Computing a perfect strategy for n × n chess requires time exponential in n

It is proved that a natural generalization of chess to an n × n board is complete in exponential time. This implies that there exist chess positions on an n × n chessboard for which the problem of determing who can win from that position requires an amount of time which is at least exponential in $\text{n}$.     

DielsAlder Cyclization of a Dihydropyridine: NMR Spectroscopy,X‐Ray Crystallography,and DFT Computations. Bent Aromatic Dimeric Clusters in the Solid Phase

Structural studies of the N‐(2,4‐dinitrophenyl) derivative of a Diels? Alder‐cyclized 1,2‐dihydropyridine both unequivocally established the polycyclic framework and revealed interesting distortions of aromatic structure and unique dimeric clustering of the aromatic entities in the solid state.     

Molecular encapsulation via metal-to-ligand coordination in a Cu(I)-folded molecular basket

A molecular basket, composed of a semirigid C3v symmetric tris-norbornadiene framework and three pyridine flaps at the rim, has been shown to coordinate to a Cu(I) cation and thereby fold in a multivalent fashion. The assembly was effective (Ka = 1.73 +/- 0.08 x 10(5) M(-1)) and driven by enthalpy (DeltaH(o) = -7.2 +/- 0.1 kcal/mol, DeltaS(o) = -0.25 eu). Variable temperature (1)H NMR studies, assisted with 2D COSY and ROESY investigations, revealed the existence of Cu(I)-folded basket 10b with a molecule of acetonitrile occupying its interior and coordinated to the metal. Interestingly, 10b is in equilibrium with Cu(I)-folded 10a , whose inner space is solvated by acetone or chloroform. The incorporation of a molecule of acetonitrile inside 10a was found to be driven by enthalpy (DeltaH(o) = -3.3 +/- 0.1 kcal/mol), with an apparent loss in entropy (DeltaS(o) = -9.4 +/- 0.4 eu); this is congruent with a complete immobilization of acetonitrile and release of a "loosely" encapsulated solvent molecule during 10a/b interconversion. From an Eyring plot, the activation enthalpy for incorporating acetonitrile into 10a was found to be positive (DeltaH(double dagger) = 6.5 +/- 0.5 kcal/mol), while the activation entropy was negative (DeltaS(double dagger) = -20 +/- 2 eu). The results are in agreement with an exchange mechanism whereby acetonitrile "slips" into an "empty" basket through its side aperture. In fact, DFT (BP86) calculations are in favor of such a mechanistic scenario; the calculations suggest that opening of the basket's rim to exchange guests is energetically demanding and therefore less feasible.