The Kernel energy method: Application to graphene and extended aromatics

Huang, Lulu; Bohórquez, Hugo J.; Matta, Chérif F.; Massa, Lou

doi:10.1002/qua.22975

Cited by 48 publications

(57 citation statements)

References 43 publications

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“…The symbols i and j are running indices and n is the number of single kernels. The validity of this has been shown in previous works (8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18)(19)(20)(21)(22)(23)(24). In this article we use the reliable accuracy of KEM to calculate the interaction energies associated with putative protoribosome molecules.…”

Section: Methods Of Calculationsmentioning

confidence: 63%

Protoribosome by quantum kernel energy method

Huang

Krupkin

Bashan

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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Experimental evidence suggests the existence of an RNA molecular prebiotic entity, called by us the "protoribosome," which may have evolved in the RNA world before evolution of the genetic code and proteins. This vestige of the RNA world, which possesses all of the capabilities required for peptide bond formation, seems to be still functioning in the heart of all of the contemporary ribosome. Within the modern ribosome this remnant includes the peptidyl transferase center. Its highly conserved nucleotide sequence is suggestive of its robustness under diverse environmental conditions, and hence on its prebiotic origin. Its twofold pseudosymmetry suggests that this entity could have been a dimer of self-folding RNA units that formed a pocket within which two activated amino acids might be accommodated, similar to the binding mode of modern tRNA molecules that carry amino acids or peptidyl moieties. Using quantum mechanics and crystal coordinates, this work studies the question of whether the putative protoribosome has properties necessary to function as an evolutionary precursor to the modern ribosome. The quantum model used in the calculations is density functional theory-B3LYP/3-21G*, implemented using the kernel energy method to make the computations practical and efficient. It occurs that the necessary conditions that would characterize a practicable protoribosome-namely (i) energetic structural stability and (ii) energetically stable attachment to substrates-are both well satisfied.bonding apparatus | puromycin | interaction energy | self-assembly | chemical model

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Section: Methods Of Calculationsmentioning

confidence: 63%

Protoribosome by quantum kernel energy method

Huang

Krupkin

Bashan

et al. 2013

Proc. Natl. Acad. Sci. U.S.A.

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“…338 More recent improvements have enabled the KEM to accurately model π-conjugated systems, most notably graphene. 339 The purpose for developing the KEM was to perform quantum calculations on systems with biological importance, such as proteins. By considering a system to be composed of individual "kernels" with known atomic coordinates, the contributions of all kernels in a system can be combined to provide properties for the full system.…”

Section: Kernel Energy Methodsmentioning

confidence: 99%

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

et al. 2011

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Theoretical chemists have always strived to perform quantum mechanics (QM) calculations on larger and larger molecules and molecular systems, as well as condensed phase species, that are frequently much larger than the current state-of-the-art would suggest is possible. The desire to study species (with acceptable accuracy) that are larger than appears to be feasible has naturally led to the development of novel methods, including semiempirical approaches, reduced scaling methods, and fragmentation methods. The focus of the present review is on fragmentation methods, in which a large molecule or molecular system is made more computationally tractable by explicitly considering only one part (fragment) of the whole in any particular calculation. If one can divide a species of interest into fragments, employ some level of ab initio QM to calculate the wave function, energy, and properties of each fragment, and then combine the results from the fragment calculations to predict the same properties for the whole, the possibility exists that the accuracy of the outcome can approach that which would be obtained from a full (nonfragmented) calculation. It is this goal that drives the development of fragmentation methods. Disciplines Chemistry CommentsReprinted (adapted) with permission from Chemical Reviews 112 (2012): 632,

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“…The normalization and the projector property must be enforced on the P matrix as follows from eqs. (3), (5), and (15). The overlap matrix S in the full molecule basis is obtained from the double and single kernel matrices through a process similar to the construction of the augmented density matrix.…”

Section: Discussionmentioning

confidence: 99%

“…[1] The kernel energy method provides softer scaling while maintaining ab initio quality results for the energy. [2][3][4][5][6] In the kernel energy method, the molecule is partitioned into disjoint subsets called kernels. A single kernel is simply a particular choice of a subset of atoms in a molecule.…”

Section: Introductionmentioning

confidence: 99%

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

Polkosnik

Massa

2017

J Comput Chem

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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.

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The Kernel energy method: Application to graphene and extended aromatics

Cited by 48 publications

References 43 publications

Protoribosome by quantum kernel energy method

Protoribosome by quantum kernel energy method

Fragmentation Methods: A Route to Accurate Calculations on Large Systems

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

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