Modern charge density studies: the entanglement of experiment and theory

This tutorial review article is intended to provide a general guidance to a reader interested to learn about the methodologies to obtain accurate electron density mapping in molecules and crystalline solids, from theory or from experiment, and to carry out a sensible interpretation of the results, for chemical, biochemical or materials science applications. The review mainly focuses on X-ray diffraction techniques and refinement of experimental models, in particular multipolar models. Neutron diffraction, which was widely used in the past to fix accurate positions of atoms, is now used for more specific purposes. The review illustrates three principal analyses of the experimental or theoretical electron density, based on quantum chemical, semi-empirical or empirical interpretation schemes, such as the quantum theory of atoms in molecules, the semi-classical evaluation of interaction energies and the Hirshfeld analysis. In particular, it is shown that a simple topological analysis based on a partition of the electron density cannot alone reveal the whole nature of chemical bonding. More information based on the pair density is necessary. A connection between quantum mechanics and observable quantities is given in order to provide the physical grounds to explain the observations and to justify the interpretations.

Charge density analysis for crystal engineering

This review reports on the application of charge density analysis in the field of crystal engineering, which is one of the most growing and productive areas of the entire field of crystallography. While methods to calculate or measure electron density are not discussed in detail, the derived quantities and tools, useful for crystal engineering analyses, are presented and their applications in the recent literature are illustrated. Potential developments and future perspectives are also highlighted and critically discussed.

Orbital currents and charge density waves in a generalized Hubbard ladder

We study a generalized Hubbard model on the two-leg ladder at zero temperature, focusing on a parameter region with staggered flux (SF)/d-density wave (DDW) order. To guide our numerical calculations, we first investigate the location of a SF/DDW phase in the phase diagram of the half-filled weakly interacting ladder using a perturbative renormalization group (RG) and bosonization approach. For hole doping 6 away from half-filling, finite-system density-matrix renormalizationgroup (DMRG) calculations are used to study ladders with up to 200 rungs for intermediate-strength interactions. In the doped SF/DDW phase, the staggered rung current and the rung electron density both show periodic spatial oscillations, with characteristic wavelengths 2/delta and 1/delta, respectively, corresponding to ordering wavevectors 2k(F) and 4k(F) for the currents and densities, where 2k(F) = pi(1 - delta). The density minima are located at the anti-phase domain walls of the staggered current. For sufficiently large dopings, SF/DDW order is suppressed. The rung density modulation also exists in neighboring phases where currents decay exponentially. We show that most of the DMRG results can be qualitatively understood from weak-coupling RG/bosonization arguments. However, while these arguments seem to suggest a crossover from non-decaying correlations to power-law decay at a length scale of order 1/delta, the DMRG results are consistent with a true long-range order scenario for the currents and densities. (c) 2005 Elsevier Inc. All rights reserved.

Injectable hydrogels with high fixed charge density and swelling pressure for nucleus pulposus repair:biomimetic glycosaminoglycan analogues

The load-bearing biomechanical role of the intervertebral disc is governed by the composition and organization of its major macromolecular components, collagen and aggrecan. The major function of aggrecan is to maintain tissue hydration, and hence disc height, under the high loads imposed by muscle activity and body weight. Key to this role is the high negative fixed charge of its glycosaminoglycan side chains, which impart a high osmotic pressure to the tissue, thus regulating and maintaining tissue hydration and hence disc height under load. In degenerate discs, aggrecan degrades and is lost from the disc, particularly centrally from the nucleus pulposus. This loss of fixed charge results in reduced hydration and loss of disc height; such changes are closely associated with low back pain. The present authors developed biomimetic glycosaminoglycan analogues based on sulphonate-containing polymers. These biomimetics are deliverable via injection into the disc where they polymerize in situ, forming a non-degradable, nuclear "implant" aimed at restoring disc height to degenerate discs, thereby relieving back pain. In vitro, these glycosaminoglycan analogues possess appropriate fixed charge density, hydration and osmotic responsiveness, thereby displaying the capacity to restore disc height and function. Preliminary biomechanical tests using a degenerate explant model showed that the implant adapts to the space into which it is injected and restores stiffness. These hydrogels mimic the role taken by glycosaminoglycans in vivo and, unlike other hydrogels, provide an intrinsic swelling pressure, which can maintain disc hydration and height under the high and variable compressive loads encountered in vivo. © 2013 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.

The relationship between charge density and polyelectrolyte brush profile using simultaneous neutron reflectivity and in situ attenuated total internal reflection FTIR

We report on a novel experimental study of a pH-responsive polyelectrolyte brush at the silicon/D2O interface. A poly[2-(diethylamino)ethyl methacrylate] brush was grown on a large silicon crystal which acted as both a substrate for a neutron reflectivity solid/liquid experiment but also as an FTIR-ATR spectroscopy crystal. This arrangement has allowed for both neutron reflectivities and FTIR spectroscopic information to be measured in parallel. The chosen polybase brush shows strong IR bands which can be assigned to the N-D+ stretch, D2O, and a carbonyl group. From such FTIR data, we are able to closely monitor the degree of protonation along the polymer chain as well as revealing information concerning the D2O concentration at the interface. The neutron reflectivity data allows us to determine the physical brush profile normal to the solid/liquid interface along with the corresponding degree of hydration. This combined approach makes it possible to quantify the charge on a polymer brush alongside the morphology adopted by the polymer chains. © 2013 American Chemical Society.

Role of charge in destabilizing AlH4 and BH4 complex anions for hydrogen storage applications : Ab initio density functional calculations

NaAlH4 and LiBH4 are potential candidate materials for mobile hydrogen storage applications, yet they have the drawback of being highly stable and desorbing hydrogen only at elevated temperatures. In this letter, ab initio density functional theory calculations reveal how the stabilities of the AlH4 and BH4 complex anions will be affected by reducing net anionic charge. Tetrahedral AlH4 and BH4 complexes are found to be distorted with the decrease of negative charge. One H-H distance becomes smaller and the charge density will overlap between them at a small anion charge. The activation energies to release of H2 from AlH4 and BH4 complexes are thus greatly decreased. We demonstrate that point defects such as neutral Na vacancies or substitution of a Na atom with Ti on the NaAlH4(001) surface can potentially cause strong distortion of neighboring AlH4 complexes and even induce spontaneous dehydrogenation. Our results help to rationalize the conjecture that the suppression of charge transfer to AlH4 and BH4 anion as a consequence of surface defects should be very effective for improving the recycling performance of H2 in NaAlH4 and LiBH4. The understanding gained here will aid in the rational design and development of hydrogen storage materials based on these two systems.

Theory of coexisting charge and spin-density waves in (TMTTF)(2)Br, (TMTSF)(2)PF6 and alpha-(BEDT-TTF)(2)MHg(SCN)(4)

We discuss a recently formulated microscopic theory of the unusual coexistence of spin density waves (SDWs) and charge density waves (CDWs) that has been seen in recent experiments on (TMTTF)2Br, (TMTSF)2PF6 and α-(BEDT-TTF)2MHg(SCN)4.

Theory of coexisting charge and spin-density waves in (TMTTF)(2)Br, (TMTSF)(2)PF6, and alpha-(BEDT-TTF)(2)MHg(SCN)(4)

Recent experiments indicate that the spin-density waves (SDWs) in (TMTTF)(2)Br, (TMTSF)(2)PF6, and alpha-(BEDT-TTF)(2)MHg(SCN)(4) are highly unconventional and coexist with charge-density waves (CDWs). We present a microscopic theory of this unusual CDW-SDW coexistence. A complete understanding requires the explicit inclusion of strong Coulomb interactions, lattice discreteness, the anisotropic two-dimensional nature of the lattice, and the correct hand filling within the starting Hamiltonian. [S0031-9007(99)08498-7].

Charge-controlled switchable CO2 capture on boron nitride nanomaterials

Increasing concerns about the atmospheric CO2 concentration and its impact on the environment are motivating researchers to discover new materials and technologies for efficient CO2 capture and conversion. Here, we report a study of the adsorption of CO2, CH4, and H2 on boron nitride (BN) nanosheets and nanotubes (NTs) with different charge states. The results show that the process of CO2 capture/release can be simply controlled by switching on/off the charges carried by BN nanomaterials. CO2 molecules form weak interactions with uncharged BN nanomaterials and are weakly adsorbed. When extra electrons are introduced to these nanomaterials (i.e., when they are negatively charged), CO2 molecules become tightly bound and strongly adsorbed. Once the electrons are removed, CO2 molecules spontaneously desorb from BN absorbents. In addition, these negatively charged BN nanosorbents show high selectivity for separating CO2 from its mixtures with CH4 and/or H2. Our study demonstrates that BN nanomaterials are excellent absorbents for controllable, highly selective, and reversible capture and release of CO2. In addition, the charge density applied in this study is of the order of 1013 cm–2 of BN nanomaterials and can be easily realized experimentally.

A density matrix renormalization group study of low-lying excitations of polythiophene within a Pariser-Parr-Pople model

Symmetrized density-matrix-renormalization-group calculations have been carried out, within Pariser-Parr-Pople Hamiltonian, to explore the nature of the ground and low-lying excited states of long polythiophene oligomers. We have exploited C-2 symmetry and spin parity of the system to obtain excited states of experimental interest, and studied the lowest dipole allowed excited state and lowest dipole forbidden two photon state, for different oligomer sizes. In the long system limit, the dipole allowed excited state always lies below the lowest dipole forbidden two-photon state which implies, by Kasha rule, that polythiophene fluoresces strongly. The lowest triplet state lies below two-photon state as usual in conjugated polymers. We have doped the system with a hole and an electron and obtained the charge excitation gap and the binding energy of the 1(1)B(u)(-) exciton. We have calculated the charge density of the ground, one-photon and two-photon states for the longer system size of 10 thiophene rings to characterize these states. We have studied bond order in these states to get an idea about the equilibrium excited state geometry of the system. We have also studied the charge density distribution of the singly and doubly doped polarons for longer system size, and observe that polythiophenes do not support bipolarons.

The Single Langmuir Probe under Orbital-Limited Conditions in a Low-Density Collisional Plasma

The cylindrical Langmuir probe under orbital-limited conditions was used to determine the charge density in a low-density collisional plasma. The Langmuir's theory was applied to both electron and ion saturation currents in their respective accelerating regions. Present study indicates that the length of the probe significantly affects the probe characteristics. A probe of suitable length under orbital-limited conditions may be useful under the experimental conditions where the radius of the probe is much smaller than the Debye lengt.

Enhanced charge and spin currents in the one-dimensional disordered mesoscopic Hubbard ring

We consider a one-dimensional mesoscopic Hubbard ring with and without disorder and compute charge and spin stiffness as a measure of the permanent currents. For finite disorder we identify critical disorder strength beyond which the charge currents in a system with repulsive interactions are larger than those for a free system. The spin currents in the disordered repulsive Hubbard model are enhanced only for small U, where the magnetic state of the system corresponds to a charge-density wave pinned to the impurities. For large U, the state of the system corresponds to localized isolated spins and the spin currents are found to be suppressed. For the attractive Hubbard model we find that the charge currents are always suppressed compared to the free system at all length scales.

Density-matrix renormalization-group study of low-lying excitations of polyacene within a Pariser-Parr-Pople model

We have carried out symmetrized density-matrix renormalization-group calculations to study the nature of excited states of long polyacene oligomers within a Pariser-Parr-Pople Hamiltonian. We have used the C-2 symmetry, the electron-hole symmetry, and the spin parity of the system in our calculations. We find that there is a crossover in the lowest dipole forbidden two-photon state and the lowest dipole allowed excited state with size of the oligomer. In the long system limit, the two-photon state lies below the lowest dipole allowed excited state. The triplet state lies well below the two-photon state and energetically does not correspond to its description as being made up of two triplets. These results are in agreement with the general trends in linear conjugated polymers. However, unlike in linear polyenes wherein the two-photon state is a localized excitation, we find that in polyacenes, the two-photon excitation is spread out over the system. We have doped the systems with a hole and an electron and have calculated the charge excitation gap. Using the charge gap and the optical gap, we estimate the binding energy of the 1(1)B(-) exciton to be 2.09 eV. We have also studied doubly doped polyacenes and find that the bipolaron in these systems, to be composed of two separated polarons, as indicated by the calculated charge-density profile and charge-charge correlation function. We have studied bond orders in various states in order to get an idea of the excited state geometry of the system. We find that the ground state, the triplet state, the dipole allowed state, and the polaron excitations correspond to lengthening of the rung bonds in the interior of the oligomer while the two-photon excitation corresponds to the rung bond lengths having two maxima in the system.

A density matrix renormalization group method study of optical properties of porphines and metalloporphines

The symmetrized density matrix renormalization group method is used to study linear and nonlinear optical properties of free base porphine and metalloporphine. Long-range interacting model, namely, Pariser-Parr-Pople model is employed to capture the quantum many-body effect in these systems. The nonlinear optical coefficients are computed within the correction vector method. The computed singlet and triplet low-lying excited state energies and their charge densities are in excellent agreement with experimental as well as many other theoretical results. The rearrangement of the charge density at carbon and nitrogen sites, on excitation, is discussed. From our bond order calculation, we conclude that porphine is well described by the 18-annulenic structure in the ground state and the molecule expands upon excitation. We have modeled the regular metalloporphine by taking an effective electric field due to the metal ion and computed the excitation spectrum. Metalloporphines have D(4h) symmetry and hence have more degenerate excited states. The ground state of metalloporphines shows 20-annulenic structure, as the charge on the metal ion increases. The linear polarizability seems to increase with the charge initially and then saturates. The same trend is observed in third order polarizability coefficients. (C) 2012 American Institute of Physics. [doi: 10.1063/1.3671946]