We develop convergence acceleration procedures that enable a gradient descent-type iteration method to efficiently simulate Hartree-Fock equations for many particles interacting both with each other and with an external potential. Our development focuses on three aspects: (i) optimization of a parameter in the preconditioning operator; (ii) adoption of a technique that eliminates the slowest-decaying mode to the case of many equations (describing many particles); and (iii) a novel extension of the above technique that allows one to eliminate multiple modes simultaneously. We illustrate performance of the numerical method for the two-dimensional model of the first layer of helium atoms above a graphene sheet.
View Article and Find Full Text PDFIn the present study, low molecular weight cyclic polyglycidol is used as a macroinitiator for hypergrafting glycidol and producing cyclic graft hyperbranched polyglycerol (cPG-g-hbPG) in the molecular weight range of 10-10 g mol. Linear graft hyperbranched polyglycerol (linPG-g-hbPG) and hyperbranched polyglycerol (hbPG) are prepared as reference samples. This creates a family of hbPG structures with cyclic, linear, and star cores, allowing to evaluate their properties in solution and in bulk.
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