Automatically generated Coulomb fitting basis sets: design and accuracy for systems containing H to Kr

For intermediate sized chemical systems the use of an auxiliary basis set (ABS) to fit the charge density provides a useful means of accelerating the performance of various quantum chemical methods. As a consequence much effort has been devoted to the design of various ABSs. This paper explores a fundamentally new approach where the ABS is created dynamically based on the specific orbital basis set (OBS) being used. The new approach includes a parameter that is used to coalesce candidate fitting functions together but which can also be used to provide some coarse grain control over the number of functions in the ABS. The accuracy of the new automatically generated ABS (auto-ABS) is systemically studied for a variety of small systems containing the elements H-Kr. Errors in the Coulomb energy computed using auto-ABS and with a variety of OBSs are shown to be small compared to errors in the Hartree-Fock energy due to incompleteness in the OBS. In contrast to fixed size ABSs, the use of auto-ABS is shown to lead to smaller errors as the size (quality) of the OBS is expanded. The performance of auto-ABS is also compared with the use of the recently proposed universal fitting sets [Weigend, Phys. Chem. Chem. Phys. 8, 1057 (2006)] for 180 compounds containing atoms from H to Kr.This work is funded by the Australian Research Council Linkage Grant Nos. LP0347178 and LP0774896, and is in association with Gaussian Inc. and Sun Microsystems

Resolving and Tuning Mechanical Anisotropy in Black Phosphorus via Nanomechanical Multimode Resonance Spectromicroscopy

Black phosphorus (P) has emerged as a layered semiconductor with a unique crystal structure featuring corrugated atomic layers and strong in-plane anisotropy in its physical properties. Here, we demonstrate that the crystal orientation and mechanical anisotropy in free-standing black P thin layers can be precisely determined by spatially resolved multimode nanomechanical resonances. This offers a new means for resolving important crystal orientation and anisotropy in black P device platforms in situ beyond conventional optical and electrical calibration techniques. Furthermore, we show that electrostatic-gating-induced straining can continuously tune the mechanical anisotropic effects on multimode resonances in black P electromechanical devices. Combined with finite element modeling (FEM), we also determine the Young's moduli of multilayer black P to be 116.1 and 46.5 GPa in the zigzag and armchair directions, respectively.Comment: Main Text: 13 Pages, 4 Figures; Supplementary Information: 5 Pages, 2 Figures, 2 Table

A new metric for rotating charged Gauss-Bonnet black holes in AdS spaces

This paper presents a new metric for slowly rotating charged Gauss-Bonnet black holes in higher dimensional anti-de Sitter spaces. Taking the angular momentum parameter $a$ up to second order, the slowly rotating charged black hole solutions are obtained by working directly in the action.Comment: 11 pages and accepted by Chin. Phys.

Shape effect on ice melting in flowing water

Iceberg melting is a critical factor for climate change, contributing to rising sea levels and climate change. However, the shape of an iceberg is an often neglected aspect of its melting process. Our study investigates the influence of different ice shapes and ambient flow velocities on melt rates by conducting direct numerical simulations. Our study focuses on the ellipsoidal shape, with the aspect ratio as the control parameter. It plays a crucial role in the melting process, resulting in significant variations in the melt rate between different shapes. Without flow, the optimal shape for a minimal melt rate is the disk (2D) or sphere (3D), due to the minimal surface area. However, as the ambient flow velocity increases, the optimal shape changes with the aspect ratio. We find that ice with an elliptical shape (when the long axis is aligned with the flow direction) can melt up to 10\% slower than a circular shape when exposed to flowing water. We provide a quantitative theoretical explanation for this optimal shape, based on the competition between surface area effects and convective heat transfer effects. Our findings provide insight into the interplay between phase transitions and ambient flows, contributing to our understanding of the iceberg melting process and highlighting the need to consider the aspect ratio effect in estimates of iceberg melt rates