Iterative approach for the moment representation of the density-density response function

Ahlert, Paul; Scherrer, Arne; Dreßler, Christian; Sebastiani, Daniel

doi:10.1140/epjb/e2018-90040-x

Cited by 4 publications

(13 citation statements)

References 35 publications

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“…Ahlert et al developed already an idea how to obtain the moment expanded states without calculation of thousands of eigenstates. In the next theorem we put this approach to the next level and show how to obtain the first N moment expand states within N ab inito calculations (by means of the a cholesky decompostion of a N × N matrix):Theorem Let

\overset{T}{true}

be the linear operator , {| P n 〉 | n ∈ ℕ} the orthonormal basis of the domain of

\overset{T}{true}

and {| ξ n 〉 | n ∈ ℕ} the moment expanded states from Theorem .…”

Section: Direct Moment Expansionmentioning

confidence: 99%

“…For the specific case of the static linear density‐density response function and a specific basis of the perturbing potential, we recently published a recipe for the calculation of the eigensystem representation as well as the moment expansion . Here, we generalize these results to an entire class of linear operators and arbitrary basis sets.…”

Section: Introductionmentioning

confidence: 98%

“…The straightforward calculation has been shown to be accurate yet computationally cumbersome. Here, we provide a mathematical study of a recently developed, considerably more efficient variant for the computation and the storage of this quantity (called the moment representation of this response function ).…”

Section: Introductionmentioning

confidence: 99%

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Efficient representation of the linear density‐density response function

et al. 2019

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We present a thorough derivation of the mathematical foundations of the representation of the molecular linear electronic density-density response function in terms of a computationally highly efficient moment expansion. Our new representation avoids the necessities of computing and storing numerous eigenfunctions of the response kernel by means of a considerable dimensionality reduction about from 10 3 to 10 1 . As the scheme is applicable to any compact, self-adjoint, and positive definite linear operator, we present a general formulation, which can be transferred to other applications with little effort. We also present an explicit application, which illustrates the actual procedure for applying the moment expansion of the linear density-density response function to a water molecule that is subject to a varying external perturbation potential.

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\overset{T}{true}

be the linear operator , {| P n 〉 | n ∈ ℕ} the orthonormal basis of the domain of

\overset{T}{true}

and {| ξ n 〉 | n ∈ ℕ} the moment expanded states from Theorem .…”

Section: Direct Moment Expansionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

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Efficient representation of the linear density‐density response function

et al. 2019

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“…Umerbekova et al look at the renormalization of energy levels and the enhancement of polarizability of molecules at surfaces with subsystem TDDFT [28]. In [29] Ahlert et al present an iterative approach for the moment representation of the densitydensity response function. Finally, Dinh et al discuss extensions of time-dependent theories in order to include incoherent dynamical correlations [30].…”

Section: This Special Issuementioning

confidence: 99%

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

et al. 2018

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“…[47] In order to tackle this problem, we developed a more efficient, iterative algorithm (referred to as direct moment expansion), which needs a single DFPT calculation per moment expanded state. [49,50] F I G U R E 1 Principal illustration of the response density of the water molecule (right) due to a perturbing water molecule (left). The potential originated from the left water molecule can be expanded at the responding (right) water molecule within a few basis functions…”

Section: Introductionmentioning

confidence: 99%

Reduced eigensystem representation of the linear density‐density response function

Dreßler

Sebastiani

2019

Int J of Quantum Chemistry

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The linear density-density response function represents a formulation of the generalized density response of a molecular (or extended) system to arbitrary perturbing potentials. We have recently established an approach for reducing the dimension of the (in principle infinite) eigenspace representation (the moment expansion) and generalized it to arbitrary self-adjoint, positive-definite, and compact linear operators. Here, we present a modified representation-the reduced eigensystem representation-which allows to define a trivial criterion for the convergence of the approximation to the density response. By means of this novel eigensystem-like structure, the remarkable reduction of the dimensionality becomes apparent for the calculation of the density-density response function.

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Iterative approach for the moment representation of the density-density response function

Cited by 4 publications

References 35 publications

Efficient representation of the linear density‐density response function

Efficient representation of the linear density‐density response function

Special issue in honor of Eberhard K.U. Gross for his 65th birthday

Reduced eigensystem representation of the linear density‐density response function

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