Moment expansion of the linear density‐density response function

Scherrer, Arne; Sebastiani, Daniel

doi:10.1002/jcc.24248

Cited by 6 publications

(26 citation statements)

References 61 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The second theorem gives rise to a much more efficient algorithm for the calculation of the moment‐expanded states (referred to as direct moment expansion). For the brute force construction of the transformation Q derived in theorem (which corresponds to the algorithm of the moment expansion published in 2016 ) a large number of M eigenstates are calculated, followed by M × N Givens rotations to condense the physically information.…”

Section: Application Of Theorem 1 and 2 To The Linear Density‐densitymentioning

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%

“…Remarks for the special case of

\overset{T}{true} : V_{pert} \mapsto n^{resp}

: For the specific choice of Racah normalized irrgelular solid harmonics as basis functions for the expression of the pertubing potential, Scherrer et al showed in 2016, the existence of the moment expansion. In this article, we put the moment expansion on a more solid mathematical fundament and generalize it to arbitrary self‐adjoint, positive, and compact operators (and arbitrary bases of the domain of these operators). The set { P n | n ∈ ℕ} denotes the basis functions for the domain of

\overset{T}{true}

, which is different for every molecule.…”

mentioning

confidence: 99%

See 3 more Smart Citations

Efficient representation of the linear density‐density response function

et al. 2019

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Section: Application Of Theorem 1 and 2 To The Linear Density‐densitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

“…Remarks for the special case of

\overset{T}{true} : V_{pert} \mapsto n^{resp}

\overset{T}{true}

, which is different for every molecule.…”

mentioning

confidence: 99%

See 2 more Smart Citations

Efficient representation of the linear density‐density response function

et al. 2019

Self Cite

View full text Add to dashboard Cite

show abstract

“…In With respect to this basis of the pertubing potential, Scherrer presented in 2016 an algorithm for a transformation of the eigenstates, which condenses the full information of the linear map into a few moment generating states. [47] We refer to the new set of states…”

Section: Introductionmentioning

confidence: 99%

Reduced eigensystem representation of the linear density‐density response function

Dreßler

Sebastiani

2019

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

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.

show abstract

Polarization Energies from Efficient Representation of the Linear Density–Density Response Function

Dreßler

Sebastiani

2021

Advcd Theory and Sims

Self Cite

View full text Add to dashboard Cite

The authors present a proof‐of‐concept study for the calculation of atomic forces on a solvated molecule by means of the linear density–density response function in its moment expanded representation. The density–density response function represents an efficient way to compute molecular forces for arbitrary external potentials via an ab initio scheme, without the need to perform an explicit self‐consistent quantum chemical calculation for each configuration of the chemical environment. Here, the authors show that it is indeed possible to determine the atomic forces of interacting bulk‐like molecular complexes due to polarization effects of the surrounding molecules with good accuracy. This study represents a significant step the practical applicability of the approach, which is still in a development phase. The potential application of the computational scheme in terms of molecular dynamics simulations is illustrated by considering a variety of cluster conformations, as they would be found within a molecular dynamics trajectory.

show abstract

Moment expansion of the linear density‐density response function

Cited by 6 publications

References 61 publications

Efficient representation of the linear density‐density response function

Efficient representation of the linear density‐density response function

Reduced eigensystem representation of the linear density‐density response function

Polarization Energies from Efficient Representation of the Linear Density–Density Response Function

Contact Info

Product

Resources

About