An efficient density-functional-theory force evaluation for large molecular systems

Reine, Simen; Krapp, Andreas; Iozzi, Maria Francesca; Bakken, Vidar; Helgaker, Trygve; Pawłowski, Filip; Sałek, Paweł

doi:10.1063/1.3459061

Cited by 22 publications

(28 citation statements)

References 59 publications

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“…Molecular gradients (forces) and Hessians (force constants) may be calculated analytically at the HF, KS, and MCSCF37,38 levels of theory, whereas analytical molecular gradients are available for the CCS, CC2, CCD, MP2, RPA, CCSD, and CCSD(T) models,18,39 also in the frozen-core approximation. Numerical differentiation may be performed automatically for these quantities when an analytical implementation is not available 40…”

Section: Molecular Propertiesmentioning

confidence: 99%

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The Dalton quantum chemistry program system

Aidas

Angeli

Bak

et al. 2013

WIREs Comput Mol Sci

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1,216

958

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Dalton is a powerful general-purpose program system for the study of molecular electronic structure at the Hartree–Fock, Kohn–Sham, multiconfigurational self-consistent-field, Møller–Plesset, configuration-interaction, and coupled-cluster levels of theory. Apart from the total energy, a wide variety of molecular properties may be calculated using these electronic-structure models. Molecular gradients and Hessians are available for geometry optimizations, molecular dynamics, and vibrational studies, whereas magnetic resonance and optical activity can be studied in a gauge-origin-invariant manner. Frequency-dependent molecular properties can be calculated using linear, quadratic, and cubic response theory. A large number of singlet and triplet perturbation operators are available for the study of one-, two-, and three-photon processes. Environmental effects may be included using various dielectric-medium and quantum-mechanics/molecular-mechanics models. Large molecules may be studied using linear-scaling and massively parallel algorithms. Dalton is distributed at no cost from http://www.daltonprogram.org for a number of UNIX platforms.

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Section: Molecular Propertiesmentioning

confidence: 99%

“…To illustrate the capabilities of Dalton for large molecules, we consider two systems—namely, the 168-atom valinomycin molecule and the 392-atom titin-I27SS model,38 see Figure 4. For valinomycin, geometry optimizations were conducted at the BP86/6-31G** and CAM-B3LYP/6-31G** levels of theory.…”

Section: Large Moleculesmentioning

confidence: 99%

The Dalton quantum chemistry program system

Aidas

Angeli

Bak

et al. 2013

WIREs Comput Mol Sci

Self Cite

1,216

958

View full text Add to dashboard Cite

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“…20 The three-center overlap routine is very efficient, especially when the contraction of integrals with the density matrix elements in Point 5b or with the d G vector in Point 8a is performed at an early stage of computation, in the spirit of the J-engine approach combined with the McMurchie-Davidson formalism. 23 The formal cubic scaling of the number of three-center overlap integrals with the system size is reduced by considering only significant three-center overlap distributions. We assume that the three-center overlap distribution is significant if, for all pairs of the three orbitals in the product, the distance between the orbital centers is smaller than the sum of their extents, as obtained with the cutoff δ = 10 −12 , see Sec.…”

Section: E Integrals Involving Only Gaussian Functionsmentioning

confidence: 99%

“…where D ab are the density-matrix elements associated with the electronic density ρ(r) and J ab are the Coulomb integrals calculated by the traditional J-engine method as implemented in the LSDALTON 18,23 or by the GFC method as described here.…”

Section: B the Choice Of α G Min And γ 1stmentioning

confidence: 99%

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals

Przybytek

Helgaker

2013

The Journal of Chemical Physics

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We analyze the accuracy of the Coulomb energy calculated using the Gaussian-and-finite-element-Coulomb (GFC) method. In this approach, the electrostatic potential associated with the molecular electronic density is obtained by solving the Poisson equation and then used to calculate matrix elements of the Coulomb operator. The molecular electrostatic potential is expanded in a mixed Gaussian-finite-element (GF) basis set consisting of Gaussian functions of s symmetry centered on the nuclei (with exponents obtained from a full optimization of the atomic potentials generated by the atomic densities from symmetry-averaged restricted open-shell Hartree-Fock theory) and shape functions defined on uniform finite elements. The quality of the GF basis is controlled by means of a small set of parameters; for a given width of the finite elements d, the highest accuracy is achieved at smallest computational cost when tricubic (n = 3) elements are used in combination with two (γ(H) = 2) and eight (γ(1st) = 8) Gaussians on hydrogen and first-row atoms, respectively, with exponents greater than a given threshold (αmin (G)=0.5). The error in the calculated Coulomb energy divided by the number of atoms in the system depends on the system type but is independent of the system size or the orbital basis set, vanishing approximately like d(4) with decreasing d. If the boundary conditions for the Poisson equation are calculated in an approximate way, the GFC method may lose its variational character when the finite elements are too small; with larger elements, it is less sensitive to inaccuracies in the boundary values. As it is possible to obtain accurate boundary conditions in linear time, the overall scaling of the GFC method for large systems is governed by another computational step-namely, the generation of the three-center overlap integrals with three Gaussian orbitals. The most unfavorable (nearly quadratic) scaling is observed for compact, truly three-dimensional systems; however, this scaling can be reduced to linear by introducing more effective techniques for recognizing significant three-center overlap distributions.

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“…Examples include the prediction of the electronic and geometrical structure of proteins from first principles [6] or modelling optical probes inside proteins [7].…”

Section: Introductionmentioning

confidence: 99%

Scaling Dalton, A Molecular Electronic Structure Program

Aguilar¹,

Schliephake²,

Vahtras³

et al. 2011

2011 IEEE Seventh International Conference on eScience

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Abstract-Dalton is a molecular electronic structure program featuring common methods of computational chemistry that are based on pure quantum mechanics (QM) as well as hybrid quantum mechanics/molecular mechanics (QM/MM). It is specialized and has a leading position in calculation of molecular properties with a large world-wide user community (over 2000 licenses issued). In this paper, we present a characterization and performance optimization of Dalton that increases the scalability and parallel efficiency of the application. We also propose a solution that helps to avoid the master/worker design of Dalton to become a performance bottleneck for larger process numbers and increase the parallel efficiency.

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An efficient density-functional-theory force evaluation for large molecular systems

Cited by 22 publications

References 59 publications

The Dalton quantum chemistry program system

The Dalton quantum chemistry program system

The accuracy of the Gaussian-and-finite-element-Coulomb (GFC) method for the calculation of Coulomb integrals

Scaling Dalton, A Molecular Electronic Structure Program

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