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• W2599571843 abstract "Recently, a general expression for Eckart-frame Hamilton operators has been obtained by the gateway Hamiltonian method [V. Szalay, J. Chem. Phys. 142, 174107 (2015) and V. Szalay, J. Chem. Phys. 143, 064104 (2015)]. The kinetic energy operator in this general Hamiltonian is nearly identical to that of the Eckart-Watson operator even when curvilinear vibrational coordinates are employed. Its different realizations correspond to different methods of calculating Eckart displacements. There are at least two different methods for calculating such displacements: rotation and projection. In this communication, the application of Eckart Hamiltonian operators constructed by rotation and projection, respectively, is numerically demonstrated in calculating vibrational energy levels. The numerical examples confirm that there is no need for rotation to construct an Eckart ro-vibrational Hamiltonian. The application of the gateway method is advantageous even when rotation is used since it obviates the need for differentiation of the matrix rotating into the Eckart frame. Simple geometrical arguments explain that there are infinitely many different methods for calculating Eckart displacements. The geometrical picture also suggests that a unique Eckart displacement vector may be defined as the shortest (mass-weighted) Eckart displacement vector among Eckart displacement vectors corresponding to configurations related by rotation. Its length, as shown analytically and demonstrated by numerical examples, is equal to or less than that of the Eckart displacement vector one can obtain by rotation to the Eckart frame." @default.
• W2599571843 created "2017-04-07" @default.
• W2599571843 creator A5079387406 @default.
• W2599571843 date "2017-03-23" @default.
• W2599571843 modified "2023-10-17" @default.
• W2599571843 title "Eckart ro-vibrational Hamiltonians via the gateway Hamilton operator: Theory and practice" @default.
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• W2599571843 doi "https://doi.org/10.1063/1.4978686" @default.
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