A minimum covariance basis for diatomic vibrational constants

An alternative semianalytical representation of diatomic vibrational energy levels to the Dunham expansion, is presented in the form of an expansion over Newton polynomials. This latter representation produces smaller variances and correlation coefficients than Dunham's representation, especially for light molecules. The method is illustrated by application to the vibrational levels of the ground state of the H₂ molecule. Extension of the method to vibrational-rotational levels is discussed briefly.