A novel definition of a molecule in a crystal

Spackman, Mark A.; Byrom, P. G.

doi:10.1016/s0009-2614(97)00100-0

Cited by 1,105 publications

(481 citation statements)

References 24 publications

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“…A disadvantage is that functions of the electron density such as the electric field can take somewhat longer to compute than the electron density. The Hirshfeld surface 17,18 possesses properties that lend it to partitioning of a crystalline electron density into molecular fragments, and it was, in fact, devised for the determination of molecular dipole moments in molecular crystals. It is based on a generalization of Hirshfeld's stockholder partitioning scheme 19 and defines a weight function for a molecule in a crystal to be the ratio of the promolecular and procystal electron densities at each point in space,…”

Section: ͑8͒mentioning

confidence: 99%

“…The Hirshfeld surface is computationally inexpensive to evaluate, and unlike partitioning schemes such as AIM, or those based on WignerSeitz or Voronoi polyhedra, the Hirshfeld surface is smooth and continuously differentiable everywhere, partitioning the crystal into molecular regions as well as small intermolecular voids, and the consequences of this latter point are discussed below. 17 For surfaces with these attributes, the time required for conventional integration over the volume would be substantially larger than the surface generation time; hence, the use of surface integrals to evaluate moments of the charge density would seem to provide an attractive alternative, and it is the purpose of this paper to present appropriate expressions for dipole, second, and quadrupole moments. Although the bulk of published work using Hirshfeld surfaces has been focused on their applications in crystal structure analysis, [21][22][23] the original publication describing this novel surface presented tentative results for dipole moments based on crude volume integrations, and the present work may be considered a refinement of that earlier approach.…”

Section: ͑8͒mentioning

confidence: 99%

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Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces

Whitten

Radford

McKinnon

et al. 2006

The Journal of Chemical Physics

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Interaction-induced dipoles of hydrogen molecules colliding with helium atoms: A new ab initio dipole surface for high-temperature applications J. Chem. Phys. 136, 044320 (2012) Elegant expressions are derived for the computation of dipole and quadrupole moments of molecules using the electrostatic potential and electric field evaluated on an oriented molecular surface. These expressions are implemented for Hirshfeld surfaces, applied to various molecular crystals, and compared with the results from the quantum theory of atoms in molecules. The effect of intermolecular interactions is also explored by examining the differences between electrostatic moments derived from a periodic Hartree-Fock electron density and an electron density resulting from a superposition of noninteracting molecules. The enhancement of the dipole moment for hydrogen bonded molecular crystals is typically 30%-40% and shown to be largely independent of the partitioning scheme. Dipole moments calculated from Hirshfeld surfaces systematically underestimate those from zero-flux surfaces, a result attributed to the translation of the Hirshfeld surface relative to the zero-flux surfaces for these molecules. For acetylene and benzene, the differences between a crystal calculation and the sum of noninteracting molecules are small, and both partitioning schemes yield quadrupole and second moment results in close agreement.

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Section: ͑8͒mentioning

confidence: 99%

Section: ͑8͒mentioning

confidence: 99%

Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces

Whitten

Radford

McKinnon

et al. 2006

The Journal of Chemical Physics

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“…Although procrystal analysis was originally developed for the examination of Hirshfeld surfaces in molecular crystals [9,10], it also performed well in the characterization of voids in metal-organic/covalent organic frameworks [11] and migration pathways in ionic solids [12]. In its course, the so-called "procrystal" is constructed from the known crystal structure by centering spherically averaged electron density at ( ) r ρ at the atomic positions.…”

Section: Procrystal-void Analysismentioning

confidence: 99%

Diffusion Pathways and Activation Energies in Crystalline Lithium-Ion Conductors

Wiedemann

Islam

Bredow

et al. 2017

Zeitschrift Für Physikalische Chemie

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Geometric information about ion migration (diffusion pathways) and knowledge about the associated energy landscape (migration activation barriers) are essential cornerstones for a comprehensive understanding of lithium transport in solids. Although many lithium-ion conductors are discussed, developed, and already used as energy-storage materials, fundamental knowledge is often still lacking. In this microreview, we give an introduction to the experimental and computational methods used in our subproject within the research unit FOR 1277, "Mobility of Lithium Ions in Solids (molife)". These comprise, amongst others, neutron diffraction, topological analyses (procrystal-void analysis and VoronoiDirichlet partitioning), examination of scattering-length density maps reconstructed via maximum-entropy methods (MEM), analysis of probability-density functions (PDFs) and one-particle potentials (OPPs), as well as climbing-image nudged-elastic-band (cNEB) computations at density-functional theory (DFT) level. The results of our studies using these approaches on ternary lithium oxides and sulfides with different conduction characteristics (fast/slow) and dimensionalities (one-/two-/three-dimensional) are summarized, focusing on the close orbit of the research unit. Not only did the investigations elucidate the lithiumdiffusion pathways and migration activation energies in the studied compounds, but we also established a versatile set of methods for the evaluation of data of differing quality.

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“…Historically, the Hirshfeld surface (HS) emerged from an effort to define the space occupied by a molecule in a crystal for the purpose of partitioning crystalline electron density into molecular fragments (Spackman and Byrom 1997). Such a surface was named in honour of F. L. Hirshfeld, who introduced the "stockholder partitioning" scheme (Hirshfeld 1977).…”

Section: Hirshfeld Surface Analysismentioning

confidence: 99%

Different molecular assemblies in two new phosphoric triamides with the same C(O)NHP(O)(NH)2 skeleton: crystallographic study and Hirshfeld surface analysis

et al. 2017

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Different molecular assemblies were compared in two new structures [4-CH 3 -C 6 H 4 C(O)NH]P(O) [NH] 2 (-CH 2 ) 3 , 1, and [4-CH 3 -C 6 H 4 C(O)NH]P(O) [NHC 6 H 3 (3, ) 2 ] 2 , 2, belonging to the families of "cyclic phosphoric triamide" and "phosphoric triamide", respectively. The differences in the hydrogen bond motifs were discussed (by single crystal X-ray diffraction) as a result of three factors: (1) action of two N atoms with a non-planar environment in 1 as an H-bond acceptor, (2) different orientations of three N-H bond vectors in two molecules and (3) different conformations of C=O and P=O groups. These differences lead to more complicated hydrogen bond pattern of 1, with respect to that of 2, as structure 1 may be considered as a model of four-acceptor-three-donor versus a two-acceptorthree-donor system in 2. The main discrepancies of 1 and 2, monitored by the Hirshfeld surface analysis, are related to the contribution portions of O···H/H···O contacts, in which compound 1 not only involves the greater existence of classical hydrogen bonds but also contains the further C-H···O weak interactions in its crystal packing with respect to compound 2. Instead, in 2, the shortage of O···H/H···O contacts has been partially compensated by the C···H/H···C interactions, due to the presence of more unsaturated carbon acceptors. The differences in assemblies are also reflected in the solid-state IR spectra, especially for the N-H vibration frequencies. The new compounds were further studied by 1D NMR experiments ( 1 H, 13 C, 31 P), 2D NMR techniques [HMQC and HMBC (H-C correlation), HSQC (N-H correlation)], high-resolution ESI-MS, EI-MS spectrometry and IR spectroscopy.

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A novel definition of a molecule in a crystal

Cited by 1,105 publications

References 24 publications

Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces

Dipole and quadrupole moments of molecules in crystals: A novel approach based on integration over Hirshfeld surfaces

Diffusion Pathways and Activation Energies in Crystalline Lithium-Ion Conductors

Different molecular assemblies in two new phosphoric triamides with the same C(O)NHP(O)(NH)2 skeleton: crystallographic study and Hirshfeld surface analysis

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