Tensor structure and transport of centrifugal distortion constants: A representation-independent framework connecting spectroscopy and quantum chemistry beyond the linear regime

Abstract

Centrifugal distortion constants provide a key link between high-resolution rotational spectroscopy and quantum-chemical rovibrational calculations. Within Watson’s Hamiltonian, the underlying structure is described in terms of tensorial objects, whereas fitted spectroscopic parameters become representation-dependent upon projection, complicating direct comparison between experiment and theory. Building on the tensorial formulation of centrifugal distortion, we show that standard quartic and sextic constants can be consistently described within a representation-independent linear tensor sector generated by first derivatives of the inverse inertia tensor so that different Watson parameterizations correspond to alternative projections of the same underlying tensorial object. An explicit inverse formulation based on a Moore–Penrose pseudoinverse enables reconstruction of tensor representatives from fitted spectroscopic parameters, leading to a lift–transport–reprojection framework for representation-independent comparison. The sextic transport problem is formulated on a canonical seven-dimensional Watson space, while the first intrinsic breakdown of the linear tensor structure is identified through the H22 contribution, marking the onset of nonlinear tensorial effects. Within this framework, we derive transformation schemes for quartic and sextic constants, introduce diagnostic indicators for nonlinearity, and show that three-index cubic force-field contributions are generally non-negligible. Applications to molecular systems of increasing size and complexity demonstrate that the tensor framework rationalizes representation dependence and provides a practical basis for multilevel and semi-experimental approaches.