Characteristics of Intermolecular Interactions between Encapsulated Molecules and the Lantern-Like Carcerand Superphanes.

The main topic of the article is to provide the characteristics of individual intermolecular interactions present between three lantern-like superphanes and the H2O, NH3, HF, HCN, and MeOH molecules trapped inside them. Despite the large cavity, the freedom of the trapped molecules is significantly limited by the presence of numerous interaction sites on the side chains of the superphane molecule. It is shown that the molecule trapped inside the superphane is stabilized mainly by only one or, less often, two strong hydrogen bonds involving the imino nitrogen atom, but QTAIM calculations also suggest the presence of many other intermolecular interactions, mainly hydrogen bonds involving imino or central hydrogen atoms from the side chains of the superphane molecule. Moreover, it is also shown that the structural simplification of the side chains does not significantly affect both the size of the superphane molecule and the obtained encapsulation energies, which is important in modeling this type of carceplexes. Noticeably, the parent superphane considered here was previously synthesized by the group of Qing He, so the results obtained will help in understanding this type and similar systems.

Halogen Bond to Experimentally Significant N-Heterocyclic Carbenes (I, IMe2, IiPr2, ItBu2, IPh2, IMes2, IDipp2, IAd2; I = Imidazol-2-ylidene).

The subjects of the article are halogen bonds between either XCN or XCCH (X = Cl, Br, I) and the carbene carbon atom in imidazol-2-ylidene (I) or its derivatives (IR2) with experimentally significant and systematically increased R substituents at both nitrogen atoms: methyl = Me, iso-propyl = iPr, tert-butyl = tBu, phenyl = Ph, mesityl = Mes, 2,6-diisopropylphenyl = Dipp, 1-adamantyl = Ad. It is shown that the halogen bond strength increases in the order Cl < Br < I and the XCN molecule forms stronger complexes than XCCH. Of all the carbenes considered, IMes2 forms the strongest and also the shortest halogen bonds with an apogee for complex IMes2⋯ICN for which D0 = 18.71 kcal/mol and dC⋯I = 2.541 Å. In many cases, IDipp2 forms as strong halogen bonds as IMes2. Quite the opposite, although characterized by the greatest nucleophilicity, ItBu2 forms the weakest complexes (and the longest halogen bonds) if X ≠ Cl. While this finding can easily be attributed to the steric hindrance exerted by the highly branched tert-butyl groups, it appears that the presence of the four C-H⋯X hydrogen bonds may also be of importance here. Similar situation occurs in the case of complexes with IAd2.

Quantitative Description of Isomorphism in the Series of Simple Compounds.

The introduction of the notion of energy change resulting from the ion exchange in apatites leads to the question: how can some simple isomorphic series be described using the mentioned idea? We concentrated on the simple isomorphic series of compounds: apatite, bioapatite, calcite, aragonite, celestine, K-, Zn- and Cu-Tutton's salts. It was demonstrated in all the series, except Tutton's salts, that the change in energy and the change in the crystal cell volume are, in a simple way, dependent on the change in the ionic radii of the introduced ions. The linear relationships between the variations in energy and in the universal crystallographic dimension d were derived from the earlier equations and proven based on available data. In many cases, except the Tutton's salts, linear dependence was discovered between the change in energy and the sinus of universal angle Θ, corresponding to the change in momentum transfer. In the same cases, linear dependencies were observed between the energy changes and the changes in the volumes of crystallographic cells, and mutually between changes in the crystallographic cell volume V, crystallographic dimension d, and diffraction angle Θ.

Studies on Chemical Composition, Structure and Potential Applications of Keratoisis Corals.

The chemical composition and structure of bamboo octocoral Keratoisis spp. skeletons were investigated by using: Scanning Electron Microscopy SEM, Raman Microscopy, X-ray Diffraction XRD, Laser Ablation-Inductively Coupled Plasma LA-ICP, and amino acid analyzers. Elements discovered in the nodes (mainly organic parts of the skeleton) of bamboo corals showed a very interesting arrangement in the growth ring areas, most probably enabling the application of bamboo corals as palaeochronometers and palaeothermometers. LA-ICP results showed that these gorgonian corals had an unusually large content of bromine, larger than any other organism yet studied. The local concentration of bromine in the organic part of the growth rings of one of the studied corals grew up to 29,000 ppm of bromine. That is over 440 times more than is contained in marine water and 35 times more than Murex contains, the species which was used to make Tyrian purple in ancient times. The organic matter of corals is called gorgonin, the specific substance that both from the XRD and Raman studies seem to be very similar to the reptile and bird keratins and less similar to the mammalian keratins. The missing cross-linking by S-S bridges, absence of aromatic rings, and significant participation of ß-turn organization of peptides differs gorgonin from keratins. Perhaps, the gorgonin belongs to the affined but still different substances concerning reptile and bird keratin and in relation to the more advanced version-the mammalian one. Chemical components of bamboo corals seem to have great medical potential, with the internodes as material substituting the hard tissues and the nodes as the components of medicines.

Contribution to Knowledge on Bioapatites: Does Mg Level Reflect the Organic Matter and Water Contents of Enamel?

The matter constituting the enamels of four types of organisms was studied. The variability of the ions was presented in molar units. It was proven that the changes in water contents of the enamel are significantly positively related to changes in Mg; inversely, there is also a strong connection with changes in Ca and P, the main components of bioapatite. The variability in the organic matter has the same strong and positive characteristics and is also coupled with changes in Mg contents. Amelogenins in organic matter, which synthesize enamel rods, likely have a role in adjusting the amount of Mg, thus establishing the amount of organic matter and water in the whole enamel; this adjustment occurs through an unknown mechanism. Ca, P, Mg, and Cl ions, as well as organic matter and water, participate in the main circulation cycle of bioapatites. The selection of variations in the composition of bioapatite occurs only along particular trajectories, where the energy of transformation linearly depends on the following factors: changes in the crystallographic d parameter; the increase in the volume, V, of the crystallographic cell; the momentum transfer, which is indirectly expressed by ΔsinΘ value. To our knowledge, these findings are novel in the literature. The obtained results indicate the different chemical and crystallographic affinities of the enamels of selected animals to the human ones. This is essential when animal bioapatites are transformed into dentistic or medical substitutes for the hard tissues. Moreover, the role of Mg is shown to control the amount of water in the apatite and in detecting organic matter in the enamels.

Bader's Topological Bond Path Does Not Necessarily Indicate Stabilizing Interaction-Proof Studies Based on the Ng@[3n]cyclophane Endohedral Complexes.

According to Bader's quantum theory of atoms in molecules (QTAIM), the simultaneous presence of a bond path and the corresponding bond critical point between any two atoms is both a necessary and sufficient condition for the atoms to be bonded to one another. In principle, this means that this pair of atoms should make a stabilizing contribution to the molecular system. However, the multitude of so-called counterintuitive bond paths strongly suggests that this statement is not necessarily true. Particularly 'troublesome' are endohedral complexes, in which encapsulation-enforced proximity between the trapped guest (e.g., an atom) and the host's cage system usually 'produces' many counterintuitive bond paths. In the author's opinion, the best evidence to demonstrate the repulsive nature of the intra-cage guest⋯host interaction is the use of some trapping systems containing small escape channels and then showing that the initially trapped entity spontaneously escapes outside the host's cage during geometry optimization of the initially built guest@host endohedral complex. For this purpose, a group of 24 Ng@[3n]cyclophane (3≤n≤6) endohedral complexes is used. As a result, arguments are presented showing that Bader's topological bond path does not necessarily indicate a stabilizing interaction.

The Ultrashort Spike-Ring Interaction in Substituted Iron Maiden Molecules.

The in forms of molecular iron maidens are known for their unique ultrashort interaction between the apical hydrogen atom or its small substituent and the surface of the benzene ring. It is generally believed that this forced ultrashort X⋯π contact is associated with high steric hindrance, which is responsible for specific properties of iron maiden molecules. The main aim of this article is to investigate the influence of significant charge enrichment or depletion of the benzene ring on the characteristics of the ultrashort C-X⋯π contact in iron maiden molecules. For this purpose, three strongly electron-donating (-NH2) or strongly electron-withdrawing (-CN) groups were inserted into the benzene ring of in-[34,10][7]metacyclophane and its halogenated (X = F, Cl, Br) derivatives. It is shown that, despite such extremely electron-donating or electron-accepting properties, the considered iron maiden molecules surprisingly reveal quite high resistance to changes in electronic properties.

Hydrogen Bonds.

The Topical Collection "Hydrogen Bonds" is a continuation of the previous Special Issue "Intramolecular Hydrogen Bonding 2021" [...].

The influence of sedentary behaviour on lumbar-pelvic kinematics during squatting and forward bending among physically active students.

Prolonged sitting may involve several mechanisms that make it a risk factor for low back pain. The aim of this study was to investigate lumbar-pelvic kinematics and multifidus muscle (MF) activity during squatting and forward bending in relation to the sedentary behaviour of physically active students. Sixty-three students were divided into two groups according to the time spent in a sitting position during the day: 'high' (>7 h/day); 'low' (≤7 h/day). Lumbar-pelvic ratios, ranges of motion, angular velocities, and MF flexion-relaxation phenomenon were investigated. Data were obtained using the optical motion analysis system, and surface electromyography. The results indicated that lumbar-pelvic ratios during both tasks and velocity of lumbar spine during squatting were significantly greater in the 'high' than in the 'low' sitting group. Muscle activity showed no differences between groups. Prolonged sitting can be considered a factor that slightly, but statistically significantly influences the lumbar-pelvic kinematics in physically active people.Practitioner summary: Lumbar-pelvic kinematics can be altered by prolonged sitting in physically active students. Lumbar-pelvic ratios during squatting and forward bending and lumbar spine velocity during squatting were significantly greater in the 'high' than in the 'low' sitting group. Sedentary behaviour should be considered during an assessment of movement patterns.Abbreviations: BMI: body mass index; ERR: extension-relaxation ratio; FRP: flexion-relaxation phenomenon; FRR: flexion-relaxation ratio; IPAQ: International Physical Activity Questionnaire; LBP: low back pain; METs: metabolic equivalent of tasks; MF: multifidus muscle; PA: physical activity; ROM: range of motion; sEMG: surface electromyography.

Endo- and exohedral complexes of superphane with cations.

Quite recently it has been shown in a previous study that superphane, that is, [2.2.2.2.2.2](1,2,3,4,5,6)cyclophane, is a very convenient molecule in the study of endohedral complexes and especially in the study of the influence of the caged entity (i.e., guest) on the structure of the host molecule. This advantage results from the presence of two parallel benzene rings joined together by six quite flexible ethylene bridges (spacers). This article examines the energetic and structural properties of endo- and exohedral complexes of superphane with the following cations: H+ , Li+ , Na+ , K+ , Be2+ , Mg2+ , Ca2+ , B3+ , Al3+ , Ga3+ . The stability of endohedral complexes has been shown to be strongly dependent on the charge and radius of the caged cation. The inclusion of the cation inside the superphane molecule causes its 'swelling', which is manifested by an increase in the distance between the benzene rings and elongations of the ring and spacer C-C bonds. In the case of exohedral complexes, three forms are investigated: with the cation above the benzene ring, with the cation interacting with the superphane window in the equatorial position, and with the cation interacting with the center of the C-C spacer bond. The first of these forms has been shown to be preferred. The cation⋯acceptor distance depends on the cation radius. Among the cations investigated, H+ and Be2+ are particularly reactive and predisposed to induce significant structural changes in the superphane molecule, forming C-H bond or C-Be-C bridges, respectively.

The physical nature of the ultrashort spike-ring interaction in iron maiden molecules.

The so-called 'iron maiden' molecules belong to one of the most interesting subgroups of cyclophanes due to the presence of the ultrashort interaction between the CX apical bond and the benzene ring. This article presents an in-depth theoretical study of 16 'iron maiden' molecules, in which X = H, F, Cl or Br and the side chains are of various lengths and types: CSC, CSCC, CCC, and CCCC. It is shown that the H → F → Cl → Br substitution leads to a significant expansion of the 'iron maiden' molecule. Shorter chains lead to more pronounced effects, while insertion of sulfur atoms into the side chains lowers them. Structural changes are associated with an increase in energetic destabilization of X. Moreover, unlike for H, in the case of X = halogen, the out → in isomerization is energetically disadvantageous. The 'iron maiden' molecules are characterized by the presence of only three X⋯CAr bond paths. Particularly noteworthy are unusually large (even up to 32) values of the X⋯CAr bond ellipticity, which results from flat electron density distribution. The X⋯π interaction in each of the investigated 'iron maiden' molecule turned out to be multi-center, stabilizing and almost purely covalent in nature as indicated by the definitely dominant percentage (94.8%-101.6%) of the exchange-correlation energy. The spatial hindrance within the 'iron maiden' molecules appears to be not so much due to the X⋯π repulsion, but due to unfavorable steric interactions between X and the CC side bonds. It is also confirmed that some CH⋯HC interactions in aliphatic chains can be very weakly stabilizing.

Acetylated Tau Protein: A New Piece in the Puzzle between Brain Ischemia and Alzheimer's Disease.

Cerebral ischemia in humans and animals is a life-threatening neuropathological event and leads to the development of dementia with the Alzheimer's disease phenotype [...].

Nature of Beryllium, Magnesium, and Zinc Bonds in Carbene⋯MX2 (M = Be, Mg, Zn; X = H, Br) Dimers Revealed by the IQA, ETS-NOCV and LED Methods.

The nature of beryllium−, magnesium− and zinc−carbene bonds in the cyclopropenylidene⋯MX2 (M = Be, Mg, Zn; X = H, Br) and imidazol-2-ylidene⋯MBr2 dimers is investigated by the joint use of the topological QTAIM-based IQA decomposition scheme, the molecular orbital-based ETS-NOCV charge and energy decomposition method, and the LED energy decomposition approach based on the state-of-the-art DLPNO-CCSD(T) method. All these methods show that the C⋯M bond strengthens according to the following order: Zn < Mg << Be. Electrostatics is proved to be the dominant bond component, whereas the orbital component is far less important. It is shown that QTAIM/IQA underestimates electrostatic contribution for zinc bonds with respect to both ETS-NOCV and LED schemes. The σ carbene→MX2 donation appears to be much more important than the MX2→ carbene back-donation of π symmetry. The substitution of hydrogen atoms by bromine (X in MX2) strengthens the metal−carbene bond in all cases. The physical origin of rotational barriers has been unveiled by the ETS-NOCV approach.

Testing of Exchange-Correlation Functionals of DFT for a Reliable Description of the Electron Density Distribution in Organic Molecules.

Researchers carrying out calculations using the DFT method face the problem of the correct choice of the exchange-correlation functional to describe the quantities they are interested in. This article deals with benchmark calculations aimed at testing various exchange-correlation functionals in terms of a reliable description of the electron density distribution in molecules. For this purpose, 30 functionals representing all rungs of Jacob's Ladder are selected and then the values of some QTAIM-based parameters are compared with their reference equivalents obtained at the CCSD/aug-cc-pVTZ level of theory. The presented results show that the DFT method undoubtedly has the greatest problems with a reliable description of the electron density distribution in multiple strongly polar bonds, such as C=O, and bonds associated with large electron charge delocalization. The performance of the tested functionals turned out to be unsystematic. Nevertheless, in terms of a reliable general description of QTAIM-based parameters, the M11, SVWN, BHHLYP, M06-HF, and, to a slightly lesser extent, also BLYP, B3LYP, and X3LYP functionals turned out to be the worst. It is alarming to find the most popular B3LYP functional in this group. On the other hand, in the case of the electron density at the bond critical point, being the most important QTAIM-based parameter, the M06-HF functional is especially discouraged due to the very poor description of the C=O bond. On the contrary, the VSXC, M06-L, SOGGA11-X, M06-2X, MN12-SX, and, to a slightly lesser extent, also TPSS, TPSSh, and B1B95 perform well in this respect. Particularly noteworthy is the overwhelming performance of double hybrids in terms of reliable values of bond delocalization indices. The results show that there is no clear improvement in the reliability of describing the electron density distribution with climbing Jacob's Ladder, as top-ranked double hybrids are also, in some cases, able to produce poor values compared to CCSD.

Hierarchy of Bioapatites.

Apatites are one of the most intensively studied materials for possible biomedical applications. New perspectives of possible application of apatites correspond with the development of nanomaterials and nanocompounds. Here, an effort to systematize different kinds of human bioapatites forming bones, dentin, and enamel was undertaken. The precursors of bioapatites and hydroxyapatite were also considered. The rigorous consideration of compositions and stoichiometry of bioapatites allowed us to establish an order in their mutual sequence. The chemical reactions describing potential transformations of biomaterials from octacalcium phosphate into hydroxyapatite via all intermediate stages were postulated. Regardless of whether the reactions occur in reality, all apatite biomaterials behave as if they participate in them. To conserve the charge, additional free charges were introduced, with an assumed meaning to be joined with the defects. The distribution of defects was coupled with the values of crystallographic parameters "a" and "c". The energetic balances of bioapatite transformations were calculated. The apatite biomaterials are surprisingly regular structures with non-integer stoichiometric coefficients. The results presented here will be helpful for the further design and development of nanomaterials.

Determining Repulsion in Cyclophane Cages.

Superphane, i.e., [2.2.2.2.2.2](1,2,3,4,5,6)cyclophane, is a very convenient molecule in studying the nature of guest⋯host interactions in endohedral complexes. Nevertheless, the presence of as many as six ethylene bridges in the superphane molecule makes it practically impossible for the trapped entity to escape out of the superphane cage. Thus, in this article, I have implemented the idea of using the superphane derivatives with a reduced number of ethylene linkers, which leads to the [2n] cyclophanes where n<6. Seven such cyclophanes are then allowed to form endohedral complexes with noble gas (Ng) atoms (He, Ne, Ar, Kr). It is shown that in the vast majority of cases, the initially trapped Ng atom spontaneously escapes from the cyclophane cage, creating an exohedral complex. This is the best proof that the Ng⋯cyclophane interaction in endohedral complexes is indeed highly repulsive, i.e., destabilizing. Apart from the 'sealed' superphane molecule, endohedral complexes are only formed in the case of the smallest He atom. However, it has been shown that in these cases, the Ng⋯cyclophane interaction inside the cyclophane cage is nonbonding, i.e., repulsive. This highly energetically unfavorable effect causes the cyclophane molecule to 'swell'.

On the Coexistence of the Carbene⋯H-D Hydrogen Bond and Other Accompanying Interactions in Forty Dimers of N-Heterocyclic-Carbenes (I, IMe2, IiPr2, ItBu2, IMes2, IDipp2, IAd2; I = imidazol-2-ylidene) and Some Fundamental Proton Donors (HF, HCN, H2O, MeOH, NH3).

The subject of research is forty dimers formed by imidazol-2-ylidene (I) or its derivative (IR2) obtained by replacing the hydrogen atoms in both N-H bonds with larger important and popular substituents of increasing complexity (methyl = Me, iso-propyl = iPr, tert-butyl = tBu, phenyl = Ph, mesityl = Mes, 2,6-diisopropylphenyl = Dipp, 1-adamantyl = Ad) and fundamental proton donor (HD) molecules (HF, HCN, H2O, MeOH, NH3). While the main goal is to characterize the generally dominant C⋯H-D hydrogen bond engaging a carbene carbon atom, an equally important issue is the often omitted analysis of the role of accompanying secondary interactions. Despite the often completely different binding possibilities of the considered carbenes, and especially HD molecules, several general trends are found. Namely, for a given carbene, the dissociation energy values of the IR2⋯HD dimers increase in the following order: NH3< H2O < HCN ≤ MeOH ≪ HF. Importantly, it is found that, for a given HD molecule, IDipp2 forms the strongest dimers. This is attributed to the multiplicity of various interactions accompanying the dominant C⋯H-D hydrogen bond. It is shown that substitution of hydrogen atoms in both N-H bonds of the imidazol-2-ylidene molecule by the investigated groups leads to stronger dimers with HF, HCN, H2O or MeOH. The presented results should contribute to increasing the knowledge about the carbene chemistry and the role of intermolecular interactions, including secondary ones.

Measurements of Energetic States Resulting from Ion Exchanges in the Isomorphic Crystals of Apatites and Bioapatites.

Developments in the field of nanostructures open new ways for designing and manufacturing innovative materials. Here, we focused on new original ways of calculating energy changes during the substitution of foreign ions into the structure of apatites and bioapatites. Using these tools, the energetic costs of ion exchanges were calculated for the exemplary cases known from the literature. It was established that the most costly were ion exchanges of some cations inside apatites and of anions, and the least costly exchanges in tetrad channel positions. Real energy expenses for bioapatites are much smaller in comparison to mineral apatites due to the limited involvement of magnesium and carbonates in the structure of hard tissues. They are of the order of several electron volts per ion. The rigorous dependences of the energy changes and crystallographic cell volumes on the ionic radii of introduced cations were proved. The differentiation of the positioning of foreign ions in locations of Ca(I) and Ca(II) could be calculated in the case of a Ca-Pb reaction in hydroxyapatite. The energetic effects of tooth aging were indicated. The ability of energy change calculation during the ion exchange for isomorphic substances widens the advantages resulting from X-ray diffraction measurements.

Dependence of the substituent energy on the level of theory.

Most often, the substituent effects are described using rather troublesome Hammett constants. Quite recently, it has been proposed to use the so-called substituent energy, which is based on total energies of the X-substituted polycyclic aromatic hydrocarbon and phenyl. This article concerns the influence of the applied level of theory (i.e., both the basis set and the method) on the determined values of the substituent energies. For this purpose, the energies of the NH2 and NO2 groups in 16 unique positions of naphthalene, anthracene, tetracene, phenanthrene, and pyrene were calculated using 10 different basis sets and 23 various exchange-correlation functionals representing the entire Jacob's Ladder, from local, through gradient- and meta-gradient-corrected, to hybrid and double-hybrid ones. Additionally, using even larger 6-311++G(2df,2p) basis set, the energies of NH2 , NO2 , CN, and Cl were also computed. Both the basis set and the method used have little effect on the substituent energy if the substituent is in the benzene-like position. On the contrary, the effect of the level of theory is pronounced especially in the case of the most spatially crowded 4-substituted phenanthrene. Substituent energies have been shown to be very useful theoretical parameters describing the proximity effect in the substituted derivatives of polycyclic aromatic hydrocarbons.

Intramolecular Hydrogen Bonding 2021.

Undoubtedly, hydrogen bonds occupy a leading place in the rich world of intermolecular interactions [...].