We present an ab-initio study of the structural and electronic properties of SnS2 stacked nanosheets using the standard LDA and GGA functionals as well as the newly developed variants of the non-local van der Waals (vdW) exchange correlation functionals, namely vdW-DF-revPBE and vdW-DF2-C09. We have examined different stacking configurations of the two, three and four SnS2 layers. The GGA-PBE functional fails to describe the interlayer binding energies and interlayer spacing of SnS2 nanosheets, while a good agreement is observed between the calculated and available experimental values when the van der Waals corrected functionals are used, mostly the vdW-DF2-C09. It is found that the interlayer interactions in the SnS2 films are not only vdW type but, the overlap of wave functions of neighboring layers have to be taken into account. We have observed a systematic reduction in the band gap with the increase in the number of stacked layers. This can be another way of controlling the band gap of SnS2 nanosheets as required for electronic devices.
The enriched triply noncentral bivariate beta type V distribution
is introduced. This distribution is constructed from independent chi-squared
random variables by using the variables-in-common (or trivariate reduction) ...
In multivariate statistics under normality, the problems of interest are random covariance matrices
(known as Wishart matrices) and "ratios" of Wishart matrices that arise in multivariate analysis of
variance (MANOVA). ...
The product moments of existing and new noncentral bimatrix variate beta distributions with
bounded domain are derived. From these, exact expressions for the distributions of statistics are obtained
by using the Mellin ...