Entropic Effects on the Free Energies of Clusters in Silane Plasmas Prasenjit Seal, Jingjing Zheng, and Donald G. Truhlar* Department of Chemistry, Supercomputing Institute, and Chemical Theory Center, University of Minnesota, Minneapolis, Minnesota 55455-0431, United States * S Supporting Information ABSTRACT: The present work demonstrates the importance of entropic effects on the thermodynamics of branched open chain silicon hydride clusters (Si n H m and Si n H m − ). These clusters are important constituents in nanodusty silane plasmas. We include all categories of such single-bonded species for n = 5 and 6, namely silyl radicals, silyl anions, silylenes and silylene anions, and silanes. We calculated the statistical mechanical partition functions by employing Kohn−Sham density functional theory with the multistructural method for torsional anharmonicity to estimate thermody- namic quantities, in particular Gibbs free energy, enthalpy, entropy, and heat capacity. For each species we included contributions from all conformational structures of all possible isomers, and we calculated the thermodynamic propeties in three ways, namely by using the multistructural quasiharmonic approximation, the multistructural method with uncoupled torsional potential anharmonicity, and the multistructural method with coupled torsional potential anharmonicity. Our results show that the entropic effects are large and are primarily due to multistructural effects, although torsional potential anharmonicities are not negligible. We find that the multiple-structure effect, which is always greater than unity, is not only very large (as large as a factor of 592) but also very isomer-dependent, so that free energy differences between isomers can be greatly affected. The torsional potential effect is relatively smaller on average but certainly not negligible; it varies from a factor of 0.2 to 1.4. 1. INTRODUCTION Silane plasmas are important in semiconductor processing, 1−4 and understanding their thermodynamics is a prerequisite for rational process design. Plasmas containing very small particles (often called nanodusty plasmas because of the particle size) are of paramount interest for this task. The most important mechanistic step that requires a better understanding in nanodusty plasmas is nucleation. It is well-known that silicon hydride anions are trapped by an ambipolar potential in plasmas, 4 and such anions are believed to be very important in the nucleation process because of their long lifetime in plasmas. It has been observed that particle formation occurred as long as the anions were trapped in the plasma and that, unlike cationic and neutral clusters, the anions can grow to large sizes (several tens of Si atoms) in silane plasmas. 3,5,6 There are numerous studies in the literature focusing on silicon hydride clusters of various sizes. Silicon-containing anionic systems have been studied both theoretically and experimentally. 7−13 Although the literature has many studies of silicon hydrides, researchers focused their attention mainly on the electron affinities, 7−11 and broader and more detailed estimation of thermodynamic quantities like Gibbs free energies, heat capacities, or the multiple-structure entropies have not been reported. Moreover, there are no explorations of the role of multiple conformational structures or entropies of these systems. Another interesting point is that none of these earlier studies considers different isomers and their corresponding conformational structures for a particular Si n H m and Si n H m − pair. Here we will examine the effect of multiple structures and torsional potential anharmonicity in determining the thermody- namic properties of all possible isomers of these clusters for the pentameric and hexameric cases (n = 5 and 6). We will especially enumerate the effect of conformational entropy on the thermo- chemistry of these branched clusters. We use the internal-coordinate multistructural (MS) approx- imation for torsional (T) anharmonicity, 14,15 which has been used previously for a variety of systems 16−28 including silanes, hydrocarbons, and other alicyclic compounds like alcohols and aldehydes. In the present study, we employed two versions of the multistructural anharmonicity (MS-T) method, in particular the recent MS-T(C) method 14 based on the coupled torsional potential and the earlier MS-T(U) method, 13 which is based on uncoupled torsional potential. In the article itself, results are given mainly for the MS-T(C) method and at a limited set of temperatures. However, a few results with the quasiharmonic approximation, with uncoupled torsional potential anharmonicity, and with the single-structure approximation are given for comparison. The Supporting Information gives full sets of results Received: January 28, 2015 Revised: April 12, 2015 Article pubs.acs.org/JPCC © XXXX American Chemical Society A DOI: 10.1021/acs.jpcc.5b00923 J. Phys. Chem. C XXXX, XXX, XXX−XXX