First-principles study of the binding energy between nanostructures and its scaling with system size

Abstract

The equilibrium van der Waals binding energy is an important factor in the design of materials and devices. However, it presents great computational challenges for materials built up from nanostructures. Here we investigate the binding-energy scaling behavior from first-principles calculations. We show that the equilibrium binding energy per atom between identical nanostructures can scale up or down with nanostructure size, but can be parametrized for large N with an analytical formula (in meV/atom), E b /N = a + b/N + c/N 2 + d/N 3 , where N is the number of atoms in a nanostructure and a, b, c, and d are fitting parameters, depending on the properties of a nanostructure. The formula is consistent with a finite large-size limit of binding energy per atom. We find that there are two competing factors in the determination of the binding energy: Nonadditivities of van der Waals coefficients and center-to-center distance between nanostructures. To decode the detail, the nonadditivity of the static multipole polarizability is investigated from an accurate spherical-shell model. We find that the higher-order multipole polarizability displays ultrastrong intrinsic nonadditivity, no matter if the dipole polarizability is additive or not.

van der Waals density functional with corrected C6 coefficients

“…We do not expect the improvement of C 6 coefficients to carry over to large nanostructures where local-field effects can be important, such as fullerenes, [54][55][56] which would require higher-order terms in S within vdW-DF. However, at binding separations such higher-order terms are generally less crucial, at least within vdW-DF, 30,57 as multipole effects are described to second order in S. Moreover, vdW-DF includes non-additive effects originating from changes in the electronic density. 58 Drawing attention to the possibility of adjusting h(y) within vdW-DF introduces a measure of flexibility that so far has been missing in standard vdW-DF.…”

Friends or strangers? Attempts at reactivating buyer–supplier relationships

“…This is documented, for example, in a previous study of parallel semiconducting nanotubes [53]. The enhancement in vdW-DF-cx attraction cannot stretch as far as in TS-MBD because the kernel contribution from an electron-XC-hole pair, at r 1 and r 2 , eventually approaches a form decaying like |r 1 − r 2 | −6 , references [4,105]. The consequence is that vdW-DF-cx and vdW-DF always have an asymptotic vdW interaction energy that decays like d −5 for parallel wires.…”

“…Depending of the intra-wire carbon-carbon separation l C-C , this problem allows a simple tuning between an insulating nature (with dimerization) and a conducting nature (with no dimerization) within a tight-binding DFT model, by simply varying the intra-wire carbon-carbon separation [246]. This leads in turn to an elegant analysis of the impact of 1D conduction on the long-range component of the vdW attraction [105,202,[246][247][248][249][250][251][252][253][254]. Reference [246] provides the analysis within a TS-based many-body-dispersion (MBD) method [80,81], denoted TS-MBD.…”

“…So far the vdW-DF-cx version has proven itself useful and accurate for descriptions of a range of dense and sparse-matter problems. Successful applications include the study of traditional bulk-matter cohesion, structure, thermo-physical properties [9,45,94,95], and vacancy formation [96], as well as of binding, structure, vibrations, polarization, elastic properties, phase transitions, defects, and dynamics in molecular, polymer, and layered materials [45,[97][98][99][100][101][102][103][104][105][106][107][108][109][110][111][112]. This is, for example, relevant for development of ionic liquids, batteries, thermo-electrics, and organic solar-cell materials [98,[113][114][115][116][117][118].…”

Atomic Vacancy Defect, Frenkel Defect and Transition Metals (Sc, V, Zr) Doping in Ti4N3 MXene Nanosheet: A First-Principles Investigation

“…In Table 2, the binding energies of Ti 4 N 3 , Ti 4 N 3 -Ti and Ti 4 N 3 -N systems are listed. The binding energy can be defined as follows [49]:…”