Electronic density response to molecular geometric changes from explicit electronic susceptibility calculations

Ihrig, Arvid Conrad; Scherrer, Arne; Sebastiani, Daniel

doi:10.1063/1.4819070

Cited by 8 publications

(20 citation statements)

References 40 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…One way to systematically improve the predictive accuracy consists of including increasingly higher-order terms. Sebastiani and coworkers [67,69,70] as well as Geerlings, De Proft and others [71][72][73] proposed promising approaches in this direction. For example, akin to our discussion above, Benoit, Sebastiani and Parrinello investigated the performance of second order linear response theory for screening the potential energy surface of the water dimer, and achieved very high predictive power.…”

Section: Linearizing Chemical Spacementioning

confidence: 99%

Quantum Mechanical Treatment of Variable Molecular Composition: From 'Alchemical' Changes of State Functions to Rational Compound Design

Chang

Lilienfeld

2014

Chimia

View full text Add to dashboard Cite

'Alchemical' interpolation paths, i.e. coupling systems along fictitious paths without realistic correspondence, are frequently used within materials and molecular modeling simulation protocols for the estimation of changes in state functions such as free energies. We discuss alchemical changes in the context of quantum chemistry, and present illustrative numerical results for the changes of HOMO eigenvalue of the He atom due to alchemical teleportation - the simultaneous annihilation and creation of nuclear charges at different locations. To demonstrate the predictive power of alchemical first order derivatives (Hellmann-Feynman) the covalent bond potential of hydrogen fluoride and hydrogen chloride is investigated, as well as the hydrogen bond in the water-water and water-hydrogen fluoride dimer, respectively. Based on converged electron densities for one configuration, the versatility of alchemical derivatives is exemplified for the screening of entire binding potentials with reasonable accuracy. Finally, we discuss new constraints for the identification of non-linear coupling potentials for which the energy's Hellmann-Feynman derivative will yield accurate predictions.

show abstract

Section: Linearizing Chemical Spacementioning

confidence: 99%

Quantum Mechanical Treatment of Variable Molecular Composition: From 'Alchemical' Changes of State Functions to Rational Compound Design

Chang

Lilienfeld

2014

Chimia

View full text Add to dashboard Cite

show abstract

“…However, preliminary results indicate that an adequate expansion in terms of normal coordinates may be able to yield accurate response functions for variable molecular geometries. In a previous work, we have already shown that the density‐density response function is capable of describing the change of the ground‐state density due to a variation of the molecular geometry . The actual dependence of the response function on the molecular geometry itself is currently under investigation.…”

Section: Discussionmentioning

confidence: 93%

Moment expansion of the linear density‐density response function

Scherrer

Sebastiani

2015

J Comput Chem

Self Cite

View full text Add to dashboard Cite

We present a low rank moment expansion of the linear density-density response function. The general interacting (fully nonlocal) density-density response function is calculated by means of its spectral decomposition via an iterative Lanczos diagonalization technique within linear density functional perturbation theory. We derive a unitary transformation in the space of the eigenfunctions yielding subspaces with well-defined moments. This transformation generates the irreducible representations of the density-density response function with respect to rotations within SO(3). This allows to separate the contributions to the electronic response density from different multipole moments of the perturbation. Our representation maximally condenses the physically relevant information of the density-density response function required for intermolecular interactions, yielding a considerable reduction in dimensionality. We illustrate the performance and accuracy of our scheme by computing the electronic response density of a water molecule to a complex interaction potential. © 2015 Wiley Periodicals, Inc.

show abstract

“…This function is very general, as it yields the response density for any perturbation potential, but in turn, it is not readily available explicitly in numerical form. Nevertheless, there is a path for the explicit calculation of this complex quantity by means of a particular mathematical representation (using the eigenfunctions and eigenvalues of the density‐density‐response function seen as a matrix operator) . The straightforward calculation has been shown to be accurate yet computationally cumbersome.…”

Section: Introductionmentioning

confidence: 99%

“…A possible attempt to overcome these problems is to apply the spectral theorem of compact and self‐adjoint operators. Thus, we can express the action of the operator

\overset{T}{true}

to a vector f ( r ) as:

\overset{T}{true} ((), f ((), r)) = \sum_{i = 1}^{\infty} χ_{i} ((), r) λ_{i} (〈〉,, χ_{i}, f)

using eigenvalues λ i and eigenfunctions χ i ( r ), which can be stored without difficulties . The eigenfunctions and eigenvalues satisfy

\overset{T}{true} χ_{i} ((), r) = λ_{i} χ_{i} ((), r)

.…”

Section: Introductionmentioning

confidence: 99%

“…For our specific example of

\overset{T}{true} : V_{pert} ((), r) \mapsto n^{resp} ((), r)

with χ ( r , r ′) equal to the molecular density‐density response function, there is a suitable way to compute and store the most significant subset of eigenvalues and eigenfunctions. We were able to calculate the eigensystem representation and could already show that the calculation of converged response densities would require several thousand eigenvalues and eigenstates . We want to emphasize that we furthermore have to calculate several thousand scalar products for the evaluation of each single perturbing potential.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

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

Electronic density response to molecular geometric changes from explicit electronic susceptibility calculations

Cited by 8 publications

References 40 publications

Quantum Mechanical Treatment of Variable Molecular Composition: From 'Alchemical' Changes of State Functions to Rational Compound Design

Quantum Mechanical Treatment of Variable Molecular Composition: From 'Alchemical' Changes of State Functions to Rational Compound Design

Moment expansion of the linear density‐density response function

Efficient representation of the linear density‐density response function

Contact Info

Product

Resources

About