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Register a new userTheory of Small Para-Hydrogen Clusters: Magic Numbers and Superfluid Sizes
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The interplay between magic number stabilities and superfluidity of small para-hydrogen clusters with sizes $N = 5$ to 40 and temperatures $0.5 K leq T leq 4.5 $K is explored with classical and quantum Path Integral Monte Carlo calculations. Clusters with $N < 26$ and T $leq 1.5 K$ have large superfluid fractions even at the stable magic numbers 13, 19, and 23. In larger clusters, superfluidity is quenched especially at the magic numbers 23, 26, 29, 32, and 37 while below 1 K, superfluidity is recovered for the pairs $(27,28)$, $(30,31)$, and $(35,36)$. For all clusters superfluidity is localized at the surface and correlates with long exchange cycles involving loosely bound surface molecules.
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We present a systematic study of the photo-absorption spectra of various Si$_{n}$H$_{m}$ clusters (n=1-10, m=1-14) using the time-dependent density functional theory (TDDFT). The method uses a real-time, real-space implementation of TDDFT involving full propagation of the time dependent Kohn-Sham equations. Our results for SiH$_{4}$ and Si$_{2}$H$_{6}$ show good agreement with the earlier calculations and experimental data. We find that for small clusters (n<7) the photo-absorption spectrum is atomic-like while for the larger clusters it shows bulk-like behaviour. We study the photo-absorption spectra of silicon clusters as a function of hydrogenation. For single hydrogenation, we find that in general, the absorption optical gap decreases and as the number of silicon atoms increase the effect of a single hydrogen atom on the optical gap diminishes. For further hydrogenation the optical gap increases and for the fully hydrogenated clusters the optical gap is larger compared to corresponding pure silicon clusters.
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Using a hydrogen molecule as a test system we demonstrate how to compute the effective potential according to the formalism of the new density functional theory (DFT), in which the basic variable is the set of spherically averaged densities instead of the total density, used in the traditional DFT. The effective potential together the external potential, nuclear Coulomb potential, can be substituted in the Schrodinger like differential equation to obtain the spherically averaged electron density of the system. In the new method instead of one three-dimensional low symmetry equation one has to solve as many spherically symmetric equations as there are atoms in the system.
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