Groves and Ledyard (Econometrica 45:783–809, 1977) constructed a mechanism attaining Pareto efficient allocations in the presence of public goods. After this path-breaking paper, many mechanisms have been proposed to attain desirable allocations with public goods. Thus, economists have thought that the free-rider problem is solved, in theory. Our view to this problem is not so optimistic. Rather, we propose fundamental impossibility theorems with public goods. In the previous mechanism design, it was implicitly assumed that every agent must participate in the mechanism that the designer provides. This approach neglects one of the basic features of public goods: non-excludability. We explicitly incorporate non-excludability and then show that it is impossible to construct a mechanism in which every agent has an incentive to participate.

We have structurally characterized a number of lithiated calix[4]arenes, where the bridge in the calix[4]arene is thia (-S-, L^SH₄), sulfinyl (-SO-, L^SOH₄), sulfonyl (-SO₂-, L^SO2H₄), dimethyleneoxa (-CH₂OCH₂-, L^COCH₄) or methylene (-CH₂-, LH₄). In the case of L^4SH₄, interaction with LiOtBu led to the isolation of the complex [Li₈(L^4S)₂(THF)₄]·5THF (1·5THF), whilst similar interaction of L^4SOH₄ led to the isolation of [Li₆(L^4SOH)₂(THF)₂]·5(THF) (2·5THF). Interestingly, the mixed sulfinyl/sulfonyl complexes [Li₈(calix[4]arene(SO)(SO₂)(SO_1.68)₂)₂(THF)₆]·8(THF) (3·8THF) and [Li₅Na(L^SO/3SO2H)₂(THF)₅]·7.5(THF) (4·7.5(THF) have also been characterized. Interaction of LiOtBu with L^SO2H₄ and L^COCH₄ afforded [Li₅L^4SO2(OH)(THF)₄]·2THF (5·2THF) and [Li₆(L^COC)₂(HOtBu)₂]·0.78THF·1.22hexane (6·0.78THF·1.22hexane), respectively. In the case of LH₄, reaction with LiOtBu in THF afforded a monoclinic polymorph [LH₂Li₂(thf)(OH₂)₂]·3THF (7·3THF) of a known triclinic form of the complex, whilst reaction of the de-butylated analogue of LH₄, namely de-BuLH₄, afforded a polymeric chain structure {[Li₅(de-BuL)(OH)(NCMe)₃]·2MeCN} _n (8·2MeCN). For comparative catalytic studies, the complex [Li₆(L^Pr)₂(H₂O)₂]·hexane (9 hexane), where L^Pr2H₂ = 1,3-di-n-propyloxycalix[4]areneH₂, was also prepared. The molecular crystal structures of 1-9 are reported, and their ability to act as catalysts for the ring opening (co-)/polymerization (ROP) of the cyclic esters ε-caprolactone, δ-valerolactone, and rac-lactide has been investigated. In most of the cases, complex 6 outperformed the other systems, allowing for higher conversions and/or greated polymer M _n.

Six novel pyrene-fused hexaarylbenzene derivatives (3a-f) were designed, synthesized, and characterized, which exhibited aggregation-induced emission enhancement (AIEE) in the aggregated state by means of THF/H2O mixtures. Techniques such as theoretical calculations, single crystal X-ray diffraction, and photophysical measurements in solution and in the solid state were employed to illustrate the tunable, variable, and sensitive AIEE features in this system. Both theoretical and experimental results revealed that the nature of the multiple photoluminescence should be taken into account when elucidating and designing the multiple photoluminescence phenomenon and molecules.

The synthesis of three new heteroditopic receptors (5a-c) which are based on thiacalix[4]arenes in the 1,3-alternate conformation is reported herein. These new receptors each have two thiourea moieties linking phenyl groups, two of which are substituted with electron-withdrawing groups at their para-positions, and at the opposite side of the thiacalix[4]arene cavity, with two 2-pyridylmethyl groups. One example (5a) was also characterized by X-ray crystallography. A limited 1H-NMR and UV-vis anion complexation study was conducted. DFT computational determinations indicated that 5c, which has strongly electron-withdrawing NO2 groups, had the most effective recognition ability towards the selected anions. The binding of Ag+ at the 2-pyridyl moieties, and the binding of the anions at the two thiourea NH groups of the p-substituted phenylthioureido moieties, respectively, was also investigated. The appearance of a positive allosteric effect with receptor 5b was also found using 1H-NMR titration experiments.

A series of pyrene-fused azaacene-type conjugated molecules containing two pyrazine units and up to eight rectilinearly arranged aromatic rings were prepared by condensation coupling reactions in moderate yields. The geometries and electronic structures associated with 2 and 5 were evaluated by DFT calculations. Photophysical properties indicated that these systems possess delocalized structures, and their optoelectronic properties can be tuned by extending the π-conjugated length and introducing electronic-withdrawing groups. The compounds were thoroughly investigated by XRD studies, electrochemistry and DFT calculations. High thermal stability and tunable energy levels make them excellent candidates as a class of organic molecular materials.

A receptor cone-1 based on a hexahomotrioxacalix[3]arene bearing three pyridyl groups was successfully synthesized, which has a C₃-symmetric conformation and is capable of binding alkylammonium and metal ions simultaneously in a cooperative fashion. It can bind alkylammonium ions through the -cavity formed by three aryl rings. This behaviour is consistent with the cone-in/cone-out conformational rearrangement needed to reorganize the cavity for endo-complexation. As a C₃-symmetrical pyridyl-substituted calixarene, receptor cone-1 can also bind an Ag⁺ ion, and the nitrogen atoms are turned towards the inside of the cavity and interact with Ag⁺. After complexation of tris(2-pyridylamide) derivative receptor cone-1 with Ag⁺, the original C₃-symmetry was retained and higher complexation selectivity for n-BuNH₃⁺ versus t-BuNH₃⁺ was observed. Thus, it is believed that this receptor will have a role to play in the sensing, detection, and recognition of Ag⁺ and n-BuNH₃⁺ ions.

Two novel receptors 5,11,17,23-tetra-tert-butyl-25,27-bis[(ethoxycarbonyl)methoxy]-26,28-bis-[1-methyl-(imidazole)meth-oxy]-2,8,14,20-tetra-thiacalix[4]arene (L1) and 5,11,17,23-tetra-tert-butyl-25,27-bis-[(benzyl)methoxy]-26,28-bis-[1-methyl-(imidazole)-methoxy]-2,8,14,20-tetrathiacalix[4]arene (L2) possessing imidazole moieties based on thiacalix[4]arene in the 1,3-alternate conformation have been synthesized and characterized. The crystal structures of L1 and L2 have been determined. The binding behaviour towards Li+, Na+, K+ and Ag+ ions has been examined by 1H NMR titration experiments in (CDCl3/CD3CN; 10:1, v/v) solution. The exclusive formation of mononuclear complexes of L1 with metal cations is of particular interest revealing a negative allosteric effect in the thiacalix[4]arene family. Liquid-liquid extraction experiments indicate that synthesized L2 can be utilized as an efficient reusable extractant for dichromate anion by controlling the pH of the aqueous solution.