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Density functional theory (DFT) is often used for simulating extended materials such as infinite crystals or surfaces, under periodic boundary conditions (PBCs). In such calculations, when the simulation cell has non-zero charge, electrical neutrality has to be imposed, and this is often done via a uniform background charge of opposite sign ("jellium"). This artificial neutralization does not occur in reality, where a different mechanism is followed as in the example of a charged electrode in electrolyte solution, where the surrounding electrolyte screens the local charge at the interface. The neutralizing effect of the surrounding electrolyte can be incorporated within a hybrid quantum-continuum model based on a modified Poisson-Boltzmann equation, where the concentrations of electrolyte ions are modified to achieve electroneutrality. Among the infinite possible ways of modifying the electrolyte charge, we propose here a physically optimal solution, which minimizes the deviation of concentrations of electrolyte ions from those in open boundary conditions (OBCs). This principle of correspondence of PBCs with OBCs leads to the correct concentration profiles of electrolyte ions, and electroneutrality within the simulation cell and in the bulk electrolyte is maintained simultaneously, as observed in experiments. MD-224 This approach, which we call the Neutralization by Electrolyte Concentration Shift (NECS), is implemented in our electrolyte model in the Order-N Electronic Total Energy Package (ONETEP) linear-scaling DFT code, which makes use of a bespoke highly parallel Poisson-Boltzmann solver, DL_MG. We further propose another neutralization scheme ("accessible jellium"), which is a simplification of NECS. We demonstrate and compare the different neutralization schemes on several examples.Mapping an atomistic configuration to a symmetrized N-point correlation of a field associated with the atomic positions (e.g., an atomic density) has emerged as an elegant and effective solution to represent structures as the input of machine-learning algorithms. While it has become clear that low-order density correlations do not provide a complete representation of an atomic environment, the exponential increase in the number of possible N-body invariants makes it difficult to design a concise and effective representation. We discuss how to exploit recursion relations between equivariant features of different order (generalizations of N-body invariants that provide a complete representation of the symmetries of improper rotations) to compute high-order terms efficiently. In combination with the automatic selection of the most expressive combination of features at each order, this approach provides a conceptual and practical framework to generate systematically improvable, symmetry adapted representations for atomistic machine learning.Using molecular dynamics simulations, we investigate how the structural and vibrational properties of the surfaces of sodo-silicate glasses depend on the sodium content as well as the nature of the surface. Two types of glass surfaces are considered A melt-formed surface (MS) in which a liquid with a free surface has been cooled down into the glass phase and a fracture surface (FS) obtained by tensile loading of a glass sample. We find that the MS is more abundant in Na and non-bridging oxygen atoms than the FS and the bulk glass, whereas the FS has higher concentration of structural defects such as two-membered rings and under-coordinated Si than the MS. We associate these structural differences to the production histories of the glasses and the mobility of the Na ions. It is also found that for Na-poor systems, the fluctuations in composition and local atomic charge density decay with a power-law as a function of distance from the surface, while Na-rich systems show an exponential decay with a typical decay length of ≈2.3 Å. The vibrational density of states shows that the presence of the surfaces leads to a decrease in the characteristic frequencies in the system. The two-membered rings give rise to a pronounce band at ≈880 cm-1, which is in good agreement with experimental observations.We compare the surface structure of linear nanopores in amorphous silica (a-SiO2) for different versions of "pore drilling" algorithms (where the pores are generated by the removal of atoms from the preformed bulk a-SiO2) and for "cylindrical resist" algorithms (where a-SiO2 is formed around a cylindrical exclusion region). After adding H to non-bridging O, the former often results in a moderate to high density of surface silanol groups, whereas the latter produces a low density. The silanol surface density for pore drilling can be lowered by a final dehydroxylation step, and that for the cylindrical resist approach can be increased by a final hydroxylation step. In this respect, the two classes of algorithms are complementary. We focus on the characterization of the chemical structure of the pore surface, decomposing the total silanol density into components corresponding to isolated and vicinal mono silanols and geminal silanols. The final dehyroxylation and hydroxylation steps can also be tuned to better align some of these populations with the target experimental values.The recently developed semistochastic heat-bath configuration interaction (SHCI) method is a systematically improvable selected configuration interaction plus perturbation theory method capable of giving essentially exact energies for larger systems than is possible with other such methods. We compute SHCI atomization energies for 55 molecules that have been used as a test set in prior studies because their atomization energies are known from experiment. Basis sets from cc-pVDZ to cc-pV5Z are used, totaling up to 500 orbitals and a Hilbert space of 1032 Slater determinants for the largest molecules. For each basis, an extrapolated energy well within chemical accuracy (1 kcal/mol or 1.6 mHa/mol) of the exact energy for that basis is computed using only a tiny fraction of the entire Hilbert space. We also use our almost exact energies to benchmark energies from the coupled cluster method with single, double, and perturbative triple excitations. The energies are extrapolated to the complete basis set limit and compared to the experimental atomization energies.

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