Multipole expansion

About: Multipole expansion is a research topic. Over the lifetime, 9675 publications have been published within this topic receiving 214783 citations.

Molecular multipole moments

Abstract: A summary and critical review of available information on molecular quadrupole and higher moments is presented. A theorem is also proved which shows that only one independent scalar quantity is required to determine a molecular electric multipole tensor of rank p for molecules with an n-fold axis of symmetry where p < n.

A quantized microwave quadrupole insulator with topologically protected corner states

Abstract: The theory of electric polarization in crystals defines the dipole moment of an insulator in terms of a Berry phase (geometric phase) associated with its electronic ground state. This concept not only solves the long-standing puzzle of how to calculate dipole moments in crystals, but also explains topological band structures in insulators and superconductors, including the quantum anomalous Hall insulator and the quantum spin Hall insulator, as well as quantized adiabatic pumping processes. A recent theoretical study has extended the Berry phase framework to also account for higher electric multipole moments, revealing the existence of higher-order topological phases that have not previously been observed. Here we demonstrate experimentally a member of this predicted class of materials-a quantized quadrupole topological insulator-produced using a gigahertz-frequency reconfigurable microwave circuit. We confirm the non-trivial topological phase using spectroscopic measurements and by identifying corner states that result from the bulk topology. In addition, we test the critical prediction that these corner states are protected by the topology of the bulk, and are not due to surface artefacts, by deforming the edges of the crystal lattice from the topological to the trivial regime. Our results provide conclusive evidence of a unique form of robustness against disorder and deformation, which is characteristic of higher-order topological insulators.

A precorrected-FFT method for electrostatic analysis of complicated 3-D structures

Abstract: In this paper we present a new algorithm for accelerating the potential calculation which occurs in the inner loop of iterative algorithms for solving electromagnetic boundary integral equations. Such integral equations arise, for example, in the extraction of coupling capacitances in three-dimensional (3-D) geometries. We present extensive experimental comparisons with the capacitance extraction code FASTCAP and demonstrate that, for a wide variety of geometries commonly encountered in integrated circuit packaging, on-chip interconnect and micro-electro-mechanical systems, the new "precorrected-FFT" algorithm is superior to the fast multipole algorithm used in FASTCAP in terms of execution time and memory use. At engineering accuracies, in terms of a speed-memory product, the new algorithm can be superior to the fast multipole based schemes by more than an order of magnitude.

Low-order scaling local electron correlation methods. I. Linear scaling local MP2

Abstract: A new implementation of local second-order Mo/ller-Plesset perturbation theory (LMP2) is presented for which asymptotically all computational resources (CPU, memory, and disk) scale only linearly with the molecular size. This is achieved by (i) using orbital domains for each electron pair that are independent of molecular size; (ii) classifying the pairs according to a distance criterion and neglecting very distant pairs; (iii) treating distant pairs by a multipole approximation, and (iv) using efficient prescreening algorithms in the integral transformation. The errors caused by the various approximations are negligible. LMP2 calculations on molecules including up to 500 correlated electrons and over 1500 basis functions in C1 symmetry are reported, all carried out on a single low-cost personal computer.