From Zero to Infinity: Customized Atomistic Calculations for Crystalline Solids —Applications to Graphene and Diamond

Toward size-dependent thermodynamics of nanoparticles from quantum chemical calculations of small atomic clusters: a case study of (B2O3)n

“…184 The energy E g characterizes the metallic ( e.g. , electroconductivity) and optoelectronic 16,24,132,187–189 properties of clusters as well.…”

“…However, in the case of a substantial departure from sphericity and with a change in the packing pattern with n increase, the dependence of the characteristic in question on the number of atoms may be more complex. 1,3,132 For instance, the expression for F S in eqn (8) can be generalized to the form F S ( n ) = 4( x surf n −1/3 + x edge n −2/3 + x corn n −1 )to include, besides the surface term involving x surf coefficient, contributions from atoms with other coordinative environments than the cluster surface, namely, edge and corner atoms with corresponding x edge and x corn factors (see ref. 9 and 19 for details).…”

“…For instance, for planar structures (as graphene and related 2D materials) the main power exponent should be −1/2, rather than −1/3 as for three-dimensional ones. 19,132…”

Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

“…To remedy this Zdetsis A. D. , Bandgaps of Atomically precise AGNRs and Occam's Razor problem we have recently suggested 25 to fit the calculated ΔΕac as a function of L efficiently and transparently 1,25 to a polynomial of the form ΔΕac(L)=A+B×L -C , where the value A corresponds to the gap at infinity, ΔΕac(∞)=A, and the constant C to some short of effective ("fractal") dimensionality (here equal to 1.20). 1,25 As we can see in the inset in Fig. 2(b), the projected ΔΕac value is 1.07 eV, which is also verified by the TDDFT result ΔΕac =1.01 eV (see Fig.…”

Bandgaps of Atomically Precise Graphene Nanoribbons and Occam’s Razor

“…[2][3] Comparing the behavior of the "bulk gap" in Figs. problem we have recently suggested 24 to fit the calculated ΔΕac as a function of L efficiently and transparently 1,24 to a polynomial of the form ΔΕac(L)=A+B×L -C , where the value A corresponds to the gap at infinity, ΔΕac(∞)=A, and the constant C to some short of effective ("fractal") dimensionality (here equal to 1.20). 1,24 As we can see in the inset in Fig.…”