AnhDis: A Scheme for Anharmonic Nuclear Ensembles and Absorption Spectra

The Nuclear Ensemble Approach (NEA), typically implemented using the harmonic Wigner approximation in Cartesian normal coordinates, has shown significant limitations when applied to molecules with large-amplitude bending and torsional motions. On the one hand, rectilinear displacements fail to follow the curvature of these motions at finite amplitudes, introducing artificial bond stretching. On the other hand, harmonic potentials can inadequately describe confinement along these motions. Both limitations can lead to artificial spectral broadening and spurious transitions. In this work, the Anharmonic-Distribution (AnhDis) scheme is presented. The method is based on constructing mode-resolved potential energy surfaces through explicit scans along curvilinear paths in internal coordinates, represented in the present implementation by polynomial fits or piecewise cubic Hermite interpolation (PCHIP). By solving the resulting one-dimensional vibrational Hamiltonians, nuclear probability densities that account for anharmonic confinement and wave function asymmetry are obtained. Temperature effects are incorporated through Boltzmann weighting of the vibrational eigenstates. AnhDis thus combines curvilinear nuclear ensembles with an independent-mode treatment of anharmonicity. Comparisons with reference simulations and experimental data across atmospherically relevant molecules demonstrate that the proposed method captures absorption spectral profiles while reducing Cartesian sampling artifacts and revealing system-dependent anharmonic effects.