Fitting of local densities in periodic systems

Maschio, Lorenzo; Usvyat, Denis

doi:10.1103/physrevb.78.073102

Cited by 60 publications

(53 citation statements)

References 29 publications

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“…In the case of extended pair lists or domains, this scheme becomes inefficient and a more advanced algorithm is desirable. In the present work, we adopt a procedure developed for density fitting in the context of periodic systems, 57,58,83,84 where local fitting is not only more efficient, but also mandatory due to the infinite nature of the physical system. The importance of a certain center X for the product charge distribution of orbitals r, s is measured by the quantity, 58 q X rs = (1 + τ rs )…”

Section: B 3-and 4-external Integralsmentioning

confidence: 99%

An efficient local coupled cluster method for accurate thermochemistry of large systems

Werner

Schütz

2011

The Journal of Chemical Physics

261

302

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An efficient local coupled cluster method with single and double excitation operators and perturbative treatment of triple excitations [DF-LCCSD(T)] is described. All required two-electron integrals are evaluated using density fitting approximations. These have a negligible effect on the accuracy but reduce the computational effort by 1-2 orders of magnitude, as compared to standard integral-direct methods. Excitations are restricted to local subsets of non-orthogonal virtual orbitals (domain approximation). Depending on distance criteria, the correlated electron pairs are classified into strong, close, weak, and very distant pairs. Only strong pairs, which typically account for more than 90% of the correlation energy, are optimized in the LCCSD treatment. The remaining close and weak pairs are approximated by LMP2 (local second-order Møller-Plesset perturbation theory); very distant pairs are neglected. It is demonstrated that the accuracy of this scheme can be significantly improved by including the close pair LMP2 amplitudes in the LCCSD equations, as well as in the perturbative treatment of the triples excitations. Using this ansatz for the wavefunction, the evaluation and transformation of the two-electron integrals scale cubically with molecular size. If local density fitting approximations are activated, this is reduced to linear scaling. The LCCSD iterations scale quadratically, but linear scaling can be achieved by neglecting some terms involving contractions of single excitations. The accuracy and efficiency of the method is systematically tested using various approximations, and calculations for molecules with up to 90 atoms and 2636 basis functions are presented.

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Section: B 3-and 4-external Integralsmentioning

confidence: 99%

An efficient local coupled cluster method for accurate thermochemistry of large systems

Werner

Schütz

2011

The Journal of Chemical Physics

261

302

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“…In particular, MP2 describes in a qualitatively correct way the dispersive interaction at long range. The implementation of fast integral evaluation techniques such as density fitting 4,[6][7][8][9][10] mean that the computational cost of a MP2 calculation is now not significantly higher than that of an HF or DFT calculation. Two other methods have been recently proposed to approximate the dispersive contribution.…”

Section: Introductionmentioning

confidence: 99%

Periodic quantum mechanical simulation of the He–MgO(100) interaction potential

Martínez-Casado

Mallia

Usvyat

et al. 2011

The Journal of Chemical Physics

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He-atom scattering is a well established and valuable tool for investigating surface structure. The correct interpretation of the experimental data requires an accurate description of the He-surface interaction potential. A quantum-mechanical treatment of the interaction potential is presented using the current dominant methodologies for computing ground state energies (Hartree-Fock, local and hybrid-exchange density functional theory) and also a novel post-Hartree-Fock ab initio technique for periodic systems (a local implementation of Møller-Plesset perturbation theory at second order). The predicted adsorption well depth and long range behavior of the interaction are compared with that deduced from experimental data in order to assess the accuracy of the interaction potential.

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“…This could be done in connection with the local-correlation CRYSCOR code, [47,48,49] which presently features a very efficient implementation of the local MP2 approach for periodic systems. This implementation makes use of advanced techniques such as density fitting [38] and orbital-specific virtuals [62], as well as efficient parallel implementation. [33] The extension to local coupled-cluster is also envisaged in the future.…”

Section: Summary and Prospectsmentioning

confidence: 99%

Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields

Maschio

Rérat

Springborg

2017

Frontiers of Quantum Chemistry

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The ab initio treatment of external field response in crystalline solids poses particular challenges, since the operator representing the external field must be reformulated so to be consistent with periodic boundary conditions. In this chapter, we review our recent work to formulate implementable working equations for polarizability and hyperpolarizabilities in solids, in the framework of a local (gaussian) basis set. This includes the combination of electric field response with geometrical distorsion, i.e. infrared and Raman intensities, as well as piezoelectricity. In addition, we outline a pathway for including magnetic fields in a consistent way, and speculate on future possible developments.

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Fitting of local densities in periodic systems

Cited by 60 publications

References 29 publications

An efficient local coupled cluster method for accurate thermochemistry of large systems

An efficient local coupled cluster method for accurate thermochemistry of large systems

Periodic quantum mechanical simulation of the He–MgO(100) interaction potential

Response Properties of Periodic Materials Subjected to External Electric and Magnetic Fields

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