Elucidating the Nuclear Quantum Dynamics of Intramolecular Double Hydrogen Transfer in Porphycene

Abstract

We address the double hydrogen transfer (DHT) dynamics of the porphycene molecule, a complex paradigmatic system in which the making and breaking of H-bonds in a highly anharmonic potential energy surface require a quantum mechanical treatment not only of the electrons but also of the nuclei. We combine density functional theory calculations, employing hybrid functionals and van der Waals corrections, with recently proposed and optimized path-integral ring-polymer methods for the approximation of quantum vibrational spectra and reaction rates. Our full-dimensional ring-polymer instanton simulations show that below 100 K the concerted DHT tunneling pathway dominates but between 100 and 300 K there is a competition between concerted and stepwise pathways when nuclear quantum effects are included. We obtain ground-state reaction rates of 2.19 × 10 11 s –1 at 150 K and 0.63 × 10 11 s –1 at 100 K, in good agreement with experiment. We also reproduce the puzzling N–H stretching band of porphycene with very good accuracy from thermostated ring-polymer molecular dynamics simulations. The position and line shape of this peak, centered at around 2600 cm –1 and spanning 750 cm –1 , stem from a combination of very strong H-bonds, the coupling to low-frequency modes, and the access to cis -like isomeric conformations, which cannot be appropriately captured with classical-nuclei dynamics. These results verify the appropriateness of our general theoretical approach and provide a framework for a deeper physical understanding of hydrogen transfer dynamics in complex systems.

Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems

“…(5) and the definitions Eqs. (22) and (24). The reactant partition function is defined in the usual way as…”

“…4,13,14 This makes semiclassical instanton theory a remarkably efficient and accurate method for studying quantum tunnelling in molecules and clusters. [15][16][17][18][19][20][21][22][23][24][25] For the atomistic simulation of reactions in solution, the semiclassical instanton method is no longer applicable, but an alternative method is provided by ringpolymer molecular dynamics (RPMD). [26][27][28][29] The excellent accuracy achieved by RPMD rate theory can be explained by its connection to instanton theory, as the instanton can be shown to be equivalent to the dominant ring-polymer configuration sampled by the RPMD scheme.…”

Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats

“…These methods ignore real time coherence but include effects arising from equilibrium quantum fluctuations and have been validated on several model systems and small molecules for which exact or highly accurate results are available [15,18,20,22]. While these methods show great promise for accurate determination of spectroscopic properties [23][24][25], their cost remains high when combined with a potential energy surface computed by ab initio electronic structure methods.Among the many methods that have been introduced in the past decade to accelerate the convergence of path integral calculations [26], those that combine path integral molecular dynamics with a generalized Langevin equation [27][28][29] can be applied transparently to empirical, machine learning or first principles simulations. They have been used to evaluate all sorts of thermodynamic properties, including structural observables [30], free energies [31], momentum distributions [28], and quantum kinetic energies [32] with a reduction in computational effort varying between a factor of 5 at ambient conditions to a factor of 100 at cryogenic temperatures [33].…”

Divide-and-Conquer Method for Instanton Rate Theory

“…Our method significantly reduces the challenge in calculating thermal reaction rates of larger chemical systems at very low temperatures where a large number of ring-polymer beads are required. 65 For Table of Contents Only…”