The IR and Raman spectra and conformations of calix[4]arene, thiacalix[4]arene and their p-tert-butyl derivatives have been analysed within the framework of scaled quantum mechanics (SQM). It is shown that the introduction of four p-tert-Bu groups into the calixarene molecules influences the relative energies of their conformers and the enthalpy of the cooperative intramolecular H-bonding (DeltaH(intra)) almost negligibly. DeltaH(intra), evaluated from Iogansen's rule, amounts to approximately 26-28 kcal mol(-1) for the calixarenes and approximately 20-21 kcal mol(-1) for the thiacalixarenes, which essentially exceeds the enthalpies of non-cooperative H-bonds formed by related phenols. As a result of this strong bonding, bands of stretching, bending and torsion vibrations of an eight-membered cyclic system (OH...)4 arise, e.g., two delta(OH)4 bands are observed in the IR spectra of the most highly symmetric C4 cone conformations of calix[4]arene and thiacalix[4]arene. The "duplication" of the number of OH infrared bands is a good new indicator of cooperativity of intramolecular H-bonding of the calixarenes.

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The (2 + p)-satisfiability (SAT) problem interpolates between different classes of complexity theory and is thought to be of basic interest in understanding the onset of typical case complexity in random combinatorics. In this paper, a tricritical point in the phase diagram of the random (2 + p)-SAT problem is analytically computed using the replica approach and found to lie in the range 2 5 p 0 0.416. These bounds on p 0 are in agreement with previous numerical simulations and rigorous results. §

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