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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Dovesi R, Saunders VR, Roetti C, Orlando R, Zicovich-Wilson CM, Pascale F, Civalleri B, Doll K, Harrison NM, Bush IJ, D’Arco Ph, Llunell M, Causà M, Noël Y. CRYSTAL14 User’s Manual. Torino: Università di Torino, 2014
Dovesi R, Orlando R, Erba A, Zicovich-Wilson CM, Civalleri B, Casassa S, Maschio L, Ferrabone M, De La Pierre M, D’Arco Ph, Noël Y, Causà M, Rérat M, Kirtman B. CRYSTAL14: A program for the ab initio investigation of crystalline solids. Int J Quantum Chem, 2014, 114: 1287–1317
Dovesi R. On the Role of symmetry in the ab initio Hartree-Fock linear-combination-of-atomic-orbitals treatment of periodic systems. Int J Quantum Chem, 1986, 29: 1755–1774
Zicovich-Wilson CM, Dovesi R. On the use of symmetry-adapted crystalline orbitals in SCF-LCAO periodic calculations. I. The Construction of the Symmetrized Orbitals. Int J Quantum Chem, 1998, 67: 299–309
Zicovich-Wilson CM, Dovesi R. On the use of symmetry-adapted crystalline orbitals in SCF-LCAO periodic calculations. II. Implementation of the Self-Consistent-Field scheme and examples. Int J Quantum Chem, 1998, 67: 311–320
Orlando R, De La Pierre M, Zicovich-Wilson CM, Erba A, Dovesi R. On the full exploitation of symmetry in periodic (as well as molecular) Self-Consistent-Field ab initio calculations. J Chem Phys, 2014, DOI: 10.1063/1.4895113
Zicovich-Wilson CM, Noël Y, Ferrari AM, Orlando R, De La Pierre M, Dovesi R. On the use of symmetry in SCF calculations. The case of fullerenes and nanotubes. AIP Conf Proc, 2012, 1456: 248–255
Pisani C, Dovesi R, Roetti C. Hartree-Fock ab-initio treatment of crystalline systems. Lect N Chem, Vol. 48. Heidelberg: Spinger Verlag, 1988
Bush IJ, Tomic S, Searle BG, Mallia G, Bailey CL, Montanari B, Bernasconi L, Carr JM, Harrison NM. Parallel implementation of the ab initio CRYSTAL program: electronic structure calculations for periodic systems. Proc R Soc A, 2011, 467: 2112–2126
Orlando R, Delle Piane M, Bush IJ, Ugliengo P, Ferrabone M, Dovesi R. A new massively parallel version of CRYSTAL for large systems on high performance computing architectures. J Comput Chem, 2012, 33: 2276–2284
Becke AD. Density functional theochemistry. III. The role of exact exchange. J Chem Phys, 1993, 98: 5648–5652
Lee C, Yang W, Parr RG. Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density. Phys Rev B, 1988, 37: 785–789
Stephens PJ, Devlin FJ, Chabalowski CF, Frisch MJ. Ab initio calculation of vibrational absorption and circular dichroism spectra using density functional force fields. J Phys Chem, 1994, 98: 11623–11627
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
De La Pierre, M., Orlando, R., Ferrabone, M. et al. Exploitation of symmetry in periodic Self-Consistent-Field ab initio calculations: application to large three-dimensional compounds. Sci. China Chem. 57, 1418–1426 (2014). https://doi.org/10.1007/s11426-014-5191-y
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11426-014-5191-y