Energy bounds for isoelectronic molecular sets and the implicated order

Daza, Edgar E.; Bernal, Andrés

doi:10.1007/s10910-005-5411-y

Cited by 8 publications

(3 citation statements)

References 9 publications

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“…Overall, exhaustive charge-neutral and isoelectronic BN doping in naphthalene leads to 2285 unique derivatives for which we have used ACE to establish energetic ranks. Having identified all alchemical enantiomers through exhaustive scanning within one stoichiometry [stoichiometries as a whole can be ranked with existing relations ( 49 – 51 )], we have ranked all possible molecules using ACE within groups of molecules approximately degenerate in electronic energy. These groups form the connected components of a graph where all molecules are nodes and only alchemical enantiomers are connected, thus allowing us to exploit the transitivity of the electronic energy degeneracy.…”

Section: Resultsmentioning

confidence: 99%

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Rudorff

Lilienfeld

2021

Sci. Adv.

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Brute-force compute campaigns relying on demanding ab initio calculations routinely search for previously unknown materials in chemical compound space (CCS), the vast set of all conceivable stable combinations of elements and structural configurations. Here, we demonstrate that four-dimensional chirality arising from antisymmetry of alchemical perturbations dissects CCS and defines approximate ranks, which reduce its formal dimensionality and break down its combinatorial scaling. The resulting “alchemical” enantiomers have the same electronic energy up to the third order, independent of respective covalent bond topology, imposing relevant constraints on chemical bonding. Alchemical chirality deepens our understanding of CCS and enables the establishment of trends without empiricism for any materials with fixed lattices. We demonstrate the efficacy for three cases: (i) new rules for electronic energy contributions to chemical bonding; (ii) analysis of the electron density of BN-doped benzene; and (iii) ranking over 2000 and 4 million BN-doped naphthalene and picene derivatives, respectively.

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Section: Resultsmentioning

confidence: 99%

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Rudorff

Lilienfeld

2021

Sci. Adv.

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“…Nevertheless, the Harris approach to employ (perturbative) approximate densities has been useful in improving convergence [11] or in deriving kinetic energy functionals in the context of orbital-free DFT [12]. Other approaches were introduced by Foldy and Wilson, Reif, Frost, and Daza [13][14][15][16][17]. The transition functional method of Nagy [18] allows to calculate energy differences of two molecules if both their electron densities are known.…”

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confidence: 99%

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

Rudorff

Lilienfeld

2019

J. Phys. Chem. B

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Based on thermodynamic integration we introduce atoms in molecules (AIM) using the orbital-free framework of alchemical perturbation density functional theory (APDFT). Within APDFT, atomic energies and electron densities in molecules are arbitrary because any arbitrary reference system and integration path can be selected as long as it meets the boundary conditions. We choose the uniform electron gas as the most generic reference, and linearly scale up all nuclear charges, situated at any query molecule's atomic coordinates. Within the approximations made when calculating one-particle electron densities, this choice affords exact and unambiguous definitions of energies and electron densities of AIMs We illustrate the approach for neutral iso-electronic diatomics (CO, N2, BF), various small molecules with different electronic hybridisation states of carbon (CH4, C2H6, C2H4, C2H2, HCN), and for all the possible BN doped mutants connecting benzene to borazine (C2nB3−nN3−nH6, 0 ≤ n ≤ 3). Analysis of the numerical results obtained suggests that APDFT based AIMs enable meaningful and new interpretations of molecular energies and electron densities.

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“…For an N -atom molecule it is a 3 × (N − 1)-dimensional space where each point corresponds to a 3D molecular conformation.2 A structure called partially ordered set (poset). Posets are widely used tools in many theoretical chemistry problems[14][15][16][17][18][19][20][21][22].…”

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confidence: 99%

A central partition of molecular conformational space. II. embedding 3D structures

Gabarro-Arpa

The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society

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Abstract-In the first work of this series [1] it was shown that the conformational space of a molecule could be described to a fair degree of accuracy by means of a central hyperplane arrangement. The hyperplanes divide the espace into a hierarchical set of cells that can be encoded by the face lattice poset of the arrangement. The model however, lacked explicit rotational symmetry which made impossible to distinguish rotated structures in conformational space. This problem was solved in a second work [2] by sorting the elementary 3D components of the molecular system into a set of morphological classes that can be properly oriented in a standard 3D reference frame. This also made possible to find a solution to the problem that is being adressed in the present work: for a molecular system immersed in a heat bath we want to enumerate the subset of cells in conformational space that are visited by the molecule in its thermal wandering. If each visited cell is a vertex on a graph with edges to the adjacent cells, here it is explained how such graph can be built.

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Energy bounds for isoelectronic molecular sets and the implicated order

Cited by 8 publications

References 9 publications

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Simplifying inverse materials design problems for fixed lattices with alchemical chirality

Atoms in Molecules from Alchemical Perturbation Density Functional Theory

A central partition of molecular conformational space. II. embedding 3D structures

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