Molecular electric moments calculated by using natural orbital functional theory

Ultrapermeable 2D-channeled graphene-wrapped zeolite molecular sieving membranes for hydrogen separation

The efficient separation of hydrogen from methane and light hydrocarbons for clean energy applications remains a technical challenge in membrane science. To address this issue, we prepared a graphene-wrapped MFI (G-MFI) molecular-sieving membrane for the ultrafast separation of hydrogen from methane at a permeability reaching 5.8 × 10⁶ barrers at a single gas selectivity of 245 and a mixed gas selectivity of 50. Our results set an upper bound for hydrogen separation. Efficient molecular sieving comes from the subnanoscale interfacial space between graphene and zeolite crystal faces according to molecular dynamic simulations. The hierarchical pore structure of the G-MFI membrane enabled rapid permeability, indicating a promising route for the ultrafast separation of hydrogen/methane and carbon dioxide/methane in view of energy-efficient industrial gas separation.

An In-Situ Neutron Diffraction and DFT Study of Hydrogen Adsorption in a Sodalite-Type Metal-Organic Framework, Cu-BTTri

Herein we present a detailed study of the hydrogen adsorption properties of Cu-BTTri, a robust crystalline metal-organic framework containing open metal-coordination sites. Diffraction techniques, carried out on the activated framework, reveal a structure that is different from what was previously reported. Further, combining standard hydrogen adsorption measurements with in-situ neutron diffraction techniques provides molecular level insight into the hydrogen adsorption process. The diffraction experiments unveil the location of four D2 adsorption sites in Cu-BTTri and shed light on the structural features that promote hydrogen adsorption in this material. Density functional theory (DFT), used to predict the location and strength of binding sites, corroborate the experimental findings. By decomposing binding energies in different sites in various energetic contributions, we show that van der Waals interactions play a crucial role, suggesting a possible route to enhancing the binding energy around open metal coordination sites.

The correct and unusual coordinate transformation rules for electromagnetic quadrupoles

Despite being studied for over a century, the use of quadrupoles have been limited to Cartesian coordinates in flat space-time due to the incorrect transformation rules used to define them. Here the correct transformation rules are derived, which are particularly unusual as they involve second derivatives of the coordinate transformation and an integral. Transformations involving integrals have not been seen before. This is significantly different from the familiar transformation rules for a dipole, where the components transform as tensors. It enables quadrupoles to be correctly defined in general relativity and to prescribe the equations of motion for a quadrupole in a coordinate system adapted to its motion and then transform them to the laboratory coordinates. An example is given of another unusual feature: a quadrupole which is free of dipole terms in polar coordinates has dipole terms in Cartesian coordinates. It is shown that dipoles, electric dipoles, quadrupoles and electric quadrupoles can be defined without reference to a metric and in a coordinates-free manner. This is particularly useful given their complicated coordinate transformation.

Analytic gradients for natural orbital functional theory

The analytic energy gradients with respect to nuclear motion are derived for the natural orbital functional (NOF) theory. The resulting equations do not require resorting to linear-response theory, so the computation of NOF energy gradients is analogous to gradient calculations at the Hartree-Fock level of theory. The structures of 15 spin-compensated systems, composed of first- and second-row atoms, are optimized employing the conjugate gradient algorithm. As functionals, two orbital-pairing approaches were used, namely, the fifth and sixth Piris NOFs (PNOF5 and PNOF6). For the latter, the obtained equilibrium geometries are compared with coupled cluster singles and doubles calculations and accurate empirical data.