Approximation of the electronic term of the diatomic molecule by the Morse function. Inversion of anharmonicity
Denisov G.S.1, Tokhadze I. K.1, Asfin R. E.1
1St. Petersburg State University, St. Petersburg, Russia
Email: iktpen1@yandex.ru
The approximation of interatomic potentials in diatomic molecules using the Morse potential typically leads to an overestimated bond energy, calculated as D'e=ωe2/4ωexe, based on known values of ωe and ωexe determined from the first two vibrational transitions, 0-1 and 1-2. This relationship holds true for a wide range of molecules, such as H2, O2, N2, HF, HCl, and many others. However, for some molecules and diatomic ions, the extrapolated value of the bond energy D'e turns out to be lower than the actual value De. In such molecules, the shape of the potential energy curve deviates significantly from the standard form due to a broadening in the lower part of the potential well, which manifests as a large anharmonicity ωexe. This feature is conveniently analyzed using the difference δ(r)=U(r)- M(r) between the actual potential and its Morse approximation. This type of approximation yields a Morse solution M1(r) that accurately describes the lower part of the potential for the simple molecules, with a monotonic increase in deviation as it approaches the dissociation asymptote. An alternative solution, M2(r), is constructed based on the known values of De and ωe, while the anharmonicity ωex'e is computed ωex'e=ωe2/4De. The M2(r) approximation provides a better description of the upper part of the potential and a satisfactory representation of the lower part. The deviation from the actual potential takes the form of a bell-shaped curve, whose maximum is typically located above the midpoint of the potential well. This paper presents several examples of potentials of a special type, for which D'e<De and ωexe>ωex'e, a behavior that can be termed the term inversion of anharmonicity. Keywords: diatomic molecules, Morse potential, anharmonicity, vibrational structure, potential function approximation.
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