Table of contents

Poisson–Boltzmann (PB) theory is the classic approach to soft matter electrostatics and has been applied to numerous physical chemistry and biophysics problems. Its essential limitations are in its neglect of correlation effects and fluid structure. Recently, several theoretical insights have allowed the formulation of approaches that go beyond PB theory in a systematic way. In this topical review, we provide an update on the developments achieved in the self-consistent formulations of correlation-corrected Poisson–Boltzmann theory. We introduce a corresponding system of coupled non-linear equations for both continuum electrostatics with a uniform dielectric constant, and a structured solvent—a dipolar Coulomb fluid—including non-local effects. While the approach is only approximate and also limited to corrections in the so-called weak fluctuation regime, it allows us to include physically relevant effects, as we show for a range of applications of these equations.

Amphetamine-type stimulants (ATS) are a group of incitation and psychedelic drugs affecting the central nervous system. Physicochemical data for these compounds are essential for understanding the stimulating mechanism, for assessing their environmental impacts, and for developing new drug detection methods. However, experimental data are scarce due to tight regulation of such illicit drugs, yet conventional methods to estimate their properties are often unreliable. Here we introduce a tailor-made multiscale procedure for predicting the hydration free energies and the solvation structures of ATS molecules by a combination of first principles calculations and the classical density functional theory. We demonstrate that the multiscale procedure performs well for a training set with similar molecular characteristics and yields good agreement with a testing set not used in the training. The theoretical predictions serve as a benchmark for the missing experimental data and, importantly, provide microscopic insights into manipulating the hydrophobicity of ATS compounds by chemical modifications.

Implicit solvent models offer an attractive way to estimate the effects of a solvent environment on the properties of small or large solutes without the complications of explicit simulations. One common test of accuracy is to compute the free energy of transfer from gas to liquid for a variety of small molecules, since many of these values have been measured. Studies of the temperature dependence of these values (i.e. solvation enthalpies and entropies) can provide additional insights into the performance of implicit solvent models. Here, we show how to compute temperature derivatives of hydration free energies for the 3D-RISM integral equation approach. We have computed hydration free energies of 1123 small drug-like molecules (both neutral and charged). Temperature derivatives were also used to calculate hydration energies and entropies of 74 of these molecules (both neutral and charged) for which experimental data is available. While direct results have rather poor agreement with experiment, we have found that several previously proposed linear hydration free energy correction schemes give good agreement with experiment. These corrections also provide good agreement for hydration energies and entropies though simple extensions are required in some cases.

For neutral hard-sphere solutes, we compare the reduced density profile of water around a solute g(r), solvation free energy μ, energy U, and entropy S under the isochoric condition predicted by the two theories: dielectrically consistent reference interaction site model (DRISM) and angle-dependent integral equation (ADIE) theories. A molecular model for water pertinent to each theory is adopted. The hypernetted-chain (HNC) closure is employed in the ADIE theory, and the HNC and Kovalenko–Hirata (K–H) closures are tested in the DRISM theory. We also calculate g(r), U, S, and μ of the same solute in a hard-sphere solvent whose molecular diameter and number density are set at those of water, in which case the radial-symmetric integral equation (RSIE) theory is employed. The dependences of μ, U, and S on the excluded volume and solvent-accessible surface area are analyzed using the morphometric approach (MA). The results from the ADIE theory are in by far better agreement with those from computer simulations available for g(r), U, and μ. For the DRISM theory, g(r) in the vicinity of the solute is quite high and becomes progressively higher as the solute diameter d_U increases. By contrast, for the ADIE theory, it is much lower and becomes further lower as d_U increases. Due to unphysically positive U and significantly larger |S|, μ from the DRISM theory becomes too high. It is interesting that μ, U, and S from the K–H closure are worse than those from the HNC closure. Overall, the results from the DRISM theory with a molecular model for water are quite similar to those from the RSIE theory with the hard-sphere solvent. Based on the results of the MA analysis, we comparatively discuss the different theoretical methods for cases where they are applied to studies on the solvation of a protein.

Complex formation between molecules in solution is the key process by which molecular interactions are translated into functional systems. These processes are governed by the binding or free energy of association which depends on both direct molecular interactions and the solvation contribution. A design goal frequently addressed in pharmaceutical sciences is the optimization of chemical properties of the complex partners in the sense of minimizing their binding free energy with respect to a change in chemical structure. Here, we demonstrate that liquid-state theory in the form of the solute–solute equation of the reference interaction site model provides all necessary information for such a task with high efficiency. In particular, computing derivatives of the potential of mean force (PMF), which defines the free-energy surface of complex formation, with respect to potential parameters can be viewed as a means to define a direction in chemical space toward better binders. We illustrate the methodology in the benchmark case of alkali ion binding to the crown ether 18-crown-6 in aqueous solution. In order to examine the validity of the underlying solute–solute theory, we first compare PMFs computed by different approaches, including explicit free-energy molecular dynamics simulations as a reference. Predictions of an optimally binding ion radius based on free-energy derivatives are then shown to yield consistent results for different ion parameter sets and to compare well with earlier, orders-of-magnitude more costly explicit simulation results. This proof-of-principle study, therefore, demonstrates the potential of liquid-state theory for molecular design problems.

The molecular recognition process of the carbohydrate-binding module family 36 (CBM36) was examined theoretically. The mechanism of xylan binding by CBM36 and the role of Ca²⁺ were investigated by the combined use of molecular dynamics simulations and the 3D reference interaction site model method. The CBM36 showed affinity for xylan after Ca²⁺ binding, but not after Mg²⁺ binding. Free-energy component analysis of the xylan-binding process revealed that the major factor for xylan-binding affinity is the electrostatic interaction between the Ca²⁺ and the hydroxyl oxygens of xylan. The van der Waals interaction between the hydrophobic side chain of CBM36 and the glucopyranose ring of xylan also contributes to the stabilization of the xylan-binding state. Dehydration on the formation of the complex has the opposite effect on these interactions. The affinity of CBM36 for xylan results from a balance of the interactions between the binding ion and solvents, hydrophilic residues around xylan, and the hydroxyl oxygens of xylan. When CBM binds Ca²⁺, these interactions are well balanced; in contrast, when CBM binds Mg²⁺, the dehydration penalty is excessively large.

In this work we have assessed the ability of a recently proposed three-dimensional integral equation approach to describe the explicit spatial distribution of molecular hydrogen confined in a crystal formed by short-capped nanotubes of C₅₀ H₁₀. To that aim we have resorted to extensive molecular simulation calculations whose results have been compared with our three-dimensional integral equation approximation. We have first tested the ability of a single C₅₀ H₁₀ nanocage for the encapsulation of H₂ by means of molecular dynamics simulations, in particular using targeted molecular dynamics to estimate the binding Gibbs energy of a host hydrogen molecule inside the nanocage. Then, we have investigated the adsorption isotherm of the nanocage crystal using grand canonical Monte Carlo simulations in order to evaluate the maximum load of molecular hydrogen. For a packing close to the maximum load explicit hydrogen density maps and density profiles have been determined using molecular dynamics simulations and the three-dimensional Ornstein–Zernike equation with a hypernetted chain closure. In these conditions of extremely tight confinement the theoretical approach has shown to be able to reproduce the three-dimensional structure of the adsorbed fluid with accuracy down to the finest details.

The interaction between any two biological molecules must compete with their interaction with water molecules. This makes water the most important molecule in medicine, as it controls the interactions of every therapeutic with its target. A small molecule binding to a protein is able to recognize a unique binding site on a protein by displacing bound water molecules from specific hydration sites. Quantifying the interactions of these water molecules allows us to estimate the potential of the protein to bind a small molecule. This is referred to as ligandability. In the study, we describe a method to predict ligandability by performing a search of all possible combinations of hydration sites on protein surfaces. We predict ligandability as the summed binding free energy for each of the constituent hydration sites, computed using inhomogeneous fluid solvation theory. We compared the predicted ligandability with the maximum observed binding affinity for 20 proteins in the human bromodomain family. Based on this comparison, it was determined that effective inhibitors have been developed for the majority of bromodomains, in the range from 10 to 100 nM. However, we predict that more potent inhibitors can be developed for the bromodomains BPTF and BRD7 with relative ease, but that further efforts to develop inhibitors for ATAD2 will be extremely challenging. We have also made predictions for the 14 bromodomains with no reported small molecule K_d values by isothermal titration calorimetry. The calculations predict that PBRM1(1) will be a challenging target, while others such as TAF1L(2), PBRM1(4) and TAF1(2), should be highly ligandable. As an outcome of this work, we assembled a database of experimental maximal K_d that can serve as a community resource assisting medicinal chemistry efforts focused on BRDs. Effective prediction of ligandability would be a very useful tool in the drug discovery process.

As an example of charged, dipolar soft matter, the ionic liquid 1-ethyl-3-methyl-imidazolium dicyanamide is studied by coarse-grained molecular dynamics simulations. We focus on the link between microscopic and mesoscopic properties for both structure and dynamics. Thereby, the generalized Kirkwood g_K-factor plays a central role in establishing this link which is not possible on the basis of molecular hydrodynamics. The decoupling between translational and rotational motion is indicative of the dynamical heterogeneity in ionic liquids.

We present a concept and ray-tracing simulation of a mechanical device that will enable inelastic neutron scattering measurements where the data at energy transfers from a few μeV to several hundred meV can be collected in a single, gapless spectrum. Besides covering 5 orders of magnitude on the energy (time) scale, the device provides data over 2 orders of magnitude on the scattering momentum (length) scale in a single measurement. Such capabilities are geared primarily toward soft and biological matter, where the broad dynamical features of relaxation origin largely overlap with vibration features, thus necessitating gapless spectral coverage over several orders of magnitude in time and space. Furthermore, neutron scattering experiments with such a device are performed with a fixed neutron final energy, which enables measurements, with neutron energy loss in the sample, at arbitrarily low temperatures over the same broad spectral range. This capability is also invaluable in biological and soft matter research, as the variable temperature dependence of different relaxation components allows their separation in the scattering spectra as a function of temperature.

We use the dielectric continuum model to obtain the polar (Fuchs–Kliewer like) interface vibration modes of toroids made of ionic materials either embedded in a different material or in vacuum, with applications to nanotoroids specially in mind. We report the frequencies of these modes and describe the electric potential they produce. We establish the quantum-mechanical Hamiltonian appropriate for their interaction with electric charges. This Hamiltonian can be used to describe the effect of this interaction on different types of charged particles either inside or outside the torus.

The electronic structure and magnetic properties of SrMn_0.5Fe_0.5O₃ powder and films grown on (1 0 0)-SrTiO₃ (STO) and (1 0 0)-LaAlO₃ (LAO) substrates by pulsed laser deposition (PLD) were investigated by temperature dependent magnetization and soft x-ray absorption. The results exhibit characteristics of 3d⁵ Fe³⁺, $\text{3}{{d}^{\text{5}}}\underline{L}\,\text{F}{{\text{e}}^{\text{4}+}}$, and 3d³  +  3d⁴$\underline{L}$ Mn⁴⁺ at room temperature in all samples. However, the features of 3d⁵ Fe³⁺ and 3d³ Mn⁴⁺ increased significantly for SMFO/LAO at 35 K, which also displayed substantial competition between antiferromagnetic and ferromagnetic order well-above the Néel temperature of SrFeO₃ (T_N ~ 134 K). We attributed this to being caused by charge disproportionation resulting from ligand-hole localization, which is more favorable to take place when the sample is under compressive strain.

We analyze the geometry and electronic structure of a series of amorphous Zn–Ir–O systems using classical molecular dynamics followed by density functional theory taking into account two different charge states of Ir (+3 and  +4). The structures obtained consist of a matrix of interconnected metal-oxygen polyhedra, with Zn adopting preferentially a coordination of 4 and Ir a mixture of coordinations between 4 and 6 that depend on the charge state of Ir and its concentration. The amorphous phases display reduced band gaps compared to crystalline ZnIr₂O₄ and exhibit localized states near the band edges, which harm their transparency and hole mobility. Increasing amounts of Ir in the Ir⁴⁺ phases decrease the band gap further while not altering it significantly in the Ir³⁺ phases. The results are consistent with recent transmittance and resistivity measurements.

The orbital symmetry of the band structure of 2H-WSe₂(0 0 0 1) has been investigated by means of angle-resolved photoelectron spectroscopy (ARPES) and density functional theory (DFT). The WSe₂(0 0 0 1) experimental band structure is found, by ARPES, to be significantly different for states of even and odd reflection parities along both the $\rm{\bar \Gamma}$–$\rm{\bar{K}}$ and $\rm{\bar \Gamma}$–$\rm{\bar{M}}$ lines, in good agreement with results obtained from DFT. The light polarization dependence of the photoemission intensities from the top of the valence band for bulk WSe₂(0 0 0 1) is explained by the dominance of W 5${{d}_{{{z}^{2}}}}$ states around the $\rm{\bar \Gamma}$-point and W 5d_xy states around the $\rm{\bar{K}}$-point, thus dominated, respectively, by states of even and odd symmetry, with respect to the $\rm{\bar \Gamma}$–$\rm{\bar{K}}$ line. The splitting of the topmost valence band at $\rm{\bar{K}}$, due to spin–orbit coupling, is measured to be 0.49  ±  0.01 eV, in agreement with the 0.48 eV value from DFT, and prior measurements for the bulk single crystal WSe₂(0 0 0 1), albeit slightly smaller than the 0.513  ±  0.01 eV observed for monolayer WSe₂.

A density functional theory study of the BiS₂ superconductors containing rare-earths: LnO_1−xF_xBiS₂ (Ln  =  La, Ce, Pr, and Nd) is presented. We find that CeO_0.5F_0.5BiS₂ has competing ferromagnetic and weak antiferromagnetic tendencies, the first one corresponding to experimental results. We show that PrO_0.5F_0.5BiS₂ has a strong tendency for magnetic order, which can be ferromagnetic or antiferromagnetic depending on subtle differences in 4f orbital occupations. We demonstrate that NdO_0.5F_0.5BiS₂ has a stable magnetic ground state with weak tendency to order. Finally, we show that the change of rare earth does not affect the Fermi surface, and predict that CeOBiS₂ should display a pressure induced phase transition to a metallic, if not superconducting, phase under pressure.

We calculate magnetic susceptibility of paramagnetic bcc Fe-Mn and Fe-V alloys by two different approaches. The first approach employs the coherent potential approximation (CPA) combined with the dynamical mean-field theory (DMFT). The material-specific Hamiltonians in the Wannier function basis are obtained by density functional theory. In the second approach, we construct supercells modeling the binary alloys and study them using DMFT. Both approaches lead to a qualitative agreement with experimental data. In particular, the decrease of Curie temperature with Mn content and a maximum at about 10 at.% V are well described in units of the Curie temperature of pure iron. In contrast to the Mn impurities, the V ones are found to be antiferromagnetically coupled to Fe atoms. Our calculations for the two-band Anderson–Hubbard model indicate that the antiferromagnetic coupling is responsible for a maximum in the concentration dependence of Curie temperature in Fe-V alloys.

Magnetization, resistivity and ¹¹B, ⁵⁹Co NMR measurements have been performed on the Pauli paramagnet $\text{LaC}{{\text{o}}_{2}}{{\text{B}}_{2}}$, and the superconductors $\text{L}{{\text{a}}_{0.9}}{{\text{Y}}_{0.1}}\text{C}{{\text{o}}_{2}}{{\text{B}}_{2}}$ (${{T}_{\text{c}}}\approx 4.2$ K) and $\text{La}{{\left(\text{C}{{\text{o}}_{0.7}}\text{F}{{\text{e}}_{0.3}}\right)}_{2}}{{\text{B}}_{2}}$ (${{T}_{\text{c}}}\approx 5.8$ K). The site selective NMR experiment reveals the multiband nature of the Fermi surface in these systems. The temperature independent Knight shift and 1/T₁T clearly indicate the absence of correlated low energy magnetic spin-fluctuations in the normal state, which is in contrast to other Fe-based pnictides. The density of states (DOS) of Co 3d electrons has been enhanced in superconducting $\text{L}{{\text{a}}_{0.9}}{{\text{Y}}_{0.1}}\text{C}{{\text{o}}_{2}}{{\text{B}}_{2}}$ and $\text{La}{{\left(\text{C}{{\text{o}}_{0.7}}\text{F}{{\text{e}}_{0.3}}\right)}_{2}}{{\text{B}}_{2}}$ with respect to the non superconducting reference compound $\text{LaC}{{\text{o}}_{2}}{{\text{B}}_{2}}$. The occurrence of superconductivity is related to the DOS enhancement.

Low field magnetoresistance is experimentally studied in a two-dimensional topological insulator (TI) in both diffusive and quasiballistic samples fabricated on top of a wide (14 nm) HgTe quantum well. In all cases a pronounced quasi-linear positive magnetoresistance is observed similar to that found previously in diffusive samples based on a narrow (8 nm) HgTe well. The experimental results are compared with the main existing theoretical models based on different types of disorder: sample edge roughness, nonmagnetic disorder in an otherwise coherent TI and metallic puddles due to locally trapped charges that act like local gate on the sample. The quasiballistic samples with resistance close to the expected quantized values also show a positive low-field magnetoresistance but with a pronounced admixture of mesoscopic effects.

⁵⁷Fe Mössbauer spectra have been recorded from the hexagonal (6H)- and trigonal (15R)- modifications of BaFeO₂F and are compared with those previously recorded from the cubic form of BaFeO₂F. The spectra, recorded over a temperature range from 15 to 650 K show that all of the iron in all the compounds is in the Fe³⁺ state. Spectra from the 6H- and 15R-modifications were successfully fitted with components that were related to the Fe(1) and Fe(2) structural sites in the 6H variant and to the Fe(1), Fe(2) and Fe(3) structural sites in the 15R form. The magnetic ordering temperatures were determined as 597  ±  3 K for 6H-BaFeO₂F and 636  ±  3 K for 15R-BaFeO₂F. These values are surprisingly close to the value of 645  ±  5 K determined for the cubic form. The magnetic interactions in the three forms are compared with a view to explaining this similarity of magnetic ordering temperature.

The nuclear magnetic resonance of ⁵⁹Co was measured over a wide frequency range in a powder sample crushed from a well-characterized single crystal of La–Co co-substituted magnetoplumbite-type strontium ferrite (SrFe₁₂O₁₉), a familiar base material for the ferrite permanent magnet. The simultaneous observation of both high- and low-frequency resonances suggests the coexistence of both high- and low-spin states of the substituted Co or the presence of Co orbital moment at a particular site. The possible presence of trivalent Co was also investigated. The results suggest that the Co atoms are distributed across different crystallographic sites with different local environments, and that the electronic state of Co is much more subtle than the conventional understanding.

We report a detailed study of the magnetic properties of CeCo_0.85Fe_0.15Si under high magnetic fields (up to 16 Tesla) measuring different physical properties such as specific heat, magnetization, electrical resistivity, thermal expansion and magnetostriction. CeCo_0.85Fe_0.15Si becomes antiferromagnetic at ${{T}_{N}}\approx 6.7$ K. However, a broad tail (onset at ${{T}_{X}}\approx 13$ K) in the specific heat precedes that second order transition. This tail is also observed in the temperature derivative of the resistivity. However, it is particularly noticeable in the thermal expansion coefficient where it takes the form of a large bump centered at T_X. A high magnetic field practically washes out that tail in the resistivity. But surprisingly, the bump in the thermal expansion coefficient becomes a well pronounced peak fully split from the magnetic transition at T_N. Concurrently, the magnetoresistance also switches from negative to positive above T_N. The magnetostriction is considerable and irreversible at low temperature ($\frac{\Delta L}{L}(16~T)\sim 4\times {{10}^{-4}}$ at 2 K) when the magnetic interactions dominate. A broad jump in the field dependence of the magnetostriction observed at low T may be the signature of a weak ongoing metamagnetic transition. Taking altogether the results indicate the importance of the lattice effects on the development of the magnetic order in these alloys.

In this work, we study the magnetization behaviors of the classical Ising model on the triangular lattice using Monte Carlo simulations, and pay particular attention to the effect of further-neighbor interactions. Several fascinating spin states are identified to be stabilized in certain magnetic field regions, respectively, resulting in the magnetization plateaus at 2/3, 5/7, 7/9 and 5/6 of the saturation magnetization M_S, in addition to the well-known plateaus at 0, 1/3 and 1/2 of M_S. The stabilization of these interesting orders can be understood as the consequence of the competition between Zeeman energy and exchange energy.