82 research outputs found

### 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

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