Full dimensional (15D) quantum-dynamical simulation of the protonated water-dimer I: Hamiltonian setup and analysis of the ground vibrational state

TL;DR

This paper presents a comprehensive 15-dimensional quantum-dynamical simulation of the protonated water dimer using MCTDH, demonstrating accurate ground state energy and capturing its fluxional, multi-minima nature.

Contribution

It introduces a detailed Hamiltonian setup with curvilinear coordinates and a modified high-dimensional potential energy surface representation for full-dimensional quantum simulations.

Findings

Accurately computed the ground vibrational state energy within 16.7 cm-1 of previous results.

Showed the system's fluxional behavior involves wagging and internal rotation motions.

Proved that a converged quantum-dynamical description of flexible, multi-minima systems is achievable.

Abstract

Quantum-dynamical full-dimensional (15D) calculations are reported for the protonated water dimer (H5O2+) using the multiconfiguration time-dependent Hartree (MCTDH) method. The dynamics is described by curvilinear coordinates. The expression of the kinetic energy operator in this set of coordinates is given and its derivation, following the polyspherical method, is discussed. The PES employed is that of Huang et al. [JCP, 122, 044308, (2005)]. A scheme for the representation of the potential energy surface (PES) is discussed which is based on a high dimensional model representation scheme (cut-HDMR), but modified to take advantage of the mode-combination representation of the vibrational wavefunction used in MCTDH. The convergence of the PES expansion used is quantified and evidence is provided that it correctly reproduces the reference PES at least for the range of energies of interest. The reported zero point energy of the system is converged with respect to the MCTDH expansion and in excellent agreement (16.7 cm-1 below) with the diffusion Monte Carlo result on the PES of Huang et al. The highly fluxional nature of the cation is accounted for through use of curvilinear coordinates. The system is found to interconvert between equivalent minima through wagging and internal rotation motions already when in the ground vibrational-state, i.e., T=0. It is shown that a converged quantum-dynamical description of such a flexible, multi-minima system is possible.