Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. I. Theory.

Reactions involving adsorbates on metallic surfaces and impurities in bulk metals are ubiquitous in a wide range of technological applications. The theoretical modeling of such reactions presents a formidable challenge for theory because nuclear quantum effects (NQEs) can play a prominent role and the coupling of the atomic motion with the electrons in the metal gives rise to important non-adiabatic effects (NAEs) that alter atomic dynamics. In this work, we derive a theoretical framework that captures both NQEs and NAEs and, due to its high efficiency, can be applied to first-principles calculations of reaction rates in high-dimensional realistic systems. More specifically, we develop a method that we coin ring polymer instanton with explicit friction (RPI-EF), starting from the ring polymer instanton formalism applied to a system-bath model. We derive general equations that incorporate the spatial and frequency dependence of the friction tensor and then combine this method with the ab initio electronic friction formalism for the calculation of thermal reaction rates. We show that the connection between RPI-EF and the form of the electronic friction tensor presented in this work does not require any further approximations, and it is expected to be valid as long as the approximations of both underlying theories remain valid.

Dissipative tunneling rates through the incorporation of first-principles electronic friction in instanton rate theory. II. Benchmarks and applications.

In Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], we presented the ring-polymer instanton with explicit friction (RPI-EF) method and showed how it can be connected to the ab initio electronic friction formalism. This framework allows for the calculation of tunneling reaction rates that incorporate the quantum nature of the nuclei and certain types of non-adiabatic effects (NAEs) present in metals. In this paper, we analyze the performance of RPI-EF on model potentials and apply it to realistic systems. For a 1D double-well model, we benchmark the method against numerically exact results obtained from multi-layer multi-configuration time-dependent Hartree calculations. We demonstrate that RPI-EF is accurate for medium and high friction strengths and less accurate for extremely low friction values. We also show quantitatively how the inclusion of NAEs lowers the crossover temperature into the deep tunneling regime, reduces the tunneling rates, and, in certain regimes, steers the quantum dynamics by modifying the tunneling pathways. As a showcase of the efficiency of this method, we present a study of hydrogen and deuterium hopping between neighboring interstitial sites in selected bulk metals. The results show that multidimensional vibrational coupling and nuclear quantum effects have a larger impact than NAEs on the tunneling rates of diffusion in metals. Together with Paper I [Litman et al., J. Chem. Phys. (in press) (2022)], these results advance the calculations of dissipative tunneling rates from first principles.

Hydrogen Recombination and Dimer Formation on Graphite from Ab Initio Molecular Dynamics Simulations.

We studied Eley-Rideal molecular hydrogen formation on graphite using ab initio molecular dynamics, in the energy range relevant for the chemistry of the interstellar medium and for terrestrial experiments employing cold plasma (0.02-1 eV). We found substantial projectile steering effects that prevent dimer formation at low energies, thereby ruling out any catalytic synthetic pathways that form hydrogen molecules. Ortho and para dimers do form efficiently thanks to preferential sticking, but only at energies that are too high to be relevant for the chemistry of the interstellar medium. Computed reaction cross sections and ro-vibrational product populations are in good agreement with available experimental data and capable of generating adsorbate configurations similar to those observed with scanning tunneling microscopy techniques.

Compact MCTDH wave functions for high-dimensional system-bath quantum dynamics.

We employ a simple multiconfiguration time-dependent Hartree (MCTDH) ansatz tailored to an effective-mode transformation of environmental variables that brings the bath into a linear chain form. In this form, important (primary) degrees of freedom can be easily identified and treated at a high correlation level, whereas secondary modes are left uncorrelated. The resulting approach scales linearly with the bath dimensions and allows us to easily access recurrence times much longer than usually possible, at a very small computational cost. Test calculations for model atom-surface problems show that the system dynamics is correctly reproduced in the relevant time window, and quantitative agreement is attained for energy relaxation and sticking, particularly in non-Markovian environments. These results pave the way for tackling realistic system-bath quantum dynamical problems on the picosecond scale.

A few simple rules governing hydrogenation of graphene dots.

We investigated binding of hydrogen atoms to small polycyclic aromatic hydrocarbons (PAHs)--i.e., graphene dots with hydrogen-terminated edges--using density functional theory and correlated wavefunction techniques. We considered a number of PAHs with three to seven hexagonal rings and computed binding energies for most of the symmetry unique sites, along with the minimum energy paths for significant cases. The chosen PAHs are small enough to not present radical character at their edges, yet show a clear preference for adsorption at the edge sites which can be attributed to electronic effects. We show how the results, as obtained at different levels of theory, can be rationalized in detail with the help of a few simple concepts derivable from a tight-binding model of the π electrons.

Unraveling a Brownian particle's memory with effective mode chains.

Memory effects in quantum dynamical processes involving structured environments are presently difficult, if not impossible, to investigate using standard approaches. Progress can be made by transforming the environmental variables to a suitable chain representation which effectively performs a Markovian embedding of the dynamics. Here, we show that this effective-mode chain representation provides a unique way of unraveling the memory kernel κ(t) as a function of time. Truncated or Markov-closed chains with n effective modes exactly reproduce κ(t) to the 4nth order in time, up to an irrelevant constant of order κ(0)/n. These favorable convergence properties pave the way for efficient quantum simulations of fast (non-Markovian) processes by reduced dynamical models.

Benchmark calculations for dissipative dynamics of a system coupled to an anharmonic bath with the multiconfiguration time-dependent Hartree method.

In this paper, we present benchmark results for dissipative dynamics of a harmonic oscillator coupled to an anharmonic bath of Morse oscillators. The microscopic Hamiltonian has been chosen so that the anharmonicity can be adjusted as a free parameter, and its effect can be isolated. This leads to a temperature dependent spectral density of the bath, which is studied for ohmic and lorentzian cases. Also, we compare numerically exact multiconfiguration time-dependent Hartree results with approximate solutions using continuous configuration time-dependent self-consistent field and local coherent state approximation.

Communication: Universal Markovian reduction of Brownian particle dynamics.

Non-Markovian processes can often be turned Markovian by enlarging the set of variables. Here we show, by an explicit construction, how this can be done for the dynamics of a Brownian particle obeying the generalized Langevin equation. Given an arbitrary bath spectral density J(0), we introduce an orthogonal transformation of the bath variables into effective modes, leading stepwise to a semi-infinite chain with nearest-neighbor interactions. The transformation is uniquely determined by J(0) and defines a sequence {J(n)}(n∈N) of residual spectral densities describing the interaction of the terminal chain mode, at each step, with the remaining bath. We derive a simple one-term recurrence relation for this sequence and show that its limit is the quasi-Ohmic expression provided by the Rubin model of dissipation. Numerical calculations show that, irrespective of the details of J(0), convergence is fast enough to be useful in practice for an effective Ohmic reduction of the dissipative dynamics.

Potential energy surface, bound states, and rotational inelastic cross sections of the He-CH4 system: a theoretical investigation.

We determined two potential energy surfaces (PES) for the He-CH(4) system by means of MP4 and Valence Bond (VB) calculations. The MP4 potential is similar to the one commonly adopted for this system [U. Buck, K. H. Kohl, A. Kolhase, M. Faubel, and U. Staemmler, Mol. Phys. 55, 1255 (1985)], while the VB PES is slightly more attractive. To evaluate the reliability of these potentials, we investigated the scattering properties by performing close coupling calculations, and concluded that: (i) the available experimental data do not permit the ranking among the PES considered; (ii) some theoretical predictions differ considerably from the experimental data, and these discrepancies cannot entirely be ascribed to the inaccuracy of the ab initio calculations; (iii) the scattering properties at low energy might discriminate between the MP4 and VB potentials.

Hot-atom versus Eley-Rideal dynamics in hydrogen recombination on Ni(100). I. The single-adsorbate case.

We compare the efficiency of the Eley-Rideal (ER) reaction with the formation of hot-atom (HA) species in the simplest case, i.e., the scattering of a projectile off a single adsorbate, considering the Hydrogen and Hydrogen-on-Ni(100) system. We use classical mechanics and the accurate embedded diatomics-in-molecules potential to study the collision system over a wide range of collision energies (0.10-1.50 eV), both with a rigid and a nonrigid Ni substrate and for impact on the occupied and neighboring empty cells. In the rigid model metastable and truly bound hot-atoms occur and we find that the cross section for the formation of bound hot-atoms is considerably higher than that for the ER reaction over the whole range of collision energies examined. Metastable hot-atoms form because of the inefficient energy transfer to the adsorbate and have lifetimes of the order 0.1-0.7 ps, depending on the collision energy. When considering the effects of lattice vibrations we find, on average, a consistent energy transfer to the substrate, say 0.1-0.2 eV, which forced us to devise a two-step dynamical model to get rid of the problems associated with the use of periodic boundary conditions. Results for long-lived HA formation due to scattering on the occupied cell at a surface temperature of 120 K agree well with those of the rigid model, suggesting that in the above process the substrate plays only a secondary role and further calculations at surface temperatures of 50 and 300 K are in line with these findings. However, considerably high cross sections for formation of long-lived hot-atoms result also from scattering off the neighboring cells where the energy transfer to the lattice cannot be neglected. Metastable hot-atoms are reduced in number and have usually lifetimes shorter than those of the rigid-model, say less than 0.3 ps. In addition, ER cross sections are only slightly affected by the lattice motion and show a little temperature dependence. Finally, we find also that absorption and reflection strongly depend on the correct consideration of lattice vibrations and the occurrence of trapping.