Van der Waals interactions in selected allotropes of phosphorus

Abstract

Selected allotropes of phosphorus are investigated by different levels of density functional theory (DFT) calculations to evaluate the relative stability orders with a special focus on the role of van der Waals interactions. Phosphorus is an excellent reference system with a large number of allotropes. Starting from low-dimensional molecular (0D, white P) and polymer structures (1D, P nanorods) to layered (2D, black P) and tubular structures (2D and 3D, crystalline forms of red P), covalent structure motifs are interconnected by van der Waals interactions. They are a key factor for the correct energetic description of all P allotropes. A comparative study is carried out within the local density approximation (LDA) and the generalized gradient approximation (GGA), with and without implementation of a dispersion correction by Grimme (GGA-D2). Our intention is to achieve a reasonable agreement of our calculations with experimental data, the plausibility of energy values, and the treatment of long-range interactions. The effect of van der Waals interactions is exemplified for the interlayer distances of black phosphorous and its electronic structure.

An Elemental Phosphorus Photocatalyst with a Record High Hydrogen Evolution Efficiency

“…The electronic structure of fibrous P was first investigated by Ruck et al . On the base of his crystal structure, we carry out the theoretical calculation to study the band structure of fibrous P. Van der Waals correction (Grimme d2) is introduced in the calculations . (Figure a,b).…”

Black Phosphorus Rediscovered: From Bulk Material to Monolayers

“…[3] Them ost common and reactive form is the metastable white phosphorus with tetrahedral P 4 molecules,w hich was originally discovered by Henning Brand in 1669. Thelowdimensional molecular structures (0D,w hite phosphorus) as well as the polymer structures (1D,p hosphorus nanorods), the layered (2D,B P), and tubular structures (2D and 3D, crystalline forms of red phosphorus) contain covalent structure motifs that are interconnected by van der Waals interactions.…”

“…Thelowdimensional molecular structures (0D,w hite phosphorus) as well as the polymer structures (1D,p hosphorus nanorods), the layered (2D,B P), and tubular structures (2D and 3D, crystalline forms of red phosphorus) contain covalent structure motifs that are interconnected by van der Waals interactions. [3,5] White phosphorus is the starting material for all the other phosphorus modifications.I ti sp roduced in millions of tons per year,i s highly reactive,t oxic, and great care must be taken when handling it. [4] Today three modifications of white phosphorus are known (a-, b-, and g-P 4 ).…”

Periodic and fragment models based on the local correlation approach

“…The effectiveness of the HL/LL protocol (section 2.6), based on the embedding models of sections 2.2–2.4 and the role of screening is studied on the interaction between the phosphorene sheets in a phosphorene bilayer (Figure a) and adsorption of a water monolayer on 2D silica (Figure b). Both black phosphorus (Bachhuber et al, ; Bachhuber et al, ; Cascella, Lin, Tavernelli, & Rothlisberger, ; Castellanos‐Gomez, ; Kim, ; Kou, Chen, & Smith, ; Li et al, ; Li et al, ; Liu et al, ; Qiao, Kong, Hu, Yang, & Ji, ; Sansone et al, ; Schütz et al, ; Shulenburger et al, ; Tran, Soklaski, Liang, & Yang, ; Wu, Fu, Zhou, Yao, & Zeng, ; Yang et al, ) which is a small gap semiconductor, and 2D silica (Björkman et al, ; Burson, Büchner, Heyde, & Freund, ; Huang et al, ; Lichtenstein et al, ; Lichtenstein, Heyde, & Freund, ; Löffler et al, ; Schlexer, Pacchioni, Wlodarczyk, & Sauer, ; Tosoni, Civalleri, & Ugliengo, ; Yu et al, ), an insulator, are promising systems from the technological point of view and are extensively studied experimentally and theoretically.…”