By John G. Verkade
Knowing molecular orbitals (MOs) is a prerequisite to appreciating many actual and chemical houses of subject. This commonly revised moment version of A Pictorial method of Molecular Bonding offers the author's leading edge method of MOs, producing them pictorially for a wide selection of molecular geometries. a massive enhancement to the second one variation is the computer- and Macintosh-compatible Nodegame software program, that is coordinated with the textual content and aids in pictorially instructing molecular orbital thought utilizing generator orbitals.
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These hybrid AOs can also be written in more general form as in Equation 2-44: (2-44) wherein the (2pfk) orbitals are defined in the case at hand by Equation 2-45: (2pfd = (2px) 1 (2pf2) = -2(2px) 1 + 2j3(2PY) (2-45) 1 1 (2pf 3) = -2(2px) - 2j3(2py). The (2pfk) orbitals point in the directions fl = (1,0,0), f2 = (-1/2,3 1/ 2 /2,0), f 3 = ( - 1/2, - 3 1 / 2 /2, 0). These vectors are of unit length so that the (2pfk) are normalized. As shown in Figure 2-17a, the unit vector directions are at 120° to one another as are the (Sp2) hybrids which point along these directions.
2-18) Since the three orbitals in Equations 2-17 are each a function of a single coordinate, Equation 2-18 can be recast into Equations 2-19 which are algebraic expressions for the projections of r onto the three coordinate axes: 35 Hybrid Orbitals I I I\ I I (x, y, z) - - - .............. ):::::=::t>--- y I! / I (~= -------~~ x 0, 1) I :\ ~==~--~*-~y e ~---+-~y ,II I ................................................. :L_V x x (a) (b) (c) Figure 2-10. Drawings depicting a vector r (a), a unit vector e (b), and the projection of r onto e (c).
A unit vector e is one unit long as measured in whatever units we are working with. In Figure 2-10b the unit vector has been placed along the y axis. Then the projection of r onto e denoted by Peer) and shown in Figure 2-lOc is given by the so-called "dot product" (e' r) which is defined in Equation 2-18: Peer) = (e' r) = ~x + 11Y + (z. (2-18) Since the three orbitals in Equations 2-17 are each a function of a single coordinate, Equation 2-18 can be recast into Equations 2-19 which are algebraic expressions for the projections of r onto the three coordinate axes: 35 Hybrid Orbitals I I I\ I I (x, y, z) - - - ..............