The measurement of frequency separations in high-resolution nuclear magnetic resonance spectra using a double-lock spectrometer

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 ?. Classical and quantum-mechanical hamiltonians and their symmetry group O ⁺⁺(3) × D _∞h are discussed. The kinetic energy matrix coefficients g_mm are found to be irrational functions of the trigonometric polynomial 3 + cos 2? in the internal coordinate ?. 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.