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Theoretical study of lithium clusters by electronic stress tensor
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Figures

Image of FIG. 1.

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FIG. 1.

The largest eigenvalue of the stress tensor (color map) and corresponding eigenvector (black rods) of H2 at various internuclear distances: (a) 0.5 Å, (b) 0.743 Å (equilibrium distance), (c) 2.20 Å (intrinsic electronic transition state) and (d) 3.0 Å. As for the eigenvectors, the projection on this plane is plotted. The red solid line denotes a contour where the eigenvalue is zero. The green dashed line denotes a contour where the kinetic energy density is zero (electronic interface).

Image of FIG. 2.

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FIG. 2.

The largest eigenvalue of the stress tensor and corresponding eigenvector of Li2 at various internuclear distances (a) 1.5 Å, (b) 2.69 Å (equilibrium distance), (c) 2.78 Å, (d) 3.31 Å, (e) 3.36 Å, (f) 4.0 Å, (g) 5.43 Å (intrinsic electronic transition state) and (h) 6.0 Å. Plotted in the same manner as Fig. 1.

Image of FIG. 3.

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FIG. 3.

The largest eigenvalue of the stress tensor and corresponding eigenvector of LiH at various internuclear distances: (a) 1.0 Å, (b) 1.61 Å (equilibrium distance), (c) 3.38 Å (intrinsic electronic transition state) and (d) 4.0 Å. Plotted in the same manner as Fig. 1.

Image of FIG. 4.

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FIG. 4.

Three eigenvalues of the stress tensor for H2 (panel (a)), Li2 (panel (b)) and LiH (panel (c)) along the internuclear axis. The red solid lines are for the largest eigenvalue (λ3), the green dashed lines are for the second largest eigenvalue (λ2) and the blue dotted lines are for the smallest eigenvalue (λ1). The internuclear distances are set to be their equilibrium distances. The origin of the abscissa corresponds to the midpoint of two nuclei.

Image of FIG. 5.

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FIG. 5.

Three eigenvalues of the stress tensor for Li2 along the internuclear axis at various internuclear distances: (a) 1.5 Å, (b) 2.78 Å, (c) 3.31 Å and (d) 6.0 Å. The red solid lines are for the largest eigenvalue (λ3), the green dashed lines are for the second largest eigenvalue (λ2) and the blue dotted lines are for the smallest eigenvalue (λ1).

Image of FIG. 6.

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FIG. 6.

Optimized structures of Li clusters: (a) Li3 (C 2v ), (b) Li4 (D 2h ), (c) Li5 (C s ), (d) Li6 (D 4h ), (e) Li7 (D 5h ) and (f) Li8 (T d ). The bonds are drawn at which the Lagrange points are found.

Image of FIG. 7.

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FIG. 7.

The largest eigenvalue of the stress tensor (color map) and corresponding eigenvector for Li clusters Li n (n = 3 ∼ 6). Plotted in similar manner to Fig. 1. The filled circles denote the positions of the atoms and the numbers in parentheses correspond to those labelled in Fig. 6.

Image of FIG. 8.

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FIG. 8.

The largest eigenvalue of the stress tensor (color map) and corresponding eigenvector for Li clusters Li n (n = 7 ∼ 8). The optimized structures are used. Plotted in similar manner to Fig. 7.

Image of FIG. 9.

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FIG. 9.

The relation between the differential eigenvalues, λ D32 = λ3 − λ2 and λ D21 = λ2 − λ1, at the Lagrange points in the Li clusters (panel (a)) and hydrocarbon molecules (panel (b)). Note that the H2 molecule has λ D32 = 0.394 and λ D21 = 0.

Tables

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Table I.

The bond length and the eigenvalues λ i (i = 1, 2, 3) of the electronic stress tensor at the Lagrange point for H2, Li2 and LiH.

Generic image for table

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Table II.

The bond length and the eigenvalues λ i (i = 1, 2, 3) of the electronic stress tensor at the Lagrange point for bonds in the Li clusters. The numbers in the second column correspond to those labelled in Fig. 6.

Generic image for table

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Table III.

The bond length and the eigenvalues λ i (i = 1, 2, 3) of the electronic stress tensor at the Lagrange point for bonds in the Na clusters. Since Na3 and Na4 respectively have C 2v and D 2h symmetry groups, which are same as the Li cluster case, one may refer to Fig. 6 for the numbers in the second column. Note that we do not find the Lagrange point between the atoms 1 and 3 (with the separation of 4.371 Å) of Na3.

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/content/aip/journal/adva/2/4/10.1063/1.4774037
2012-12-28
2014-04-18

Abstract

We study the electronic structure of small lithium clusters Li n (n = 2 ∼ 8) using the electronic stress tensor. We find that the three eigenvalues of the electronic stress tensor of the Li clusters are negative and degenerate, just like the stress tensor of liquid. This leads us to propose that we may characterize a metallic bond in terms of the electronic stress tensor. Our proposal is that in addition to the negativity of the three eigenvalues of the electronic stress tensor, their degeneracy characterizes some aspects of the metallic nature of chemical bonding. To quantify the degree of degeneracy, we use the differential eigenvalues of the electronic stress tensor. By comparing the Li clusters and hydrocarbon molecules, we show that the sign of the largest eigenvalue and the differential eigenvalues could be useful indices to evaluate the metallicity or covalency of a chemical bond.

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Scitation: Theoretical study of lithium clusters by electronic stress tensor
http://aip.metastore.ingenta.com/content/aip/journal/adva/2/4/10.1063/1.4774037
10.1063/1.4774037
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