ClusterES swMATH ID: 18311 Software Authors: Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D. Description: A spectral scheme for Kohn-Sham density functional theory of clusters. Starting from the observation that one of the most successful methods for solving the Kohn-Sham equations for periodic systems - the plane-wave method - is a spectral method based on eigenfunction expansion, we formulate a spectral method designed towards solving the Kohn-Sham equations for clusters. This allows for efficient calculation of the electronic structure of clusters (and molecules) with high accuracy and systematic convergence properties without the need for any artificial periodicity. The basis functions in this method form a complete orthonormal set and are expressible in terms of spherical harmonics and spherical Bessel functions. Computation of the occupied eigenstates of the discretized Kohn-Sham Hamiltonian is carried out using a combination of preconditioned block eigensolvers and Chebyshev polynomial filter accelerated subspace iterations. Several algorithmic and computational aspects of the method, including computation of the electrostatics terms and parallelization are discussed. We have implemented these methods and algorithms into an efficient and reliable package called ClusterES (Cluster Electronic Structure). A variety of benchmark calculations employing local and non-local pseudopotentials are carried out using our package and the results are compared to the literature. Convergence properties of the basis set are discussed through numerical examples. Computations involving large systems that contain thousands of electrons are demonstrated to highlight the efficacy of our methodology. The use of our method to study clusters with arbitrary point group symmetries is briefly discussed. Homepage: http://www.sciencedirect.com/science/article/pii/S0021999115000704 Keywords: spectral scheme; Kohn-Sham density functional theory; spherical harmonics; spherical Bessel functions; computational efficiency; spectral convergence; parallel scaling performance; eigenvalue problem; lobpcg; Chebyshev filtering; nano clusters; super atoms Related Software: CheFSI; ABINIT; Quantum Espresso; CASTEP; PARSEC; Matlab; RESCU; Libxc; ISOGAT; LAPACK; lobpcg.m; CRYSTAL; SPARC; Lightspeed; RELION; Bilbao Crystallography Server; Chimera; EMan; DLMF; fhi98PP Cited in: 10 Publications Standard Articles 1 Publication describing the Software, including 1 Publication in zbMATH Year A spectral scheme for Kohn-Sham density functional theory of clusters. Zbl 1351.81014Banerjee, Amartya S.; Elliott, Ryan S.; James, Richard D. 2015 all top 5 Cited by 19 Authors 3 Banerjee, Amartya S. 2 James, Richard D. 2 Temizer, Ilker 1 Bodroški, Žarko 1 Doerschuk, Peter C. 1 Elliott, Ryan S. 1 Feng, Fan 1 Gavini, Vikram 1 Li, Rencang 1 Motamarri, Phani 1 Pérez-Jordá, José M. 1 Plucinsky, Paul 1 Škrbić, Srđan 1 Suryanarayana, Phanish 1 Teng, Zhongming 1 Vukmirović, Nenad 1 Xu, Nan 1 Yu, Hsuan Ming 1 Zhou, Yunkai all top 5 Cited in 6 Serials 4 Journal of Computational Physics 2 Journal of the Mechanics and Physics of Solids 1 Computers & Mathematics with Applications 1 Computer Methods in Applied Mechanics and Engineering 1 SIAM Journal on Scientific Computing 1 Advances in Computational Mathematics all top 5 Cited in 8 Fields 6 Numerical analysis (65-XX) 2 Partial differential equations (35-XX) 2 Mechanics of deformable solids (74-XX) 2 Quantum theory (81-XX) 2 Statistical mechanics, structure of matter (82-XX) 1 Real functions (26-XX) 1 Manifolds and cell complexes (57-XX) 1 Biology and other natural sciences (92-XX) Citations by Year