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A Universal Two‐Parameter Kratzer‐Potential and Its Superiority over Morse's for Calculating and Scaling First‐Order Spectroscopic Constants of 300 Diatomic Bonds
Author(s) -
Van Hooydonk Guido
Publication year - 1999
Publication title -
european journal of inorganic chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.667
H-Index - 136
eISSN - 1099-0682
pISSN - 1434-1948
DOI - 10.1002/(sici)1099-0682(199910)1999:10<1617::aid-ejic1617>3.0.co;2-1
Subject(s) - asymptote , scaling , diatomic molecule , chemistry , morse potential , ionic bonding , quantum mechanics , statistical physics , computational chemistry , mathematical physics , thermodynamics , physics , mathematics , molecule , mathematical analysis , geometry , ion
Abstract After decades of intensive research, the question remains whether or not a universal two‐ or three‐parameter potential exists. For a large number of about 300 bonds, we now critically review the constraints for potentials and asymptotes, involved in three available scaling processes (Varshni, Calder–Ruedenberg, and Graves–Parr). We show that the covalent Sutherland parameter can never be a universal scaling factor. This implies that the usual constraint U ( R ) = – D e at R = ∞ for potentials is only desirable and that the natural asymptote D e is not even needed to explain the relations between the constants. We show that ionic potentials of generalized Kratzer‐type (Varshni's V th potential) and their ionic Coulomb‐like asymptotes Ae 2 / R e (with A close to 1) behave as simple universal two‐parameter potentials. For both α e and ω e x e , this potential gives percentage deviations 2 to 3 times smaller than Morse's three parameter potential for hundreds of bonds. We also prove that the Graves–Parr scaling hypothesis is valid, despite these authors' own conclusion. We discuss various new relations between spectroscopic constants.