Progress in the atomic-scale modelling of matter over the past decade has been tremendous. This progress has been brought about by improvements in methods for evaluating interatomic forces that work by either solving the electronic structure problem explicitly, or by computing accurate approximations of the solution and by the development of techniques that use the Born-Oppenheimer (BO) forces to move the atoms on the BO potential energy surface. As a consequence of these developments it is now possible to identify stable or metastable states, to sample configurations consistent with the appropriate thermodynamic ensemble, and to estimate the kinetics of reactions and phase transitions. All too often, however, progress is slowed down by the bottleneck associated with implementing new optimization algorithms and/or sampling techniques into the many existing electronic-structure and empirical-potential codes. To address this problem, we are thus releasing a new version of the i-PI software. This piece of software is an easily extensible framework for implementing advanced atomistic simulation techniques using interatomic potentials and forces calculated by an external driver code. While the original version of the code[1] was developed with a focus on path integral molecular dynamics techniques, this second release of i-PI not only includes several new advanced path integral methods, but also offers other classes of algorithms. In other words, i-PI is moving towards becoming a universal force engine that is both modular and tightly coupled to the driver codes that evaluate the potential energy surface and its derivatives.

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.

Water molecules adsorbed on inorganic substrates play an important role in several technological applications. In the presence of light atoms in adsorbates, nuclear quantum effects (NQE) influence the structural stability and the dynamical properties of these systems. In this work, we explore the impact of NQE on the dissociation of water wires on stepped Pt(221) surfaces. By performing ab initio molecular dynamics simulations with van der Waals corrected density functional theory, we note that several competing minima for both intact and dissociated structures are accessible at finite temperatures, making it important to assess whether harmonic estimates of the quantum free energy are sufficient to determine the relative stability of the different states. We thus perform ab initio path integral molecular dynamics (PIMD) in order to calculate these contributions taking into account conformational entropy and anharmonicities at finite temperatures. We propose that when when adsorption is weak and NQE on the substrate are negligible, PIMD simulations can be performed through a simple partition of the system, resulting in considerable computational savings. We then calculate the full contribution of NQE to the free energies, including also anharmonic terms. We find that they result in an increase of up to 20% of the quantum contribution to the dissociation free energy compared to the harmonic estimates. We also find that the dissociation process has a negligible contribution from tunneling, but is dominated by ZPE, which can enhance the rate of dissociation by three orders of magnitude. Finally we highlight how both temperature and NQE indirectly impact dipoles and the redistribution of electron density, causing work function to changes of up to 0.4 eV with respect to static estimates. This quantitative determination of the change in work function provides a possible approach to determine experimentally the most stable configurations of water oligomers on the stepped surfaces.

Tautomerization in single porphycene molecules is investigated on Cu(111), Ag(111), and Au(111) surfaces by a combination of low-temperature scanning tunneling microscopy (STM) experiments and density functional theory (DFT) calculations. It is revealed that the trans configuration is the thermodynamically stable form of porphycene on Cu(111) and Ag(111), whereas the cis configuration occurs as a meta-stable form. The trans → cis or cis → trans conversion on Cu(111) can be induced in an unidirectional fashion by injecting tunneling electrons from the STM tip or heating the surface, respectively. We find that the cis ↔ cis tautomerization on Cu(111) occurs spontaneously via tunneling, verified by the negligible temperature dependence of the tautomerization rate below ∼23 K. Van der Waals corrected DFT calculations are used to characterize the adsorption structures of porphycene and to map the potential energy surface of the tautomerization on Cu(111). The calculated barriers are too high to be thermally overcome at cryogenic temperatures used in the experiment and zero-point energy corrections do not change this picture, leaving tunneling as the most likely mechanism. On Ag(111), the reversible trans ↔ cis conversion occurs spontaneously at 5 K and the cis ↔ cis tautomerization rate is much higher than on Cu(111), indicating a significantly smaller tautomerization barrier on Ag(111) due to the weaker interaction between porphycene and the surface compared to Cu(111). Additionally, the STM experiments and DFT calculations reveal that tautomerization on Cu(111) and Ag(111) occurs with migration of porphycene along the surface; thus, the translational motion couples with the tautomerization coordinate. On the other hand, the trans and cis configurations are not discernible in the STM image and no tautomerization is observed for porphycene on Au(111). The weak interaction of porphycene with Au(111) is closest to the gas-phase limit and therefore the absence of trans and cis configurations in the STM images is explained either by the rapid tautomerization rate or the similar character of the molecular frontier orbitals of the trans and cis configurations.

Approximate quantum dynamics succeed in predicting a temperature-dependent blue-shift of the high-frequency stretch bands that arise from vibrational coupling between low-frequency thermally activated modes and high-frequency quantized ones. Classical nuclei molecular dynamics fail and instead predict a red-shift.