Corresponding Orbitals Derived from Periodic Bloch States for Electron Transfer Calculations of Transition Metal Oxides

Implementation and Validation of Constrained Density Functional Theory Forces in the CP2K Package

Constrained density functional theory (CDFT) is a powerful tool for the prediction of electron transfer parameters in condensed phase simulations at a reasonable computational cost. In this work we present an extension to CDFT in the popular mixed Gaussian/plane wave electronic structure package CP2K, implementing the additional force terms arising from a constraint based on Hirshfeld charge partitioning. This improves upon the existing Becke partitioning scheme, which is prone to give unphysical atomic charges. We verify this implementation for a variety of systems: electron transfer in (H₂O)₂⁺ in a vacuum, electron tunnelling between oxygen vacancy centers in solid MgO, and electron self-exchange in aqueous Ru²⁺–Ru³⁺. We find good agreement with previous plane-wave CDFT results for the same systems, but at a significantly lower computational cost, and we discuss the general reliability of condensed phase CDFT calculations.

Electron and Hole Mobilities in Bulk Hematite from Spin-Constrained Density Functional Theory

Transition metal oxide materials have attracted much attention for photoelectrochemical water splitting, but problems remain, e.g. the sluggish transport of excess charge carriers in these materials, which is not well understood. Here we use periodic, spin-constrained and gap-optimized hybrid density functional theory to uncover the nature and transport mechanism of holes and excess electrons in a widely used water splitting material, bulk-hematite (α-Fe₂O₃). We find that upon ionization the hole relaxes from a delocalized band state to a polaron localized on a single iron atom with localization induced by tetragonal distortion of the six surrounding iron-oxygen bonds. This distortion is responsible for sluggish hopping transport in the Fe-bilayer, characterized by an activation energy of 70 meV and a hole mobility of 0.031 cm²/(V s). By contrast, the excess electron induces a smaller distortion of the iron-oxygen bonds resulting in delocalization over two neighboring Fe units. We find that 2-site delocalization is advantageous for charge transport due to the larger spatial displacements per transfer step. As a result, the electron mobility is predicted to be a factor of 3 higher than the hole mobility, 0.098 cm²/(V s), in qualitative agreement with experimental observations. This work provides new fundamental insight into charge carrier transport in hematite with implications for its photocatalytic activity.

How the Donor/Acceptor Spin States Affect the Electronic Couplings in Molecular Charge-Transfer Processes?

The electronic coupling matrix element H_AB is an essential ingredient of most electron-transfer theories. H_AB depends on the overlap between donor and acceptor wave functions and is affected by the involved states’ spin. We classify the spin-state effects into three categories: orbital occupation, spin-dependent electron density, and density delocalization. The orbital occupancy reflects the diverse chemical nature and reactivity of the spin states of interest. The effect of spin-dependent density is related to a more compact electron density cloud at lower spin states due to decreased exchange interactions between electrons. Density delocalization is strongly connected with the covalency concept that increases the spatial extent of the diabatic state’s electron density in specific directions. We illustrate these effects with high-level ab initio calculations on model direct donor–acceptor systems relevant to metal oxide materials and biological electron transfer. Obtained results can be used to benchmark existing methods for H_AB calculations in complicated cases such as spin-crossover materials or antiferromagnetically coupled systems.

Quantum Solvers for Plane-Wave Hamiltonians: Abridging Virtual Spaces Through the Optimization of Pairwise Correlations

For many-body methods such as MCSCF and CASSCF, in which the number of one-electron orbitals is optimized and independent of the basis set used, there are no problems with using plane-wave basis sets. However, for methods currently used in quantum computing such as select configuration interaction (CI) and coupled cluster (CC) methods, it is necessary to have a virtual space that is able to capture a significant amount of electron-electron correlation in the system. The virtual orbitals in a pseudopotential plane-wave Hartree-Fock calculation, because of Coulomb repulsion, are often scattering states that interact very weakly with the filled orbitals. As a result, very little correlation energy is captured from them. The use of virtual spaces derived from the one-electron operators has also been tried, and while some correlations are captured, the amount is quite low. To overcome these limitations, we have been developing new classes of algorithms to define virtual spaces by optimizing orbitals from small pairwise CI Hamiltonians, which we term as correlation optimized virtual orbitals with the abbreviation COVOs. With these procedures, we have been able to derive virtual spaces, containing only a few orbitals, which are able to capture a significant amount of correlation. The focus in this manuscript is on using these derived basis sets to target full CI (FCI) quality results for H2 on near-term quantum computers. However, the initial results for this approach were promising. We were able to obtain good agreement with FCI/cc-pVTZ results for this system with just 4 virtual orbitals, using both FCI and quantum simulations. The quality of the results using COVOs suggests that it may be possible to use them in other many-body approaches, including coupled cluster and Møller-Plesset perturbation theories, and open up the door to many-body calculations for pseudopotential plane-wave basis set methods.

NWChem: Past, present, and future

Specialized computational chemistry packages have permanently reshaped the landscape of chemical and materials science by providing tools to support and guide experimental efforts and for the prediction of atomistic and electronic properties. In this regard, electronic structure packages have played a special role by using first-principle-driven methodologies to model complex chemical and materials processes. Over the past few decades, the rapid development of computing technologies and the tremendous increase in computational power have offered a unique chance to study complex transformations using sophisticated and predictive many-body techniques that describe correlated behavior of electrons in molecular and condensed phase systems at different levels of theory. In enabling these simulations, novel parallel algorithms have been able to take advantage of computational resources to address the polynomial scaling of electronic structure methods. In this paper, we briefly review the NWChem computational chemistry suite, including its history, design principles, parallel tools, current capabilities, outreach, and outlook.

Polaronic structure of excess electrons and holes for a series of bulk iron oxides

With the use of a gap-optimized hybrid functional and large supercells, it is found that while the electron hole polaron generally localises onto a single iron site, the electron polaron localises across two iron sites of the same spin layer.

Electron transfer in extended systems: characterization by periodic density functional theory including the electronic coupling

We describe a new computer implementation of electron transfer (ET) theory in extended systems treated by periodic density functional theory (DFT), including the calculation of the electronic coupling transition element V_AB. In particular, the development opens up the full characterization of electron transfer in the solid state. The approach is valid for any single-determinant wavefunction with localized character representing the electronic structure of the system, from Hartree-Fock (HF) theory, to density functional theory (DFT), hybrid DFT theory, DFT+U theory, and constrained DFT (cDFT) theory. The implementation in CP2K reuses the high-performance functions of the code. The computational cost is equivalent to only one iteration of an HF calculation. We present test calculations for electron transfer in a number of systems, including a 1D-model of ferric oxide, hematite Fe₂O₃, rutile TiO₂, and finally bismuth vanadate BiVO₄.