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. This Perspective focuses on two path-integral based tunneling splitting methods whose computational cost scales well with the system size, namely, the ring-polymer instanton method and the path-integral molecular dynamics (PIMD) method. From a simple derivation, we show that the former is a semiclassical approximation to the latter, despite that the two methods are derived very differently. Currently, the PIMD method is considered to be an ideal route to rigorously compute the ground-state tunneling splitting, while the instanton method sacrifices some accuracy for a significantly smaller computational cost. An application scenario of such a quantitatively rigorous calculation is to test and calibrate the potential energy surfaces of molecular systems by spectroscopic accuracy. Recent progress in water clusters is reviewed, and the current challenges are discussed.

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. The technique is tested on small molecules and water trimer to justify its applicability and reliability. Results show that the CCFD method can effectively extract the vibrational eigenvalues from short trajectories and reproduce the original spectra conventionally obtained from long-time ones, with no loss on accuracy while the numerical behavior is much better. This work demonstrates the possibility to apply the combined method of CCFD and SC-IVR to real molecular potential surfaces, which might be a new way to overcome the numerical instabilities caused by the increase of dimensions.

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-1. 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. With such an ab initio endeavor, we examine the quality of the water potential developed and provide a rigorous scheme to decipher the experimental spectra with unprecedented accuracy, which is applicable to more general systems.