Tetrahedron orientation

J. M. Tedder and J. C. Walton, The Importance of Polarity and Steric Effects in Determining the Rate and Orientation of Free Radical Addition to Olefins Rules for Determining the Rate and Preferred Orientation , Tetrahedron, 1980, 36, 701. 

FIGURE 3.16 Three common hybridization schemes shown as outlines of the amplitude of the wavefunction and in terms of the orientations of the hybrid orbitals, (a) An s-orbital and a p-orbital hybridize into two sp hybrid orbitals that >oint in opposite direc tions, forming a linear molecular shape, (b) An s-orbital and two p-orbitals can blend together to give three ip hybrid orbitals that point to the corners of an equilateral triangle, (c) An s-orbital and three p-orbitals can blend together to give four sp hybrid orbitals that point to the corners of a tetrahedron. 

The arrangement of the centers of the molecules in the crystal is that corresponding to the diamond structure. Each molecule is surrounded tetrahedrally by four molecules. If we consider a molecule as roughly tetrahedral in shape with similar orientation to the tetrahedron formed by the four beryllium atoms, then the adjacent molecules are so oriented as to present tetrahedral faces to one another. 

The functions % to X4 correspond to orbitals having preferential alignments oriented towards the vertices of an circumscribed tetrahedron. Their combinations with the wave functions of four hydrogen atoms placed in these vertices yield the following functions, the insignificant coefficient c3 being neglected ... 

The most probable distribution of the four a electrons—the distribution that keeps them as far apart as possible—is at the vertices of a tetrahedron (Fig. 7a). The most probable arrangement of the four (3 electrons is also at the vertices of a tetrahedron (Fig. 7b). In a free atom these two tetrahedra are independent, so they can have any relative orientation giving, an overall spherical density. 

Amico V, Oriente G, Piattelli M, Tringali C, Fattorusso E, Magno S, Mayol L (1978) Tetrahedron Lett 3593... 

L. D. S. Yadav, V. P. Srivastava, V. K. Rai, and R. Patel, Diversity oriented synthesis of fused-ring 1, 3-oxazines from carbohydrates as biorenewable feedstocks, Tetrahedron, 64 (2008) 4246-4253. 

M. Nardelli, P. Caubere, Tetrahedron Lett. 1990, 31, 7603-7606 the formula of the enol cycloadduct 7 displays the wrong orientation (personal communication from Prof. 

But it was not really until 1931, when Slater and Pauling independently developed methods to explain directed chemical valence by orbital orientation that it can truly be said that a chemical quantum mechanics, rather than an application of quantum mechanics to chemistry, had been created. In a study of Slater, S. S. Schweber notes the distinction between the Heitler-London-Pauling-Slater theory and the Heitler-London theory. Heitler and London successfully explained the electron-valence pair on the basis of the Goudsmit-Uhlenbeck theory of spin. Slater and Pauling explained the carbon tetrahedron. This second explanation distinguishes quantum chemistry from quantum physics.2... 

Fig. 2.1 Configurations of the tetrahedral units and chain, double chain, and sheet structures in the silicate and aluminosilicate minerals. (A) Two-dimensional representation of a single silicate tetrahedron. (A ) Two-dimensional representation of an extended silicate chain. (B) Three-dimensional representations of single tetra-hedra in two orientations. The apexes of the tetrahedra point above or below the plane of the paper. (B ) Three-dimensional representations of extended silicate chains showing different orientations of the tetrahedra in two of the many possible configurations. Single chain pyroxenes (C), wollastonite (D), rhodonite (E). Double chains amphiboles (F). Sheets as found in the serpentines, micas, and clays (G).

Spatz JH, Bach T, Umkehrer M, Bardin J, Ross G, Burdack C, Kolb J (2007) Diversity oriented synthesis of henzoxazoles and benzothiazoles. Tetrahedron Lett 48 9030-9034... 

S. D. Markad, S. M. Miller, M. Morton, and M. W. Peczuh, Hydroxyl group orientation affects hydrolysis rates of methyl [alpha]-septanosides, Tetrahedron Lett., 51 (2010) 1209-1212. 

Fig. 14. High-temperature K2SO4 structure projected on (1120) of hexagonal unit cell = (100) of orthohexagonal cell (a = a -I- b, b = - a -I- b, c = c ). Large, medium and small circles = K, S and O open/filled at = 1/2/0 dotted at heights indicated in units of aJlOO. There are twice as many 0 sites as atoms because there are two (obvious) possibilities for orienting each SO4 tetrahedron. Top, B8(,- (Nijin-) like K2S anay. Compare Fig. 11 and Fig. 16.

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