Linear system-size scaling methods for electronic-structure calculations

Ordejón, Pablo; Drabold, D. A.; Martin, Richard M.; Grumbach, Matthew P.

doi:10.1103/physrevb.51.1456

Cited by 269 publications

(233 citation statements)

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“…The method is validated below for DFT liquid water, including the localization approximations required for linear scaling. [19][20][21] After the characterization of the equilibrium properties, we present results on nonequilibrium relaxation processes, which provide insights into why the simulations need longer times, how to look at the DFT deficiencies, and, more importantly, into the nature of liquid water itself.…”

Section: Introductionmentioning

confidence: 99%

Network equilibration and first-principles liquid water

Fernández-Serra

Artacho

2004

The Journal of Chemical Physics

164

175

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Motivated by the very low diffusivity recently found in ab initio simulations of liquid water, we have studied its dependence with temperature, system size, and duration of the simulations. We use ab initio molecular dynamics ͑AIMD͒, following the Born-Oppenheimer forces obtained from density-functional theory ͑DFT͒. The linear-scaling capability of our method allows the consideration of larger system sizes ͑up to 128 molecules in this study͒, even if the main emphasis of this work is in the time scale. We obtain diffusivities that are substantially lower than the experimental values, in agreement with recent findings using similar methods. A fairly good agreement with D(T) experiments is obtained if the simulation temperature is scaled down by Ϸ20%. It is still an open question whether the deviation is due to the limited accuracy of present density functionals or to quantum fluctuations, but neither technical approximations ͑basis set, localization for linear scaling͒ nor the system size ͑down to 32 molecules͒ deteriorate the DFT description in an appreciable way. We find that the need for long equilibration times is consequence of the slow process of rearranging the H-bond network ͑at least 20 ps at AIMDs room temperature͒. The diffusivity is observed to be very directly linked to network imperfection. This link does not appear an artifact of the simulations, but a genuine property of liquid water.

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Section: Introductionmentioning

confidence: 99%

Network equilibration and first-principles liquid water

Fernández-Serra

Artacho

2004

The Journal of Chemical Physics

164

175

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“…(2) exhibits extremely slow convergence 3,21,24,26,32 rendering such an approach impractical ( Figure 1). …”

Section: Theoretical Approachmentioning

confidence: 99%

Efficient Linear-Scaling Density Functional Theory for Molecular Systems

Khaliullin

VandeVondele

Hutter

2013

J. Chem. Theory Comput.

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Despite recent progress in linear scaling (LS) density function theory (DFT), the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate nonself-consistent approach. We demonstrate that, even for challenging condensed-phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those previously treated. Efficient linear-scaling density functional theory for molecular systems Despite recent progress in linear scaling (LS) density function theory (DFT) the computational cost of the existing LS methods remains too high for a widespread adoption at present. In this work, we exploit nonorthogonal localized molecular orbitals to develop a series of LS methods for molecular systems with a low computational overhead. High efficiency of the proposed methods is achieved with a new robust two-stage variational procedure or by replacing the optimization altogether with an accurate non-self-consistent approach. We demonstrate that even for challenging condensed phase systems, the implemented LS methods are capable of extending the range of accurate DFT simulations to molecular systems that are an order of magnitude larger than those treated before.

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“…The second step is extracting dynamic properties such as linear and nonlinear-response functions from this Hamiltonian. While the first step has been extensively studied [1][2][3][4][5][6][7][8] and also comprehensive reviews are available [9,10], the second step has been studied by only few papers [11][12][13][14][15], including the particle source method [16,17] and the projection method [18][19][20][21], which use the numerical solution of the time-dependent Schrödinger equation [22], and projected random vectors [23].…”

Section: Introductionmentioning

confidence: 99%