{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T00:57:53Z","timestamp":1760057873383,"version":"build-2065373602"},"reference-count":19,"publisher":"MDPI AG","issue":"3","license":[{"start":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T00:00:00Z","timestamp":1740441600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This review discusses two triatomic Hamiltonians and their applications to some non-adiabatic spectroscopic and collision problems. Carter and Handy in 1984 presented the first Hamiltonian in bond lengths\u2013bond angle coordinates, that is here applied for studying the NO2 spectroscopy: vibronic states, internal dynamics, and interaction with the radiation due to the X\u02dc2A\u2032(A1)\u2212A\u02dc2A\u2032(B2) conical intersection. The second Hamiltonian was reported by Tennyson and Sutcliffe in 1983 in Jacobi coordinates and is here employed in the study of the Kr + OH(A2\u03a3+) electronic quenching due to conical intersection and Renner\u2013Teller interactions among the 12A\u2032, 22A\u2032, and 12A\u2033 electronic species. Within the non-relativistic approximation and the expansion method in diabatic electronic representations, the formalism is exact and allows a unified study of various non-adiabatic interactions between electronic states. The rotation, inversion, and nuclear permutation symmetries are considered for defining rovibronic representations, which are symmetry adapted for ABC and AB2 molecules, and the matrix elements of the Hamiltonians are then computed.<\/jats:p>","DOI":"10.3390\/sym17030346","type":"journal-article","created":{"date-parts":[[2025,2,25]],"date-time":"2025-02-25T07:45:08Z","timestamp":1740469508000},"page":"346","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Two Quantum Triatomic Hamiltonians: Applications to Non-Adiabatic Effects in NO2 Spectroscopy and in Kr + OH(A2\u03a3+) Electronic Quenching"],"prefix":"10.3390","volume":"17","author":[{"given":"Carlo","family":"Petrongolo","sequence":"first","affiliation":[{"name":"Istituto per i Processi Chimico-Fisici, Consiglio Nazionale delle Ricerche, Via G. Moruzzi 1, 56124 Pisa, Italy"}]}],"member":"1968","published-online":{"date-parts":[[2025,2,25]]},"reference":[{"key":"ref_1","first-page":"99","article-title":"Some problems in defining a nuclear motion Hamiltonian and their relation to the problem of the molecular shape","volume":"Volume 21","year":"1982","journal-title":"Current Aspects of Quantum Chemistry 1981"},{"key":"ref_2","unstructured":"Davydov, A.S. (1976). Quantum Mechanics, Pergamon. [2nd ed.]."},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Wilson, E.B., Decius, J.C., and Cross, P.C. (1955). Molecular Vibrations, the Theory of Infrared and Raman Vibrational Spectra, McGraw-Hill.","DOI":"10.1149\/1.2430134"},{"key":"ref_4","unstructured":"Kemble, E.C. (1937). 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