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.

A deep neural network for molecular wave functions in quasi-atomic minimal basis representation.

The emergence of machine learning methods in quantum chemistry provides new methods to revisit an old problem: Can the predictive accuracy of electronic structure calculations be decoupled from their numerical bottlenecks? Previous attempts to answer this question have, among other methods, given rise to semi-empirical quantum chemistry in minimal basis representation. We present an adaptation of the recently proposed SchNet for Orbitals (SchNOrb) deep convolutional neural network model [K. T. Schütt et al., Nat. Commun. 10, 5024 (2019)] for electronic wave functions in an optimized quasi-atomic minimal basis representation. For five organic molecules ranging from 5 to 13 heavy atoms, the model accurately predicts molecular orbital energies and wave functions and provides access to derived properties for chemical bonding analysis. Particularly for larger molecules, the model outperforms the original atomic-orbital-based SchNOrb method in terms of accuracy and scaling. We conclude by discussing the future potential of this approach in quantum chemical workflows.

DFTB+, a software package for efficient approximate density functional theory based atomistic simulations.

DFTB+ is a versatile community developed open source software package offering fast and efficient methods for carrying out atomistic quantum mechanical simulations. By implementing various methods approximating density functional theory (DFT), such as the density functional based tight binding (DFTB) and the extended tight binding method, it enables simulations of large systems and long timescales with reasonable accuracy while being considerably faster for typical simulations than the respective ab initio methods. Based on the DFTB framework, it additionally offers approximated versions of various DFT extensions including hybrid functionals, time dependent formalism for treating excited systems, electron transport using non-equilibrium Green's functions, and many more. DFTB+ can be used as a user-friendly standalone application in addition to being embedded into other software packages as a library or acting as a calculation-server accessed by socket communication. We give an overview of the recently developed capabilities of the DFTB+ code, demonstrating with a few use case examples, discuss the strengths and weaknesses of the various features, and also discuss on-going developments and possible future perspectives.

Donor-Acceptor Co-Adsorption Ratio Controls the Structure and Electronic Properties of Two-Dimensional Alkali-Organic Networks on Ag(100).

The results are presented of a detailed combined experimental and theoretical investigation of the influence of coadsorbed electron-donating alkali atoms and the prototypical electron acceptor molecule 7,7,8,8-tetracyanoquinodimethane (TCNQ) on the Ag(100) surface. Several coadsorption phases were characterized by scanning tunneling microscopy, low-energy electron diffraction, and soft X-ray photoelectron spectroscopy. Quantitative structural data were obtained using normal-incidence X-ray standing wave (NIXSW) measurements and compared with the results of density functional theory (DFT) calculations using several different methods of dispersion correction. Generally, good agreement between theory and experiment was achieved for the quantitative structures, albeit with the prediction of the alkali atom heights being challenging for some methods. The adsorption structures depend sensitively on the interplay of molecule-metal charge transfer and long-range dispersion forces, which are controlled by the composition ratio between alkali atoms and TCNQ. The large difference in atomic size between K and Cs has negligible effects on stability, whereas increasing the ratio of K/TCNQ from 1:4 to 1:1 leads to a weakening of molecule-metal interaction strength in favor of stronger ionic bonds within the two-dimensional alkali-organic network. A strong dependence of the work function on the alkali donor-TCNQ acceptor coadsorption ratio is predicted.

Unifying machine learning and quantum chemistry with a deep neural network for molecular wavefunctions.

Machine learning advances chemistry and materials science by enabling large-scale exploration of chemical space based on quantum chemical calculations. While these models supply fast and accurate predictions of atomistic chemical properties, they do not explicitly capture the electronic degrees of freedom of a molecule, which limits their applicability for reactive chemistry and chemical analysis. Here we present a deep learning framework for the prediction of the quantum mechanical wavefunction in a local basis of atomic orbitals from which all other ground-state properties can be derived. This approach retains full access to the electronic structure via the wavefunction at force-field-like efficiency and captures quantum mechanics in an analytically differentiable representation. On several examples, we demonstrate that this opens promising avenues to perform inverse design of molecular structures for targeting electronic property optimisation and a clear path towards increased synergy of machine learning and quantum chemistry.

The Structure of VOPc on Cu(111): Does V=O Point Up, or Down, or Both?

The local structure of the nonplanar phthalocyanine, vanadyl phthalocyanine (VOPc), adsorbed on Cu(111) at a coverage of approximately one-half of a saturated molecular layer, has been investigated by a combination of normal-incidence X-ray standing waves (NIXSW), scanned-energy mode photoelectron diffraction (PhD), and density-functional theory (DFT), complemented by scanning tunnelling microscopy (STM). Qualitative assessment of the NIXSW data clearly shows that both "up" and "down" orientations of the molecule (with V=O pointing out of, and into, the surface) must coexist on the surface. O 1s PhD proves to be inconclusive regarding the molecular orientation. DFT calculations, using two different dispersion correction schemes, show good quantitative agreement with the NIXSW structural results for equal co-occupation of the two different molecular orientations and clearly favor the many body dispersion (MBD) method to deal with long-range dispersion forces. The calculated relative adsorption energies of the differently oriented molecules at the lowest coverage show a strong preference for the "up" orientation, but at higher local coverages, this energetic difference decreases, and mixed orientation phases are almost energetically equivalent to pure "up"-oriented phases. DFT-based Tersoff-Hamann simulations of STM topographs for the two orientations cast some light on the extent to which such images provide a reliable guide to molecular orientation.

Case report 704: Extraskeletal osteosarcoma of the thigh with several suspected skeletal metastases and extensive metastases to the chest.

A case of extraskeletal osteosarcoma occurring in its most common location, the thigh, is reported. Particular emphasis is given to demonstrating the spectrum of radiological findings, including CT, MRI, and scintigraphy and to illustrate that this entity can metastasize to bone.