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The molecular dipole polarizability describes the tendency of a molecule to change its dipole moment in response to an applied electric field. This quantity governs key intra- and intermolecular interactions, such as induction and dispersion; plays a vital role in determining the spectroscopic signatures of molecules; and is an essential ingredient in polarizable force fields. Compared with other ground-state properties, an accurate prediction of the molecular polarizability is considerably more difficult, as this response quantity is quite sensitive to the underlying electronic structure description. In this work, we present highly accurate quantum mechanical calculations of the static dipole polarizability tensors of 7,211 small organic molecules computed using linear response coupled cluster singles and doubles theory (LRCCSD). Using a symmetry-adapted machine-learning approach, we demonstrate that it is possible to predict the LR-CCSD molecular polarizabilities of these small molecules with an error that is an order of magnitude smaller than that of hybrid density functional theory (DFT) at a negligible computational cost. The resultant model is robust and transferable, yielding molecular polarizabilities for a diverse set of 52 larger molecules (including challenging conjugated systems, carbohydrates, small drugs, amino acids, nucleobases, and hydrocarbon isomers) at an accuracy that exceeds that of hybrid DFT. The atom-centered decomposition implicit in our machine-learning approach offers some insight into the shortcomings of DFT in the prediction of this fundamental quantity of interest.

Invariance under time translation (or stationarity) is probably one of the most important assumptions made when investigating electromagnetic phenomena. Breaking this assumption is expected to open up novel possibilities and result in exceeding conventional limitations. However, to explore the field of time-varying electromagnetic structures, we primarily need to contemplate the fundamental principles and concepts from a nonstationarity perspective. Here, we revisit one of those key concepts: the polarizability of a small particle, assuming that its properties vary in time. We describe the creation of induced dipole moment by external fields in a nonstationary, causal way, and introduce a complex-valued function, called temporal complex polarizability, for elucidating a nonstationary Hertzian dipole under time-harmonic illumination. This approach can be extended to any subwavelength particle exhibiting electric response. In addition, we also study the classical model of the polarizability of an oscillating electron using the equation of motion whose damping coefficient and natural frequency are changing in time. Next, we theoretically derive the effective permittivity corresponding to time-varying media (comprising free or bound electrons, or dipolar meta-atoms) and explicitly show the differences with the conventional macroscopic Drude–Lorentz model. This paper will hopefully pave the road towards better understanding of nonstationary scattering from small particles and homogenization of time-varying materials, metamaterials, and metasurfaces.

The coarse-grained Martini force field is widely used in biomolecular simulations. Here we present the refined model, Martini 3 (http://cgmartini.nl), with an improved interaction balance, new bead types and expanded ability to include specific interactions representing, for example, hydrogen bonding and electronic polarizability. The updated model allows more accurate predictions of molecular packing and interactions in general, which is exemplified with a vast and diverse set of applications, ranging from oil/water partitioning and miscibility data to complex molecular systems, involving protein–protein and protein–lipid interactions and material science applications as ionic liquids and aedamers.Martini 3.0 is an updated and reparametrized force field for coarse-grained molecular dynamics simulations with new bead types and an expanded ability to model molecular packing and interactions.

The polarizability of twisted bilayer graphene, due to the combined effect of electron–hole pairs, plasmons, and acoustic phonons, is analyzed. The screened Coulomb interaction allows for the formation of Cooper pairs and superconductivity in a significant range of twist angles and fillings. The tendency toward superconductivity is enhanced by the coupling between longitudinal phonons and electron–hole pairs. Scattering processes involving large momentum transfers, Umklapp processes, play a crucial role in the formation of Cooper pairs. The magnitude of the superconducting gap changes among the different pockets of the Fermi surface.

To use natural gas as a feedstock alternative to coal and oil, its main constituent, methane, needs to be isolated with high purity 1 . In particular, nitrogen dilutes the heating value of natural gas and is, therefore, of prime importance for removal 2 . However, the inertness of nitrogen and its similarities to methane in terms of kinetic size, polarizability and boiling point pose particular challenges for the development of energy-efficient nitrogen-removing processes 3 . Here we report a mixed-linker metal–organic framework (MOF) membrane based on fumarate ( fum ) and mesaconate ( mes ) linkers, Zr- fum 67 - mes 33 - fcu -MOF, with a pore aperture shape specific for effective nitrogen removal from natural gas. The deliberate introduction of asymmetry in the parent trefoil-shaped pore aperture induces a shape irregularity, blocking the transport of tetrahedral methane while allowing linear nitrogen to permeate. Zr- fum 67 - mes 33 - fcu -MOF membranes exhibit record-high nitrogen/methane selectivity and nitrogen permeance under practical pressures up to 50 bar, removing both carbon dioxide and nitrogen from natural gas. Techno-economic analysis shows that our membranes offer the potential to reduce methane purification costs by about 66% for nitrogen rejection and about 73% for simultaneous removal of carbon dioxide and nitrogen, relative to cryogenic distillation and amine-based carbon dioxide capture. A metal–organic framework membrane based on fumarate and mesaconate linkers is shown to have a pore aperture shape that enables efficient and cost-effective removal of nitrogen and carbon dioxide from methane.

Polarizability exaltation is typical for (C60)n nanostructures. It relates to the ratio between the mean polarizabilities of (C60)n and C60: the first one is higher than the n-fold mean polarizability of the original fullerene. This phenomenon is used in the design of novel fullerene compounds and the understanding of its properties but still has no chemical rationalization. In the present work, we studied the distributed polarizability of (C60)2 and isomeric (C60)3 nanoaggregates with the density functional theory method. We found that polarizability exaltation increases with the size of the nanostructure and originates from the response of the sp2-hybridized carbon atoms to the external electric field. The highest contributions to the dipole polarizability of (C60)2 and (C60)3 come from the most remote atoms of the marginal fullerene cores. The sp3-hybridized carbon atoms of cyclobutane bridges negligibly contribute to the molecular property. A similar major contribution to the molecular polarizability from the marginal atoms is observed for related carbon nanostructures isomeric to (C60)2 (tubular fullerene and nanopeanut). Additionally, we discuss the analogy between the polarizability exaltation of covalently bonded (C60)n and the increase in the polarizability found in experiments on fullerene nanoclusters/films as compared with the isolated molecules.

We present detailed measurements of the double-layer capacitance of the Pt(111)–electrolyte interface close to the potential of zero charge (PZC) in the presence of several different electrolytes consisting of anions and cations that are considered to be nonspecifically adsorbed. For low electrolyte concentrations, we show strong deviations from traditional Gouy–Chapman–Stern (GCS) behavior that appear to be independent of the nature of the electrolyte ions. Focusing on the capacitance further away from PZC and the trends for increasing ion concentration, we observe ion-specific capacitance effects that appear to be related to the size or hydration strength of the ions. We formulate a model for the structure of the electric double layer of the Pt(111)–electrolyte interface that goes significantly beyond the GCS theory. By combining two existing models, namely, one capturing the water reorganization on Pt close to the PZC and one accounting for an attractive ion–surface interaction not included in the GCS model, we can reproduce and interpret the main features the experimental capacitance of the Pt(111)–electrolyte interface. The model suggests a picture of the double layer with an increased ion concentration close to the interface as a consequence of a weak attractive ion–surface interaction, and a changing polarizability of the Pt(111)–water interface due to the potential-dependent water adsorption and orientation.

Optical anisotropy is a fundamental building block for linear and nonlinear optical components such as polarizers, wave plates, and phase-matching elements1–4. In solid homogeneous materials, the strongest optical anisotropy is found in crystals such as calcite and rutile5,6. Attempts to enhance anisotropic light–matter interaction often rely on artificial anisotropic micro/nanostructures (form birefringence)7–11. Here, we demonstrate rationally designed, giant optical anisotropy in single crystals of barium titanium sulfide (BaTiS3). This material shows an unprecedented, broadband birefringence of up to 0.76 in the mid- to long-wave infrared, as well as a large dichroism window with absorption edges at 1.6 μm and 4.5 μm for light with polarization along two crystallographic axes on an easily accessible cleavage plane. The unusually large anisotropy is a result of the quasi-one-dimensional structure, combined with rational selection of the constituent ions to maximize the polarizability difference along different axes.

In this perspective, we review the theory and methodology of the derivation of force fields (FFs), and their validity, for molecular simulations, from their inception in the second half of the twentieth century to the improved representations at the end of the century. We examine the representations of the physics embodied in various force fields, their accuracy and deficiencies. The early days in the 1950s and 60s saw FFs first introduced to analyze vibrational spectra. The advent of computers was soon followed by the first molecular mechanics machine calculations. From the very first papers it was recognized that the accuracy with which the FFs represented the physics was critical if meaningful calculated structural and thermodynamic properties were to be achieved. We discuss the rigorous methodology formulated by Lifson, and later Allinger to derive molecular FFs, not only obtain optimal parameters but also uncover deficiencies in the representation of the physics and improve the functional form to account for this physics. In this context, the known coupling between valence coordinates and the importance of coupling terms to describe the physics of this coupling is evaluated. Early simplified, truncated FFs introduced to allow simulations of macromolecular systems are reviewed and their subsequent improvement assessed. We examine in some depth: the basis of the reformulation of the H-bond to its current description; the early introduction of QM in FF development methodology to calculate partial charges and rotational barriers; the powerful and abundant information provided by crystal structure and energetic observables to derive and test all aspects of a FF including both nonbond and intramolecular functional forms; the combined use of QM, along with crystallography and lattice energy calculations to derive rotational barriers about ɸ and ψ; the development and results of methodologies to derive “QM FFs” by sampling the QM energy surface, either by calculating energies at hundreds of configurations, or by describing the energy surface by energies, first and second derivatives sampled over the surface; and the use of the latter to probe the validity of the representations of the physics, reveal flaws and assess improved functional forms. Research demonstrating significant effects of the flaws in the use of the improper torsion angle to represent out of plane deformations, and the standard Lorentz–Berthelot combining rules for nonbonded interactions, and the more accurate descriptions presented are also reviewed. Finally, we discuss the thorough studies involved in deriving the 2nd generation all-atom versions of the CHARMm, AMBER and OPLS FFs, and how the extensive set of observables used in these studies allowed, in the spirit of Lifson, a characterization of both the abilities, but more importantly the deficiencies in the diagonal 12-6-1 FFs used. The significant contribution made by the extensive set of observables compiled in these papers as a basis to test improved forms is noted. In the following paper, we discuss the progress in improving the FFs and representations of the physics that have been investigated in the years following the research described above.