Charge constrained density functional molecular dynamics for simulation of condensed phase electron transfer reactions

We present a plane-wave basis set implementation of charge constrained density functional molecular dynamics (CDFT-MD) for simulation of electron transfer reactions in condensed phase systems. Following earlier work of Wu et al. Phys. Rev. A 72, 024502 (2005), the density functional is minimized under the constraint that the charge difference between donor and acceptor is equal to a given value. The classical ion dynamics is propagated on the Born-Oppenheimer surface of the charge constrained state. We investigate the dependence of the constrained energy and of the energy gap on the definition of the charge, and present expressions for the constraint forces. The method is applied to the Ru2+-Ru3+ electron self-exchange reaction in aqueous solution. Sampling the vertical energy gap along CDFT-MD trajectories, and correcting for finite size effects, a reorganization free energy of 1.6 eV is obtained. This is 0.1-0.2 eV lower than a previous estimate based on a continuum model for solvation. smaller value for reorganization free energy can be explained by fact that the Ru-O distances of the divalent and trivalent Ru-hexahydrates are predicted to be more similar in the electron transfer complex than for the separated aqua-ions.Comment: 12 pages, 7 figure

First-principles embedded-cluster calculations of the neutral and charged oxygen vacancy at the rutile TiO₂(110) surface

We perform full-potential screened-hybrid density-functional theory calculations to compare the thermodynamic stability of neutral and charged states of the surface oxygen vacancy at the rutile TiO2(110) surface. Solid-state (QM/MM) embedded-cluster calculations are employed to account for the strong TiO2 polarization response to the charged defect states. Similarly to the situation for the bulk O vacancy, the +2 charge state VO2+ is found to be energetically by far the most stable. Only for Fermi-level positions very close to the conduction band, small polarons may at best be trapped by the charged vacancy. The large decrease in the VO2+ formation energy with decreasing Fermi-level position indicates strongly enhanced surface O vacancy concentrations for p-doped samples

First-Principles Free-Energy Barriers for Photoelectrochemical Surface Reactions: Proton Abstraction at TiO₂(110)

We explicitly calculate the free-energy barrier for the initial proton abstraction in the water splitting reaction at rutile TiO2(110) through ab initio molecular dynamics. Combining solid-state embedding, an energy based reaction coordinate and state-of-the-art free-energy reconstruction techniques renders the calculation tractable at the hybrid density-functional theory level. The obtained free-energy barrier of approximately 0.2 eV, depending slightly on the orientation of the first acceptor water molecule, suggests a hindered reaction on the pristine rutile surface

Transferable ionic parameters for first-principles Poisson-Boltzmann solvation calculations: Neutral solutes in aqueous monovalent salt solutions

Implicit solvation calculations based on a Stern-layer corrected size-modified Poisson-Boltzmann (SMPB) model are an effective approach to capture electrolytic effects in first-principles electronic structure calculations. For a given salt solution, they require a range of ion-specific parameters, which describe the size of the dissolved ions as well as thickness and shape of the Stern layer. Out of this defined parameter space, we show that the Stern layer thickness expressed in terms of the solute’s electron density and the resulting ionic cavity volume completely determine ion effects on the stability of neutral solutes. Using the efficient SMPB functionality of the full-potential density-functional theory package FHI-aims, we derive optimized such Stern layer parameters for neutral solutes in various aqueous monovalent electrolytes. The parametrization protocol relies on fitting to reference Setschenow coefficients that describe solvation free energy changes with ionic strength at low to medium concentrations. The availability of such data for NaCl solutions yields a highly predictive SMPB model that allows to recover the measured Setschenow coefficients with an accuracy that is comparable to prevalent quantitative regression models. Correspondingly derived SMPB parameters for other salts suffer from a much scarcer experimental data base but lead to Stern layer properties that follow a physically reasonable trend with ionic hydration numbers

Perspective: On the active site model in computational catalyst screening

First-principles screening approaches exploiting energy trends in surface adsorption represent an unparalleled success story in recent computational catalysis research. Here we argue that our still limited understanding of the structure of active sites is one of the major bottlenecks towards an ever extended and reliable use of such computational screening for catalyst discovery. For low-index transition metal surfaces, the prevalently chosen high-symmetry (terrace and step) sites offered by the nominal bulk-truncated crystal lattice might be justified. For more complex surfaces and composite catalyst materials, computational screening studies will need to actively embrace a considerable uncertainty with respect to what truly are the active sites. By systematically exploring the space of possible active site motifs, such studies might eventually contribute towards a targeted design of optimized sites in future catalysts

Implicit Solvation Methods for Catalysis at Electrified Interfaces

Implicit solvation is an effective, highly coarse-grained approach in atomic-scale simulations to account for a surrounding liquid electrolyte on the level of a continuous polarizable medium. Originating in molecular chemistry with finite solutes, implicit solvation techniques are now increasingly used in the context of first-principles modeling of electrochemistry and electrocatalysis at extended (often metallic) electrodes. The prevalent ansatz to model the latter electrodes and the reactive surface chemistry at them through slabs in periodic boundary condition supercells brings its specific challenges. Foremost this concerns the difficulty of describing the entire double layer forming at the electrified solid–liquid interface (SLI) within supercell sizes tractable by commonly employed density functional theory (DFT). We review liquid solvation methodology from this specific application angle, highlighting in particular its use in the widespread ab initio thermodynamics approach to surface catalysis. Notably, implicit solvation can be employed to mimic a polarization of the electrode’s electronic density under the applied potential and the concomitant capacitive charging of the entire double layer beyond the limitations of the employed DFT supercell. Most critical for continuing advances of this effective methodology for the SLI context is the lack of pertinent (experimental or high-level theoretical) reference data needed for parametrization

Equilibrium free energies from fast-switching trajectories with large time steps

Jarzynski's identity for the free energy difference between two equilibrium states can be viewed as a special case of a more general procedure based on phase space mappings. Solving a system's equation of motion by approximate means generates a mapping that is perfectly valid for this purpose, regardless of how closely the solution mimics true time evolution. We exploit this fact, using crudely dynamical trajectories to compute free energy differences that are in principle exact. Numerical simulations show that Newton's equation can be discretized to low order over very large time steps (limited only by the computer's ability to represent resulting values of dynamical variables) without sacrificing thermodynamic accuracy. For computing the reversible work required to move a particle through a dense liquid, these calculations are more efficient than conventional fast switching simulations by more than an order of magnitude. We also explore consequences of the phase space mapping perspective for systems at equilibrium, deriving an exact expression for the statistics of energy fluctuations in simulated conservative systems

Active discovery of organic semiconductors

The versatility of organic molecules generates a rich design space for organic semiconductors (OSCs) considered for electronics applications. Offering unparalleled promise for materials discovery, the vastness of this design space also dictates efficient search strategies. Here, we present an active machine learning (AML) approach that explores an unlimited search space through consecutive application of molecular morphing operations. Evaluating the suitability of OSC candidates on the basis of charge injection and mobility descriptors, the approach successively queries predictive-quality first-principles calculations to build a refining surrogate model. The AML approach is optimized in a truncated test space, providing deep methodological insight by visualizing it as a chemical space network. Significantly outperforming a conventional computational funnel, the optimized AML approach rapidly identifies well-known and hitherto unknown molecular OSC candidates with superior charge conduction properties. Most importantly, it constantly finds further candidates with highest efficiency while continuing its exploration of the endless design space

Finding the Right Bricks for Molecular Legos: A Data Mining Approach to Organic Semiconductor Design

Improving charge carrier mobilities in organic semiconductors is a challenging task that has hitherto primarily been tackled by empirical structural tuning of promising core compounds. Knowledge-based methods can greatly accelerate such local exploration, while a systematic analysis of large chemical databases can point toward promising design strategies. Here, we demonstrate such data mining by clustering an in-house database of >64,000 organic molecular crystals for which two charge-transport descriptors, the electronic coupling and the reorganization energy, have been calculated from first principles. The clustering is performed according to the Bemis–Murcko scaffolds of the constituting molecules and according to the side groups with which these molecular backbones are functionalized. In both cases, we obtain statistically significant structure–property relationships with certain scaffolds (side groups) consistently leading to favorable charge-transport properties. Functionalizing promising scaffolds with favorable side groups results in engineered molecular crystals for which we indeed compute improved charge-transport properties

Size-Extensive Molecular Machine Learning with Global Representations

Machine learning (ML) models are increasingly used in combination with electronic structure calculations to predict molecular properties at a much lower computational cost in high-throughput settings. Such ML models require representations that encode the molecular structure, which are generally designed to respect the symmetries and invariances of the target property. However, size-extensivity is usually not guaranteed for so-called global representations. In this contribution, we show how extensivity can be built into global ML models using, e. g., the Many-Body Tensor Representation. Properties of extensive and non-extensive models for the atomization energy are systematically explored by training on small molecules and testing on small, medium and large molecules. Our results show that non-extensive models are only useful in the size-range of their training set, whereas extensive models provide reasonable predictions across large size differences. Remaining sources of error for extensive models are discussed