Self-consistent Density Functional Calculations Research Articles

Reticular Synthesis of Metal‐Organic Frameworks by 8‐Connected Quadrangular Prism Ligands for Water Harvesting

AbstractUtilization of rigid, highly connected organic linkers is critical for the reticular synthesis of functional metal–organic frameworks (MOFs). However, highly‐stable MOFs (e.g. Al/Cr/Zr‐based MOFs) based on rigid ligands with more than 6 coordinating functions have been rarely achieved thus far. Herein, we describe the construction of two bcu Zr‐based MOFs (named ZrMOF‐1 and ZrMOF‐2) from peripherally extended pentiptycene ligands (H8PEP‐1 and H8PEP‐2) with rigid quadrangular prism shape possessing 8 carboxylic groups at the prism vertices. Particularly, ZrMOF‐1 exhibits microporous structure with large Bruno‐Emmett‐Teller surface area and high water stability, endowing it a promising water harvesting material with a high water uptake capacity of 0.83 gH2O gMOF−1 at P/P0=0.90 and 25 °C, a steep uptake at a low P/P0 of 0.30, and excellent durability over 500 water adsorption‐desorption cycles. Moreover, self‐consistent charge density functional tight‐binding calculations were carried out, rationalizing the water adsorbing process and amount in ZrMOF‐1.

Reticular Synthesis of Metal-Organic Frameworks by 8-Connected Quadrangular Prism Ligands for Water Harvesting.

Utilization of rigid, highly connected organic linkers is critical for the reticular synthesis of functional metal-organic frameworks (MOFs). However, highly-stable MOFs (e.g. Al/Cr/Zr-based MOFs) based on rigid ligands with more than 6 coordinating functions have been rarely achieved thus far. Herein, we describe the construction of two bcu Zr-based MOFs (named ZrMOF-1 and ZrMOF-2) from peripherally extended pentiptycene ligands (H8 PEP-1 and H8 PEP-2) with rigid quadrangular prism shape possessing 8 carboxylic groups at the prism vertices. Particularly, ZrMOF-1 exhibits microporous structure with large Bruno-Emmett-Teller surface area and high water stability, endowing it a promising water harvesting material with a high water uptake capacity of 0.83 gH2O gMOF -1 at P/P0 =0.90 and 25 °C, a steep uptake at a low P/P0 of 0.30, and excellent durability over 500 water adsorption-desorption cycles. Moreover, self-consistent charge density functional tight-binding calculations were carried out, rationalizing the water adsorbing process and amount in ZrMOF-1.

Understanding Density-Driven Errors for Reaction Barrier Heights.

Delocalization errors, such as charge-transfer and some self-interaction errors, plague computationally efficient and otherwise accurate density functional approximations (DFAs). Evaluating a semilocal DFA non-self-consistently on the Hartree-Fock (HF) density is often recommended as a computationally inexpensive remedy for delocalization errors. For sophisticated meta-GGAs like SCAN, this approach can achieve remarkable accuracy. This HF-DFT (also known as DFA@HF) is often presumed to work, when it significantly improves over the DFA, because the HF density is more accurate than the self-consistent DFA density in those cases. By applying the metrics of density-corrected density functional theory (DFT), we show that HF-DFT works for barrier heights by making a localizing charge-transfer error or density overcorrection, thereby producing a somewhat reliable cancellation of density- and functional-driven errors for the energy. A quantitative analysis of the charge-transfer errors in a few randomly selected transition states confirms this trend. We do not have the exact functional and electron densities that would be needed to evaluate the exact density- and functional-driven errors for the large BH76 database of barrier heights. Instead, we have identified and employed three fully nonlocal proxy functionals (SCAN 50% global hybrid, range-separated hybrid LC-ωPBE, and SCAN-FLOSIC) and their self-consistent proxy densities. These functionals are chosen because they yield reasonably accurate self-consistent barrier heights and because their self-consistent total energies are nearly piecewise linear in fractional electron number─two important points of similarity to the exact functional. We argue that density-driven errors of the energy in a self-consistent density functional calculation are second order in the density error and that large density-driven errors arise primarily from incorrect electron transfers over length scales larger than the diameter of an atom.

Reduced spin-orbit splitting in 35Si: Weak binding or density-depletion effect?

The reduction of the neutron spin-orbit (SO) splitting 2p3/2−2p1/2 between the 41Ca and 35Si isotones is a unique feature throughout the chart of nuclides, as the SO splitting usually increases with decreasing A. The way it is reduced, either gradually between 41Ca and 35Si or abruptly between 37S and 35Si, as well as the origin of its reduction, whether from the weak binding energy of the p states or from the sudden depletion in the central proton density moving to 35Si, are subject of debate. The results reported here using the self-consistent Covariant Energy Density Functional calculations with the DD-ME2 parametrization rather point to an abrupt, local decrease in 35Si, and to the large dominance of the central density depletion effect. It is concluded that weak binding, central density depletion as well as correlations must be taken into account to fully evaluate the amplitude and causes of this SO splitting reduction. To broaden the scope of the present work, discussions also include the recent experimental results of proton and neutron SO splittings around 132Sn and 56Ni.

Weak ferromagnetism in hexagonal Mn3Z alloys (Z=Sn,Ge,Ga)

We present combined spin model and first principles electronic structure calculations to study the weak ferromagnetism in bulk Mn$_3$Z (Z=Sn, Ge, Ga) compounds. The spin model parameters were determined from a spin-cluster expansion technique based on the relativistic disordered local moment formalism implemented in the screened Korringa--Kohn--Rostoker method. We describe the magnetic ground state of the system within a three-sublattice model and investigate the formation of the weak ferromagnetic states in terms of the relevant model parameters. First, we give a group-theoretical argument how the point-group symmetry of the lattice leads to the formation of weak ferromagnetic states. Then we study the ground states of the classical spin model and derive analytical expressions for the weak ferromagnetic distortions by recovering the main results of the group-theoretical analysis. As a third approach we obtain the weak ferromagnetic ground states from self-consistent density functional calculations and compare our results with previous first principles calculations and with available experimental data. In particular, we demonstrate that the orbital moments follow a decomposition predicted by group theory. For a deeper understanding of the formation of weak ferromagnetism we selectively trace the effect of the spin-orbit coupling at the Mn and Z sites. In addition, for the case of Mn$_3$Ga, we gain information on the role of the induced moment of Ga from constrained local density functional calculations.

Interaction of Hydrogen with MB6 (M = Ba, Ca, La, and Sr) Surfaces from First Principles.

We show results of basic energetics and interacting behavior of hydrogen with metal hexaboride surfaces using a combination of self-consistent density functional calculations and dynamics based on the Car–Parrinello method. Our results show that hydrogen is strongly attracted to localized exposed boron atoms and interactions with the terminal cations are strictly repulsive. From these, preliminary local adsorption energy calculations suggest that a single hydrogen molecule per surface unit-cell is possible (one ML). Strongest bonds are found when hydrogen is above the terminal boron atoms affected by reduced coordination and dangling bonds. This location serves to restore the hexaboride unit to a more stable structure by providing electronic density to the deficient surface octahedra. Additionally, trajectories from dynamic simulations provide insight into how hydrogen recombination reactions occur on the surface through dissociative adsorption and the method of travel prior to recombination to be along the octahedral face and bridging sites connecting separate unit cells on the surface. Upon adsorption, a single hydrogen atom becomes localized at the dangling bond site while the second interacts with the surface along a weaker potential energy path. Desorption at lower temperatures occurs when migrating atoms from separate adsorption sites intersect to form a new pair.

Local probe of irradiation-induced structural changes and orbital magnetism in Fe60Al40 thin films via an order-disorder phase transition

Hard x-ray absorption and magnetic circular dichroism spectroscopy have been applied to study the consequential changes of the local environment around Fe atoms and their orbital polarizations in 40 nm thick ${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ thin films along the order-disorder $(B2\ensuremath{\rightarrow}A2)$ phase transition initiated by 20-keV ${\mathrm{Ne}}^{+}$ ion irradiation with fluences of $(0.75--6)\ifmmode\times\else\texttimes\fi{}{10}^{14}\phantom{\rule{4pt}{0ex}}\text{ions}\phantom{\rule{0.28em}{0ex}}{\mathrm{cm}}^{\ensuremath{-}2}$. The analysis of the extended x-ray absorption fine structure spectra measured at the Fe K edge at room temperature revealed an increased number of Fe-Fe nearest neighbors from 3.47(7) to 5.0(1) and $\ensuremath{\sim}1%$ of volume expansion through the transition. The visualization of the Fe and Al nearest-neighbor rearrangement in the first coordination shell of Fe absorbers via the transition was carried out by wavelet transformations. The obtained changes in Fe coordination are evidently reflected in the x-ray magnetic circular dichroism spectra which show an increased orbital magnetic moment of Fe atoms and a pronounced magnetic multielectronic excitations peak at $\ensuremath{\sim}60$ eV above the edge. The amplitudes of both peaks demonstrated similar dependencies on the irradiation fluence. The results of self-consistent density functional calculations on relaxed ${\mathrm{Fe}}_{60}{\mathrm{Al}}_{40}$ model structures for the ordered $(B2)$ and the disordered $(A2)$ phases are consistent with the experimental findings and point to the formation of Fe-rich regions in the films studied.

Theoretical and experimental study of ethanol adsorption and dissociation on β-Mo2C surfaces

The adsorption and dissociation of ethanol over molybdenum carbide were studied in the context of the production of H2 from alcohols. A β-Mo2C catalyst was prepared from char and Mo salts. The sample was characterized by N2 sorptometry at 77K, temperature programmed reaction of H2, X-ray diffraction (applying Rietveld approximation) and X-ray photoelectron spectroscopy for investigating on the catalytic properties of the prepared sample. The catalyst would be active and stable for H2 dissociation at 500–600K. The value of ethanol adsorption energy was −0.92eV, as calculated on β-Mo2C (001) surface by means of self-consistent density functional calculations. A transfer of electron density from the surface to adsorbed ethanol was concluded from calculations. Plausible reaction pathways corresponding to ethanol dissociation to ethoxy were theoretically studied by using the Climbing Image Nudged Elastic Band (CI-NEB), which shows and activation energy value of 0.57eV.

Computational insight into the capacitive performance of graphene edge planes

Recent experiments have shown that electric double-layer capacitors utilizing electrodes consisting of graphene edge plane exhibit higher capacitance than graphene basal plane. However, theoretical understanding of this capacitance enhancement is still limited. Here we applied a self-consistent joint density functional theory calculation on the electrode/electrolyte interface and found that the capacitance of graphene edge plane depends on the edge type: zigzag edge has higher capacitance than armchair edge due to the difference in their electronic structures. We further examined the quantum, dielectric, and electric double-layer (EDL) contributions to the total capacitance of the edge-plane electrodes. Classical molecular dynamics simulation found that the edge planes have higher EDL capacitance than the basal plane due to better adsorption of counter-ions and higher solvent accessible surface area. Our work therefore has elucidated the capacitive energy storage in graphene edge planes that take into account both the electrode's electronic structure and the EDL structure.

Multiple adsorption of molecular oxygen on small Au/Pd cationic clusters at finite temperature. A van der Waals density functional study.

The adsorption of molecular oxygen on cationic bimetallic palladium/gold clusters, AunPdm (+) (n + m ≤ 5), is studied by means of self-consistent density functional calculations including long range van der Waals non-local interactions. A single O2 molecule is adsorbed preferably on top of Pd sites for m = 0, 1, but bridge or hollow locations between Pd atoms are preferred for m ≥ 2. In the later cases, both the O2 electronic charge and the O-O distance increase as compared with the values for free O2, leading to negatively charged O2 superoxo species which facilitates the CO oxidation. Multiple sequential adsorption of several O2 is considered for the n + m ≤ 3 clusters, which occurs with decreasing adsorption energy, except when severe distortion of the bimetallic support appears. The Gibbs free energy of AunPd2-n (+)O2x complexes with n = 1-2 and x = 1-5 is computed at temperatures 0 K, 50 K, 150 K, and 300 K. We obtain that Pd2 (+) (PdAu(+)) can adsorb 5 (4) oxygen molecules at ambient temperature; however, Au2 (+) can adsorb up to three O2 molecules when the temperature is lower than 150 K.

Self-consistent density functional calculations of the crystal field levels in lanthanide and actinide dioxides

Using a recently developed method combining a nonspherical self-interaction corrected LDA $+$ $U$ scheme and an on-site multibody Hamiltonian [Phys. Rev. B 83, 085106 (2011)], we calculate the crystal field parameters and crystal field (CF) excitation levels of $f$-element dioxides in the fluorite structure with ${f}^{n}$ electronic configurations, including $n=1$ (PaO${}_{2}$, PrO${}_{2}$), $n=2$ (UO${}_{2}$), $n=3$ (NpO${}_{2}$), and $n=4$ (PuO${}_{2}$). It is shown that good agreement with experimental data (within approximately 10--20 meV) can be obtained in all cases. The properties of the multielectron CF ground states are analyzed.

Investigation of the Conducting Properties of a Photoswitching Dithienylethene Molecule

Photoswitching molecules are attractive candidates as organic materials for optoelectronics applications because light impulses can switch them between states with different conducting characteristics. Here, we report a fully self-consistent density functional theory calculation of the electron transport properties of photoswitching dithienylethene attached to Au leads in both the open and closed conformations. The molecule is found to be a good conductor in both conformations, with the low-bias current for the closed one being about 20 times larger than that of the open. Importantly, the current-voltage characteristics away from the linear response are largely determined by molecular orbital rehybridization in an electric field, in close analogy to what happens for Mn(12) molecules. However, in the case of dithienylethene attached to Au, such a mechanism is effective also in conditions of strong electronic coupling to the electrodes. This makes the dithienylethene family an intriguing materials platform for constructing highly conducting organic optoelectronics switches.

Gating of a Three-Leg Molecule

We study the use of a simple three-leg molecule, triphenylene, as a transistor. This configuration allows increased voltage gain to be achieved. We analyze control of the transport between electrodes attached to two of the legs by a gate closely coupled electrostatically to the third leg, using self-consistent density functional calculations. In spite of the close coupling, the maximum voltage gain was less than unity, and this was attributed to efficient screening of the internal potential due to polarization of the molecular states. The transistor current vs. voltage characteristics were able to be reproduced using a simple electrostatic model.

Dielectric properties of 1,1,1-trifluoroethane (HFC-143a) in the liquid phase

The relative permittivity ( ɛ r) data of 1,1,1-trifluoroethane (HFC-143a), (CAS N# 420-46-2), a hydrofluorocarbon (HFC) developed as a refrigerant that has zero ozone depletion potential, is reported. The relative permittivity of HFC-143a in the liquid phase was measured using a direct capacitance method at temperatures from T = 218 to 294 K and at pressures up to P = 15 MPa, for a frequency of 10 kHz. The uncertainty of the ɛ r measurements is estimated to be better than ±1.2 × 10 −2. A complete set of tables of experimental data as a function of temperature, pressure and density, is presented that covers the dielectric property needs for most engineering applications. To study the dependence of ɛ r on density and temperature on a molecular basis, the theory developed by Vedam et al. and adapted by Diguet was applied to analyse the data. The Kirkwood modification of the Onsager equation was used to obtain the value of its dipole moment in the liquid phase ( μ*). The apparent dipole moment obtained was μ* = 3.293 D. The effective dipole in the liquid state predicted by the Kirkwood–Frölich theory is 2.530 D. The measured values are compared with density functional and density functional self-consistent calculations (SCIPCM) of the electronic distribution and of the dipole moment of HFC-143a. Finally, the values of the isobaric thermal expansion and isothermal compressibility were estimated from the reported measurements.

The Biphenyl Molecule as a Model Transistor

We study transport and charge control in a gated 4,4'-biphenyl diradical molecular transistor using self-consistent density-functional calculations. We track both electron-like and hole-like conduction and relate it to the field dependence of current-carrying pi-derived states. Owing to the coupling between the two benzene rings, the pi-states become segregated into extended, current-carrying states and localized states. Under application of the source/drain field, along the axis of the molecule, the localized pi-states become split, while the extended states become polarized and screen the field. The localized states act like isolated islands within the molecule--while they make a substantial contribution to the density of states, they make only a small contribution to transport.

Relative Permittivities of 1,1,1,2,3,3,3-Heptafluoropropane (HFC-227ea), 1,1,1,2,3,3-Hexafluoropropane (HFC-236ea), and 1,1,1,3,3-Pentafluorobutane (HFC-365mfc) in the Liquid Phase

Relative permittivity measurements of 1,1,1,2,3,3,3-heptafluoropropane (HFC-227ea), 1,1,1,2,3,3-hexafluoropropane (HFC-236ea), and 1,1,1,3,3-pentafluorobutane (HFC-365mfc) in the liquid phase are reported. Measurements were performed by using a direct capacitance method at temperatures from 223 K to 303 K and pressures up to 16 MPa for HFC-227ea and HFC-236ea and at temperatures from 263 K to 303 K up to 16 MPa for HFC-365mfc. The uncertainty of the relative permittivity measurements is estimated to be better than ±1.1·10-2. The theory developed by Vedam et al., and adapted by Diguet, and the Kirkwood modification of the Onsager were applied to obtain the apparent dipole moment of HFC-227ea, HFC-236ea, and HFC-365mfc in the liquid state, found to be 2.356 D for HFC-227ea, 2.624 D for HFC-236ea, and 4.917 D for HFC-365mfc. The effective dipole in the liquid state of HFC-236ea predicted by the Kirkwood−Frölich theory is 2.065 D. Density functional and density functional self-consistent calculations (SCIPCM) of the electronic distribution and of the dipole moment are reported for HFC-227ea.

Lagrange-Lobatto interpolating polynomials in the discrete variable representation

The discrete variable representation (DVR) is a well known and widely used computational technique in many areas of physics. Recently, the Lagrange-Lobatto basis has attracted increasing attention, especially for radial Hamiltonians with a singular potential at the origin and finite element DVR constructions. However, unlike standard DVR functions, the Lagrange-Lobatto basis functions are not orthogonal. The overlap matrix is usually approximated as the identity using the same quadrature approximation as for the potential. Based on the special properties of overlap matrix of Lagrange-Lobatto polynomials, an explanation of the success of the identity approximation, including error bounds, is presented. Results for hydrogen and the more nontrivial potentials of self-consistent all-electron density functional atomic calculations are also given.

Reply to “Comment on ‘Band structures and optical spectra of InN polymorphs: Influence of quasiparticle and excitonic effects’ ”

In their Comment, Bagayoko et al. [Phys. Rev. B 76, 037101 (2007)] criticized the three-step electronic-structure calculations of Furthm\uller et al. [Phys. Rev. B 72, 205106 (2005)] to calculate the band structures and hence the fundamental energy gaps of crystalline InN polymorphs of $0.82\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (wurtzite InN) or $0.55\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ (zinc-blende InN) [J. Furthm\uller et al., Phys. Rev. B 72, 205106 (2005); F. Bechstedt and J. Furthm\uller, J. Cryst. Growth 246, 315 (2002)]. In contrast, in their self-consistent density-functional calculations they compute the fundamental gaps at the theoretical lattice constants to 0.88 or $0.65\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ in one step, already on the density-functional theory (DFT)--local-density approximation (LDA) level of approximation [D. Bagayoko and L. Franklin, J. Appl. Phys. 97, 123708 (2005); D. Bagayoko et al., J. Appl. Phys. 96, 4297 (2004)].

Self-consistent density functional calculation of the image potential at a metalsurface

It is well known that the exchange–correlation (XC) potential ata metal surface has an image-like asymptotic behaviour given by−1/4(z−z0),where z is the coordinate perpendicular to the surface. Using a suitable fully non-localfunctional prescription, we evaluate self-consistently the XC potential with the correctimage behaviour for simple jellium surfaces in the range of metallic densities. Thisallows a proper comparison between the corresponding image-plane position,z0, and other related quantities such as the centroid of an induced charge by anexternal perturbation. As a by-product, we assess the routinely used local densityapproximation when evaluating electron density profiles, work functions, andsurface energies by focusing on the XC effects included in the fully non-localdescription.

Local electronic structure of threading screw dislocation in wurtzite GaN

The atomic and electronic structure of the full-core threading screw dislocation in wurzite GaN has been investigated using a self-consistent density-functional tight-binding calculation. It is shown that the atoms are severely strained in a hexagonal atomic core, and an extra charge transfer of 0.12 e occurs at the core atoms from Ga to N, in addition to the typical charge transfer of 0.56 e for bulk GaN. Filled and unfilled gap states are found to be spread over the entire band gap. The p states of the core N-atom mostly contribute to the tail states of valence and conduction bands, whereas the deep levels are heavily localized at the Ga and N core atoms. The coexistence of acceptor and donor gap states in the vicinity of the screw dislocations could be an origin of the leakage currents observed in GaN-based devices.