Isotope effect in the Morse approximation of the ground state term of hydrogen molecule nH2, n = 1-7. Herzberg anomaly and anharmonicity

TL;DR

This study investigates how isotopic mass variations affect Morse potential approximations of hydrogen molecules' ground states, revealing systematic deviations, Herzberg anomalies, and anharmonic effects across isotopologues.

Contribution

It introduces a systematic analysis of Morse approximation deviations and Herzberg anomalies in hydrogen isotopologues, highlighting their impact on potential modeling.

Findings

Morse approximation deviations increase with isotopic mass.

Herzberg anomalies occur at specific internuclear distances.

Divergence between models M1(r) and M2(r) is minimal across isotopologues.

Abstract

The influence of the reduced mass on the results of the approximation by the Morse function of the ground electronic state term potential U(r) of hydrogen molecule nH2 for seven symmetrical isotopologues n = 1-7 is investigated. For each isotopologue, two alternative model solutions of the Schroedinger equation are obtained, namely, M1(r) and M2(r) functions, which differ by the selection of the primary fitting parameters in the Morse approximation. The U(r) - M(r) functions are shown to clearly visualize the differences between the shapes of the potential at its approximation. The concept of systematic deviation of Morse functions from the real potential is introduced. This deviation is always present in the approximation of simple terms, for which U(r) curve lies between M1(r) and M2(r) without crossings. In case of nH2, for M1(r) the systematic monotonous deviation increases, reaching 1700-2770 cm-1 (for 7H2-1H2) at the level of the asymptote. For M2(r) the systematic deviation decreases at larger distances: it is dome-shaped with a maximum of ca. 1500 cm-1 in the upper part of the term, after which it falls to zero. The M2(r) curves for different isotopologues diverge by less than 20 cm-1. There are also anomalies, where M1(r) and M2(r) cross U(r), called "Herzberg anomaly". For example, at around r = 1.08 A the U(r) - M2(r) function shows anomalous negative values ranging from -125 cm-1 (for 1H2) to -142 cm-1 (for 7H2). The diagnostic value of Herzberg anomaly and anharmonicities for various isotopologues is discussed.