Four-dimensional model calculation of torsional levels of cyclic water tetramer

Quantum four-dimensional model calculations of the coupled intermolecular torsional vibrations of the cyclic homodromic water tetramers (H₂O)₄ and (D₂O)₄ are presented, based on the analytical modEPEN4B potential energy surface [S. Graf and S. Leutwyler, J. Chem. Phys. 109, 5393 (1998), preceding paper] and a four-dimensional discrete variable representation approach. The lowest 50 torsional levels were calculated up to 420 and 500cm^-1 for (D₂O)₄ and (H₂O)₄, respectively. For both clusters, the torsional ground state is split by a synchronous O-H torsional inversion process, similar to inversion tunneling in ammonia, with calculated tunnel splittings of 21.8 and 0.00012 MHz for (H₂O)₄ and (D₂O)₄, respectively. As for the cyclic water trimer and pentamer, the four torsional fundamentals of the tetramer lie above the torsional interconversion barriers, between 185-200cm^-1 for (D₂O)₄ and 229-242cm^-1 for (H₂O)₄, but also lie below the one-dimensional torsionally adiabatic barriers. The anharmonic fundamental frequencies lie both above and below the normal-mode frequencies, by up to 33%. Slightly above the fundamental torsional excitations, at 257-260 and 280-281cm^-1 for (H₂O)₄ and (D₂O)₄, respectively, lie four states corresponding to four versions of the uudd isomer, which form a pseudorotational manifold; the torsional interconversion occurs by a sequence of double O-H flips. Higher excited pseudorotational states are calculated up to a vibrational angular momentum of k=3. At ≈295 and ≈300cm^-1, a further group of eight states is found, corresponding to the eight permutationally equivalent versions of yet another isomer, the uuud structure. The four uudd and eight uuud states of (H₂O)₄ exhibit inverse isotope effects, and lie at lower energy than their (D₂O)₄ counterparts.