To verify whether attractive metallophilic interactions exist in the dimer-of-dimers [Cu(2)(ophen)(2)](2) (Hophen=1H-[1,10]phenanthrolin-2-one) (1), we designed and synthesized a series of such [M(2)L(2)](2) structures by varying the d(10) metal and/or the ligand (M=Cu(I) or Ag(I), L=ophen or obpy; Hobpy=1H-[2,2']bipyridinyl-6-one), and have successfully obtained three dimers-of-dimers: [Ag(2)(ophen)(2)](2).6 H(2)O (2), [Cu(2)(obpy)(2)](2) (3), and [Ag(2)(obpy)(2)](2).4.5 H(2)O.0.5 DMF (4). X-ray analyses of these structures show that interdimer M-M separations in [Ag(2)-(ophen)(2)](2) (3.199 A) are remarkably shorter than those in [Cu(2)(ophen)(2)](2) (3.595 A). Shorter interdimer M-M separations are found in the structures of [M(2)(obpy)(2)](2) (2.986 and 2.993 A in [Cu(2)(obpy)(2)](2), 3.037 to 3.093 A in [Ag(2)(obpy)(2)](2)), in which the pi systems are smaller than in the complexes with the ophen ligand. Detailed structural comparison of these dimers-of-dimers indicates that the interdimer, face-to-face pi-pi interactions repulse rather than support the interdimer metal-metal attractive interactions. This study also yields qualitative comparison of the strengths between argentophilic, cuprophilic, and face-to-face pi-pi interactions. DFT calculations on the four dimers-of-dimers further support the above deduction. The structure of a trimer-of-dimers [Ag(2)(obpy)(2)](3) (Ag-Ag 3.171 to 3.274 A) is further evidence that the oligomerization of the [M(2)L(2)] molecules is favored by stronger metallophilic and weaker face-to-face pi-pi interactions.

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Selecting the saturated graphene fragment as a model of graphene, we have investigated seven popular density functionals, including ωB97X-D, B97-D, B-LYP-D3, M05-2X, M06-2X, M11-L, and N12, for their performance in describing the adsorption of aromatic molecules on graphene. The best performing functionals are B97-D, B-LYP-D3, and ωB97X-D. M05-2X, M06-2X, and M11-L significantly underestimate the adsorption strengths, while N12 fails completely in this respect. The effects of the basis sets and size of the saturated graphene fragments on the geometries, energies, and properties for the adsorption of aromatic molecules on graphene have also been studied. It was found that the small basis sets such as 6-31G(d) and jun-cc-pVDZ are not suitable for the accurate description of the adsorption of aromatic molecules on graphene. The size of selected graphene fragments has a little effect on both the ωB97X-D and SCS-SAPT0 interaction energies, but the effects of the size of selected graphene fragments on the energy components are significant in some cases of the adsorption of aromatic molecules on graphene. The surprising weakness of electrostatic interactions by F substitution for the adsorption of F-substituted benzenes on graphene was explained using the energy component analysis.

In fractured reservoirs, seismic wave velocity and amplitude depend on frequency and incidence angle. Frequency dependence is believed to be principally caused by the wave‐induced flow of pore fluid at the mesoscopic scale. In recent years, two particular phenomena, i.e., patchy saturation and flow between fractures and pores, have been identified as significant mechanisms of wave‐induced flow. However, these two phenomena are studied separately. Recently, a unified model has been proposed for a porous rock with a set of aligned fractures, with pores and fractures filled with two different fluids. Existing models treat waves propagating perpendicular to the fractures. In this paper, we extend the model to all propagation angles by assuming that the flow direction is perpendicular to the layering plane and is independent of the loading direction. We first consider the limiting cases through poroelastic Backus averaging, and then we obtain the five complex and frequency‐dependent stiffness values of the equivalent transversely isotropic medium as a function of the frequency. The numerical results show that, when the bulk modulus of the fracture‐filling fluid is relatively large, the dispersion and attenuation of P‐waves are mainly caused by fractures, and the values decrease as angles increase, almost vanishing when the incidence angle is 90° (propagation parallel to the fracture plane). While the bulk modulus of fluid in fractures is much smaller than that of matrix pores, the attenuation due to the “partial saturation” mechanism makes the fluid flow from pores into fractures, which is almost independent of the incidence angle.