Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cui, Ganglong; Fang, Wei‐Hai; Yang, Weitao

doi:10.1039/b916688b

Cited by 32 publications

(46 citation statements)

References 35 publications

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“…10,27,39 The ground-state calculations not only demonstrate that NOLMOs are more compact/localized in space than OLMOs but also illustrate that accurate results can be achieved with smaller cutoff radii. Moreover, solution of the time-domain NOLMO-TDDFT equations, with low-scaling effort, was also investigated where NOLMO construction is repeatedly performed to maintain the sparsity of NOLMOs in a system.…”

Section: Introductionmentioning

confidence: 86%

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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Section: Introductionmentioning

confidence: 86%

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

Cui¹,

Fang²,

Yang³

2010

J. Phys. Chem. A

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“…Rewriting Eqs. (16) and (17) in the new non-orthogonal MO representation of Eqs. (20) and 21, one obtains after some rearrangement…”

Section: Lr-tddft With Non-orthogonal Mosmentioning

confidence: 99%

“…Neugebauer and co-workers later extended this method. 14,15 Chen et al 16 developed a linear-scaling TDDFT method using the localized density matrix in an orthogonal AO representation, which Yang et al 17 later extended to use non-orthogonal localized molecular orbitals (LMOs). Liu et al 18 derived LMOs from capped fragment canonical MOs and used them to realize a) herbert@chemistry.ohio-state.edu a linear-scaling TDDFT method.…”

Section: Introductionmentioning

confidence: 99%

“…The equation of motion for the time-dependent ALMOs that is derived herein turns out to be the same as in the nonorthogonal LMO treatment of Yang et al 17 Those authors pursued a time-domain approach, which can be advantageous in large systems where numerous excited states are desired, because it does not require propagation of virtual orbitals and therefore sidesteps a significant memory bottleneck in the more traditional frequency-domain approach, at the expense of a large increase in computer time.…”

Section: Introductionmentioning

confidence: 99%

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An efficient and accurate approximation to time-dependent density functional theory for systems of weakly coupled monomers

Liu

Herbert

2015

The Journal of Chemical Physics

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A novel formulation of time-dependent density functional theory (TDDFT) is derived, based on non-orthogonal, absolutely-localized molecular orbitals (ALMOs). We call this approach TDDFT(MI), in reference to ALMO-based methods for describing molecular interactions (MI) that have been developed for ground-state applications. TDDFT(MI) is intended for efficient excited-state calculations in systems composed of multiple, weakly interacting chromophores. The efficiency is based upon (1) a local excitation approximation; (2) monomer-based, singly-excited basis states; (3) an efficient localization procedure; and (4) a one-step Davidson method to solve the TDDFT(MI) working equation. We apply this methodology to study molecular dimers, water clusters, solvated chromophores, and aggregates of naphthalene diimide that form the building blocks of self-assembling organic nanotubes. Absolute errors of 0.1-0.3 eV with respect to supersystem methods are achievable for these systems, especially for cases involving an excited chromophore that is weakly coupled to several explicit solvent molecules. Excited-state calculations in an aggregate of nine naphthalene diimide monomers are ∼40 times faster than traditional TDDFT calculations.

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“…It is shown that the error in the excitation energies due to the frozen orbital approximation is less than 0.01 eV. 28 proposed an alternative O(N) method for excited states. Instead of the density matrix, time-evolution of LMOs is solved by integrating the corresponding TDKS equation.…”

Section: Linear-scaling Calculations Of the Fock Matrixmentioning

confidence: 99%

Linear-scaling quantum mechanical methods for excited states

et al. 2012

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The poor scaling of many existing quantum mechanical methods with respect to the system size hinders their applications to large systems. In this tutorial review, we focus on latest research on linear-scaling or O(N) quantum mechanical methods for excited states. Based on the locality of quantum mechanical systems, O(N) quantum mechanical methods for excited states are comprised of two categories, the time-domain and frequency-domain methods. The former solves the dynamics of the electronic systems in real time while the latter involves direct evaluation of electronic response in the frequency-domain. The localized density matrix (LDM) method is the first and most mature linear-scaling quantum mechanical method for excited states. It has been implemented in time- and frequency-domains. The O(N) time-domain methods also include the approach that solves the time-dependent Kohn-Sham (TDKS) equation using the non-orthogonal localized molecular orbitals (NOLMOs). Besides the frequency-domain LDM method, other O(N) frequency-domain methods have been proposed and implemented at the first-principles level. Except one-dimensional or quasi-one-dimensional systems, the O(N) frequency-domain methods are often not applicable to resonant responses because of the convergence problem. For linear response, the most efficient O(N) first-principles method is found to be the LDM method with Chebyshev expansion for time integration. For off-resonant response (including nonlinear properties) at a specific frequency, the frequency-domain methods with iterative solvers are quite efficient and thus practical. For nonlinear response, both on-resonance and off-resonance, the time-domain methods can be used, however, as the time-domain first-principles methods are quite expensive, time-domain O(N) semi-empirical methods are often the practical choice. Compared to the O(N) frequency-domain methods, the O(N) time-domain methods for excited states are much more mature and numerically stable, and have been applied widely to investigate the dynamics of complex molecular systems.

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Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cited by 32 publications

References 35 publications

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

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

An efficient and accurate approximation to time-dependent density functional theory for systems of weakly coupled monomers

Linear-scaling quantum mechanical methods for excited states

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Reformulating time-dependent density functional theory with non-orthogonal localized molecular orbitals

Cited by 32 publications

References 35 publications

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

An efficient and accurate approximation to time-dependent density functional theory for systems of weakly coupled monomers

Linear-scaling quantum mechanical methods for excited states

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

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