Topological analysis of the charge density of solids:<i>bcc</i>sodium and lithium

Mei, Changjiang; Edgecombe, Kenneth E.; Smith, Vedene H.; Heilingbrunner, Andrea

doi:10.1002/qua.560480503

Cited by 51 publications

(44 citation statements)

References 12 publications

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“…Although in most molecules nuclei are the sole attractors of the charge density and the atomic form is dominant, 2 there have been found systems, both in the gas phase 5,35,36 and in the condensed phase, [37][38][39][40][41] where maxima at position other than nuclei also occur in their charge distribution. These maxima have been called 5 nonnuclear attractors (NNAs) and the union of a (3,Ϫ3) nonnuclear attractor and of the R 3 space traversed by the ٌ paths terminating at the (3,Ϫ3) attractor, has been termed a nonnuclear basin 5 or a pseudoatom 42 because its behavior mimics that of a regular atom in a molecule, but it cannot exist in isolation.…”

Section: Clustersmentioning

confidence: 99%

Chemical information from the source function

2003

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The source function, which enables one to equate the value of the electron density at any point within a molecule to a sum of atomic contributions, has been applied to a number of cases. The source function is a model-independent, quantitative measure of the relative importance of an atom's or group's contribution to the density at any point in a system, and it represents a potentially interesting tool to provide chemical information. It is shown that the source contribution from H to the electron density rho(b) at the bond critical point in HX diatomics decreases with increasing X's electronegativity, and that this decrease is a result of significant changes in the Laplacian distribution within the H-basin. It is also demonstrated that the source function from Li to rho(b) in LiX diatomics is a more sensitive index of atomic transferability than it is the lithium atomic energy or population. The observed changes are such as to ensure a constant percentage source contribution from Li to rho(b) throughout the LiX series, rather than a constant source as one would expect in the limit of perfect atomic transferability. Application of the source function to planar lithium clusters has revealed that the source function clearly discriminates between a nonnuclear electron density maximum and a maximum associated to a nucleus, on the basis of the relative weight of the source contributions from the basin associated to the maximum and from the remaining basins in the cluster. The source function has also allowed for a classification of hydrogen bonds in terms of characteristic source contributions to the density at the H-bond critical point from the H involved in the H-bond, the H-donor D, and the H-acceptor A. The source contribution from the H appears as the most distinctive marker of the H-bond strength, being highly negative for isolated H-bonds, slightly negative for polarized assisted H-bonds, close to zero for resonance-assisted H-bonds, and largely positive for charge-assisted H-bonds. The contributions from atoms other than H, D, and A strongly increase with decreasing H-bond strength, consistently with the parallel increased electrostatic character of the interaction. The correspondence between the classification provided by the Electron Localization Function topologic approach and by the source function has been highlighted. It is concluded that the source function represents a practical tool to disclose the local and nonlocal character of the electron density distributions and to quantify such a locality and nonlocality in terms of a physically sound and appealing chemical partitioning.

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Section: Clustersmentioning

confidence: 99%

Chemical information from the source function

2003

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“…7,8 This method is computationally expensive, it does not describe correctly the atomic charges for polar bonds and for certain systems it gives a nonchemical partitioning. 9 To its defense one might mention that the local properties are transferable, a feature which can not be underestimated if the analysis has to give chemical insight. An alternative method for calculating localized charges has been developed by Cioslowski 10 based on the generalized atomic polar tensor, and Lazzeretti and co-workers 11 have used a similar approach to partition the total molecular polarizability into local contributions.…”

Section: Introductionmentioning

confidence: 99%

Local properties of quantum chemical systems: The LoProp approach

Gagliardi¹,

Lindh²,

Karlström

2004

The Journal of Chemical Physics

342

419

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A new method is presented, which makes it possible to partition molecular properties like multipole moments and polarizabilities, into atomic and interatomic contributions. The method requires a subdivision of the atomic basis set into occupied and virtual basis functions for each atom in the molecular system. The localization procedure is organized into a series of orthogonalizations of the original basis set, which will have as a final result a localized orthonormal basis set. The new localization procedure is demonstrated to be stable with various basis sets, and to provide physically meaningful localized properties. Transferability of the methyl properties for the alkane series and of the carbon and hydrogen properties for the benzene, naphtalene, and anthracene series is demonstrated.

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“…In reality, perturbation of the periodicity by the presence either of a surface or of impurities cause oscillations in the EDD, the so-called Friedel oscillations. In the present paper, however, we refer to non-nuclear maxima with the periodicity of the lattice, such as found by Mei et al [5] in the bcc lattices of lithium and sodium, using the HartreeFock program CRYSTAL [6]. In 1990 Sakata and Sato [7] analyzed the highly accurate x-ray Pendellösung data on Si measured by Saka and Kato [8] with the maximum entropy method (MEM).…”

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confidence: 99%

Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method

1996

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Experimental evidence for the existence of non-nuclear maxima in charge densities is questioned. It is shown that the non-nuclear maxima reported for silicon are artifacts of the maximum entropy method that was used to analyze the x-ray diffraction data. This method can be improved by the use of appropriate prior information. We report systematic tests of the improved method leading to the absence of non-nuclear maxima in Si. Likewise, the non-nuclear maxima reported earlier in beryllium are not substantiated. [S0031-9007(96) [4] recently reported that the presence of the non-nuclear maxima in the Na clusters appears to be a basis-set or method-dependent effect. Unfortunately, no experimental methods exist to confirm or invalidate these theoretical results.We now turn to crystals. Periodicity allows accurate studies of the EDD by x-ray diffraction. In reality, perturbation of the periodicity by the presence either of a surface or of impurities cause oscillations in the EDD, the so-called Friedel oscillations. In the present paper, however, we refer to non-nuclear maxima with the periodicity of the lattice, such as found by Mei et al. [5] in the bcc lattices of lithium and sodium, using the HartreeFock program CRYSTAL [6]. In 1990 Sakata and Sato [7] analyzed the highly accurate x-ray Pendellösung data on Si measured by Saka and Kato [8] with the maximum entropy method (MEM). They found maxima in the electron density in the Si-Si bond. Recently, non-nuclear maxima were also found in Be by Iversen et al. [9], applying the MEM to structure factors that were measured by Larsen and Hansen [10]. These two findings are the first and only experimental support for the rather elusive non-nuclear maxima. They constitute a considerable challenge to theoretical solid state physics, since the many present wave-function calculations on Si, including our own [11], do not corroborate the result. Since we do not doubt the quality of the primary data in the MEM analysis, we decided to reassess the MEM procedure itself and test its ability to bring to light subtle features in electron density maps. In the course of the work we discovered the essential role of the prior assumptions in the analysis, a role that has not yet received the attention it deserves.Structure factors, obtained from a single crystal x-ray experiment, are directly related to the EDD by means of a Fourier transform. The problems one is facing when performing the inverse Fourier transformation are that (i) the experiment provides us with a limited number of structure factors, (ii) all structure factors are determined within a certain experimental error, and (iii) the phase of the structure factors is unknown. In case the crystal is centrosymmetric the phases can usually be derived without any ambiguity and only the first two problems remain.The traditional way to extract the EDD from a limited set of noisy data is to fit the structure factors by a model. The drawback of this method is that features which are not allowed by the model will never show up in the ED...

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Topological analysis of the charge density of solids:bccsodium and lithium

Cited by 51 publications

References 12 publications

Chemical information from the source function

Chemical information from the source function

Local properties of quantum chemical systems: The LoProp approach

Critical Analysis of Non-Nuclear Electron-Density Maxima and the Maximum Entropy Method

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