A graphene flake under external electric fields reconstructed from field-perturbed kernels

Huang, Lulu; Massa, Lou; Matta, Chérif F.

doi:10.1016/j.carbon.2014.04.082

Cited by 40 publications

(46 citation statements)

References 56 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[33] The method has been extended to estimate electric field-induced changes in the properties (ie, response properties) of a finite graphene flake. [34] There is, thus, strong evidence supporting the confidence in that the extension of KEM to estimate the total molecular electron density and the total molecular ESP is only awaiting automation, a current interest in our group.…”

Section: The Kernel Energy Methods (Kem)mentioning

confidence: 85%

“…KEM has been shown to be capable of delivering electron densities sampled at bond and ring critical points in addition to the complete localization‐delocalization matrix of a graphene nanoribbon . The method has been extended to estimate electric field‐induced changes in the properties (ie, response properties) of a finite graphene flake . There is, thus, strong evidence supporting the confidence in that the extension of KEM to estimate the total molecular electron density and the total molecular ESP is only awaiting automation, a current interest in our group.…”

Section: The Kernel Energy Methods (Kem)mentioning

confidence: 96%

See 1 more Smart Citation

Fast quantum crystallography

Polkosnik

Matta

Huang

et al. 2019

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

Typical contemporary X‐ray crystallography delivers the geometries and, at best, the electron densities of molecules or periodic systems in the crystalline phase. Energies, electron momentum densities, and information relating to the pair density such as electron delocalization measures—all crucial to chemistry—are simply missed. Quantum crystallography (QCr) is an emerging line of research aimed at filling this gap by solving the crystallographic problem under the constraints of quantum mechanics. In this way, not only geometries and electron densities become experimentally accessible but also the entire panoply of quantum mechanical properties that are in the output of any quantum chemical software package. However, QCr remains limited to smaller systems (small molecules or small unit cells) due to the exponential bottleneck that plagues quantum mechanical calculations. When combined with a fragmentation technique, termed the “kernel energy method (KEM)”, QCr's reach to larger molecules is extended considerably to almost “any size”, that is, systems of up to many hundreds of thousands of atoms. KEM has made this doable with any chemical model and is capable of providing the entire quantum mechanics of large molecular systems. The smallness of the R‐factor adjudicates the accuracy of the quantum mechanics extracted from the crystallography.

show abstract

Section: The Kernel Energy Methods (Kem)mentioning

confidence: 85%

Section: The Kernel Energy Methods (Kem)mentioning

confidence: 96%

Fast quantum crystallography

Polkosnik

Matta

Huang

et al. 2019

Int J of Quantum Chemistry

Self Cite

View full text Add to dashboard Cite

show abstract

“…Details of the Clinton algorithm iterations are presented in Tables (3)(4)(5)(6)(7). Iteration number n 5 0 corresponds to the initial P KEM matrix obtained from the augmented kernel density matrix sum while the last iteration corresponds to P projector .…”

Section: Results Of Kem Energy Calculations On Are Shown Inmentioning

confidence: 99%

“…The details for the four cases that violate the variational theorem are presented in Tables (4)(5)(6)(7). As the iterations progress the P matrix quickly converges to a normalized projector.…”

Section: Results Of Kem Energy Calculations On Are Shown Inmentioning

confidence: 99%

See 1 more Smart Citation

Single determinant N‐representability and the kernel energy method applied to water clusters

Polkosnik

Massa

2017

J Comput Chem

Self Cite

View full text Add to dashboard Cite

The Kernel energy method (KEM) is a quantum chemical calculation method that has been shown to provide accurate energies for large molecules. KEM performs calculations on subsets of a molecule (called kernels) and so the computational difficulty of KEM calculations scales more softly than full molecule methods. Although KEM provides accurate energies those energies are not required to satisfy the variational theorem. In this article, KEM is extended to provide a full molecule single-determinant N-representable one-body density matrix. A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined. This matrix is converted to a normalized projector by an algorithm due to Clinton. The resulting single-determinant N-representable density matrix maps to a quantum mechanically valid wavefunction which satisfies the variational theorem. The process is demonstrated on clusters of three to twenty water molecules. The resulting energies are more accurate than the straightforward KEM energy results and all violations of the variational theorem are resolved. The N-representability studied in this article is applicable to the study of quantum crystallography. © 2017 Wiley Periodicals, Inc.

show abstract