Charged‐cell periodic DFT simulations via an impurity model based on density embedding: Application to the ionization potential of liquid water

Abstract

Calculations of charged systems in periodic boundary conditions (PBC) are problematic because there are spurious interactions between the charges in different periodic images that can affect the physical picture. In addition, the intuitive limit of Coulomb interactions decaying to zero as the interacting charges are placed at infinite separation no longer applies, and for example total energies become undefined. Leveraging subsystem density functional theory (also known as density embedding) we define an impurity model that embeds a finite neutral or charged subsystem within an extended (infinite) surrounding subsystem. The combination of the impurity model and a consistent choice of the Coulomb reference provides us with an algorithm for evaluating the ionization potential (IP) in extended systems. We demonstrate our approach in a pilot calculation of the IP of liquid water, based on a configuration from a prior ab initio molecular dynamics (AIMD) simulation of liquid water (Genova et al., J. Chem. Phys. 2016, 144, 234105). The calculations with the impurity model capture the broadening on the ionization energies introduced by the interactions between the water molecules. Furthermore, the calculated average IP value (10.5 eV) compare favorably to experiments (9.9-10.06 eV) and very recent simulations based on the GW approximation (10.55 eV), while at the same time outperforming density embedding calculations carried out with a naïve handling of the electrostatic interactions (about 7 eV). K E Y W O R D S DFT, embedding, periodic boundary conditions, water 1 | INTRODUCTION Atomistic models of extended systems (such as solids and liquids) typically prescribe the use of periodic boundary conditions (PBC). Once PBC are invoked, one has the choice of evaluating Coulomb interactions in real space or in reciprocal space. If real space is chosen, considering r, r 0 2R 3 then the Coulomb kernel is w r, r 0 ð Þ¼ 1 jr− r 0 j hinting that it decays to zero when two charges are far away. Despite the decay feature of the kernel, Coulomb potentials and energies for extended systems involve conditionally convergent integrals [1] -a complication which is dealt with by switching to reciprocal space. From a purely theoretical standpoint, in PBC, distance is not a well-defined quantity [2] and the physical kernel is only the one represented in reciprocal space, w G ð Þ¼ 4π G j j 2 (G 2 R 3 an element of the reciprocal space). Thus, complications arise because when G = 0, as the Coulomb kernel becomes undefined. In Ewald summations, [3] this is dealt with using a two-prongued approach: the short-range interactions are dealt with in real space (using a cut-off function, typically the error function), and the long-range interactions are dealt with in reciprocal space.In practice, however, the kernel singularity at G = 0 is not problematic because, although w(G) is singular for G = 0, the total charge density ρ(G) is zero for G = 0. We note that neutrality of the charge density in each unit cell is the only physical choice in PBC, beca...

Probing Interfacial Effects on Ionization Energies: The Surprising Banality of Anion-Water Hydrogen Bonding at the Air/Water Interface

“…86 The present calculations, however, are free of issues related to the use of periodic electronic structure for ionization or redox processes. [126][127][128][129][130][131][132][133][134][135] Having validated the accuracy of our computational protocol with respect to experimental data, we next turn to the most interesting aspect of the calculations, namely, the similarity between VIEs computed for isotropic versus slab simulations, for the same ion. These differences are < 0.3 eV for each of the ions in our data set, and often much smaller.…”

“…This is comparable to the accuracy of the best existing periodic DFT calculations of the same quantities, 86 but without the complexities posed by the periodic treatment when the number of electrons changes. [128][129][130][131][132][133][134][135] The protocol reported here is also readily extensible to wave function-based quantum chemistry.…”

Frozen‐density embedding‐based many‐body expansions

“…As the theory is formulated only in terms of the subsystem electron densities, it is particularly easy to combine with different QC methods and MBE strategies, without introducing problems due to a potential double counting of energy contributions. In combination with periodic density-based embedding schemes, [28,97] the db-MBE thus provides an intriguing approach for the accurate QC treatment of molecular crystals. In such applications, the use of accurate nonlocal kinetic energy functionals recently developed by Pavanello and coworkers [98,99] might be particularly promising.…”

Frozen-Density Embedding Based Many-Body Expansions

“…As the theory is formulated only in terms of the subsystem electron densities, it is particularly easy to combine with different quantum-chemical methods and MBE strategies, without introducing problems due to a potential double counting of energy contributions. In combination with periodic densitybased embedding schemes [28,97], the db-MBE thus provides a intriguing approach for the accurate quantum-chemical treatment of molecular crystals. In such applications, the use of accurate nonlocal kinetic-energy functionals recently developed by Pavanello and coworkers [98,99] might be particularly promising.…”