Phosphorus nanoclusters and insight into the formation of phosphorus allotropes

Abstract

Elemental phosphorus possesses a striking variety of allotropes, which we analyze by looking at stable phosphorus clusters. We determine the ground-state structures of Pn clusters in a wide range of...

Lithiation of phosphorus at the nanoscale: a computational study of LinPm clusters

“…Many studies of single-element nanoclusters have shown that compounds with high values of Δ 2 E are indeed more likely to appear in experiments. [48][49][50][51] For multicomponent systems, such as the considered Li n P m clusters, this criterion can be generalized by calculating the energy differences with respect to the number of atoms of different types and taking the lowest value among them:…”

“…and E(n, m) is the total energy of the Li n P m cluster ground state. In our previous studies we applied this approach to various multicomponent systems 38,[52][53][54][55] and found that higher values of Δ 2 min indicate higher abundance of the corresponding clusters or molecules in experiments.…”

“…For example, a similar approach allowed us to identify the most stable structural fragments of 1D-tubular phosphorus nanoclusters. 50 Fig. 1b shows the interpolated map of Δ 2 ext (n, m).…”

Lone Pair Electrons with Weak Nuclear Binding Inducing Sensitive Nonlinear Optical Responses in Phosphorus Clusters

“…The determination of ground-state structures for phosphorus clusters is challenging, particularly for larger clusters with numerous isomers, even with state-of-the-art structural searches. Therefore, for the sake of simplicity, this work selected the most energetically stable structures reported in the literature as the focus was not on determining stable structures. − In the case of some controversial isomers mentioned in the literature (Figure S1), − the system energy was evaluated to identify the ground-state structure of the phosphorus clusters at specific sizes (Table S1). The Supporting Information provides a comprehensive presentation of the results and discussion of the nonlinear optical behaviors of clusters with odd numbers of atoms.…”

Prediction and Rationalization of Abundant C–N–H Molecules in Different Environments

“…In our previous works − we elucidated the stability of the clusters and molecules using criteria that showed great success in the studies of nanoparticles and atomic nuclei (which, like molecules, are finite metastable aggregates of particles). These criteria are based on second-order energy differences and fragmentation energies.…”