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EnglishWhen solving the Møller-Plesset second order perturbation theory (MP2) equations for periodic systems using a local-correlation approach [J. Chem. Phys. 122 (2005) 094113], the computational bottleneck is represented by the evaluation of the two-electron Coulomb interaction integrals between product distributions, each involving a Wannier function and a projected atomic orbital. While for distant product distributions a multipolar approximation performs very efficiently, the four index transformation for close-by distributions, which by far constitutes the bottleneck of correlated electronic structure calculations of crystals, can be avoided through the use of density fitting techniques. An adaptation of that scheme to translationally periodic systems is described, based on Fourier transformation techniques. The formulas and algorithms adopted allow the point symmetry of the crystal to be exploited. Problems related to the possible divergency of lattice sums of integrals involving fitting functions are identified and eliminated through the use of Poisson transformed fitting functions and of dipole-corrected product distributions. The iterative scheme for solving the linear local MP2 (LMP2) equations is revisited. Prescreening in the evaluation of the residual matrix is introduced, which significantly lowers the scaling of the LMP2 equations.
| Titolo: | Fast local-MP2 method with density-fitting for crystals. I. Theory and algorithms |
| Autori Riconosciuti: | |
| Autori: | L. MASCHIO; D. USVYAT; C. PISANI; F. MANBY; S. CASASSA; M. SCHUETZ |
| Data di pubblicazione: | 2007 |
| Abstract: | When solving the Møller-Plesset second order perturbation theory (MP2) equations for periodic systems using a local-correlation approach [J. Chem. Phys. 122 (2005) 094113], the computational bottleneck is represented by the evaluation of the two-electron Coulomb interaction integrals between product distributions, each involving a Wannier function and a projected atomic orbital. While for distant product distributions a multipolar approximation performs very efficiently, the four index transformation for close-by distributions, which by far constitutes the bottleneck of correlated electronic structure calculations of crystals, can be avoided through the use of density fitting techniques. An adaptation of that scheme to translationally periodic systems is described, based on Fourier transformation techniques. The formulas and algorithms adopted allow the point symmetry of the crystal to be exploited. Problems related to the possible divergency of lattice sums of integrals involving fitting functions are identified and eliminated through the use of Poisson transformed fitting functions and of dipole-corrected product distributions. The iterative scheme for solving the linear local MP2 (LMP2) equations is revisited. Prescreening in the evaluation of the residual matrix is introduced, which significantly lowers the scaling of the LMP2 equations. |
| Editore: | American Institute of Physics:2 Huntington Quadrangle, Suite 1NO1:Melville, NY 11747:(800)344-6902, (631)576-2287, EMAIL: subs@aip.org, INTERNET: http://www.aip.org, Fax: (516)349-9704 |
| Volume: | 76 |
| Pagina iniziale: | 075101-1 |
| Pagina finale: | 075101-9 |
| Digital Object Identifier (DOI): | 10.1103/PhysRevB.76.075101 |
| Parole Chiave: | periodic local MP2; electronic correlation |
| Rivista: | PHYSICAL REVIEW. B, CONDENSED MATTER AND MATERIALS PHYSICS |
| Appare nelle tipologie: | 03A-Articolo su Rivista |
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