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Explicit algebraic expressions for the expansion of the vibrational matrixelements in series of matrix elements on the wave functions of the groundvibrational state have been obtained for arbitrary sufficiently differentiablefunctions of the internuclear distance, arbitrary values v and v', and thepotential curves whose ladder operators can be constructed. A diagram techniquehave been developed for it that consists in: 1) the numeration of the matrixelements by points of the 2D diagram with coordinates (l, k), 2) the drawingarrows between points of this diagram corresponding to the action of theannihilation operators on the wave functions; 3) total taking into account ofall possible path vectors formed by the continuous sequences of arrows frompoint (v, v) towards points (0, k). The only requirement is that the action ofthe operator on the wave functions should give the wave functions of theSchr\"odinger equation with the potential curve having the same parametervalues. All necessary data for algebraic calculations of the vibrationaldependence of matrix elements for the harmonic oscillator and the Morsepotential have been given. Obtained expressions can be used to determine theabsolute values and vibrational dependences of various spectroscopiccharacteristics of both ground and electronically excited states of diatomicmolecules.

Algebraic Determination of Spectral Characteristics of Rovibrational  States of Diatomic Molecules. I. Diagram Technique for Determination of  Vibrational Dependences of Matrix Elements