Triangle, equilateral

Hence, the same teclmiques used to calculate are also used for Cg. Note that equation (A1.5.28) has a geometrical factor whose sign depends upon the geometry, and that, unlike tlie case of the two-body dispersion interaction, the triple-dipole dispersion energy has no minus sign in front of the positive coefficient Cg. For example, for an equilateral triangle configuration the triple-dipole dispersion is repulsive and varies... 

The ADT matrix for the lowest two electronic states of H3 has recently been obtained [55]. These states display a conical intersection at equilateral triangle geometi ies, but the GP effect can be easily built into the treatment of the reactive scattering equations. Since, for two electronic states, there is only one nonzero first-derivative coupling vector, w5 2 (Rl), we will refer to it in the rest of this... 

Figure 4. The H3 and H4 loops. Ac the center, the conical intersections are shown schematically an equilateral triangle for H3 and a perfect tetrahedron for Kt, <2p> Jid Q, are the phase-preserving and phase-inverting coordinates, respectively.

The two coordinates defined for H4 apply also for the H3 system, and the conical intersection in both is the most symmetric structure possible by the combination of the three equivalent structures An equilateral triangle for H3 and a perfect tetrahedron for H4. These sbnctures lie on the ground-state potential surface, at the point connecting it with the excited state. This result is generalized in the Section. IV. 

The effect of the Axilrod-Teller term (also known as the triple-dipole correction) is to make the interaction energy more negative when three molecules are linear but to weaken it when the molecules form an equilateral triangle. This is because the linear arrangement enhances the correlations of the motions of the electrons, whereas the equilateral arrangement reduces it. 

The 4 point group is that to which a regular icosahedron, illustrated in Figure 4.13(a), belongs. It contains 20 equilateral triangles arranged in a three-dimensional sttucture. This is the conformation of the anion, in which there is a boron atom, with a hydrogen atom... 

Triangular—Joining the centers of 3 adjacent tubes forms an equilateral triangle. Any side of this triangle is the tube pitch c. 

Draw the equilateral triangle connecting three adjacent tube centers. Any side of the triangle is the tube pitch (recall 1.25 Do is minimum). 

The icosahedron is a roughly spherical object that is built up from 20 identical equilateral triangles. These triangular tiles are arranged side by side in such a way that they enclose the volume inside the icosahedron. Figure 16.3 shows a view of an icosahedron where there are 5 tiles at the top, 5 at the bottom, and 10 in a band around the middle region. These faces are identical in other words, identical icosahedra are obtained irrespective of which of the vertices is at the top in Figure 16.3a. 

The problem must be simplified considerably to permit solution in the context of this book. Suppose an equilateral triangle is subjected to some loads in the vertical direction as in Figure 7-22. A load P of 100 lb (445 N) is applied to the top joint, and that load can go in either the downward or upward direction (in the diagram, not in space ). This truss must take its reversible load with, say, a factor of safety of two against whatever event would cause it to fail. What material, size, and weight of truss element would you select to satisfy the design requirements that include building the structure for the lowest cost ... 

Caps should be arranged on the plate in 60° equilateral layout, with the liquid flowing into Ae apex of the triangle rather than parallel to the base. The liquid flows normal to each row of caps. 

A great deal of evidence has shown that carbocations are planar. The divalent carbon is 5p2-hybridized, and the three substituents are oriented to the corners of an equilateral triangle, as indicated in Figure 6.9. Because there are only six valence electrons on carbon and all six are used in the three a bonds, the p orbital extending above and below the plane is unoccupied. 

Two electron pairs are as far apart as possible when they are directed at 180° to one another. This gives BeF2 a linear structure. The three electron pairs around the boron atom in BF3 are directed toward the comers of an equilateral triangle the bond angles are 120°. We describe this geometry as trigonal planar. 

Trigonal planar The geometry of an AXj molecule where A is at the center of the equilateral triangle formed by three X atoms, 176,185,187t, 191 Trigonal pyramid The geometry of an... 

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