A highly-efficient technique for evaluating bond-orientational order parameters

We propose a novel, highly-efficient approach for the evaluation of bond-orientational order parameters (BOPs). Our approach exploits the properties of spherical harmonics and Wigner 3j-symbols to reduce the number of terms in the expressions for BOPs, and employs simultaneous interpolation of normalised associated Legendre polynomials and trigonometric functions to dramatically reduce the total number of arithmetic operations. Using realistic test cases, we show how the above, combined with a CPU-cache-friendly data structure, leads to a 10 to 50-fold performance increase over approaches currently in use, depending on the size of the interpolation grids and the machine used. As the proposed approach is an approximation, we demonstrate that the errors it introduces are well-behaved, controllable and essentially negligible for practical grid sizes. We benchmark our approach against other structure identification methods (centro-symmetry parameter (CSP), common neighbour analysis (CNA), common neighbourhood parameter (CNP) and Voronoi analysis), generally regarded as much faster than BOPs, and demonstrate that our formulation is able to outperform them for all studied systems.