Eckart rovibrational Hamiltonians via the gateway Hamilton operator: Theory and practice
Abstract
Recently, a general expression for Eckartframe 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 EckartWatson 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 rovibrational 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 (massweighted) 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.
 Publication:

Journal of Chemical Physics
 Pub Date:
 March 2017
 DOI:
 10.1063/1.4978686
 arXiv:
 arXiv:1701.01823
 Bibcode:
 2017JChPh.146l4107S
 Keywords:

 Physics  Chemical Physics
 EPrint:
 The Journal of Chemical Physics 146, 124107 (2017)