A new basis set for the representation of angular degrees of freedom

A new set of angular basis functions is presented that yields a straightforward representation of the bending kinetic energy operator. The basis functions vanish at the interval limits and are therefore appropriate for the description of librational but not rotational motion. The basis set can be derived from Chebychev polynomials of the second kind and is related to an equidistantly spaced quadrature grid. We compare the performance of these functions to the standard basis for bending operators, Legendre functions Pl(cos(x)), for the description of the pure bending motion of water and the vibrational states associated with the ground state potential of ozone.