Kinetic energy operator triatomic molecules

The essential step in (4.20) is the repeated application of the Hamiltonian. While the application of the potential is simply a multiplication, application of the kinetic energy operator, which for the linear triatomic molecule has the form... 

H. Wei and T. Carrington, Jr., An exact Eckart-embedded kinetic energy operator in Radau coordinates for triatomic molecules. Chem. Phys. Lett. 287, 289—300 (1998). 

As an example of the split-operator method, we here consider the time propagation of the vibrational wavefunction of a triatomic molecule, such as NO2 (Sec. 5.4). The two bond lengths of the molecule are ri and r2, and the bond angle is / . The total kinetic energy operator TV is represented in a convenient form by taking the Jacobi coordinates (r, R, 6) as depicted in Fig. 3.4, in which the length R is the distance between the upper O atom and the centroid of the N and the lower O atoms, and r is the bond length of one NO moiety. It is... 

For triatomic molecules it is possible to find orthogonal coordinates in terms of which the kinetic energy operator has no cross terms. Three possibilities are Jacobi coordinates, Radau coordinates, and hyperspherical coordinates, The form of the kinetic energy operator in Jacobi and Radau coordinates is the same. 

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