Exact solution to the rotation-ring-puckering problem ofD4h-D2dfour-membered ring molecules by infinite matrix diagonalization

The rotation-ring-puckering problem of four-membered ring cyclobutane-type molecules with D 4h -D 2d conformations is formulated as a dynamical system in the eulerian angles and the polar coordinate ϑ. Classical and quantum-mechanical hamiltonians and their symmetry group O ++(3) × D ∞h are discussed. The kinetic energy matrix coefficients gmm are found to be irrational functions of the trigonometric polynomial 3 + cos 2ϑ in the internal coordinate ϑ. It is shown that the energy matrix coefficients may all be expressed as Laurent coefficients by means of the hypergeometric function 2 F 1, the convergence being determined by the roots of the kinetic determinant. Selection rules and matrix elements for rotation-ring-puckering Raman transitions are given.