This article discusses the coupling of angular momentum in spherical top molecules with excited triply degenerate vibrations. The authors introduce a new quantum number R that combines the total angular momentum J and the vibrational angular momentum Ls. This coupling is described using vector coupling techniques and leads to a modified rotational Hamiltonian.
The rotational energy of the molecule is given by the product of a rotational constant B and the square of the combined angular momentum [J + ζsLs]². The matrix elements of the rotational Hamiltonian are diagonal in the basis set and depend on the quantum numbers J, Ls, and R.
The article shows that when no vibrational quanta are excited (υ = 0), the quantum number R equals J. When one vibrational quantum is excited (υs = 1), R can take values of J + 1, J, or J – 1. The Coriolis operator in the Hamiltonian leads to a natural grouping of rovibrational levels according to their R values.
The authors conclude that the coupling of angular momentum in spherical top molecules with excited triply degenerate vibrations can be described using a modified rotational Hamiltonian and quantum numbers. This approach provides a more complete understanding of the rotational energy levels and their dependence on the vibrational excitation.
Source: https://www.nist.gov/pml/methane-symmetry-operations/methane-symmetry-operations-coupling-j-and-ls
Keywords: quantum computing, algorithms, sensing
