Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds |
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Authors: | Marco De La Pierre Roberto Orlando Matteo Ferrabone Claudio M. Zicovich-Wilson Roberto Dovesi |
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Affiliation: | 1. Dipartimento di Chimica, Università di Torino and NIS, Nanostructured Interfaces and Surfaces, Centre of Excellence, Via P. Giuria 7, 10125, Torino, Italy 2. Nanochemistry Research Institute, Department of Chemistry, Curtin University, GPO Box U1987, Perth, WA, 6845, Australia 3. Facultad de Ciencias, Universidad Autónoma del Estado de Morelos, Av. Universidad, 1001, Col. Chamilpa, 62209, Cuernavaca (Morelos), Mexico
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Abstract: | Symmetry can dramatically reduce the computational cost (running time and memory allocation) of Self-Consistent-Field ab initio calculations for crystalline systems. Crucial for running time is use of symmetry in the evaluation of one- and two-electron integrals, diagonalization of the Fock matrix at selected points in reciprocal space, reconstruction of the density matrix. As regards memory allocation, full square matrices (overlap, Fock and density) in the Atomic Orbital (AO) basis are avoided and a direct transformation from the packed AO to the SACO (Symmetry Adapted Crystalline Orbital) basis is performed, so that the largest matrix to be handled has the size of the largest sub-block in the latter basis. We here illustrate the effectiveness of this scheme, following recent advancements in the CRYSTAL code, concerning memory allocation and direct basis set transformation. Quantitative examples are given for large unit cell systems, such as zeolites (all-silica faujasite and silicalite MFI) and garnets (pyrope). It is shown that the full SCF of 3D systems containing up to 576 atoms and 11136 Atomic Orbitals in the cell can be run with a hybrid functional on a single core PC with 500 MB RAM in about 8 h. |
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Keywords: | point symmetry Symmetry Adapted Crystalline Orbitals Fock matrix density matrix CPU time memory allocation quantum-mechanical calculations CRYSTAL code |
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