Bader Method Research Articles

Counting Electrons in Electrides.

The selection and design of charge integration methods remain an outstanding challenge in materials chemistry. In complex materials like electrides, this challenge is amplified by the small charge and complex shape of electride wave functions. For these reasons, popular integration methods, such as the Bader method, usually fail to assign any charge to the bare electrons in an electride. To address this challenge, we developed an algorithm that instead partitions the charge based on the electron localization function (ELF), a popular scheme for visualizing chemically important features in molecules and solids. The algorithm uses Bader segmentation of the ELF to find the electride electrons and Voronoi segmentation of the ELF to identify atoms. We apply this method, "BadELF", to the quantification of atomic radii and oxidation states in both ionic compounds and electrides. For ionic compounds, we find that the BadELF method yields radii that agree closely with Shannon crystal radii, while the oxidation states agree closely with the Bader method. When they are applied to electrides, however, only the BadELF algorithm yields chemically meaningful charges. We argue that the BadELF method provides a useful strategy to identify electrides and obtain new insight into their most essential property: the quantity of electrons within them.

A DFT study of ZnO, Al2O3 and SiO2; combining X-ray spectroscopy, chemical bonding and Wannier functions

The electronic properties of a group of oxides with important technological applications were studied performing ab initio calculations. Al2O3 is an important ceramic and catalyst, suitable insulator for electronic applications and nano scale access memory. SiO2 is important from both geological and materials science point of view. Pure and doped ZnO structures have direct industrial applications in lasers, sensors, and infra-red and luminescence sensitive devices.A Full Potential Linearized Augmented Plane Waves (FP-LAPW) method within the Density Functional Theory (DFT) formalism was applied to study electronic properties of these oxides and different post-processing tasks as contour plots of electronic charge density, projected densities of states, band structure, Bader's method and Maximally Localized Wannier Functions were used to analyse the electronic charge transfer and bonding properties of the systems. The positions of these Wannier functions, shown in histograms and 3D plots, opened the possibility to calculate the bonding ionicity trend of materials. We report X-ray spectra obtained from self consistent ab initio calculations. K and L2,3 edges were calculated including the fractional electronic core-hole and double core-hole providing similar features as in the reported experimental X-ray absorption near edge structure (XANES).

Comparisons of NH…O and OH…O hydrogen bonds in various ethanolammonium–based protic ionic liquids

The effect of a number of terminal OH groups in tertiary ammonium cations (triethanolammonium, ethyldiethanolammonium, diethylethanolammonium, and triethylammonium) on structural and energetic characteristics of the ion pairs resulted from the acid–amine interaction with six different sulfonic acids was investigated. The ion pairs have been studied in detail from energetic and structural point of view by means of the B3LYP-GD3 dispersion-corrected density functional theory with further analysis of electron density function based on the Bader method. The topological properties of the electron density distributions for NH…O and ОH…O bonding interactions have been considered as well as their energies estimated by Espinosa approach. It was shown that the presence of OH groups in the cation leads to increasing structural stability of the ion pairs due to additional hydrogen bonding with acid anion. While the number of hydrogen bonds between cation and anion in the ion pair raises, the strength of each NH…O and ОH…O interaction is becoming weaker. The stronger interactions of the NH proton of the cation are evident in all the ion pairs studied. A thorough analysis of the interaction data on the ion pairs allows us to make the conclusion that the interaction energy of the ion pairs increases in the cation order TEA < DEEOA < EDEOA < TEOA, with the sequence of anions being TfO < NBsu < SA < Bsu < MTN < MsO.

Synthesis, Molecular Structure, and Spectral Characteristics of Lead(II) Complexes with 1,5-Dimethyl-4-[2-(3-methyl-5-oxo-1-phenyl-1,5-dihydro-4H-pyrazol-4-ylidene)hydrazinyl]-2-phenyl-1,2-dihydro-3H-pyrazol-3-one

Pb(II) cations form complexes with 1,5-dimethyl-4-[2-(3-methyl-5-oxo-1-phenyl-1,5-dihydro-4H-pyrazol-4-ylidene)hydrazinyl]-2-phenyl-1,2-dihydro-3H-pyrazol-3-one (HL) in an aqueous-ethanolic solution. The C42H41N13O9Pb2 compound has been isolated in the crystalline state and its spectral characteristics have been determined. As per X-ray diffraction analysis data, it is a cocrystallizate of the Pb2L2(OH)2·(H2O)2 binuclear complex and the PbLNO3 dimeric associate. According to the simulation using the Bader method, the lead cations both in the binuclear structure and in the dimeric associate have not interacted.

Manganese hydrides and superhydrides at high pressure

Manganese hydrides and superhydrides have been studied from ambient up to high pressures by the ab initio random structure searching algorithm. At ambient pressure conditions and room temperature, the subhydride ${\mathrm{Mn}}_{2}\mathrm{H}$ (space group $P\overline{3}m1$) is the only compound found stable among those studied, since $\ensuremath{\epsilon}$-MnH (hcp structure, space group $P{6}_{3}/mmc$), although stable at 0 K, is destabilized by thermal effects. With increasing pressure, MnH is stabilized, and then hydrogen-rich hydrides appear: first ${\mathrm{MnH}}_{2}$ around 30 GPa, then ${\mathrm{MnH}}_{7}$ around 40 GPa, and finally ${\mathrm{MnH}}_{3}$ around 90 GPa. ${\mathrm{MnH}}_{8}$ is likely to become stable around 150 GPa. The body-centered tetragonal structure of ${\mathrm{MnH}}_{2}$ (space group $I4/mmm$) is identical to that of ${\mathrm{FeH}}_{2}$ and ${\mathrm{CoH}}_{2}$. ${\mathrm{MnH}}_{3}$ has an original body-centered tetragonal structure, with space group $I4/m$ and 4 formula units per primitive cell. It contains a structural unit ${\mathrm{H}}_{8}$ with rather short H-H distances. ${\mathrm{MnH}}_{7}$ is extremely stable at high pressure. ${\mathrm{MnH}}_{7}$ and ${\mathrm{MnH}}_{8}$ exhibit a mixed structure, with one hydrogen being under the molecular form (1/2 ${\mathrm{H}}_{2}$) and the other ones under an atomic (hydrided) form. Atomic charges computed by the Bader method confirm the electron transfer from Mn to H, with Mn oxidation increasing from MnH to ${\mathrm{MnH}}_{3}$, and then saturating beyond. At high pressure, nuclear quantum effects tend to stabilize ${\mathrm{MnH}}_{4}$ and increase the stability of ${\mathrm{MnH}}_{8}$.

Evaluation of the Apparent Interfacial Shear Strength of Nanocellulose/PVA Composites

Nanocellulose in the form of whiskers and nanofibers has become a promising reinforcement material for polymer composites due to its high mechanical characteristics and sustainability. For optimization of composite properties, efficient means of characterization of the stress transfer between fibrous nanofiller and the polymer matrix are needed. In the current work, the apparent interfacial shear strength (IFSS) of cellulose nanofiber/PVA is evaluated by a modified Bowyer and Bader method based on an analysis of the stress–strain curve of a composite film in uniaxial tension. The IFSS is found to exceed shear yield strength of the neat polymer, suggesting good adhesion.

C-H···O Hydrogen Bonding. The Prototypical Methane-Formaldehyde System: A Critical Assessment.

Distinguishing the functionality of C-H···O hydrogen bonds (HBs) remains challenging, because their properties are difficult to quantify reliably. Herein, we present a study of the model methane-formaldehyde complex (MFC). Six stationary points on the MFC potential energy surface (PES) were obtained at the CCSD(T)/ANO2 level. The CCSDT(Q)/CBS interaction energies of the conformers range from only -1.12 kcal mol-1 to -0.33 kcal mol-1, denoting a very flat PES. Notably, only the lowest energy stationary point (MFC1) corresponds to a genuine minimum, whereas all other stationary points-including the previously studied ideal case of ae(C-H···O) = 180°-exhibit some degree of freedom that leads to MFC1. Despite the flat PES, we clearly see that the HB properties of MFC1 align with those of the prototypical water dimer O-H···O HB. Each HB property generally becomes less prominent in the higher-energy conformers. Only the MFC1 conformer prominently exhibits (1) elongated C-H donor bonds, (2) attractive C-H···O═C interactions, (3) n(O) → σ*(C-H) hyperconjugation, (4) critical points in the electron density from Bader's method and from the noncovalent interactions method, (5) positively charged donor hydrogen, and (6) downfield NMR chemical shifts and nonzero 2J(CM-HM···OF) coupling constants. Based on this research, some issues merit further study. The flat PES hinders reliable determinations of the HB-induced shifts of the C-H stretches; a similarly difficult challenge is observed for the experiment. The role of charge transfer in HBs remains an intriguing open question, although our BLW and NBO computations suggest that it is relevant to the C-H···O HB geometries. These issues notwithstanding, the prominence of the HB properties in MFC1 serves as clear evidence that the MFC is predominantly bound by a C-H···O HB.

Effects of glass fibers on mechanical and thermal properties of poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate)

This study investigates the effects of glass fiber on the mechanical and thermal properties of bacterial polyester, poly(3‐hydroxybutyrate‐co‐3‐hydroxyhexanoate) (PHBH). PHBH composites were prepared by melt‐compounding and injection molding, using PHBH with 3‐hydroxyhexanoate (3HH) molar fractions of 5.6% and 11.1%, and short glass fiber content varying from 0 to 23 volume percent. Tensile test results suggested that the glass fiber addition significantly increased Young's modulus and strength of PHBH. The Halpin–Tsai and Tsai–Pagano equations were used to predict Young's modulus of PHBH composites while the modified Kelly–Tyson model with the Bowyer–Bader method were used for strength prediction. These predictions gave reasonable estimates for the mechanical properties of PHBH composites. Differential scanning calorimetry results suggested that glass fiber addition had little effect on the degree of crystallinity of PHBH, as well as on the crystallization half‐time of PHBH containing 5.6 mol% 3HH. POLYM. COMPOS., 39:491–503, 2018. © 2016 Society of Plastics Engineers

Apparent interfacial shear strength of short-flax-fiber/starch acetate composites

The paper deals with an indirect industry-friendly method for identification of the interfacial shear strength (IFSS) in a fully bio-based composite. The IFSS of flax fiber/starch acetate is evaluated by a modified Bowyer and Bader method based on an analysis of the stress–strain curve of a short-fiber-reinforced composite in tension. A shear lag model is developed for the tensile stress–strain response of short-fiber-reinforced composites allowing for an elastic-perfectly plastic stress transfer. Composites with different fiber volume fractions and a variable content of plasticizer have been analyzed. The apparent IFSS of flax/starch acetate is within the range of 5.5–20.5MPa, depending on composition of the material. The IFSS is found to be greater for composites with a higher fiber loading and to decrease with increasing content of plasticizer. The IFSS is equal or greater than the yield strength of the neat polymer, suggesting good adhesion, as expected for the chemically compatible constituents.

Tuning electrochemical potential of LiCoO2 with cation substitution: first-principles predictions and electronic origin

With a goal to improve the performance of LiCoO2 as a cathode material in Li-ion batteries, we simulate substitution of various elements (X = Be, Mg, Al, Ga, Si and Ti) for Co using first-principles density functional theory and predict changes in its electrochemical potential. While the electrochemical potential of LiCoO2 is enhanced with substitution of Be, Mg, Al and Ga for Co, an opposite effect is predicted of Si and Ti substitution. We determine the electronic origin of these changes in electrochemical potential using (a) Bader method of topological analysis of charge density, (b) partial density of electronic states to estimate oxidation states of metal and oxygen, and charge re-distribution upon lithiation. We find that the distribution of electronic charge donated by Li is influenced by the nature of the X–O bond. A larger electron transfer to O (in XO6 octahedron) upon lithiation leads to stronger Li intercalation and thereby higher electrochemical voltage. Our findings provide a platform for a rational design of cathode materials in Li batteries with enhanced voltage.

P-type reduced graphene oxide membranes induced by iodine doping

Reduced graphene oxide membranes with electrical conductivity of 201 S/cm were successfully fabricated by a simple hydriodic acid reducing method. It has been shown that the obtained graphene oxide membranes exhibit a p-type conductive property with a hole carrier concentration of 3.66 × 1017 cm−2 and a mobility of 13.7 cm2/Vs. The p-type conductive property was mainly attributed to iodine atom adsorption on C atom layer, supported by the energy dispersive X-ray spectrometry and the first-principles calculations based on the density functional theory. The Bader method was used to analyze charge density of each atom. It has been shown that 0.38 electrons per unit cell are transferred to I atom from the C atom layer which leaves a lot of holes.

Modeling and evaluation of tensile properties of randomly oriented banana/epoxy composite

The main aim of this study is to compare the experimentally observed tensile properties of banana/epoxy composite with those obtained using various theories of reinforcement. Models used for the comparison are Hirsch, Halpin–Tsai, Nielson, Bowyer and Bader’s, and Modified Rule of Mixture. Further, the effect of fiber length on the tensile properties of the composite was compared with Bowyer and Bader method. Of the used theories of reinforcement, it is found that Modified rule of mixture predicts tensile properties closer to experimental values and next comes Bowyer and Bader method.

Interstitial Diffusion of C Interacting with Ambient H in Tungsten Crystals

Negative binding energies between interstitial C (octahedral) and H (tetrahedral) in a bulk crystal of W (bcc) were obtained with the first-principle calculations, which indicate repulsive interaction in the interstitial C-H pair. The electron cloud associated to the each interstitial atom was analyzed with Bader's method. This analysis gives negative fractional charges of −0.35 and −0.37 for the interstitial C and H, respectively, supporting the repulsive interaction between them. Interstitial diffusion of C was studied including influences of ambient H atoms in the mean field approximation and the ergodic assumption. The calculated diffusion coefficients are significantly increased by the repulsive interaction with the H atoms.

A Density Functional Theory study on gold cyanide interactions: The fundamentals of ore cleaning

We have employed Density Functional Theory calculations to study the adsorption of CN, CN − and KCN on Au(111) and Au(211) surfaces and compare the obtained results to CO. The adsorption of CN, CN −, and KCN are exothermic with respect to the gas-phase moieties, and the adsorption energy increases at steps. Our results show that the binding mechanism of CN − is different from that of CO. The projected LDOS indicates that the bond between the flat surface and CN shows very small overlap between metal and CN states. This overlap increases provided that extra charge is present or low-coordinated Au atoms are available. Charge transfer is analyzed via the Bader method and the Electron Localization Function. Both suggest that Au–CN bonding resembles that in the gas-phase [Au(CN) 2] −, which has been identified as covalent. The present study justifies the mechanism described in the literature involving a first CN − adsorption, electron transfer to form AuCN, and second adsorption of a CN − to form the soluble species and dissolve gold atoms from low grade ores.

Atomvolumina und Ladungsverteilungen in Nitridometallaten

AbstractAtom Volumina and Charge Distributions in NitridometalatesThe linear relation between the nitride volumina calculated by use of the QTAIM‐method developed by Bader and those derived from the tables of volume increments reported by Biltz does not hold for nitridometalates Aa[MmNn] (A = alkali or alkaline earth metal, M = transition metal). The clear deviation from linearity is caused by the different kinds of chemical bonds being present within the complex [MmNn] anions on the one hand and between the complex anions and the cations on the other hand. The significant covalency of the chemical bonds within the complex [MmNn] anions is reflected by the calculated volumina and the charge distributions between the M and N atoms using the Bader method. By comparing the oxidation numbers of the atoms forming the complex anions with their calculated charge assignments (QTAIM method) a significant charge reduction becomes evident.

Density functional study of the charge on Aun clusters (n=1–7) supported on a partially reduced rutile TiO2(110): Are all clusters negatively charged?

It is widely believed that small gold clusters supported on an oxide surface and adsorbed at the site of an oxygen vacancy are negatively charged. It has been suggested that this negative charge helps a gold cluster adsorb oxygen and weakens the O-O bond to make oxidation reactions more efficient. Given the fact that an oxygen vacancy is electron rich and that Au is a very electronegative element, the assumption that the Au cluster will take electron density from the vacancy is plausible. However, the density functional calculations presented here show that the situation is more complicated. The authors have used the Bader method to examine the charge redistribution when a Aun cluster (n=1-7) binds next to or at an oxygen vacancy on rutile TiO2(110). For the lowest energy isomers they find that Au1 and Au3 are negatively charged, Au5 and Au7 are positively charged, and Au2, Au4, and Au6 exchange practically no charge. The behavior of the Aun isomers having the second-lowest energy is also unexpected. Au2, Au3, Au5, and Au7 are negatively charged upon adsorption and very little charge is transferred when Au4 and Au6 are adsorbed. These observations can be explained in terms of the overlap between the frontier molecular orbitals of the gold cluster and the eigenstates of the support. Aun with even n becomes negatively charged when the lowest unoccupied molecular orbital has a lobe pointing in the direction of the oxygen vacancy or towards a fivefold coordinated Ti (5c-Ti) located in the surface layer; otherwise it stays neutral. Aun with odd n becomes negatively charged when the singly occupied molecular orbital has a lobe pointing in the direction of a 5c-Ti located at the vacancy site or in the surface layer, otherwise it donates electron density into the conduction band of rutile TiO2(110) becoming positively charged.

Charge Transfer and Chemical Hardness along a Substitution Path in Metastable Au‐Sb Alloys

AbstractIn the present study the synthesis of metastable alloys of the noble metal Au and the semimetal Sb is realized by using high pressure techniques. The influence of Au on bulk Sb is shown experimentally by stepwise substitution. In addition to the effect of the most electronegative noble metal on Pauling's scale in the binary Au‐Sb phases, some ternary compounds with In, Sn, As, and Te in addition to Au and Sb are discussed. The experiments are planned to obtain a better knowledge on the reasons for building up a simple cubic Sb partial lattice, and their crystallographic results are used to construct model structures for new electronic structure calculations from first principles on the metastable π‐phases. Using the LCAO‐CO ansatz and density‐functional methods, we study total energies, band structures, densities of states and charge transfer properties according to Bader's method by integrating zero flux surfaces. Finally, from electronic band structure analysis, the quantities “chemical potential” μ, and “chemical hardness”, η, are derived according to the original ideas of Pearson and Parr and are applied to solid state problems using special points of the Brillouin zones within a band structure approximation for the first time. The results are shown to support the experimental findings about the substitution path within the system Au‐Sb.

Electron density distribution in molecules of 4-aryl-substituted [2.2]paracyclophanes and regioselectivity of their complexation with Cr(CO)3

Charges on carbon atoms in the molecules of 4-aryl-substituted [2.2]paracyclophanes were estimated and the role of charge control as a kinetic factor in regioselectivity of their complexation with (NH3)3Cr(CO)3 was investigated using electron density distribution analysis by the Bader, Weinhold-Reed (NPA), and Mulliken methods. The most plausible picture of the electron density distribution in substituted [2.2]paracyclophanes was obtained by the Bader method and compared with experimental data on the yields of reaction products. Topological analysis of the electron density distribution in the [2.2]paracyclophane molecule by the Bader method confirmed the existence of a weak antibonding interaction between the stacked benzene rings.

Ring Structure Formation in Transition-Metal Nitrido Chlorides by Donor−Acceptor Formation

According to quantum chemical calculations, nitrido chlorides constituted from d6 transition metals form ring structures which are best described as weak donor−acceptor complexes between the lone pair at nitrogen and the empty d orbitals at the transition metal. The stabilities of the ring structures increase in the order Cr < Mo < W. The transition metal Cr forms only endothermic ring systems, and these in turn decompose into monomers. A comparison of several homologous oligomers of NMoCl3 shows maximum stability for the tetramer, in agreement with the experimental findings. This particular stability of the tetramer is due to a perfect alignment of the nitrogens between two metal centers. The vibrational analyses reveal that the character of the monomers is nearly conserved in the ring systems. An analysis of the electron densities on the basis of Bader's method of atoms in molecules as well as of the natural bond orbitals (NBO) substantiates the weak ring stabilities.

Molecular structure and charge density analysis of p-methoxybenzoic acid (anisic acid)

A concerted X-ray and ab initio SCF-MO study of the structure and charge density of p-methoxybenzoic acid (anisic acid) is reported. An extensive X-ray data set (7401 reflections) was measured on a single crystal using Mo K α radiation and the structure refined with 2121 unique reflections, leading to a final R( F)-factor of 0.047 calculated for reflections with I>2 σ. The molecular geometry of crystalline anisic acid, where the molecules dimerize via a moderately strong CO–H⋯O hydrogen bond, is compared with that of the isolated molecule, resulting from SCF-MO ab initio calculations. A topological analysis of the molecular charge density was performed using Bader's method to gain insight into the dominant intra- and intermolecular interactions in this compound. In particular, the effects of the substituents on the observed distortions of the benzene ring were investigated as well as the internal rotation of the methyl group.