Real-space Analysis Research Articles

Critic2: A program for real-space analysis of quantum chemical interactions in solids

We present critic2, a program for the analysis of quantum-mechanical atomic and molecular interactions in periodic solids. This code, a greatly improved version of the previous critic program (Otero-de-la Roza et al., 2009), can: (i) find critical points of the electron density and related scalar fields such as the electron localization function (ELF), Laplacian, … (ii) integrate atomic properties in the framework of Bader’s Atoms-in-Molecules theory (QTAIM), (iii) visualize non-covalent interactions in crystals using the non-covalent interactions (NCI) index, (iv) generate relevant graphical representations including lines, planes, gradient paths, contour plots, atomic basins, … and (v) perform transformations between file formats describing scalar fields and crystal structures. Critic2 can interface with the output produced by a variety of electronic structure programs including WIEN2k, elk, PI, abinit, Quantum ESPRESSO, VASP, Gaussian, and, in general, any other code capable of writing the scalar field under study to a three-dimensional grid. Critic2 is parallelized, completely documented (including illustrative test cases) and publicly available under the GNU General Public License. Program summaryProgram title: CRITIC2Catalogue identifier: AECB_v2_0Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AECB_v2_0.htmlProgram obtainable from: CPC Program Library, Queen’s University, Belfast, N. IrelandLicensing provisions: yesNo. of lines in distributed program, including test data, etc.: 11686949No. of bytes in distributed program, including test data, etc.: 337020731Distribution format: tar.gzProgramming language: Fortran 77 and 90.Computer: Workstations.Operating system: Unix, GNU/Linux.Has the code been vectorized or parallelized?: Shared-memory parallelization can be used for most tasks.Classification: 7.3.Catalogue identifier of previous version: AECB_v1_0Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 157Nature of problem:Analysis of quantum-chemical interactions in periodic solids by means of atoms-in-molecules and related formalisms.Solution method:Critical point search using Newton’s algorithm, atomic basin integration using bisection, qtree and grid-based algorithms, diverse graphical representations and computation of the non-covalent interactions index on a three-dimensional grid.Additional comments:!!!!! The distribution file for this program is over 330 Mbytes and therefore is not delivered directly when download or Email is requested. Instead a html file giving details of how the program can be obtained is sent. !!!!!Running time:Variable, depending on the crystal and the source of the underlying scalar field.

Structure-property relationships for three indoline dyes used in dye-sensitized solar cells: TDDFT study of visible absorption and photoinduced charge-transfer processes

The electronic structures of three D-A-π-A indoline dyes (WS-2, WS-6, and WS-11) used in dye-sensitized solar cells (DSSCs) were studied by performing quantum chemistry calculations. The coplanarity of the A-π-A segment and distinct noncoplanarity of the indoline donor part of each dye were confirmed by checking the calculated geometric parameters. The relationships between molecular modifications and the optical properties of the dyes were derived in terms of the partial density of states, absorption spectrum, frontier molecular orbital, and excited-state charge transfer. 3D real-space analysis of the transition density (TD) and charge difference density (CDD) was also performed to further investigate the excited-state features of the molecular systems, as they provide visualized physical pictures of the charge separation and transfer. It was found that modifying the alkyl chain of the bridge unit near the acceptor unit is an efficient way to decrease dye aggregation and improve DSSC efficiency. Inserting a hexylthiophene group next to the donor unit leads to a complicated molecular structure and a decrease in the charge-transfer ability of the system, which has an unfavorable impact on DSSC performance.

Construction of a general semilocal exchange-correlation hole model: Application to nonempirical meta-GGA functionals

Using a reverse-engineering method, we construct a meta-generalized gradient approximation (meta-GGA) angle-averaged exchange-correlation (XC) hole model which has a general applicability. It satisfies known exact hole constraints and can exactly recover the exchange-correlation energy density of any reasonable meta-GGA exchange-correlation energy functional satisfying a minimal set of exact properties. The hole model is applied to several nonempirical meta-GGA functionals: the Tao-Perdew-Staroverov-Scuseria (TPSS), the revised TPSS (revTPSS), and the recently Balanced LOCalization (BLOC) meta-GGA [L. A. Constantin, E. Fabiano, and F. Della Sala, J. Chem. Theory Comput. 9, 2256 (2013)]. The empirical M06-L meta-GGA functional is also considered. Real-space analyses of atoms and ions as well as wave-vector analyses of jellium surface energies show that the meta-GGA hole models, in particular the BLOC one, are very realistic and can reproduce many features of benchmark XC holes. In addition, the BLOC hole model can be used to estimate with good accuracy the Coulomb hole radius of small atoms and ions. Thus, the proposed meta-GGA hole models provide a valuable tool to validate in detail existing meta-GGA functionals, and can be further used in the development of density functional theory methods beyond the semilocal level of theory.

Comparison of CMB lensing efficiency of gravitational waves and large scale structure

We provide a detailed treatment and comparison of the weak lensing effects due to large scale structure (LSS), or scalar density perturbations and those due to gravitational waves (GWs) or tensor perturbations, on the temperature and polarization power spectra of the cosmic microwave background (CMB). We carry out the analysis both in real space by using the correlation function method, as well as in the spherical harmonic space. We find an intriguing similarity between the lensing kernels associated with LSS lensing and GW lensing. It is found that the lensing kernels only differ in relative negative signs and their form is very reminiscent of even and odd parity bipolar spherical harmonic coefficients. Through a numerical study of these lensing kernels, we establish that lensing due to GW is more efficient at distorting the CMB spectra as compared to LSS lensing, particularly for the polarization power spectra. Finally we argue that the CMB $B$-mode power spectra measurements can be used to place interesting constraints on GW energy densities.

Charge transfer and optoelectronic properties in the triarylamine-based donor–π bridge–acceptor dyes for dye-sensitised solar cells

The triarylamine–based donor–π bridge–acceptor dyes (namely, Ds-3, Ds-5 and Ds-6), with the higher conversion efficiency of sunlight to electricity, have been studied with quantum chemistry methods. The geometrical structure, frontier molecular orbital and electronic vertical excitation energies were calculated by using the density functional theory (DFT) and the time-dependent DFT with the Cam-B3LYP and PBE0 functional. From the calculated results, we perform a three-dimensional real-space analysis, which demonstrates that the lowest energy excited state of the triarylamine-based dye is a charge transfer (CT) excited state and electrons shift from triarylamine to cyanoacrylic acid group. The excited-state oxidation potentials and driving force energy are identified as the essential parameters to study the electron injection ability of the excited dyes. The evaluation of photochemical parameter and the visualised study of CT process provide the important information for revealing the relationship between structure and photochemical property of the triarylamine-based dyes.

Real-space approach to cosmic microwave background deboosting

The effect of our Galaxy's motion through the Cosmic Microwave Background rest frame, which aberrates and Doppler shifts incoming photons measured by current CMB experiments, has been shown to produce mode-mixing in the multipole space temperature coefficients. However, multipole space determinations are subject to many difficulties, and a real-space analysis can provide a straightforward alternative. In this work we describe a numerical method for removing Lorentz- boost effects from real-space temperature maps. We show that to deboost a map so that one can accurately extract the temperature power spectrum requires calculating the boost kernel at a finer pixelization than one might naively expect. In idealized cases that allow for easy comparison to analytic results, we have confirmed that there is indeed mode mixing among the spherical harmonic coefficients of the temperature. We find that using a boost kernel calculated at Nside=8192 leads to a 1% bias in the binned boosted power spectrum at l~2000, while individual Cls exhibit ~5% fluctuations around the binned average. However, this bias is dominated by pixelization effects and not the aberration and Doppler shift of CMB photons that causes the fluctuations. Performing analysis on maps with galactic cuts does not induce any additional error in the boosted, binned power spectra over the full sky analysis. For multipoles that are free of resolution effects, there is no detectable deviation between the binned boosted and unboosted spectra. This result arises because the power spectrum is a slowly varying function of and does not show that, in general, Lorentz boosts can be neglected for other cosmological quantities such as polarization maps or higher-point functions.

Compton profile study and electronic properties of tantalum diboride

We have reported the first-ever experimental Compton profile (CP) of TaB2 using 20 Ci137Cs Compton spectrometer. To compare the experimental data, we have also computed the theoretical CPs using density functional theory (DFT) and hybridization of DFT and Hartree–Fock (HF) within linear combination of the atomic orbitals (LCAO) method. In addition, we have reported energy bands and density of states of TaB2 using LCAO and full potential-linearized augmented plane wave (FP-LAPW) methods. A real space analysis of CP of TaB2 confirms its metallic character which is in tune with the cross-overs of Fermi level by energy bands and Fermi surface topology. A comparison of equal-valence-electron-density (EVED) experimental profiles of isoelectronic TaB2 and NbB2 show more covalent (or less ionic) character of TaB2 than that of NbB2 which is in agreement with available ionicity data.

In situ XRD studies of nanocrystallization of Fe-based metallic glass: a comparative study by reciprocal and direct space methods

Structural changes occurring in an Fe(72.5)Cu1Nb2Mo2Si(15.5)B7 alloy during a combination of constant rate heating (20 K min(-1)) and isothermal holding at 500 and 520 °C were investigated using in situ high-energy X-ray diffraction. We found that the ferromagnetic-to-paramagnetic transition of the amorphous phase is revealed as a change in the slope of the thermal expansion curve when heating a sample at a constant rate up to 520 °C. Real space analysis by means of the atomic pair distribution function (PDF) demonstrated that the rate and extent of the thermal expansion strongly depend on the interatomic separation. The PDF proved to be a reliable method for the description of crystallization kinetics. Further it allows determination of sizes of ultrafine nanocrystals with grain sizes well below 8 nm and thus makes observation of early stages of nanocrystallization possible. Following grain growth kinetics during isothermal annealing at 500 and 520 °C we found that the activation energy of the process is 357 ± 12 kJ mol(-1).

TDDFT studies of electronic spectra and excited states of the triphenylamine-based organic sensitizers and organic sensitizer–titanium dioxide cluster complexes

The absorption spectra and excited states of four triphenylamine-based organic dye molecules (TC1, TC2, TC3 and TC4) for dye sensitized solar cells (DSSC) have been theoretically investigated with density function theory (DFT) and time-dependent density function theory (TDDFT). In order to simulate the optical properties of the real DSSCs, sensitizer/titanium dioxide cluster interface systems TC4-(TiO2)n (n = 1–8) are also modeled. It is found that different adsorption sites and sizes of the clusters will exert critical effects on the molecular orbital energy levels of the complexes, and ultimately on their light-harvesting capabilities. In all the tested sensitizer/titanium dioxide cluster interface systems, the binding of the organic dye molecule to the 3-fold-coordinated titanium of the cluster (TiO2)6 could most benefit the widening of the spectrum response region and the interactions between the sensitizer and the cluster. From the intuitive physical pictures given by the three-dimensional (3D) real-space analysis methods of transition and charge difference densities, one reveals the photo-induced charge transfer microcosmic process of the sampled organic sensitizer/titanium dioxide cluster system TC4-(TiO2)6.

Electronic structure and electron momentum density in TiSi

We report the electron momentum density in titanium monosilicide using 241Am Compton spectrometer. Experimental Compton profile has been compared with the theoretical profiles computed using linear combination of atomic orbitals (LCAO). The energy bands, density of states and Fermi surface structures of TiSi are reported using the LCAO and the full potential linearized augmented plane wave methods. Theoretical anisotropies in directional Compton profiles are interpreted in terms of energy bands. To confirm the conducting behavior, we also report the real space analysis of experimental Compton profile of TiSi.

Grazing incidence small-angle neutron scattering: challenges and possibilities

The enhancement of surface sensitivity by grazing incidence geometry facilitates the investigation of nanostructures in thin films and at surfaces. The technique provides information about the surface roughness, lateral correlations, sizes and shapes of objects (such as, nanoparticles and nanostructures) positioned on top of the surface or in a region near the surface. Grazing incidence small-angle neutron scattering (GISANS) overcomes the limitations of conventional small-angle neutron scattering for extremely small sample volumes in the thin-film geometry. Although real space analysis techniques, such as atomic force microscopy, provide easy access to surface structures, reciprocal space analysis techniques, such as GISANS, provide several advantages: (i) average statistical information over the large illuminated sample surface can be detected and (ii) buried lateral structures can be probed without damage, using the variable-probed depth as a function of the incident angle. To illustrate the potential applications and challenges of GISANS, several different examples of thin nanostructured polymer films are reviewed. Nanostructures in triblock copolymer thin films are studied in the bulk as well as at the polymer-air and the silicon–polymer interface. Confined nanostructures in a dewetted diblock copolymer film are also discussed in terms of contrast and experimental settings.

Molecular modeling of two-photon absorption and third-order nonlinearities of polymethine dyes for all-optical switching

Stimulated by a recent experimental report [Hales JM et al. (2010) Science 327:1485-1488], two-photon absorption and third-order optical nonlinearities of selenopyrylium- and bis(dioxaborine)-terminated polymethine dyes (called SE-7C and DOB-9C) used for all-optical switching were investigated theoretically with time-dependent DFT (TD-DFT) and response theory as well as visualized real-space analysis. The calculated results for the first hyperpolarizability and second hyperpolarizability demonstrated that the two molecules both have large third-order optical nonlinearities. Using real-space analysis, we were able to visually determine that in the one-photon absorption (OPA) process, the first singlet excited state of SE-7C and DOB-9C is an intramolecular charge transfer (ICT) excited state with strong absorption, while the second excited state of these dyes (also termed the "ICT state") shows weak absorption. However, in the two-photon absorption (TPA) process, a larger TPA absorption cross-section was predicted for the second excited state. In this paper, we describe the properties of the S2 excited state, incorporating charge transfer and the transition moment, via real-space analysis, which was very important for understanding the TPA characteristics of the S(2) state.

Real space and wave-number space studies of the phase structure and morphology of iPP/PEOc blends using phase contrast microscopy

Phase contrast microscopy (PCM) was used to study the relation of the phase structure and morphology of isotactic polypropylene/poly(ethylene- co-octene) (iPP/PEOc) blends and the composition and the shear rate. The digital image analysis containing the analysis both in real space and wave-number space was introduced to deal with the PCM micrographs. The average characteristic length, Lm, in real space and the mean square radius of gyration, [Formula: see text], in wave-number space were defined and calculated to discuss the phase structure and morphology of iPP/PEOc blends. In addition, the fractal dimension, Dc, was introduced to describe spatial distribution uniformity of the dispersed phase. The results showed that these parameters were effective to study the size and its distribution of the dispersed phase particles.

A Compton scattering study of refractory niobium diborides

Isotropic Compton profile of NbB2 using 20 Ci 137Cs Compton spectrometer is compared with our theoretical profiles obtained from the density functional theory (DFT) within the first and the second order generalized gradient approximation (GGA) and the hybridization of Hartree–Fock and DFT. A good agreement between GGA based profiles and the experiment validates the applicability of second order GGA in momentum densities. Energy bands, density of states and real space analysis of the experimental profile show metallic character of NbB2.

Neutron scattering study of the magnetic microstructure of nanocrystalline gadolinium

We report grain-size-dependent results on nanocrystalline bulk Gd obtained by magnetic small-angle neutron scattering (SANS) and magnetometry. This approach allows one to study systematically how the magnetic microstructure of this rare-earth metal is affected by defects in the atomic microstructure, which are largely present in nanocrystalline materials, predominantly in the form of grain boundaries. The neutron scattering data reveal two types of angular anisotropies in the magnetic-field-dependent scattering cross section that are typically not seen in the coarse-grained polycrystal. In particular, a cloverleaf-shaped anisotropy and an elongation of the scattering pattern in the direction of the applied magnetic field have been detected. While the first result, which is an exceptional finding even in the nanocrystalline state, can be attributed to pronounced spin disorder in the vicinity of the Gd grain boundaries, the second anisotropy is related to spin misalignment due to the random magnetocrystalline anisotropy within the individual crystallites. Furthermore, we have calculated the correlation function of the spin misalignment from the radially averaged data, which gives access to the characteristic length scales on which the magnetization is perturbed by crystal defects. The results of this real-space analysis independently support the findings from magnetometry and field-dependent SANS. Wide-angle x-ray diffraction data indicate that stacking faults may limit the range of spin-misalignment fluctuations due to random anisotropy in this material.

Effects of transition-metal substitution in the iron-based superconductor LaFeAsO: Momentum- and real-space analysis from first principles

We study how transition-metal substitution changes the electronic structure of the iron-based superconductor LaFeAsO in real and momentum space. We first perform ab initio density functional calculation for various sizes of supercells with one transition-metal impurity. For various substitutes (Mn, Co, Ni, Zn, and Ru), we derive effective tight-binding models by constructing the maximally localized Wannier functions from the d bands around the Fermi level. The local electronic structure around the impurity site is quantitatively characterized by their onsite potential and transfer hoppings to neighboring sites. We find that the impurities are classified into three groups according to the derived parameters. For Mn, Co, and Ni, their impurity 3d levels measured from the Fe 3d level are ∼0.3, −0.3, and −0.8 eV, respectively, while, for the Zn case, its d level is extremely deep as ∼8 eV. For the Ru case, although the onsite-level difference is much smaller (∼O(0.1) eV), the transfer integrals around the impurity ion are larger than those of the pure system by 20% ∼ 30%, due to the large spatial spread of the Ru 4d orbitals. We also show that the charge distribution of the extra d electrons is confined around the impurity ion. We then unfold the first Brillouin zone (BZ) for the supercell to calculate the spectral function in the BZ for the normal cell for the case of Co and Ni doping. While the charge distribution seems to suggest that Co and Ni impurities do not change the amount of mobile carriers in the system, the momentum-space analysis clearly shows that the Fermi-surface volume indeed expands by Co and Ni substitutions, which can be well described by the rigid-band shift approximation.

Synthesis of fluorescent monodisperse non-spherical dumbbell-like model colloids

We describe a facile and flexible approach for synthesizing uniform non-spherical micron sized PMMA (poly(methyl methacrylate)) colloids with well-controlled protrusions. When homogeneously cross-linked PMMA spheres were used as seeds in a swelling process using again a methyl methacrylate monomer, they were found to transform into non-spherical particles with a single or multiple protrusions mainly depending on the cross-link density of the seeds. Alternatively, if core–shell PMMA spheres bearing a highly cross-linked shell around an uncross-linked ‘soft’ core were employed as seed particles, they always developed just a single protrusion. Precise control over the anisotropy of the particles was achieved by varying the amount and composition of the swelling mixture as well as the concentration of the stabilizer. Subsequently, the phase separation was enhanced and protrusions could be readily polymerized through temperature elevation of the system, yielding PMMA ‘snowman’-like or dumbbell-like colloids. Furthermore, these particles could be labeled with fluorescent dyes either before or after the polymerization, and transferred into apolar, refractive index and density matching liquids (cyclohexyl bromide (CHB) and/or decalin), enabling their use in quantitative confocal fluorescence microscopy studies in concentrated systems. Some examples of the use of these particles as a model system for real space analysis are given. These examples include the formation of plastic crystals, a special form of a colloidal crystal where the particles are positionally ordered but orientationally disordered. Additionally, the non-spherical particles could be organized into semi-flexibly bonded colloidal chains aided by an electric field in a polar solvent (formamide). Such chains of anisotropic particles are interesting as polymer analogs and for the preparation of new materials.

Dynamic heterogeneity in hard and soft sphere colloidal glasses

The nature of dynamic correlations in glasses and jammed soft matter remains a puzzle. Despite the strong increase in viscosity, hard-spheres exhibit only moderate increase of dynamic correlations at the glass transition, while recent experiments on soft-spheres suggest that in these systems, correlations grow to macroscopic length. Here, we present a direct real-space analysis of dynamic correlations in hard and soft-sphere glasses. The motion of the particles is imaged directly with confocal microscopy, and the maximum dynamical susceptibility is determined systematically over a range of probe length and time scales. We elucidate the displacement vector field, and analyze correlations in the particles' direction of motion. This allows us to demonstrate the different nature of relaxations in hard and soft-sphere systems. We find that the deeply jammed soft sphere suspension shows by far longer-range dynamic correlations that are characterized by small, remarkably coherent displacements. These observations provide direct evidence of the internal elasticity that governs long-range relaxation modes in soft systems.

Systematic Study on the Effect of Solvent Removal Rate on the Morphology of Solvent Vapor Annealed ABA Triblock Copolymer Thin Films

Nanoscale self-assembly of block copolymer thin films has garnered significant research interest for nanotemplate design and membrane applications. To fulfill these roles, control of thin film morphology and orientation is critical. Solvent vapor annealing (SVA) treatments can be used to kinetically trap morphologies in thin films not achievable by traditional thermal treatments, but many variables affect the outcome of SVA, including solvent choice, total solvent concentration/swollen film thickness, and solvent removal rate. In this work, we systematically examined the effect of solvent removal rate on the final thin film morphology of a cylinder-forming ABA triblock copolymer. By kinetically trapping the film morphologies at key points during the solvent removal process and then using successive ultraviolet ozone (UVO) etching steps followed by atomic force microscopy (AFM) imaging to examine the through-film morphologies of the films, we determined that the mechanism for cylinder reorientation from substrate-parallel to substrate-perpendicular involved the propagation of changes at the free surface through the film toward the substrate as a front. The degree of reorientation increased with successively slower solvent removal rates. Furthermore, the AFM/UVO etching scheme permitted facile real-space analysis of the thin film internal structure in comparison to cross-sectional transmission electron microscopy.

Theoretical study of charge transfer mechanism in fullerene-phenyl-phenothiazine compound: A real-space analysis

Quantum chemistry methods as well as two-dimensional (2D) and three-dimensional (3D) real-space analysis have been conducted to study the photo-induced intramolecular charge-transfer (ICT) and excited state properties of fullerene-phenylphenothiazine, which has recently been developed for solar cells. Firstly, we obtained the energy levels and spatial distributions of HOMO/LUMO, energy gap ( Δ E H – L ) and excitation energies on the basis of quantum chemistry study. Secondly, two-dimensional (2D) and three-dimensional (3D) real-space analysis were used to visualize the CT process and to reveal the nature of the excited states. In the above analyses, the 2D real-space analysis of the transition density matrix provided information about the electron-hole coherence, and the 3D real-space analysis of charge difference density enabled the visualization of the orientation and result of the ICT. The results of real-space analysis directly indicate that some states are ICT states, and others belong to locally excited states. Moreover, according to the generalized Mulliken Hush theory, we calculated the electronic coupling matrix elements and predict that electron transfer for some ICT states more easily takes place than that for some locally excited states.