Linear-scaling computation of ground state with time-domain localized-density-matrix method

Yokojima, Satoshi; Zhou, DongHao; Chen, Guanhua

doi:10.1016/s0009-2614(99)00167-0

Cited by 19 publications

(19 citation statements)

References 32 publications

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“…To achieve the linear-scaling computation for the ground state, we adopt the following approximation: 3,4 where r ij is the distance between two atomic orbitals i and j, and l 1 is a critical length for the density matrix. 1,2 Consequently…”

Section: Model and Time-dependent Hartree-fock Approximationmentioning

confidence: 99%

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

et al. 1999

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The localized-density-matrix method Chen, G. H. Chem. Phys. Lett. 1998, 292, 379) is employed to simulate the optical responses of very large carbon nanotubes and polyacetylene oligomers containing 10 000 carbon atoms. The Pariser-Parr-Pople Hamiltonian is used to describe the π electrons in these systems, and the time-dependent Hartree-Fock approximation is employed to calculate the linear optical responses. In the calculation, the fast multipole method or the cell multipole method is employed to evaluate the effects of Coulomb interaction. It is illustrated that the computational time scales linearly with the system size for carbon nanotubes while high accuracy is achieved.

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Section: Model and Time-dependent Hartree-fock Approximationmentioning

confidence: 99%

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

et al. 1999

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18] Development of linear-scaling techniques, in particular for excited states, remains an active area of electronic structure theory. With sparse matrix techniques, linear-scaling calculations can be achieved by means of DAC-style fragment methods, localized molecular orbitals (LMOs), and density matrices.…”

Section: Introductionmentioning

confidence: 99%

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Cui¹,

Fang²,

Yang³

2010

J. Phys. Chem. A

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Localized molecular orbitals (LMOs) are much more compact representations of electronic degrees of freedom than canonical molecular orbitals (CMOs). The most compact representation is provided by nonorthogonal localized molecular orbitals (NOLMOs), which are linearly independent but are not orthogonal. Both LMOs and NOLMOs are thus useful for linear-scaling calculations of electronic structures for large systems. Recently, NOLMOs have been successfully applied to linear-scaling calculations with density functional theory (DFT) and to reformulating time-dependent density functional theory (TDDFT) for calculations of excited states and spectroscopy. However, a challenge remains as NOLMO construction from CMOs is still inefficient for large systems. In this work, we develop an efficient method to accelerate the NOLMO construction by using predefined centroids of the NOLMO and thereby removing the nonlinear equality constraints in the original method (J. Chem. Phys. 2004, 120, 9458 and J. Chem. Phys. 2000, 112, 4). Thus, NOLMO construction becomes an unconstrained optimization. Its efficiency is demonstrated for the selected saturated and conjugated molecules. Our method for fast NOLMO construction should lead to efficient DFT and NOLMO-TDDFT applications to large systems.

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“…To avoid unphysical results for the excited state properties, it is important that the relation [h (0) , H (0) ] = 0 is satisfied to a high accuracy. A new linear-scaling procedure is to be devised to determine the [27]. To calculate H (0) , we start with Eq.…”

Section: Localized-density-matrix Methodsmentioning

confidence: 99%

Localized-density-matrix method and its application to nanomaterials

Chen

Yokojima

Liang

et al. 2000

Pure and Applied Chemistry

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The localized-density-matrix (LDM) method has been developed to calculate the excited state properties of very large systems containing thousands of atoms. It is particularly suitable for simulating the dynamic electronic processes in nanoscale materials, and has been applied to poly(p-phenylenevynelene) (PPV) aggregates and carbon nanotubes. Absorption spectra of PPVs and carbon nanotubes have been calculated and compared to the experiments.

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Linear-scaling computation of ground state with time-domain localized-density-matrix method

Cited by 19 publications

References 32 publications

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†

Localized-density-matrix method and its application to nanomaterials

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Linear-scaling computation of ground state with time-domain localized-density-matrix method

Cited by 19 publications

References 32 publications

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

Localized-Density-Matrix Method and Its Application to Carbon Nanotubes

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

Localized-density-matrix method and its application to nanomaterials

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Product

Resources

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Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems^†