In order to explore the essence of the hydration process of chitin or chitosan in the presence of cation, the cooperativity effects between the H-bonding and Na+···molecule interactions in the 1,4-dimethoxy-D-glucosamine (DMGA) complexes with H2O and Na+ were investigated at the B3LYP/6-311++G(d,p), M06-2X/6-311++G(2df,2p), and ωB97X-D/6-311++G(2df,2p) levels. The result shows that the complexes in which Na+ or H2O is bonded simultaneously to the -NH and -OH groups connected to the C3 atom of DMGA are the most stable. The cooperativity and anti-cooperativity effects occur in DMGA···H2O···DMGA and DMGA···Na+···H2O, while only the cooperativities are confirmed in DMGA···Na+···DMGA. The cooperativity occurs in the DMGA···Na+···H2O complexes without the hydration, while the anti-cooperativity occurs in those with the hydration. Furthermore, the cooperativity and anti-cooperativity in DMGA···Na+···H2O are far stronger than those in DMGA···Na+···DMGA or DMGA···H2O···DMGA. Therefore, a deduction is given that the cooperativity and anti-cooperativity effects play an important role in the hydration of chitin or chitosan in the presence of Na+. When only Na+ is linked with -OH and -NH groups of chitosan or chitin, due to the cooperativity effect, the hydration does not occur. When both Na+ and H2O are linked with -OH and -NH groups, the anti-cooperativities are dominant in controlling of the aggregation process of Na+, H2O, chitosan, and chitin, leading to the possible hydration. Atoms in molecules (AIM) analysis confirms the cooperativity and anti-cooperativity effects. Graphical abstract.

The reaction pathway of the cyclization of 2-phenoxybenzophenone into 9-phenyl-9H-xanthen-9-ol in the presence of acid and an excess of AlCl33 was studied using density functional theory. This type of reaction is known to occur during the Friedel-Crafts polycondensation of poly(aryl ether ketones) following the undesired benzoylation of nucleophilic positions ortho- to the growing polymer\'s ether groups. The formed defect acts as an undesired terminator of the polymer chain, causing severe problems in the polymer\'s melt state. A branched, multistep mechanism reminiscent of the Friedel-Crafts acylation reaction is discovered; the reaction starts with the protonation of the carbonyl oxygen, followed by intramolecular electrophilic attack on the carbonyl carbon that determines the turnover frequency of the catalytic cycle and ends by deprotonation of the Wheland intermediate.