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.