Electronic excitation energies of smallZniSiclusters

Abstract

Improvements in the characterization of II-VI compound-based solar cells, and a recent experimental characterization of small clusters and nanoparticles, make the study of small II-VI clusters very interesting. In a previous work the global minima of small ${\mathrm{Zn}}_{i}{\mathrm{S}}_{i}$ clusters $i=1--9$ were characterized. In order to calculate the excitation energies of these clusters, basically two methods are available: on the one hand, the traditionally used configuration interaction singles (CIS) theory, and on the other hand the recently developed time dependent density-functional theory (TDDFT). Calculations of the excitation energies of small ${\mathrm{Zn}}_{i}{\mathrm{S}}_{i}$ clusters, $i=1--3,$ were performed with both methods in an attempt to find the most appropriate one. The relativistic compact effective core potentials and shared-exponent basis set of Stevens, Krauss, Basch and Jasien (SKBJ) [Can J. Chem. 70, 612 (1992)], systematically enlarged with extra functions, were used in this work. These larger basis sets are labeled according to the number of added functions. Thus, as an example, if two extra $\mathrm{sp}$ functions and one d function are added, the final basis set is denoted $\mathrm{SKBJ}(2sp1d).$ These basis sets were combined with both methods. In this way the most appropriate method and basis-set combination was chosen, for further excitation energy calculations on larger ${\mathrm{Zn}}_{i}{\mathrm{S}}_{i}$ clusters. It was seen in both methods that more than one polarization function was needed. Combined with the CIS method, the smallest basis yielding good results was $\mathrm{SKBJ}(1sp2d3f),$ and with TDDFT $\mathrm{SKBJ}(1sp2d2f).$ In the CIS case, this basis was too large even for ${\mathrm{Zn}}_{3}{\mathrm{S}}_{3}.$ In addition to this, in the literature TDDFT was seen to provide a better description of the excitations, and therefore a $\mathrm{TDDFT}\ensuremath{-}\mathrm{SKBJ}(1sp2d2f)$ combination was chosen for further calculations. However, due to the fact that no experimental data are available, some results confirming the TDDFT results are necessary, in this way ensuring that our choice is the correct one. Multireference configuration interaction calculations, combined with a triple-\ensuremath{\zeta} double polarization (TZ2P) basis set, were carried out for ${\mathrm{Zn}}_{i}{\mathrm{S}}_{i}, i=1$ and 2. For $i=3,$ a TZ basis without polarization was used; otherwise the limit of 255 on the basis function number was exceeded. These results were clearly in agreement with the TDDFT results, and confirm our previous choice.