Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems<sup>†</sup>

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

doi:10.1021/jp1027838

Cited by 12 publications

(26 citation statements)

References 45 publications

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“…The relative reduction in localization between OLMOs and NLMOs is similar to that obtained with the algorithms that fix NLMO localization centers [33,34]. Since the NLMOs centers were previously fixed at the position of OLMOs centers this implies that the locations of the centers of NLMOs and OLMOs are very similar.…”

Section: Compromise Between Locality and Orthogonalitysupporting

confidence: 71%

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

Luo

Khaliullin

2020

J. Chem. Theory Comput.

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Spatially localized one-electron orbitals, orthogonal and nonorthogonal, are widely used in electronic structure theory to describe chemical bonding and speed up calculations. In order to avoid linear dependencies of localized orbitals, the existing localization methods either constrain orbital transformations to be unitary, that is, metric preserving, or, in the case of variable-metric methods, fix the centers of nonorthogonal localized orbitals. Here, we developed a different approach to orbital localization, in which these constraints are replaced with a single restriction that specifies the maximum allowed deviation from the orthogonality for the final set of localized orbitals. This reformulation, which can be viewed as a generalization of existing localization methods, enables one to choose the desired balance between the orthogonality and locality of the orbitals. Furthermore, the approach is conceptually and practically simple as it obviates the necessity in unitary transformations and allows to determine optimal positions of the centers of nonorthogonal orbitals in a unconstrained and straightforward minimization procedure. It is demonstrated to produce welllocalized orthogonal and nonorthogonal orbitals with the Berghold and Pipek-Mezey localization functions for a variety of molecules and periodic materials including large systems with non-trivial bonding.

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Section: Compromise Between Locality and Orthogonalitysupporting

confidence: 71%

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

Luo

Khaliullin

2020

J. Chem. Theory Comput.

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“…In addition to the traditional localization techniques, CP2K offers localization methods that produce nonorthogonal LMOs (NLMOs) [199]. In these methods, matrix A is not restricted to be unitary and the minimized objective function contains two terms: a localization functional Ω L given by Eq.…”

Section: A Localization Of Orthogonal and Non-orthogonal Molecular Or...mentioning

confidence: 99%

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

Kühne,

Iannuzzi,

Del Ben

et al. 2020

Preprint

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CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular and biological systems. It is especially aimed at massively-parallel and linear-scaling electronic structure methods and state-of-the-art ab-initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

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“…Density operator, r(t), can also be constructed with NOLMOs, |j i |, which are the most localized representation of electronic degrees of freedom, because the orthogonality constraints between MOs are removed among NOLMOs. 56 With NOLMOs, the density operator is expressed as…”

Section: O(n)mentioning

confidence: 99%

“…Moreover, the Fock matrix F in the LMO representation is a sparse matrix. Thus, the time-domain integration of eqn (56) needs only O(N) floatingpoint calculations. Fig.…”

Section: O(n)mentioning

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

Cited by 12 publications

References 45 publications

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

Linear-scaling quantum mechanical methods for excited states

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Efficient Construction of Nonorthogonal Localized Molecular Orbitals in Large Systems†

Cited by 12 publications

References 45 publications

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

Direct Unconstrained Variable-Metric Localization of One-Electron Orbitals

CP2K: An Electronic Structure and Molecular Dynamics Software Package -- Quickstep: Efficient and Accurate Electronic Structure Calculations

Linear-scaling quantum mechanical methods for excited states

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