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Macrocyclic arenes laid the foundations of supramolecular chemistry and their study established the fundamentals of noncovalent interactions. Advancing their frontier, here we designed rigidified resorcin[4]arenes that serve as hosts for large nonspherical anions. In one synthetic step, we vary the host's anion affinity properties by more than seven orders of magnitude. This is possible by engineering electropositive aromatic C-H bond donors in an idealized square planar geometry embedded within the host's inner cavity. The hydrogen atom's electropositivity is tuned by introducing fluorine atoms as electron withdrawing groups. These novel macrocycles, termed fluorocages, are engineered to sequester large anions. Indeed, experimental data shows an increase in the anion association constant (

Naturally sourced 2-picolinic acid was discovered as an off-the-shelf, non-toxic, and inexpensive HBD catalyst for the cycloaddition of CO2 to both internal and terminal epoxides to prepare cyclic carbonates at low catalyst loadings.

A transition-metal-free postmodification of the Groebke-Blackburn-Bienayme (GBB) reaction for the synthesis of spiro[chromene-imidazo[1,2-a]pyridin]-3'-imine was discovered. The unusual transformation represents the first example of activation and the reaction of the imidazole carbon atom. In this postcondensational modification, KOt-Bu acts as a base, which, after the isomerization of an alkyne moiety to allene, causes the next unique nucleophilic reaction of the imidazole carbon atom that results in spirocyclic structures. The proposed reaction mechanism was confirmed based on the DFT calculations.

We employed density functional theory (DFT) methods to investigate the most plausible mechanism of cyclization/ring expansion of proline with

Molecular compounds with permanent tubular architectures displaying radial π-conjugation are exceedingly rare. Their radial and axial delocalization presents them with unique optical and electronic properties, such as remarkable tuning of their Stokes shifts, and redox switching between global and local aromaticity. Although these tubular compounds display large internal void spaces, these attributes have not been extensively explored, thus presenting future opportunities in the development of materials. By using cutting-edge synthetic methodologies to bend aromatic surfaces, large opportunities in synthesis, property discovery, and applications are expected in new members of this family of conjugated molecular nanotubes.

Mechanism-based inactivation (MBI) refers to the metabolic bioactivation of a xenobiotic by cytochrome P450s to a highly reactive intermediate which subsequently binds to the enzyme and leads to the quasi-irreversible or irreversible inhibition. Xenobiotics, mainly drugs with specific functional units, are the major sources of MBI. Two possible consequences of MBI by medicinal compounds are drug-drug interaction and severe toxicity that are observed and highlighted by clinical experiments. Today almost all of these latent functional groups (e.g., thiophene, furan, alkylamines, etc.) are known, and their features and mechanisms of action, owing to the vast experimental and theoretical studies, are determined. In the past decade, molecular modeling techniques, mostly density functional theory, have revealed the most feasible mechanism that a drug undergoes by P450 enzymes to generate a highly reactive intermediate. In this review, we provide a comprehensive and detailed picture of computational advances toward the elucidation of the activation mechanisms of various known groups with MBI activity. To this aim, we briefly describe the computational concepts to carry out and analyze the mechanistic investigations, and then, we summarize the studies on compounds with known inhibition activity including thiophene, furan, alkylamines, terminal acetylene, etc. This study can be reference literature for both theoretical and experimental (bio)chemists in several different fields including rational drug design, the process of toxicity prevention, and the discovery of novel inhibitors and catalysts.

Here, we report two series (denoted as meta and para) of π-extended dibenzo[g,p]chrysenes (DBCs) with different substituents (H, Me and OMe). These six novel compounds benefit from the presence of eight methyl groups on the sp3 bridges which improve the solubility and rigidify the extended phenylenes. Their optoelectronic properties were determined using electrochemistry and spectroscopic (UV-vis and emission) techniques and further confirmed by DFT calculations. The results showed that both the position and nature of substituents on the π-extended moieties exert significant effects on the optoelectronic properties and the charge delocalization mechanism. In addition, isomerism (meta and para) leads to different packings in the solid state structure; interestingly, the crystal structure of the hydrogen substituted para molecule showed a permanent three-dimensional porous structure.

We report the discovery of a novel metastable polymorph of a propyloxy substituted calix[4]arene molecule which undergoes two distinct transformations to form different conformers and packing arrangements. The first transition was found as a reversible thermal-induced rotation (180°) in two propyloxy moieties of the closed-I form upon cooling (from 298 K to 100 K) which resulted in a new polymorph (closed-II) and is an example of single-crystal-to-single-crystal transformation (SCSC). The second transition is an irreversible and remarkable change in packing and conformation (from close to open) at room temperature which was observed after keeping the mother crystals for few days in the liquor which resulted in an open conformer; this transformation is following the Ostwald's rule of stages and is the outcome of dissolvation/recrystallization of the metastable conformer (closed-I).

Molecular compounds with zigzag carbon nanotube geometries are exceedingly rare. Here we report the synthesis and characterization of carbon-based nanotubes with zigzag geometry, best described as radially oriented [n]cyclo-meta-phenylenes, extending the tubularene family of compounds. By the incorporation of edge-sharing benzene rings into the tubularene's radial π-surface, we have uncovered the first step to give rise to the emergence of radial orbital distribution in zigzag nanorings.

Herein, we report the synthesis of two new series of angular (all-syn) ladder-type meta-[n]phenylenes (LMP, n = 3-8). One series contains keto groups at the termini bridges, denoted angular keto (AKn), the second contains alkyl groups at all bridge sp3 carbons, denoted angular alkyl (AAn). Their electronic and structural properties were delineated by a combination of electrochemistry and spectroscopic (UV-Vis and emission) methods and further supported by DFT calculations. Interestingly, experimental and DFT data show that changing the bridging group at the termini from alkyl (AAn) to keto (AKn) gives an increase in the first reduction potentials and LUMO energies, as the π-system is extended. Also, the charge (de)localization behavior is different for these two species; while the AAn compounds stablize charge with Robin-Day class III, the AKn compounds show a clear switch from class III to class II. In comparison with the linear analogues (LKn and LAn), DFT results reveal a shape independency of the charge (de)localization mechanism in acceptor-π-acceptor series (AKn/LKn).

A transition-metal-free postmodification of the Groebke-Blackburn-Bienaymé (GBB) reaction for the synthesis of spiro[chromene-imidazo[1,2

We employed the density functionaly theory (DFT)-predicted regioselectivity of the intramolecular Scholl reaction in phenanthrene and dibenzo[g,p]chrysene frameworks to obtain π-extended mono and double [7]helicenes, respectively. The formation of these helical structures occurs despite the buildup of a large strain energy up to 30 kcal/mol compared with their most stable isomers. The twisted and strained structures were characterized and analyzed by experimental (NMR, UV-vis, emission, electrochemistry, and single-crystal X-ray diffraction) techniques and were further supported by DFT calculations.

We report the synthesis and characterization of conjugated, conformationally rigid, and electroactive carbon-based nanotubes that we term tubularenes. These structures are constructed from a resorcin[nb]arene base. Cyclization of the conjugated aromatic nanotube is achieved in one-pot eight-fold C–C bond formation via Suzuki–Miyaura cross-coupling. DFT calculations indicate a buildup of strain energy in excess of 90 kcal mol−1. The resulting architectures contain large internal void spaces >260 Å3, are fluorescent, and able to accept up to 4 electrons. This represents the first scaffolding approach that provides conjugated nanotube architectures., First scaffolding approach to obtain tubular-shaped contorted aromatic architectures.

Calculation of the solvation free energy of ionic molecules is the principal source of errors in the quantum chemical evaluation of pKa values using implicit polarizable continuum solvent models. O...

A simple model has been developed for predicting the regioselectivity of arynes using orbital electronegativity. Based on this model, the nucleophile attacks the terminus possessing lower orbital electronegativity.

Herein, we report the synthesis of two new series of angular (all-syn) ladder-type meta-[n]phenylenes (LMP, n = 3–8). One series contains keto groups at the termini bridges, denoted angular keto (AKn), the second contains alkyl groups at all bridge sp(3) carbons, denoted angular alkyl (AAn). Their electronic and structural properties were delineated by a combination of electrochemistry and spectroscopic (UV-Vis and emission) methods and further supported by DFT calculations. Interestingly, experimental and DFT data show that changing the bridging group at the termini from alkyl (AAn) to keto (AKn) gives an increase in the first reduction potentials and LUMO energies, as the π-system is extended. Also, the charge (de)localization behavior is different for these two species; while the AAn compounds stablize charge with Robin-Day class III, the AKn compounds show a clear switch from class III to class II. In comparison with the linear analogues (LKn and LAn), DFT results reveal a shape independency of the charge (de)localization mechanism in acceptor-π-acceptor series (AKn/LKn).

Molecular compounds with zigzag carbon nanotube geometries are exceedingly rare. Here we report the synthesis and characterization of carbon-based nanotubes with zigzag geometry, best described as radially oriented [

The design and synthesis of a new molecular tweezer (T-tmp) with electron-rich pincers are reported. The stable monocationic radicals and self-assembled dimeric radicals of this molecular tweezer platform were prepared by chemical oxidative titration. With the aid of DFT calculations, it was found that the dimeric radicals with syn-syn-syn conformer has the most stable structure, with the hole primarily delocalized between parallel stacked pyrenyl groups.

Calixarenes have found widespread application as building blocks for the design and synthesis of functional materials in host-guest chemistry. The ongoing desire to develop a detailed understanding of the nature of NO bonding to multichromophoric π-stacked assemblies led us to develop an electron-rich methoxy derivative of calix[4]arene (3), which we show exists as a single conformer in solution at ambient temperature. Here, we examine the redox properties of this derivative, generate its cation radical (3+. ) using robust chemical oxidants, and determine the relative efficacy of its NO binding in comparison with model calixarenes. We find that 3/3+. is a remarkable receptor for NO+ /NO, with unprecedented binding efficacy. The availability of precise experimental structures of this calixarene derivative and its NO complex, obtained by X-ray crystallography, is critically important both for developing novel functional NO biosensors, and understanding the role of stacked aromatic donors in efficient NO binding, which may have relevance to biological NO transport.

There is much current interest in the design of molecular actuators, which undergo reversible, controlled motion in response to an external stimulus (light, heat, oxidation, etc.). Here we describe the design and synthesis of a series of cofacially arrayed polyfluorenes (MeFnHm) with varied end-capping groups, which undergo redox-controlled electromechanical actuation. Such cofacially arrayed polyfluorenes are a model molecular scaffold to investigate fundamental processes of charge and energy transfer across a π-stacked assembly, and we show with the aid of NMR and optical spectroscopies, X-ray crystallography and DFT calculations that in the neutral state the conformation of MeFnH1 and MeFnH2 is open rather than cofacial, with a conformational dependence that is highly influenced by the local environment. Upon (electro)chemical oxidation, these systems undergo a reversible transformation into a closed fully π-stacked conformation, driven by charge-resonance stabilization of the cationic charge. These fi...

Electro-active polychromophoric assemblies that undergo clam-like electromechanic actuation represent an important class of organic functional materials. Here, we show that the readily available cyclotetraveratrylene (CTTV) undergoes oxidation-induced folding, consistent with interconversion from a non-cofacial "sofa" conformation to a cofacial "boat" conformer. It is found that the non-cofacial "sofa" conformer of CTTV forms stable electron donor-acceptor complexes with chloranil and DDQ. Electron-transfer induced conformational transformation in CTTV provides a framework for the rational design of novel organic functional molecules.

The regioselectivity of nucleophilic addition to substituted arynes was predicted using frontier molecular orbital contribution analysis. This model indicates that the percentage of the LUMO on the reacting terminus of the aryne is responsible for the observed regioselectivity; the nucleophile attacks the carbon possessing higher contribution of the LUMO.

We report a practical two-step approach for the synthesis of hybrid-bridge macrocyclic molecules that has been used to synthesize two novel oxy-alternate-bridged macrocyclic molecules, oxy-alternate cyclotetraveratrylene (

Calculation of the solvation free energy of ionic molecules is the principal source of errors in the quantum chemical evaluation of p

Conformational analysis is one of the significant subjects in the organic chemistry curriculum. Since this subject may be intricate for some beginner students, a concrete model (an activity) has been devised to explain the conformational concepts with an intriguing and simple method. This model is based on geometric shapes (particularly triangles) in which the revolution of each shape on its axis at the centroid (around its vertices and edges) simulates the rotation about a single bond in a molecule. If we take edges as lower energy (more stable) and vertices as higher energy (less stable), this revolution gives a graph almost identical to the actual conformational energy diagram of that molecule. These shapes can also incorporate into the Newman projections to form a tangible representation of these notations. Most of the participants, who got familiar with these newly modified Newman projections, found them beneficial in enhancing the students’ perception of the basic conformational properties of the molecules. Furthermore, searching for a relevant shape to match the right molecule serves as an activity that in addition to being enjoyable can encourage the students to get engaged with the topic. This model is applicable to a large variety of molecules such as the hydrocarbon, aldehyde and ketone molecules, which can also generalize to more functional groups and compounds.

The reassembling of a simple connected graph G = (V,E) is an abstraction of a problem arising in earlier studies of network analysis. Its simplest formulation is in two steps: (1) We cut every edge of G into two halves, thus obtaining a collection of n=|V| one-vertex components. (2) We splice the two halves of every edge together, not of all the edges at once, but in some ordering \Theta of the edges that minimizes two measures that depend on the edge-boundary degrees of assembled components. The edge-boundary degree of a component A (subset of V) is the number of edges in G with one endpoint in A and one endpoint in V-A. We call the maximum edge-boundary degree encountered during the reassembling process the alpha-measure of the reassembling, and the sum of all edge-boundary degrees is its beta-measure. The alpha-optimization (resp. beta-optimization) of the reassembling of G is to determine an order \Theta for splicing the edges that minimizes its alpha-measure (resp. beta-measure). There are different forms of reassembling. We consider only cases satisfying the condition that if the an edge between disjoint components A and B is spliced, then all the edges between A and B are spliced at the same time. In this report, we examine the particular case of linear reassembling, which requires that the next edge to be spliced must be adjacent to an already spliced edge. We delay other forms of reassembling to follow-up reports. We prove that alpha-optimization of linear reassembling and minimum-cutwidth linear arrangment (CutWidth) are polynomially reducible to each other, and that beta-optimization of linear reassembling and minimum-cost linear arrangement (MinArr) are polynomially reducible to each other.

The intrinsic reactivity of allopurinol oxidation is calculated using the active-site models of aldehyde oxidase and xanthine oxidase (molybdopterin cofactor, MoCo) enzymes. The effects of substrate tautomerization, deprotonation and its orientation with respect to the active-site were considered. Among several mechanistic approaches, the most favorable mechanisms are the stepwise pathways. The transition barrier for the most stable tautomer of allopurinol is around 19.83 kcal mol−1. The stepwise approaches indicate the significant role of glutamate → glutamic acid conversion in the catabolism of allopurinol. Both aldehyde oxidase (AO) and xanthine oxidase (XO) could metabolize the allopurinol to oxypurinol through the self-inhibitory mechanism. This pathway is not in accordance with the experimental results which showed the release of oxypurinol with a low half-life. This phenomenon and also the presence of experimental evidence of allopurinol interaction with cytochrome P450 and drugs which are metabolized with P450 encouraged us to investigate allopurinol oxidation using the active species of P450 enzyme, compound I (Cpd I). The P450 enzymes are responsible for the catabolism of the overwhelming majority of drugs. The detailed understanding of the P450-catalyzed mechanism could result in more precise predictions about the drug metabolism and also the drug–drug interactions. The results of this study reveal that cytochrome P450 can successfully metabolize allopurinol with both a thermodynamically and kinetically feasible mechanism. The rate-determining step of this mechanism is around 22.77 kcal mol−1. Allopurinol oxidation with P450 will lead to the release of oxypurinol, not a self-inhibitory mechanism. The outcomes of this investigation can be extended to the other purine or pyrimidine containing compounds (especially hypoxanthine) which are metabolized by this group of enzymes.

Correction for ‘Tubularenes’ by Saber Mirzaei et al., Chem. Sci., 2020, 11, 8089–8094, DOI: 10.1039/d0sc03384g.

An efficient and highly selective synthetic method toward the preparation of pillar[ n]arenes ( n = 5, 6) is reported, based upon a high solvent-dependent selectivity found in the condensation reaction between 1,4-dialkyloxybenzene and paraformaldehyde, involving methanesulfonic acid as catalyst. Pillar[6]arene (P6) is obtained as the major product when using chloroform as solvent, while in dichloromethane pillar[5]arene (P5) is the dominant product. Accordingly, a series of P5 and P6 have been selectively synthesized with excellent yield.

Temozolomide, an anticancer and chemotherapy prodrug, undergoes pH dependent ring-opening under both acidic and alkaline conditions. While the rate of degradation accelerates with an increase in pH, it never comes to a complete halt under acidic conditions. Herein, the ring-opening of temozolomide is investigated, in both neutral and acidic conditions, to find out the energy differences and the effects of an acidic environment on its activation energy. Two possible and different pathways have been considered for the ring-opening reaction. When compared to path-2, the rate-determining step (first TS) for path-1 is about 15 kcal mol−1 more favourable. However, the second path led to a more stable product. It seems that the energy-favoured overall mechanism is a combination of the two paths (tautomerization may occur during the process). Moreover, in order to elucidate the role of the acidic conditions on the increased stability and mechanism of the drug, the protonation of all possible sites was examined. This predicts that the protonation of the oxygen of the amide group is the preferable site for protonation that would stabilize the system by about 1.23 kcal mol−1 more than the next favourable protonation site (protonated nitrogen in the imidazole ring). The low energy barrier (6 kcal mol−1) for proton exchange in these two sites results in the simultaneous existence of both N-protonated and O-protonated structures. In addition, the pKa values were calculated and averaged out at −2.625. This value indicates the extremely acidic feature of the protonated temozolomide that does not protonate or deprotonate over the normal pH range. The protonation and degradation mechanism were treated using density functional theory (B3LYP) and by employing the complete basis set (CBS-4M) method. Moreover, the high-level G3MP2 level was used on some occasions.

Thiosemicarbazones (TSC) have been the subject of a large number of investigations, either because of their pharmacological effects in a wide variety of compounds or because of their intriguing and controversial coordination behaviour. These features make TSC derivatives significant, particularly in complexes and coordination chemistry. Because some of the TSC ligands have shown E–Z interconversion about the CN double bond during the coordination process, a comprehensive study on the coordination mechanism of these TSCs has been conducted on several model molecules with the aim of applying it to other TSC derivatives, and also of providing new views on the complexation behaviour of these compounds. The density functional theory (DFT) computations (B3LYP/6-311++G(2d,p) and B3LYP/6-31+G(d)) have been used for these investigations. Initially, all the conformational and tautomeric structures were obtained and then the mechanistic studies were performed on the optimized structures. Additionally, the influence of terminal nitrogen substitution on the conformation of TSCs was also investigated. All possible mechanisms: rotation (direct isomerisation), inversion (lateral shift) mechanism, and tautomerization, which subdivides into two paths (catalysed and non-catalysed), were explored to reach the energy favoured mechanism. The DFT calculations reveal that the solvents have a strong impact on the E–Z isomerisation of TSCs in which the inversion mechanism is the most likely mechanism in aprotic (and less polar) solvents, whereas the catalytic tautomerization mechanism prevails in protic (and polar) solutions. This is because of the retardation and the acceleration effects of the protic solvent (and the acidic condition) on inversion and catalytic tautomerization mechanism, respectively. These findings are consistent with the experimental evidence obtained. Furthermore, because the E–Z isomerisation (and TSC binding modes) was under the influence of terminal N-substitution in several experiments (e.g., 3-methoxy salicylaldehyde and 2-oxo-1,2-dihydroquinoline-3-carbaldehyde TSC), the underlying reasons for this suspicious and contradictory behaviour have been also assessed and interpreted using the results obtained.

Synthesizing novel electron-rich calix[n]arene derivatives to alter the electronic properties of calixarene-based materials has been one of the long-standing interests. Herein, two new electron-rich calix[n]arenes (n = 4 and 8) with different sizes were synthesized by acid-catalyzed condensation reaction of 1,3,5-tripropoxybenzene and paraformaldehyde. Both derivatives were fully characterized with 1H and 13C NMR, mass spectrometry and X-ray crystallography. Furthermore, their electrochemical properties and oxidized product (cation radicals) have also been investigated.

Stochastic activity networks (SANs) are a well-known petri net-based formalism used for the performance and dependability modeling of a wide range of systems. On the other hand, the growing complexity of timed systems makes it imperative to apply formal analysis techniques in the early stages of the system's development. Finding a suitable framework for the modeling, evaluation, and verification of these systems is still a great challenge. In this paper, we introduce a new formalism named timed activity networks (TANs), which are based on the activity networks that are the nondeterministic settings of the SANs. The advantages of TANs are 2-fold: 1) allowing the construction of more compact petri net-based models of timed systems and 2) allowing the assignment of time intervals to timed activities where the activity completion rates are marking-dependent, which makes TANs a better model for timed systems. Thanks to the presence of the input/output gates, TANs are capable of describing a situation whose specification using petri net-based formalisms was not practical, due to the naivety of the enabling and firing rules in these models. In addition, a great benefit of TANs is the similarity of their primitives and notations to ordinary SANs, which allows us to easily obtaining these 2 models from each other. Accordingly, SANs can be used for performance, and dependability modeling and evaluation, while TANs can be used for the model checking of timed systems. In this paper, we present the definitions, semantics, and model checking techniques of the proposed formalism. In order to model check TAN models, a transformation procedure is given for translating TAN models into the equivalent linear hybrid automaton, which can then be used with the existing techniques and tools.

The electronic features of anti-tumor agent, temozolomide, and its degradation products (MTIC and metabolite AIC) have been traced by means of UV absorption spectroscopy in vacuo and aqueous media. For comparison, electronic spectra of related structures and drugs (e.g., dacarbazine) were also investigated. These investigations were carried out using time-dependent density functional theory (TD-DFT) method while the conductor like screening model (COSMO) were applied for the inclusion of solvent effects in electronic spectra. From functional benchmarking, two methods; B3LYP and O3LYP were selected among several other methods with 6-311+G(2d,p) basis set aiming to get the best results in accord with the experimental values. An assessment of the obtained spectra has shown that O3LYP functional gives a mean absolute error (MAE) from experimental absorption peaks of 4.3 nm compared to the 7.2 nm MAE value at B3LYP level in aqueous media. Furthermore, since the structural and tautomeric conformers affect the electronic spectra, conformational preferences have been analyzed in temozolomide, dacarbazine, and their related structures. Temozolomide structure possesses two rotamers that differ in the orientation of carboxamide moiety with a small energy difference (energy difference of 1.39 kcal mol-1 in vacuo and 0.35 kcal mol-1 in aqueous media at B3LYP/6-311++G(2df,3pd). The more stable and meta-stable TMZ rotamer have shown their absorption maxima at 329-334 nm, respectively, at O3LYP level in aqueous media. Applying statistical calculation according to Boltzmann population formula at 25 °C and computed weighed mean estimates the λmax of temozolomide at 331 nm, which is in notable agreement with the experimental value (330 nm). Moreover, molecular orbital composition analysis has been conducted in order to interpret these findings. Graphical Abstract Temozolomide and dacarbazine.

In recent decades, the roles of government have changed greatly and consequently systems of national planning have also changed. Governments still have roles but they must play soft roles and therefore, they need new tools for these new roles. This paper proposes a model to make it possible to establish which actions needs to be planned at the national level (particularly for science and technology development) by compounding three government roles (providing policy intelligence, making policy decisions and policy implementation) with four tools (direct intervention, regulations, offering incentives and promotion). The National Iranian Nanotechnology Initiative is used as a case study. Copyright , Beech Tree Publishing.

Max Consensus-based Auction (MCA) protocols are an elegant approach to establish conflict-free distributed allocations in a wide range of network utility maximization problems. A set of agents independently bid on a set of items, and exchange their bids with their first hop-neighbors for a distributed (max-consensus) winner determination. MCAprotocols have been proposed, e.g., To solve the task allocation problem for a fleet of unmanned aerial vehicles, in smart grids, or in distributed virtual network management applications. Misconfigured or malicious agents participating in a MCAor an incorrect combination of policy instantiations can lead to oscillations of the protocol, causing, e.g., Service Level Agreement (SLA) violations. In this paper we propose a formal, machine-readable, Max-Consensus Auction model encoded in the Alloy light weight modeling language. The model consists of a network of agents applying the MCA mechanisms instantiated with potentially different policies, and a set of predicates to analyze its convergence properties. We were able to verify that even when all agents follow the protocol, MCA is not resilient against rebidding attacks, and that the protocol fails (to achieve a conflict-free resource allocation) for some specific combinations of policies. Our model can be used to verify, with a "push-button" analysis, the convergence of the MCA mechanism to a conflict-free allocation under a wide range of policy instantiations.