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.

From the chiral magnetic wave to the charge dependence of elliptic flow

The quark-gluon plasma formed in heavy ion collisions contains charged chiral fermions evolving in an external magnetic field. At finite density of electric charge or baryon number (resulting either from nuclear stopping or from fluctuations), the triangle anomaly induces in the plasma the Chiral Magnetic Wave (CMW). The CMW first induces a separation of the right and left chiral charges along the magnetic field; the resulting dipolar axial charge density in turn induces the oppositely directed vector charge currents leading to an electric quadrupole moment of the quark-gluon plasma. Boosted by the strong collective flow, the electric quadrupole moment translates into the charge dependence of the elliptic flow coefficients, so that $v_2(\pi^+) < v_2(\pi^-)$ (at positive net charge). Using the latest quantitative simulations of the produced magnetic field and solving the CMW equation, we make further quantitative estimates of the produced $v_2$ splitting and its centrality dependence. We compare the results with the available experimental data.

Experimental and Theoretical Electron Density Analysis of Copper Pyrazine Nitrate Quasi-Low-Dimensional Quantum Magnets

The accurate electron density distribution and magnetic properties of two metal-organic polymeric magnets, the quasi-one-dimensional (1D) Cu(pyz)(NO3)2 and the quasi-two-dimensional (2D) [Cu(pyz)2(NO3)]NO3·H2O, have been investigated by high-resolution single-crystal X-ray diffraction and density functional theory calculations on the whole periodic systems and on selected fragments. Topological analyses, based on quantum theory of atoms in molecules, enabled the characterization of possible magnetic exchange pathways and the establishment of relationships between the electron (charge and spin) densities and the exchange-coupling constants. In both compounds, the experimentally observed antiferromagnetic coupling can be quantitatively explained by the Cu-Cu superexchange pathway mediated by the pyrazine bridging ligands, via a σ-type interaction. From topological analyses of experimental charge-density data, we show for the first time that the pyrazine tilt angle does not play a role in determining the strength of the magnetic interaction. Taken in combination with molecular orbital analysis and spin density calculations, we find a synergistic relationship between spin delocalization and spin polarization mechanisms and that both determine the bulk magnetic behavior of these Cu(II)-pyz coordination polymers.

Delayed gadolinium-enhanced magnetic resonance imaging of hip joint cartilage: pearls and pitfalls

With the increasing advances in hip joint preservation surgery, accurate diagnosis and assessment of femoral head and acetabular cartilage status is becoming increasingly important. Magnetic resonance imaging (MRI) of the hip does present technical difficulties. The fairly thin cartilage lining necessitates high image resolution and high contrast-to-noise ratio (CNR). With MR arthrography (MRA) using intraarticular injected gadolinium, labral tears and cartilage clefts may be better identified through the contrast medium filling into the clefts. However, the ability of MRA to detect varying grades of cartilage damage is fairly limited and early histological and biochemical changes in the beginning of osteoarthritis (OA) cannot be accurately delineated. Traditional MRI thus lacks the ability to analyze the biological status of cartilage degeneration. The technique of delayed gadolinium-enhanced MRI of cartilage (dGEMRIC) is sensitive to the charge density of cartilage contributed by glycosaminoglycans (GAGs), which are lost early in the process of OA. Therefore, the dGEMRIC technique has a potential to detect early cartilage damage that is obviously critical for decision-making regarding time and extent of intervention for joint-preservation. In the last decade, cartilage imaging with dGEMRIC has been established as an accurate and reliable tool for assessment of cartilage status in the knee and hip joint.This review outlines the current status of dGEMRIC for assessment of hip joint cartilage. Practical modifications of the standard technique including three-dimensional (3D) dGEMRIC and dGEMRIC after intra-articular gadolinium instead of iv-dGEMRIC will also be addressed.

Probing Charge Transfer in Benzodifuran-C-60 Dumbbell-Type Electron Donor-Acceptor Conjugates: Ground- and Excited-State Assays

Rigid electron donor-acceptor conjugates (1-3) that combine -extended benzodifurans as electron donors and C-60 molecules as electron acceptors with different linkers have been synthesized and investigated with respect to intramolecular charge-transfer events. Electrochemistry, fluorescence, and transient absorption measurements revealed tunable and structure-dependent charge-transfer processes in the ground and excited states. Our experimental findings are underpinned by density-functional theory calculations.

Surface charge of polymer coated SPIONs influences the serum protein adsorption, colloidal stability and subsequent cell interaction in vitro

It is known that the nanoparticle-cell interaction strongly depends on the physicochemical properties of the investigated particles. In addition, medium density and viscosity influence the colloidal behaviour of nanoparticles. Here, we show how nanoparticle-protein interactions are related to the particular physicochemical characteristics of the particles, such as their colloidal stability, and how this significantly influences the subsequent nanoparticle-cell interaction in vitro. Therefore, different surface charged superparamagnetic iron oxide nanoparticles were synthesized and characterized. Similar adsorbed protein profiles were identified following incubation in supplemented cell culture media, although cellular uptake varied significantly between the different particles. However, positively charged nanoparticles displayed a significantly lower colloidal stability than neutral and negatively charged particles while showing higher non-sedimentation driven cell-internalization in vitro without any significant cytotoxic effects. The results of this study strongly indicate therefore that an understanding of the aggregation state of NPs in biological fluids is crucial in regards to their biological interaction(s).

Numerical study of Anderson localization of terahertz waves in disordered waveguides

We present a numerical study of electromagnetic wave transport in disordered quasi-one-dimensional waveguides at terahertz frequencies. Finite element method calculations of terahertz wave propagation within LiNbO3 waveguides with randomly arranged air-filled circular scatterers exhibit an onset of Anderson localization at experimentally accessible length scales. Results for the average transmission as a function of waveguide length and scatterer density demonstrate a clear crossover from diffusive to localized transport regime. In addition, we find that transmission fluctuations grow dramatically when crossing into the localized regime. Our numerical results are in good quantitative agreement with theory over a wide range of experimentally accessible parameters both in the diffusive and localized regime opening the path towards experimental observation of terahertz wave localization.

Solvation-Driven Charge Transfer and Localization in Metal Complexes

In any physicochemical process in liquids, the dynamical response of the solvent to the solutes out of equilibrium plays a crucial role in the rates and products: the solvent molecules react to the changes in volume and electron density of the solutes to minimize the free energy of the solution, thus modulating the activation barriers and stabilizing (or destabilizing) intermediate states. In charge transfer (CT) processes in polar solvents, the response of the solvent always assists the formation of charge separation states by stabilizing the energy of the localized charges. A deep understanding of the solvation mechanisms and time scales is therefore essential for a correct description of any photochemical process in dense phase and for designing molecular devices based on photosensitizers with CT excited states. In the last two decades, with the advent of ultrafast time-resolved spectroscopies, microscopic models describing the relevant case of polar solvation (where both the solvent and the solute molecules have a permanent electric dipole and the mutual interaction is mainly dipole−dipole) have dramatically progressed. Regardless of the details of each model, they all assume that the effect of the electrostatic fields of the solvent molecules on the internal electronic dynamics of the solute are perturbative and that the solvent−solute coupling is mainly an electrostatic interaction between the constant permanent dipoles of the solute and the solvent molecules. This well-established picture has proven to quantitatively rationalize spectroscopic effects of environmental and electric dynamics (time-resolved Stokes shifts, inhomogeneous broadening, etc.). However, recent computational and experimental studies, including ours, have shown that further improvement is required. Indeed, in the last years we investigated several molecular complexes exhibiting photoexcited CT states, and we found that the current description of the formation and stabilization of CT states in an important group of molecules such as transition metal complexes is inaccurate. In particular, we proved that the solvent molecules are not just spectators of intramolecular electron density redistribution but significantly modulate it. Our results solicit further development of quantum mechanics computational methods to treat the solute and (at least) the closest solvent molecules including the nonperturbative treatment of the effects of local electrostatics and direct solvent−solute interactions to describe the dynamical changes of the solute excited states during the solvent response.

Experimental and Calculated Spectra of π-Stacked Mild Charge-Transfer Complexes: Jet-Cooled Perylene·(Tetrachloroethene) n , n = 1,2

The S0 ↔ S1 spectra of the mild charge-transfer (CT) complexes perylene·tetrachloroethene (P·4ClE) and perylene·(tetrachloroethene)2 (P·(4ClE)2) are investigated by two-color resonant two-photon ionization (2C-R2PI) and dispersed fluorescence spectroscopy in supersonic jets. The S0 → S1 vibrationless transitions of P·4ClE and P·(4ClE)2 are shifted by δν = −451 and −858 cm–1 relative to perylene, translating to excited-state dissociation energy increases of 5.4 and 10.3 kJ/mol, respectively. The red shift is ∼30% larger than that of perylene·trans-1,2-dichloroethene; therefore, the increase in chlorination increases the excited-state stabilization and CT character of the interaction, but the electronic excitation remains largely confined to the perylene moiety. The 2C-R2PI and fluorescence spectra of P·4ClE exhibit strong progressions in the perylene intramolecular twist (1au) vibration (42 cm–1 in S0 and 55 cm–1 in S1), signaling that perylene deforms along its twist coordinate upon electronic excitation. The intermolecular stretching (Tz) and internal rotation (Rc) vibrations are weak; therefore, the P·4ClE intermolecular potential energy surface (IPES) changes little during the S0 ↔ S1 transition. The minimum-energy structures and inter- and intramolecular vibrational frequencies of P·4ClE and P·(4ClE)2 are calculated with the dispersion-corrected density functional theory (DFT) methods B97-D3, ωB97X-D, M06, and M06-2X and the spin-consistent-scaled (SCS) variant of the approximate second-order coupled-cluster method, SCS-CC2. All methods predict the global minima to be π-stacked centered coplanar structures with the long axis of tetrachloroethene rotated by τ ≈ 60° relative to the perylene long axis. The calculated binding energies are in the range of −D0 = 28–35 kJ/mol. A second minimum is predicted with τ ≈ 25°, with ∼1 kJ/mol smaller binding energy. Although both monomers are achiral, both the P·4ClE and P·(4ClE)2 complexes are chiral. The best agreement for adiabatic excitation energies and vibrational frequencies is observed for the ωB97X-D and M06-2X DFT methods.

On the CFT operator spectrum at large global charge

We calculate the anomalous dimensions of operators with large global charge J in certain strongly coupled conformal field theories in three dimensions, such as the O(2) model and the supersymmetric fixed point with a single chiral superfield and a W = Φ3 superpotential. Working in a 1/J expansion, we find that the large-J sector of both examples is controlled by a conformally invariant effective Lagrangian for a Goldstone boson of the global symmetry. For both these theories, we find that the lowest state with charge J is always a scalar operator whose dimension ΔJ satisfies the sum rule J2ΔJ−(J22+J4+316)ΔJ−1−(J22+J4+316)ΔJ+1=0.04067 up to corrections that vanish at large J . The spectrum of low-lying excited states is also calculable explcitly: for example, the second-lowest primary operator has spin two and dimension ΔJ+3√. In the supersymmetric case, the dimensions of all half-integer-spin operators lie above the dimensions of the integer-spin operators by a gap of order J+12. The propagation speeds of the Goldstone waves and heavy fermions are 12√ and ±12 times the speed of light, respectively. These values, including the negative one, are necessary for the consistent realization of the superconformal symmetry at large J.