Revisiting an approximation in the Wilson G-matrix formalism and its impact on molecular quantum dynamics

Quantum dynamics simulations of reactive molecular processes are commonly performed in a low-dimensional space spanned by highly optimized reactive coordinates. Usually, these sets of reactive coordinates consist of non-linear coordinates. The Wilson G-matrix formalism allows to formulate the Hamiltonian in arbitrary coordinates. In our present work, we revisit an approximation in this formalism, namely the assumption that the Jacobian determinant is constant. We show that the approximation can introduce an error and illustrate it for a harmonic oscillator. Finally, we present a strategy to prevent this error.