Raoult's law revisited: accurately predicting equilibrium relative humidity points for humidity control experiments

The humidity surrounding a sample is an important variable in scientific experiments. Biological samples in particular require not just a humid atmosphere but often a relative humidity (RH) that is in equilibrium with a stabilizing solution required to maintain the sample in the same state during measurements. The controlled dehydration of macromolecular crystals can lead to significant increases in crystal order, leading to higher diffraction quality. Devices that can accurately control the humidity surrounding crystals while monitoring diffraction have led to this technique being increasingly adopted, as the experiments become easier and more reproducible. Matching the RH to the mother liquor is the first step in allowing the stable mounting of a crystal. In previous work [Wheeler, Russi, Bowler & Bowler (2012). Acta Cryst. F68, 111– 114], the equilibrium RHs were measured for a range of concentrations of the most commonly used precipitants in macromolecular crystallography and it was shown how these related to Raoult’s law for the equilibrium vapour pressure of water above a solution. However, a discrepancy between the measured values and those predicted by theory could not be explained. Here, a more precise humidity control device has been used to determine equilibrium RH points. The new results are in agreement with Raoult’s law. A simple argument in statistical mechanics is also presented, demonstrating that the equilibrium vapour pressure of a solvent is proportional to its mole fraction in an ideal solution: Raoult’s law. The same argument can be extended to the case where the solvent and solute molecules are of different sizes, as is the case with polymers. The results provide a framework for the correct maintenance of the RH surrounding a sample

First-principles soft-mode lattice dynamics of PbZr₀.₅Ti₀.₅O₃ and shortcomings of the virtual crystal approximation

A comparative study of PbTiO 3 , PbZrO 3 , and the solid solution PbZr 0.5 Ti 0.5 O 3 is performed on the soft-mode lattice dynamics within the first Brillouin zone. We consider the six unique B-site orderings for PbZr 0.5 Ti 0.5 O 3 representable within the 2 × 2 × 2 primitive perovskite supercell as well as the virtual crystal approximation (VCA) to extract the phonon dispersion relations of a high-symmetry cubic-constrained form using density functional perturbation theory. We find that the most unstable modes in the rock-salt ordered structure and the VCA, like pure PbZrO 3 , are antiferrodistortive (AFD) while lower symmetry arrangements are dominated by Γ -point ferroelectric (FE) instabilities like pure PbTiO 3 . Despite similarities in the phonon dispersion relations between the rock-salt ordered supercell and the VCA, the character of modes at high symmetry points are found to be different. In particular, the a 0 a 0 c − and a 0 a 0 c + AFD instabilities of the rock-salt ordering are replaced with a − b − c − and a + b + c + instabilities within the VCA. Such a rotation pattern is not seen in any of the supercell-based calculations, thus serving as a quantitative example of the inability of the method to accurately represent local structural distortions. Single modes are found exhibiting dual order parameters. At the zone center, some arrangements show mixed FE and antipolar soft modes (due to Pb motion transverse to the polar axis), and at long wavelengths all arrangements have soft modes of a mixed antipolar and AFD character. These are described with direct analysis of the eigendisplacements

DFT study of undoped and As-doped Si nanowires approaching the bulk limit

The electronic properties of pure and As-doped Si nanowires (NWs) with radii up to 9.53 nm are studied using large scale density functional theory (DFT) calculations. We show that, for the undoped NWs, the DFT bandgap reduces with increasing diameter and converges to its bulk value, a trend in agreement with experimental data. Moreover, we show that the atoms closest to the surface of the nanowire (NW) contribute less to the states near the band edges, when compared with atoms close to the centre; this is shown to be due to differences in Si-Si atomic distances, as well as surface passivation effects. When considering As-doped Si NWs we show that dopant placement within the NW plays an important role in deciding electronic properties. We show that a low velocity band is introduced by As doping, in the gap, but close to the conduction band edge. The curvature of this low velocity band depends on the dopant location, with the curvature reducing when the dopant is placed closer to the center. We also show that asymmetry of dopant location with the NW leads to splitting of the valence band edge

Origin of Ferroelectric Domain Wall Alignment with Surface Trenches in Ultrathin Films

Engraving trenches on the surfaces of ultrathin ferroelectric (FE) films and superlattices promises control over the orientation and direction of FE domain walls (DWs). Through exploiting the phenomenon of DW-surface trench (ST) parallel alignment, systems where DWs are known for becoming electrical conductors could now become useful nanocircuits using only standard lithographical techniques. Despite this clear application, the microscopic mechanism responsible for the alignment phenomenon has remained elusive. Using ultrathin PbTiO3 films as a model system, we explore this mechanism with large scale density functional theory simulations on as many as 5,136 atoms. Although we expect multiple contributing factors, we show that parallel DW-ST alignment can be well explained by this configuration giving rise to an arrangement of electric dipole moments which best restore polar continuity to the film. These moments preserve the polar texture of the pristine film, thus minimizing ST-induced depolarizing fields. Given the generality of this mechanism, we suggest that STs could be used to engineer other exotic polar textures in a variety of FE nanostructures as supported by the appearance of ST-induced polar cycloidal modulations in this Letter. Our simulations also support experimental observations of ST-induced negative strains which have been suggested to play a role in the alignment mechanism

Communication: Generalized canonical purification for density matrix minimization

A Lagrangian formulation for the constrained search for the N-representable one-particle density matrix based on the McWeeny idempotency error minimization is proposed, which converges systematically to the ground state. A closed form of the canonical purification is derived for which no a posteriori adjustment on the trace of the density matrix is needed. The relationship with comparable methods is discussed, showing their possible generalization through the hole-particle duality. The appealing simplicity of this self-consistent recursion relation along with its low computational complexity could prove useful as an alternative to diagonalization in solving dense and sparse matrix eigenvalue problems

The pseudoatomic orbital basis: electronic accuracy and soft-mode distortions in ABO3 perovskites

The perovskite oxides are known to be susceptible to structural distortions over a long wavelength when compared to their parent cubic structures. From an ab initio simulation perspective, this requires accurate calculations including many thousands of atoms; a task well beyond the remit of traditional plane wave-based density functional theory (DFT). We suggest that this void can be filled using the methodology implemented in the large-scale DFT code, CONQUEST, using a local pseudoatomic orbital (PAO) basis. Whilst this basis has been tested before for some structural and energetic properties, none have treated the most fundamental quantity to the theory, the charge density n(r) itself. An accurate description of n(r) is vital to the perovskite oxides due to the crucial role played by short-range restoring forces (characterised by bond covalency) and long range Coulomb forces as suggested by the soft-mode theory of Cochran and Anderson. We find that modestly sized basis sets of PAOs can reproduce the plane-wave charge density to a total integrated error of better than 0.5% and provide Bader partitioned ionic charges, volumes and average charge densities to similar degree of accuracy. Further, the multi-mode antiferroelectric distortion of PbZrO3 and its associated energetics are reproduced by better than 99% when compared to plane-waves. This work suggests that electronic structure calculations using efficient and compact basis sets of pseudoatomic orbitals can achieve the same accuracy as high cutoff energy plane-wave calculations. When paired with the CONQUEST code, calculations with high electronic and structural accuracy can now be performed on many thousands of atoms, even on systems as delicate as the perovskite oxides

Notes on density matrix perturbation theory

Density matrix perturbation theory (DMPT) is known as a promising alternative to the Rayleigh-Schrödinger perturbation theory, in which the sum-over-states (SOS) is replaced by algorithms with perturbed density matrices as the input variables. In this article, we formulate and discuss three types of DMPT, with two of them based only on density matrices: the approach of Kussmann and Ochsenfeld [J. Chem. Phys. 127, 054103 (2007)] is reformulated via the Sylvester equation and the recursive DMPT of Niklasson and Challacombe [Phys. Rev. Lett. 92, 193001 (2004)] is extended to the hole-particle canonical purification (HPCP) from Truflandier et al. [J. Chem. Phys. 144, 091102 (2016)]. A comparison of the computational performances shows that the aforementioned methods outperform the standard SOS. The HPCP-DMPT demonstrates stable convergence profiles but at a higher computational cost when compared to the original recursive polynomial method

Linear-scaling first-principles molecular dynamics of complex biological systems with the CONQUEST code

The recent progress of linear-scaling or $\mathcal{O}(N)$ methods in density functional theory (DFT) is remarkable. In this paper, we show that all-atom molecular dynamics simulations of complex biological systems based on DFT are now possible using our linear-scaling DFT code Conquest. We first overview the calculation methods used in Conquest and explain the method introduced recently to realise efficient and robust first-principles molecular dynamics (FPMD) with $\mathcal{O}(N)$ DFT. Then, we show that we can perform reliable all-atom FPMD simulations of a hydrated DNA model containing about 3400 atoms. We also report that the velocity scaling method is both reliable and useful for controlling the temperature of the FPMD simulation of this system. From these results, we conclude that reliable FPMD simulations of complex biological systems are now possible with Conquest

Subatomic electronic feature from dynamic motion of Si dimer defects in Bi nanolines on Si(001)

Scanning tunneling microscopy (STM) reveals unusual sharp features in otherwise defect-free Bi nanolines self-assembled on Si(001). They appear as subatomic thin lines perpendicular to the Bi nanoline at positive biases and as atomic size beads at negative biases. Density functional theory (DFT) simulations show that these features can be attributed to buckled Si dimers substituting for Bi dimers in the nanoline, where the sharp feature is the counterintuitive signature of these dimers flipping during scanning. The perfect correspondence between the STM data and the DFT simulation demonstrated in this paper highlights the detailed understanding we have of the complex Bi-Si(001) Haiku system. This discovery has applications in the patterning of Si dangling bonds for nanoscale electronic