2021•arXiv (Cornell University)Open access

Modelling the Vibration-Rotation Energy Levels of D218O molecule with Effective Hamiltonian Method

Irina A. Vasilenko, O. V. Naumenko, Elena R. Polovtseva, А. Д. Быков

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Abstract

Using the effective rotational Hamiltonian method, we have conducted an analysis of the D218O ground and the first excited vibration state rotational energy levels. The analysis was based on the effective Hamiltonians represented in several forms: the Watson Hamiltonian, the Hamiltonian expressed in terms of Padé-Borel approximants, and the Hamiltonian in terms of generating function expansions. The rotational and centrifugal constants have been determined from the fitting, which describe the rotational energy levels with an accuracy close to that of the experimental data. The predictive performance of the model with respect to highly excited rotational states has been evaluated against the global variation calculations. The radii of convergence of the effective rotation Hamiltonian series have been determined.

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Using the effective rotational Hamiltonian method, we have conducted an analysis of the D218O ground and the first excited vibration state rotational energy levels. The analysis was based on the effective Hamiltonians represented in several forms: the Watson Hamiltonian, the Hamiltonian expressed in terms of Padé-Borel approximants, and the Hamiltonian in terms of generating function expansions. The rotational and centrifugal constants have been determined from the fitting, which describe the rotational energy levels with an accuracy close to that of the experimental data. The predictive performance of the model with respect to highly excited rotational states has been evaluated against the global variation calculations. The radii of convergence of the effective rotation Hamiltonian series have been determined.

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Available abstract

Using the effective rotational Hamiltonian method, we have conducted an analysis of the D218O ground and the first excited vibration state rotational energy levels. The analysis was based on the effective Hamiltonians represented in several forms: the Watson Hamiltonian, the Hamiltonian expressed in terms of Padé-Borel approximants, and the Hamiltonian in terms of generating function expansions. The rotational and centrifugal constants have been determined from the fitting, which describe the rotational energy levels with an accuracy close to that of the experimental data. The predictive performance of the model with respect to highly excited rotational states has been evaluated against the global variation calculations. The radii of convergence of the effective rotation Hamiltonian series have been determined.

Key concepts: Vibration, Hamiltonian (control theory), Molecule, Physics, Classical mechanics, Acoustics, Mathematics, Quantum mechanics

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