Design-of-Experiments Optimizations Supplemented by Machine Learning

A saddle-shaped nanocarbon molecule was synthesized, which revealed the existence of negative Gauss curvatures on a >3-nm molecular structure possessing 192 π-electrons. The synthesis was facilitated by a protocol developed with Design-of-Experiments optimizations and machine-learning predictions, and spectroscopy and crystallography were used to reveal the saddle-shaped structure of the molecule. Solution-phase analyses showed the presence of dimeric assembly, and crystallographic analyses revealed the stacked dimeric structures. The stacked crystal structure was scrutinized by various methods, including Gauss curvatures derived from the discrete surface theory of geometry, to reveal the important role of the molecular Gauss curvature in dimeric assembly.

Singly and Triply Linked Magnetic Porphyrin Lanthanide Arrays

The introduction of paramagnetic metal centers into a conjugated π-system is a promising approach toward engineering spintronic materials. Here, we report an investigation of two types of spin-bearing dysprosium(III) and gadolinium(III) porphyrin dimers: singly meso–meso-linked dimers with twisted conformations and planar edge-fused β,meso,β-linked tapes. The rare-earth spin centers sit out of the plane of the porphyrin, so that the singly linked dimers are chiral, and their enantiomers can be resolved, whereas the edge-fused tape complexes can be separated into syn and anti stereoisomers. We compare the crystal structures, UV–vis–NIR absorption spectra, electrochemistry, EPR spectroscopy, and magnetic behavior of these complexes. Low-temperature SQUID magnetometry measurements reveal intramolecular antiferromagnetic exchange coupling between the Gd^III centers in the edge-fused dimers (syn isomer: J = −51 ± 2 MHz; anti isomer: J = −19 ± 3 MHz), whereas no exchange coupling is detected in the singly linked twisted complex. The phase-memory times, T_m, are in the range of 8–10 μs at 3 K, which is long enough to test quantum computational schemes using microwave pulses. Both the syn and anti Dy₂ edge-fused tapes exhibit single-molecule magnetic hysteresis cycles at temperatures below 0.5 K with slow magnetization dynamics.

Activation of positive cooperativity by size-mismatch assembly via inclination of guests in a single-site receptor

A halogenated bowl-shaped guest, corannulene, was encapsulated in a cylindrical host, [4]cyclochrysenylene, to form a bowl-in-tube complex, which mimicked supramolecular complexes between bowl guests and carbon nanotubes. As was the case with carbon nanotubes, the cylindrical space of [4]cyclochrysenylene trapped multiple corannulene molecules in an array, and 1:2 complexes were commonly obtained with the corannulene guests with various halogen substituents (F, Cl, Br and I). Careful statistical analyses of isothermal titration calorimetry titration data succeeded in revealing the stoichiometry, and the molecular structures of the 1:2 complexes were further clarified by X-ray crystallographic analyses. Two fluorinated corannulene guests were stacked perpendicular to the cylinder axis, while two chlorinated guests were stacked with inclined orientations. The structural difference resulted in a large difference in the cooperativity of the two-stage association in solution: fluorinated corannulene guests showed negative cooperativity for the 1:2 complexation, and the other, larger halogenated corannulene guests showed positive cooperativity.

A Defective Nanotube Molecule of C552 H496 N24 with Pyridinic and Pyrrolic Nitrogen Atoms

A 3-nm molecule comprising a cylindrical core and cross-shaped rims was designed and synthesized by developing a modular synthetic route. By using a cyclic precursor from previous studies as a starting material, multiple carbazole units were installed at the rims of the defective cylinder. The defective cylinder was synthetically doped with two types of nitrogen atoms, that is, pyridinic and pyrrolic nitrogen atoms, which resulted in solvatochromic shifts in fluorescence by charge-transfer interactions. The structure of the large, C₅₅₂ H₄₉₆ N₂₄ molecule was fully disclosed by crystallographic analyses, and the unique helical arrangement of nitrogen-doped cylinders in the crystal was revealed.

Synthesis and Chiral Resolution of Twisted Carbon Nanobelts

Twisted carbon nanobelts could display persistent chirality, which is desirable for material applications, but their synthesis is very challenging. Herein, we report the successful synthesis and chiral resolution of such a kind of molecules (1-H and 1) with a figure-eight configuration. 1-H was synthesized first by macrocyclization through Suzuki coupling reaction followed by benzannulation via Bi(OTf)₃-mediated cyclization reaction of vinyl ether. Oxidative dehydrogenation of 1-H gave the fully π-conjugated 1. Their twisted structures were confirmed by X-ray crystallographic analysis and calculations, and they can be resolved by chiral high-performance liquid chromatography. The isolated enantiomers showed persistent chiroptical properties according to the circular dichroism measurements, with moderate |g_abs| values (0.0016 for 1-H and 0.005-0.007 for 1). Their photophysical properties were also briefly studied.

Metal-Templated Oligomeric Macrocyclization via Coupling for Metal-Doped π-Systems

A method for the synthesis of metal-doped aromatic macrocycles has been developed. The method, i.e., metal-templated oligomeric macrocyclization via coupling, adopts Ni as the template and assembles five pyridine units via a Ni-mediated coupling reaction to form aryl-aryl linkages. A pentameric oligopyridyl macrocycle was selectively obtained in good yield, and the reaction was also applicable to a gram-scale synthesis. The pentameric oligopyridyl macrocycle captured d⁸-Ni(II) at the center to form a paramagnetic pentagonal-bipyramidal complex. The method was applied to the synthesis of a large π-molecule to afford a nanometer-sized, bowl-shaped molecule having a unique combination of 120π and 8d electrons.

A hybrid molecular peapod of sp2- and sp3-nanocarbons enabling ultrafast terahertz rotations

The internal hollow space of carbon nanotubes provides a unique nanometre-sized space to capture various molecular entities. The inner space circumfused by sp²-carbon networks can also encapsulate diamondoid molecules to afford sp²/sp³-hybrid nanocarbon peapods that have recently emerged as unique nanostructures. In this study, the sp²/sp³-hybrid peapods have been mimicked by adopting a cylindrical molecule and the smallest diamondoid, i.e., adamantane, to demonstrate the existence of ultrafast rotational motion. The solid-state rotational frequency is measured by NMR spectroscopy to record 1.06 THz that is, to the best of our knowledge, the largest value recorded for solid-state rotations of molecules. Theoretical calculations reveal that multivalent CH-π hydrogen bonds anchored the diamondoid guest on the π-wall of the cylindrical host. The weak hydrogen bonds are prone not only to cleave but also to regenerate at the interfaces, which give freedom to the guest for ultrafast isotropic rotations in the inertial regime.

Mechanical motions in hybrid sp²/sp³ -hybrid nanocarbon peapods might lead to promising materials applications, but have been insufficiently explored. Here the authors demonstrate that a diamondoid molecule trapped inside a carbonaceous cylinder undergoes solid-state rotations at terahertz frequencies.

Manipulations of Chiroptical Properties in Belt-Persistent Cycloarylenes via Desymmetrization with Heteroatom Doping

A desymmetrization strategy has been devised in the design of molecular cylinders to maximize the dissymmetry factor relevant to circularly polarized light. Although the highest dissymmetry factor of organic molecules was previously achieved with a chiral belt-persistent cycloarylene having magnetic and electric transition dipole moments in parallel, we noticed that an unbalanced magnitude of two moments was detrimental for higher dissymmetry factors. In this study, a molecular cylinder was desymmetrized by arraying doped and undoped panels via stereoselective cross-coupling macrocyclization. The desymmetrization succeeded in balancing two moments by reducing the electric transition moment at the global minimum but failed to maximize the dissymmetry factor. Structural studies revealed that the dissymmetry factor is sensitive to subtle structural fluctuations, while the rotatory strength is not affected. This study is important for the development of chiroptical materials.

Chemical Reduction of a Nanosized [6]Cyclo-2,7-naphthylene Macrocycle

Chemical reduction of a naphthylene macrocycle, [6]cyclo-2,7-naphthylene ([6]CNAP, 1), with alkali metals, Li and K, revealed the accessibility of the doubly-reduced state of 1. The macrocyclic 1^2- anion was isolated in different coordination environments and crystallographically characterized. The single-crystal X-ray diffraction confirmed the formation of contact-ion complexes with one Li⁺ and two K⁺ ions in THF, and a "naked" dianion in the solvent-separated ion product with K⁺ ions in the presence of 18-crown-6 ether. The detailed structural analysis of 1^2- showed that the π-conjugation over the biaryl linkages between naphthylene panels were enhanced upon two-fold reduction, which was rationally explained by theoretical calculations.

Fused Quinoidal Dithiophene-Based Helicenes: Synthesis by Intramolecular Radical-Radical Coupling Reactions and Dynamics of Interconversion of Enantiomers

A series of fused quinoidal dithiophene-based double and triple helicenes (1-M, 2-M, 2-M-Cl, 3-M, 3-M-Cl) were synthesized by intramolecular radical-radical coupling followed by oxidative dehydrogenation reaction. These helical molecules show dynamic interconversion of enantiomers in solution as revealed by variable-temperature NMR measurements, and the energy barriers are correlated to the substituents and topological structures. Notably, dynamic high performance liquid chromatography was used to quantitatively investigate the room-temperature racemization process between the (P,P,M)- and (P,M,M)- enantiomers of the triple helical 3-M-Cl, which gave an interconversion energy barrier in consistent with density functional theory calculations. Their optical and electrochemical properties are dependent on the fusion mode. Our studies provide both new synthetic strategy and new dynamic analytical method for helicenes with unique electronic structure.

Synthesis and stereoisomerism of [n]cyclo-2,9-phenanthrenylene congeners possessing alternating E/Z- and R/S-biaryl linkages

The synthesis and cyclostereoisomerism of [n]cyclo-2,9-phenanthrenylenes ([n]CPhen2,9, n = 4, 6 and 8), possessing hybrid E/Z- and R/S-biaryl linkages, were elaborated. The dimer of a phenanthrene derivative was used as a starting material and underwent Ni-mediated Yamamoto-type coupling to afford [6]CPhen2,9 as a major cyclic product, as well as [4]CPhen2,9 and [8]CPhen2,9 as minor products. The stereoisomers of [n]CPhen2,9 were isolated and characterized, and the number of stereoisomers indicated that E/Z linkages did not provide any experimentally separable isomers, whereas the chirality in [n]CPhen2,9 originated from the intrinsic axial chirality at constrained R/S linkages. Theoretical calculations predicted that the 2,2'-linkages in [n]CPhen2,9 adopted a fixed Z- or E-configuration, which suggested a novel type of dynamics of atropisomerism in contrast to the reported rigid or flexible behavior. This study enriches our understanding of the stereochemical features of E/Z linkages in aromatic macrocycles.

Stereoselectivity in spontaneous assembly of rolled incommensurate carbon bilayers

The periodicity of two-dimensional entities can be manipulated by their stacking assembly, and incommensurate stacks of bilayers are attracting considerable interest in materials science. Stereoisomerism in incommensurate bilayers was first noted with incommensurate double-wall carbon nanotubes composed of helical carbon networks, but the lack of structural information hampered the chemical understanding such as the stereoselectivity during bilayer formation. In this study, we construct a finite molecular version of incommensurate carbon bilayers by assembling two helical cylindrical molecules in solution. An outer cylindrical molecule is designed to encapsulate a small-bore helical cylindrical molecule, and the spontaneous assembly of coaxial complexes proceeds in a stereoselective manner in solution with a preference for heterohelical combinations over diastereomeric, homohelical combinations. The rational design of incommensurate bilayers for material applications may be facilitated by the design and development of molecular versions with discrete structures with atomic precision.

Electronic and spin structures of CaMn4Ox clusters in the S0 state of the oxygen evolving complex of photosystem II. Domain-based local pair natural orbital (DLPNO) coupled-cluster (CC) calculations using optimized geometries and natural orbitals (UNO) by hybrid density functional theory (HDFT) calculations

Domain-based local pair natural orbital (DLPNO) coupled cluster single and double (CCSD) with triple perturbation (T) correction methods were performed to elucidate the relative stabilities of ten different intermediate structures of the CaMn4Ox cluster in the S0 state of the oxygen evolving complex (OEC) of photosystem II (PSII). Full geometry optimizations of all the S0 intermediates were performed by the UB3LYP-D3/Def2-TZVP methods, providing the assumed geometrical structures and starting natural orbitals (UNO) for DLPNO-CCSD(T)/Def2TZVP calculations. The effective exchange integrals (J) for the spin Hamiltonian models for the ten intermediates were obtained by the UB3LYP/Def2-TZVP calculations followed by the general spin projections. DLPNO-CCSD(T) calculations followed by the CBS extrapolation procedure elucidated that the (II, III, IV, IV) and (III, III, III, IV) valence states in the CaMn4O5 cluster of the OEC of the PS II were nearly degenerated in energy in the S0 state, indicating an important role of dynamical electron correlation effects for the valence and spin fluctuations in strongly correlated electron systems (SCESs) consisting of 3d transition metals.

Crystalline Naphthylene Macrocycles Capturing Gaseous Small Molecules in Chiral Nanopores

A series of chiral naphthylene macrocycles, [n]cyclo-epi-naphthylenes ([n]CeNAPs), possessing epi-linkages were synthesized by one-pot macrocyclization. With chiral (R)- or (S)-1,1'-linkages embedded in binaphthyl precursors, the macrocycles were assembled in polygonal structures possessing chiral hinges as corners. Among four chiral [n]CeNAP variants, [8]CeNAP with eight naphthylene panels formed robust columnar assemblies in crystals. The nanoporous crystals maintained a columnar assembly structure even after the removal of encapsulated solvent molecules, and their gas adsorption behavior was thoroughly investigated. Gas adsorption, including state-of-the-art in situ crystallographic analyses, revealed accurate atomic-level structures of the nanopores trapping gaseous N₂ molecules in chiral C₂ arrangements. With macrocycles as basic frameworks, functional nanopores may be exploited for chiral small-molecule alignments.

Acyclic, Linear Oligo-meta-phenylenes as Multipotent Base Materials for Highly Efficient Single-layer Organic Light-emitting Devices

Oligo-meta-phenylenes have been designed and synthesized as multipotent base materials of single-layer organic light-emitting devices. Simple molecular structures of oligo-meta-phenylenes composed of linear phenylene arrays benefited from the wealth of modern reactions available for biaryl couplings and were concisely synthesized in a series. Structure-performance relationship studies with the first seven congeners revealed key features important for the multipotent materials in single-layer devices. As a result, highly efficient phosphorescent electroluminescence was made possible in a highly simplified device architecture comprising one-region, single-layer configurations. Detailed investigations with hole-only devices disclosed that the hole mobility was effectively retarded by potent materials, which should facilitate hole/electron recombination for electroluminescence.

Synthesis of a Hemispherical Geodesic Phenine Framework by a Polygon Assembling Strategy

A synthetic strategy to construct large geodesic structures of phenine (1,3,5-trisubstituted benzene) was devised. In this strategy, five pentagons were assembled on an omphalos pentagon, and bridging peripheral pentagons furnished five additional hexagons. Thirty phenine units were synthetically assembled to afford a large C₂₂₀ H₁₈₀ molecule with a phenine framework isoreticular to a hemispherical, bisected segment of C₆₀ . Although a hemispherical structure of the phenine framework was suggested by solution-phase NMR spectra, crystallographic analysis revealed an oval-like deformation of the molecular shape. In-depth structural analyses, including theoretical calculations, showed that structural fluctuations observed as variations in the biaryl torsion angles allowed structural deformations and, at the same time, that the dynamic fluctuations resulted in the spectroscopic observation of a hemisphere as a time-averaged structure.