Accurate calculation of tunneling splittings in water clusters using path-integral based methods.

Tunneling splittings observed in molecular rovibrational spectra are significant evidence for tunneling motion of hydrogen nuclei in water clusters. Accurate calculations of the splitting sizes from first principles require a combination of high-quality inter-atomic interactions and rigorous methods to treat the nuclei with quantum mechanics. Many theoretical efforts have been made in recent decades.

Semiclassical Vibrational Spectroscopy of Real Molecular Systems by Means of Cross-Correlation Filter Diagonalization.

We applied the harmonic inversion technique to extract vibrational eigenvalues from the semiclassical initial value representation (SC-IVR) propagator of molecular systems described by explicit potential surfaces. The cross-correlation filter-diagonalization (CCFD) method is used for the inversion problem instead of the Fourier transformation, which allows much shorter propagation time and is thus capable of avoiding numerical divergence issues while getting rid of approximations like the separable one to the pre-exponential factor. We also used the "Divide-and-Conquer" technique to control the total dimensions under consideration, which helps to further enhance the numerical behavior of SC-IVR calculations and the stability of harmonic inversion methods.

Torsional Tunneling Splitting in a Water Trimer.

Using a full-dimensional quantum method for nuclei and a new first-principles water potential, we show that the torsional tunneling splitting in a water trimer can be reproduced with accuracy up to ∼1 cm. We quantify the coupling constants of the nuclear quantum states between nonadjacent wells and show that they are the main reason for shifting the quartet-split levels in spectra from a 1:2:1 spacing. This demonstrates the limitation of treatments using simplified models such as the Hückel model and emphasizes the nonlocal nature of the quantum interactions in this system.