The ionization potential of aqueous hydroxide computed using many-body perturbation theory

Investigation of Ionization Potential in Quantum Dots Using the Stratified Stochastic Enumeration of Molecular Orbitals Method

The overarching goal of this work is to investigate the size-dependent characteristics of the ionization potential of PbS and CdS quantum dots. The ionization potentials of quantum dots provide critical information about the energies of occupied states, which can then be used to quantify the electron-removal characteristics of quantum dots. The energy of the highest-occupied molecular orbital is used to understand electron-transfer processes when invesigating the energy-level alignment between quantum dots and electron-accepting ligands. Ionization potential is also important for investigating and interpreting electron-detachment processes induced by light (photoelectron spectra), external voltage (chemiresistance), and collision with other electrons (impact ionization). Accurate first-principles calculations of ionization potential continue to be challenging because of the computational cost associated with the construction of the frequency-dependent self-energy operator and the numerical solution of the associated Dyson equation. The computational cost becomes prohibitive as the system size increases because of the large number of 2particle-1hole (2p1h) and 1particle-2hole (1p2h) terms needed for the calculation. In this work, we present the Stratified Stochastic Enumeration of Molecular Orbitals (SSE-MO) method for efficient construction of the self-energy operator. The SSE-MO method is a real-space method and the central strategy of this method is to use stochastically enumerated sampling of molecular orbitals and molecular-orbital indices for the construction of the 2p1h and 1p2h terms. This is achieved by first constructing a composite MO-index Cartesian coordinate space followed by transformation of the frequency-dependent self-energy operator to this composite space. The evaluation of both the real and imaginary components of the self-energy operator is performed using a stratified Monte Carlo technique. The SSE-MO method was used to calculate the ionization potentials and the frequency-dependent spectral functions for a series of PbS and CdS quantum dots by solving the Dyson equation using both single-shot and iterative procedures. The ionization potentials for both PbS and CdS quantum dots were found to decrease with increasing dot size. Analysis of the frequency-dependent spectral functions revealed that for PbS quantum dots the intermediate dot size exhibited a longer relative lifetime whereas in CdS the smallest dot size had the longest relative lifetime. The results from these calculations demonstrate the efficacy of the SSE-MO method for calculating accurate ionization potentials and spectral functions of chemical systems.

Photoelectron spectra of water and simple aqueous solutions at extreme conditions

Determining the electronic structure of aqueous solutions at extreme conditions is an important step towards understanding chemical bonding and reactions in water under pressure (P) and at high temperature (T)....

Beyond Koopmans' theorem: electron binding energies in disordered materials

The topical review focuses on calculating ionization energies (IE), or electronic polarons in quasi-particle terminology, in large disordered systems, e.g. for a solute dissolved in a molecular solvent. The simplest estimate of the ionization energy is provided by one-electron energies in the Hartree-Fock theory, but the calculated quantities are not accurate. Density functional theory as many-body theory provides a principal opportunity for calculating one-electron energies including correlation and relaxation effects, i.e. the true energies of electronic polarons. We argue that such a principal possibility materializes within the concept of optimally tuned range-separated hybrid functionals (OT-RSH). We describe various schemes for optimal tuning. Importantly, the OT-RSH scheme is investigated for systems capped with dielectric continuum, providing a consistent picture on the QM/dielectric boundary. Finally, some limitations and open issues of the OT-RSH approach are addressed.

Understanding the apparent fractional charge of protons in the aqueous electrochemical double layer

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. In this work, we investigate the charge of solvated protons at the Pt(111) | H₂O and Al(111) | H₂O interfaces. Using semi-local density-functional theory as well as hybrid functionals and embedded correlated wavefunction methods as higher-level benchmarks, we show that the effective charge of a solvated proton in the electrochemical double layer or outer Helmholtz plane at all levels of theory is fractional, when the solvated proton and solvent band edges are aligned correctly with the Fermi level of the metal (E_F). The observed fractional charge in the absence of frontier band misalignment arises from a significant overlap between the proton and the electron density from the metal surface, and results in an energetic difference between protons in bulk solution and those in the outer Helmholtz plane.

A detailed atomic-scale description of the electrochemical interface is essential to the understanding of electrochemical energy transformations. Here, the authors investigate the solvated proton at the electrochemical interface and show that it unexpectedly carries a fractional charge.

Absolute Energy Levels of Liquid Water

We determine the ionization potential (IP) and the electron affinity (EA) of liquid water together with the absolute redox level of the standard hydrogen electrode (SHE) by combining advanced electronic-structure calculations, ab initio molecular dynamics simulations, thermodynamic integration, and potential alignment at the water-vacuum interface. The calculated SHE level lies at 4.56 eV below the vacuum level, close to the experimental reference of 4.44 eV inferred by Trasatti. The band edges are determined through a hybrid functional designed to reproduce the band gap achieved with highly accurate GW calculations. Our analysis yields IP = 9.7 eV and EA = 0.8 eV, consistent with both photoemission spectra of liquid water and thermodynamical data for the hydrated electron.

Electron affinity of liquid water

Understanding redox and photochemical reactions in aqueous environments requires a precise knowledge of the ionization potential and electron affinity of liquid water. The former has been measured, but not the latter. We predict the electron affinity of liquid water and of its surface from first principles, coupling path-integral molecular dynamics with ab initio potentials, and many-body perturbation theory. Our results for the surface (0.8 eV) agree well with recent pump-probe spectroscopy measurements on amorphous ice. Those for the bulk (0.1-0.3 eV) differ from several estimates adopted in the literature, which we critically revisit. We show that the ionization potential of the bulk and surface are almost identical; instead their electron affinities differ substantially, with the conduction band edge of the surface much deeper in energy than that of the bulk. We also discuss the significant impact of nuclear quantum effects on the fundamental gap and band edges of the liquid.

Integrating Ab Initio Simulations and X-ray Photoelectron Spectroscopy: Toward A Realistic Description of Oxidized Solid/Liquid Interfaces

Many energy storage and conversion devices rely on processes that take place at complex interfaces, where structural and chemical properties are often difficult to probe under operating conditions. A primary example is solar water splitting using high-performance photoelectrochemical cells, where surface chemistry, including native oxide formation, affects hydrogen generation. In this Perspective, we discuss some of the challenges associated with interrogating interface chemistry, and how they may be overcome by integrating high-level first-principles calculations of explicit interfaces with ambient pressure X-ray photoelectron spectroscopy and direct spectroscopic simulations. We illustrate the benefit of this combined approach toward insights into native oxide chemistry at prototypical InP/water and GaP/water interfaces. This example suggests a more general roadmap for obtaining a realistic and reliable description of the chemistry of complex interfaces by combining state-of-the-art computational and experimental techniques.

Electronic structure of aqueous solutions: Bridging the gap between theory and experiments

Predicting the electronic properties of aqueous liquids has been a long-standing challenge for quantum mechanical methods. However, it is a crucial step in understanding and predicting the key role played by aqueous solutions and electrolytes in a wide variety of emerging energy and environmental technologies, including battery and photoelectrochemical cell design. We propose an efficient and accurate approach to predict the electronic properties of aqueous solutions, on the basis of the combination of first-principles methods and experimental validation using state-of-the-art spectroscopic measurements. We present results of the photoelectron spectra of a broad range of solvated ions, showing that first-principles molecular dynamics simulations and electronic structure calculations using dielectric hybrid functionals provide a quantitative description of the electronic properties of the solvent and solutes, including excitation energies. The proposed computational framework is general and applicable to other liquids, thereby offering great promise in understanding and engineering solutions and liquid electrolytes for a variety of important energy technologies.

Modelling heterogeneous interfaces for solar water splitting

The generation of hydrogen from water and sunlight offers a promising approach for producing scalable and sustainable carbon-free energy. The key of a successful solar-to-fuel technology is the design of efficient, long-lasting and low-cost photoelectrochemical cells, which are responsible for absorbing sunlight and driving water splitting reactions. To this end, a detailed understanding and control of heterogeneous interfaces between photoabsorbers, electrolytes and catalysts present in photoelectrochemical cells is essential. Here we review recent progress and open challenges in predicting physicochemical properties of heterogeneous interfaces for solar water splitting applications using first-principles-based approaches, and highlights the key role of these calculations in interpreting increasingly complex experiments.

Dehydrogenation Free Energy of Co2+(aq) from Density Functional Theory-Based Molecular Dynamics

Electron and proton transfers are important steps occurring in chemical reactions. The often used approach of calculating the energy differences of those steps using methods based on geometry optimizations neglects the influence of dynamic effects. To further investigate this issue and inspired by research in water oxidation, we calculate in the present study the dehydrogenation free energy of aqueous Co²⁺, which is the free energy change associated with the first step of the water oxidation reaction mechanism of recently investigated model Co(II)-aqua catalysts. We employ a method based on a thermodynamic integration scheme with strong ties to Marcus theory to obtain free energy differences, solvent reorganization free energies, and dynamic structural information on the systems from density functional theory-based molecular dynamics. While this method is computationally orders of magnitude more expensive than a static approach, it potentially allows for predicting the validity of the approximation of neglecting dynamic effects.

Ab initio Electronic Structure of Liquid Water

Self-consistent GW calculations with efficient vertex corrections are employed to determine the electronic structure of liquid water. Nuclear quantum effects are taken into account through ab initio path-integral molecular dynamics simulations. We reveal a sizable band-gap renormalization of up to 0.7 eV due to hydrogen-bond quantum fluctuations. Our calculations lead to a band gap of 8.9 eV, in accord with the experimental estimate. We further resolve the ambiguities in the band-edge positions of liquid water. The valence-band maximum and the conduction-band minimum are found at -9.4 and -0.5  eV with respect to the vacuum level, respectively.

Photoelectron Spectra of Aqueous Solutions from First Principles

We present a combined computational and experimental study of the photoelectron spectrum of a simple aqueous solution of NaCl. Measurements were conducted on microjets, and first-principles calculations were performed using hybrid functionals and many-body perturbation theory at the G0W0 level, starting with wave functions computed in ab initio molecular dynamics simulations. We show excellent agreement between theory and experiments for the positions of both the solute and solvent excitation energies on an absolute energy scale and for peak intensities. The best comparison was obtained using wave functions obtained with dielectric-dependent self-consistent and range-separated hybrid functionals. Our computational protocol opens the way to accurate, predictive calculations of the electronic properties of electrolytes, of interest to a variety of energy problems.

Density Functional Theory Calculation of the Band Alignment of (101̅0) In(x)Ga(1-x)N/Water Interfaces

Conduction band edge (CBE) and valence band edge (VBE) positions of InxGa1-xN photoelectrodes were computed using density functional theory methods. The band edges of fully solvated GaN and InN model systems were aligned with respect to the standard hydrogen electrode using a molecular dynamics hydrogen electrode scheme applied earlier to TiO2/water interfaces. Similar to the findings for TiO2, we found that the Purdew-Burke-Ernzerhof (PBE) functional gives a VBE potential which is too negative by 1 V. This cathodic bias is largely corrected by application of the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional containing a fraction of Hartree-Fock exchange. The effect of a change of composition was investigated using simplified model systems consisting of vacuum slabs covered on both sides by one monolayer of H2O. The CBE was found to vary linearly with In content. The VBE, in comparison, is much less sensitive to composition. The data show that the band edges straddle the hydrogen and oxygen evolution potentials for In fractions less than 47%. The band gap was found to exceed 2 eV for an In fraction less than 54%.

Calculation of Electrochemical Energy Levels in Water Using the Random Phase Approximation and a Double Hybrid Functional

Understanding charge transfer at electrochemical interfaces requires consistent treatment of electronic energy levels in solids and in water at the same level of the electronic structure theory. Using density-functional-theory-based molecular dynamics and thermodynamic integration, the free energy levels of six redox couples in water are calculated at the level of the random phase approximation and a double hybrid density functional. The redox levels, together with the water band positions, are aligned against a computational standard hydrogen electrode, allowing for critical analysis of errors compared to the experiment. It is encouraging that both methods offer a good description of the electronic structures of the solutes and water, showing promise for a full treatment of electrochemical interfaces.

Colloidal Nanoparticles for Intermediate Band Solar Cells

The Intermediate Band (IB) solar cell concept is a promising idea to transcend the Shockley-Queisser limit. Using the results of first-principles calculations, we propose that colloidal nanoparticles (CNPs) are a viable and efficient platform for the implementation of the IB solar cell concept. We focused on CdSe CNPs and we showed that intragap states present in the isolated CNPs with reconstructed surfaces combine to form an IB in arrays of CNPs, which is well separated from the valence and conduction band edges. We demonstrated that optical transitions to and from the IB are active. We also showed that the IB can be electron doped in a solution, e.g., by decamethylcobaltocene, thus activating an IB-induced absorption process. Our results, together with the recent report of a nearly 10% efficient CNP solar cell, indicate that colloidal nanoparticle intermediate band solar cells are a promising platform to overcome the Shockley-Queisser limit.

Predicting the voltage dependence of interfacial electrochemical processes at lithium-intercalated graphite edge planes

The voltage of lithium-intercalated graphite with edge planes exposed to a liquid electrolyte is calibrated and applied to examine electrolyte decomposition reactions.

Redox potentials and acidity constants from density functional theory based molecular dynamics

CONSPECTUS: All-atom methods treat solute and solvent at the same level of electronic structure theory and statistical mechanics. All-atom computation of acidity constants (pKa) and redox potentials is still a challenge. In this Account, we review such a method combining density functional theory based molecular dynamics (DFTMD) and free energy perturbation (FEP) methods. The key computational tool is a FEP based method for reversible insertion of a proton or electron in a periodic DFTMD model system. The free energy of insertion (work function) is computed by thermodynamic integration of vertical energy gaps obtained from total energy differences. The problem of the loss of a physical reference for ionization energies under periodic boundary conditions is solved by comparing with the proton work function computed for the same supercell. The scheme acts as a computational hydrogen electrode, and the DFTMD redox energies can be directly compared with experimental redox potentials. Consistent with the closed shell nature of acid dissociation, pKa estimates computed using the proton insertion/removal scheme are found to be significantly more accurate than the redox potential calculations. This enables us to separate the DFT error from other sources of uncertainty such as finite system size and sampling errors. Drawing an analogy with charged defects in solids, we trace the error in redox potentials back to underestimation of the energy gap of the extended states of the solvent. Accordingly the improvement in the redox potential as calculated by hybrid functionals is explained as a consequence of the opening up of the bandgap by the Hartree-Fock exchange component in hybrids. Test calculations for a number of small inorganic and organic molecules show that the hybrid functional implementation of our method can reproduce acidity constants with an uncertainty of 1-2 pKa units (0.1 eV). The error for redox potentials is in the order of 0.2 V.