Model density approach to the Kohn–Sham problem: Efficient extension of the density fitting technique

Birkenheuer, U.; Gordienko, A. B.; Наслузов, Владимир А.; Fuchs-Rohr, Monika K.; Rösch, Notker

doi:10.1002/qua.20447

Cited by 28 publications

(27 citation statements)

References 68 publications

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“…Richer fitting basis sets gave further reductions in these errors for various observables, reaching essentially the results of the numerical procedure employing the exact density [81]. Atomisation energies have been reproduced up to about 1 kcal/mol for optimised molecular structures for standard auxiliary basis sets [81].…”

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 97%

“…For a moderate-sized fitting basis, it has been shown that the mean absolute errors of the model density approach, compared to using the KS density, were less than 0.5 pm for bond lengths and 0.3 for angles on a large set of molecules for both the local density and gradient corrected XC approximations [81,82]. Richer fitting basis sets gave further reductions in these errors for various observables, reaching essentially the results of the numerical procedure employing the exact density [81].…”

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 98%

“…More recently, some of the developers of the ParaGauss and deMon2k molecular DFT codes have made an even bolder use of the fitted density, or in their respective terminology, the 'model density' [81] 3176 B.I. Dunlap et al or 'auxiliary density' [82].…”

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

“…Overall, this 'model density approach' [81] reduces the computational effort of the numerical treatment of the XC interaction in the KS procedure from a problem formally scaling as O(N 3 ) to an easier one scaling as O(N 2 ). Matrix elements of both terms of the potential v ee can be evaluated by using the same threecentre integrals h jCi C [81].…”

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

“…Matrix elements of both terms of the potential v ee can be evaluated by using the same threecentre integrals h jCi C [81]. For this approach, gradients with respect to nuclear positions also have been derived [81,82], and the linear polarisibility evaluated [84].…”

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

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Variational fitting methods for electronic structure calculations

Dunlap¹,

Rösch²,

Trickey³

2010

Molecular Physics

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101

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We review the basics and the evolution of a powerful and widely applicable general approach to the systematic reduction of computational burden in many-electron calculations. Variational fitting of electron densities (either total or partial) has the great advantage, for quantum mechanical calculations, that it respects the stationarity property, which is at the heart of the success of the basis set expansion methods ubiquitous in computational chemistry and materials physics. The key point is easy. In a finite system, independent of whether the fitted charge distribution is constrained to contain the proper amount of charge, variational fitting guarantees that the quantum mechanical total energy retains the stationarity property. Thus, many-electron quantum mechanics with variational fitting of an electronic density in an incomplete density-fitting basis set behaves similarly as the exact quantum mechanical energy does when evaluated with an incomplete basis set to fit wavefunctions or spinorbitals. Periodically bounded systems are a bit more subtle but the essential stationarity is preserved. This preservation of an exact property is quite distinct from truncation of the resolution of the identity in a basis. Variational fitting has proven to have benefits far beyond the original objective of making a Gaussian-orbital basis calculation of an early density functional computationally feasible. We survey many of those developments briefly, with guidance to the pertinent literature and a few remarks about the connections with Quantum Theory Project.

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Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 97%

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 98%

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

Section: Using the Fitted Density And Charge Distributionsmentioning

confidence: 99%

See 3 more Smart Citations

Variational fitting methods for electronic structure calculations

Dunlap¹,

Rösch²,

Trickey³

2010

Molecular Physics

Self Cite

101

View full text Add to dashboard Cite

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Optimization of auxiliary basis sets for the LEDO expansion and a projection technique for LEDO–DFT

2005

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We present a systematic procedure for the optimization of the expansion basis for the limited expansion of diatomic overlap density functional theory (LEDO-DFT) and report on optimized auxiliary orbitals for the Ahlrichs split valence plus polarization basis set (SVP) for the elements H, Li--F, and Na--Cl. A new method to deal with near-linear dependences in the LEDO expansion basis is introduced, which greatly reduces the computational effort of LEDO-DFT calculations. Numerical results for a test set of small molecules demonstrate the accuracy of electronic energies, structural parameters, dipole moments, and harmonic frequencies. For larger molecular systems the numerical errors introduced by the LEDO approximation can lead to an uncontrollable behavior of the self-consistent field (SCF) process. A projection technique suggested by Löwdin is presented in the framework of LEDO-DFT, which guarantees for SCF convergence. Numerical results on some critical test molecules suggest the general applicability of the auxiliary orbitals presented in combination with this projection technique. Timing results indicate that LEDO-DFT is competitive with conventional density fitting methods.

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