Optimization of constrained density functional theory

Constrained density functional theory (cDFT) is a versatile electronic structure method that enables ground-state calculations to be performed subject to physical constraints. It thereby broadens their applicability and utility. Automated Lagrange multiplier optimisation is necessary for multiple constraints to be applied efficiently in cDFT, for it to be used in tandem with geometry optimization, or with molecular dynamics. In order to facilitate this, we comprehensively develop the connection between cDFT energy derivatives and response functions, providing a rigorous assessment of the uniqueness and character of cDFT stationary points while accounting for electronic interactions and screening. In particular, we provide a new, non-perturbative proof that stable stationary points of linear density constraints occur only at energy maxima with respect to their Lagrange multipliers. We show that multiple solutions, hysteresis, and energy discontinuities may occur in cDFT. Expressions are derived, in terms of convenient by-products of cDFT optimization, for quantities such as the dielectric function and a condition number quantifying ill-definition in multi-constraint cDFT.Comment: 15 pages, 6 figure

What is the orientation of the tip in a scanning tunneling microscope?

We introduce a statistical correlation analysis method to obtain information on the local geometry and orientation of the tip used in scanning tunneling microscopy (STM) experiments based on large scale simulations. The key quantity is the relative brightness correlation of constant-current topographs between experimental and simulated data. This correlation can be analyzed statistically for a large number of modeled tip orientations and geometries. Assuming a stable tip during the STM scans and based on the correlation distribution, it is possible to determine the tip orientations that are most likely present in an STM experiment, and exclude other orientations. This is especially important for substrates such as highly oriented pyrolytic graphite (HOPG) since its STM contrast is strongly tip dependent, which makes interpretation and comparison of STM images very challenging. We illustrate the applicability of our method considering the HOPG surface in combination with tungsten tip models of two different apex geometries and 18144 different orientations. We calculate constant-current profiles along the $$ direction of the HOPG(0001) surface in the $|V|\le 1$ V bias voltage range, and compare them with experimental data. We find that a blunt tip model provides better correlation with the experiment for a wider range of tip orientations and bias voltages than a sharp tip model. Such a combination of experiments and large scale simulations opens up the way for obtaining more detailed information on the structure of the tip apex and more reliable interpretation of STM data in the view of local tip geometry effects.Comment: Progress in Surface Science, accepted for publication, 25 pages manuscript, 9 figures, abstract shortene

Density Functional Theory screening of gas-treatment strategies for stabilization of high energy-density lithium metal anodes

To explore the potential of molecular gas treatment of freshly cut lithium foils in non-electrolyte based passivation of high energy-density Li anodes, density functional theory (DFT) has been used to study the decomposition of molecular gases on metallic lithium surfaces. By combining DFT geometry optimization and Molecular Dynamics, the effects of atmospheric (N2, O2, CO2) and hazardous (F2, SO2) gas decomposition on Li(bcc) (100), (110), and (111) surfaces on relative surface energies, work functions, and emerging electronic and elastic properties are investigated. The simulations suggest that exposure to different molecular gases can be used to induce and control reconstructions of the metal Li surface and substantial changes (up to over 1 eV) in the work function of the passivated system. Contrary to the other considered gases, which form metallic adlayers, SO2 treatment emerges as the most effective in creating an insulating passivation layer for dosages <= 1 mono-layer. The substantial Li->adsorbate charge transfer and adlayer relaxation produce marked elastic stiffening of the interface, with the smallest change shown by nitrogen-treated adlayers

Chemically Selective Alternatives to Photoferroelectrics for Polarization-Enhanced Photocatalysis: the Untapped Potential of Hybrid Inorganic Nanotubes

Linear-scaling Density Functional Theory simulation of methylated imogolite nanotubes (NTs) elucidates the interplay between wall-polarization, bands separation, charge-transfer excitation, and tunable electrostatics inside and outside the NT-cavity. The results suggest that integration of polarization-enhanced selective photocatalysis and chemical separation into one overall dipole-free material should be possible. Strategies are proposed to increase the NT polarization for maximally enhanced electron-hole separation

Contrast stability and "stripe" formation in Scanning Tunnelling Microscopy imaging of highly oriented pyrolytic graphite: The role of STM-tip orientations

Highly oriented pyrolytic graphite (HOPG) is an important substrate in many technological applications and is routinely used as a standard in Scanning Tunnelling Microscopy (STM) calibration, which makes the accurate interpretation of the HOPG STM contrast of great fundamental and applicative importance. We demonstrate by STM simulations based on electronic structure obtained from first principles that the relative local orientation of the STM-tip apex with respect to the HOPG substrate has a considerable effect on the HOPG STM contrast. Importantly for experimental STM analysis of HOPG, the simulations indicate that local tip-rotations maintaining a major contribution of the $d_{3z^2-r^2}$ tip-apex state to the STM current affect only the secondary features of the HOPG STM contrast resulting in "stripe" formation and leaving the primary contrast unaltered. Conversely, tip-rotations leading to enhanced contributions from $m\ne 0$ tip-apex electronic states can cause a triangular-hexagonal change in the primary contrast. We also report a comparison of two STM simulation models with experiments in terms of bias-voltage-dependent STM topography brightness correlations, and discuss our findings for the HOPG(0001) surface in combination with tungsten tip models of different sharpnesses and terminations.Comment: 20 pages manuscript, 7 Figures, 2 Tables, accepted for publication in J. Phys. Condens. Matte

A self-consistent ground-state formulation of the first-principles Hubbard U parameter validated on one-electron self-interaction error

In electronic structure methods based on the correction of approximate density-functional theory (DFT) for systematic inaccuracies, Hubbard $U$ parameters may be used to quantify and amend the self-interaction errors ascribed to selected subspaces. Here, in order to enable the accurate, computationally convenient calculation of $U$ by means of DFT algorithms that locate the ground-state by direct total-energy minimization, we introduce a reformulation of the successful linear-response method for $U$ in terms of the fully-relaxed constrained ground-state density. Defining $U$ as an implicit functional of the ground-state density implies the comparability of DFT + Hubbard $U$ (DFT+$U$) total-energies, and related properties, as external parameters such as ionic positions are varied together with their corresponding first-principles $U$ values. Our approach provides a framework in which to address the partially unresolved question of self-consistency over $U$, for which plausible schemes have been proposed, and to precisely define the energy associated with subspace many-body self-interaction error. We demonstrate that DFT+$U$ precisely corrects the total energy for self-interaction error under ideal conditions, but only if a simple self-consistency condition is applied. Such parameters also promote to first-principles a recently proposed DFT+$U$ based method for enforcing Koopmans' theorem

Inapplicability of exact constraints and a minimal two-parameter generalization to the DFT plus U based correction of self-interaction error

In approximate density functional theory (DFT), the self-interaction error is an electron delocalization anomaly associated with underestimated insulating gaps. It exhibits a predominantly quadratic energy-density curve that is amenable to correction using efficient, constraint-resembling methods such as DFT + Hubbard $U$ (DFT+$U$). Constrained DFT (cDFT) enforces conditions on DFT exactly, by means of self-consistently optimized Lagrange multipliers, and while its use to automate error corrections is a compelling possibility, we show that it is limited by a fundamental incompatibility with constraints beyond linear order. We circumvent this problem by utilizing separate linear and quadratic correction terms, which may be interpreted either as distinct constraints, each with its own Hubbard $U$ type Lagrange multiplier, or as the components of a generalized DFT+$U$ functional. The latter approach prevails in our tests on a model one-electron system, $H_2^+$, in that it readily recovers the exact total-energy while symmetry-preserving pure constraints fail to do so. The generalized DFT+$U$ functional moreover enables the simultaneous correction of the total-energy and ionization potential or the correction of either together with the enforcement of Koopmans condition. For the latter case, we outline a practical, approximate scheme by which the required pair of Hubbard parameters, denoted as U1 and U2, may be calculated from first-principles.Comment: 7 pages, 5 figures. Accepted for Physical Review B Rapid Communications on 30th November 201

Constrained density-functional theory extended to finite temperatures, non-integer particle numbers, and non-local constraints

We present a generalization of the constrained density-functional theory approach to metallic and finite-temperature electronic systems, both in the canonical and grand-canonical ensembles. We find that the free-energy attains a unique maximum with respect to Lagrange multipliers whenever the applied constraints are satisfied, in each case. Analytical expressions are provided for the free-energy curvatures with respect to the Lagrange multipliers, as required for their automated non-linear optimization. Our extension is general to arbitrary constraints on the spin-polarized density, or on the density-matrix in the case of orbital-dependent constrained density-functional theory constrained non-locally. Our conclusion that the ground-state free-energy is concave with respect to Lagrange multipliers for finite-temperature systems is corroborated by numerical tests on a disparate pair of systems, namely a metallic hydrogen chain and a ferromagnetic metal oxide

Creating pseudo Kondo-resonances by field-induced diffusion of atomic hydrogen

In low temperature scanning tunneling microscopy (STM) experiments a cerium adatom on Ag(100) possesses two discrete states with significantly different apparent heights. These atomic switches also exhibit a Kondo-like feature in spectroscopy experiments. By extensive theoretical simulations we find that this behavior is due to diffusion of hydrogen from the surface onto the Ce adatom in the presence of the STM tip field. The cerium adatom possesses vibrational modes of very low energy (3-4meV) and very high efficiency (> 20%), which are due to the large changes of Ce-states in the presence of hydrogen. The atomic vibrations lead to a Kondo-like feature at very low bias voltages. We predict that the same low-frequency/high-efficiency modes can also be observed at lanthanum adatoms.Comment: five pages and four figure