Atomic orbitals lobes

The following figures show HOMOs of each. Shaded vs. unshaded atomic orbital lobes represent opposite signs of the wavefunctions. A relatively large atomic orbital represents the major contribution to the molecular orbital. 

Molecular modeling helps students understand physical and chemical properties by providing a way to visualize the three-dimensional arrangement of atoms. This model set uses polyhedra to represent atoms, and plastic connectors to represent bonds (scaled to correct bond length). Plastic plates representing orbital lobes are included for indicating lone pairs of electrons, radicals, and multiple bonds—a feature unique to this set. 

Since these new orbitals are a mixture of the two original orbitals, they are called hybrid orbitals. Each is called an sp orbital, since a merger of an s and a p orbital was required to form it. The sp orbitals, each of which consists of a large lobe and a very small one, are atomic orbitals, although they arise only in the bonding process and... 

There are two simple atomic orbitals i and p orbitals (we don t really deal with d and/orbitals in organic chemistry), i orbitals are spherical and p orbitals have two lobes (one front lobe and one back lobe) ... 

As there are 6 ir electrons to accommodate—two per orbital—the HOMO will be ip3 (11). To form the C—C a bond on cyclisation, the orbital lobes on the terminal carbon atoms of the conjugated system (C2 and C7—the C atoms carrying the Me substituents) must each rotate through 90° if mutual overlap is to occur (p/sp2— sp3 re-hybridisation must also occur). This necessary rotation could be either (a) both in the same direction—conrotatory (12), or (b) each in opposite directions—disrotatory (13) ... 

The difference in stereochemical outcome of these reactions is determined, therefore, by the relative phase of the lobes—at the terminal carbon atoms—of the MOs of these (and other similar) mre systems by the symmetry of their orbitals, that is. As we have seen, the orbital lobes, at the two terminal carbon atoms, have the same phase in the HOMO (tf 3) of the triene (67re), and in the HOMO after irradiation (i/i3) of the diene (4ire) while these orbital lobes have opposite phases in the HOMO (i/r2) of the diene and in the HOMO after irradiation (ifi4) of the triene. Two such terminal lobes with the same phase require disrotatory movement before bond-making/bond-breaking can occur, while two terminal lobes with... 

Figure 1.5 The shapes of some s and p orbitals. Pure, unhybridized p orbitals are almost-touching spheres. The p orbitals in hybridized atoms are lobe-shaped (Section 1.14).

The antibonding tt MO results when orbital lobes of opposite sign overlap between adjacent carbon atoms => there is a node between each pair of carbon atoms. 

Figure 10.4 Shapes of the s, p, and d atomic orbitals. The s orbital (a) is spherically symmetrical about the nucleus. The three p orbitals (b) are figure-of-eight lobes orientated along the three orthogonal axes (only z axis shown). The five d orbitals (c, d, and e) are four quatrefoil lobes, one orientated along the x-y axes, three between the axes, and the fifth (e) a figure-of-eight along the z axis with an additional donut around the nucleus. The orbitals are not drawn to the same scale.

It is to be noted that o orbitals are formed not only by the overlap of two 5 orbitals but by the overlap of any of the atomic orbitals (s, p. d or f) whether same or different, but the two lobes must have the same sign. A + s orbital can form a bond only by overlapping with another positive 5 orbital or with a + lobe of a p, d or / orbital. 

The orbital angular-momentum quantum number, , defines the shape of the atomic orbital (for example, s-orbitals have a spherical boundary surface, while p-orbitals are represented by a two-lobed shaped boundary surface). can have integral values from 0 to (n - 1) for each value of n. The value of for a particular orbital is designated by the letters s, p, d and f, corresponding to values of 0, 1, 2 and 3 respectively (Table 1.2). 

The principal quantum number n is the most important determinant of the radius and energy of the electron atomic orbital. The orbital shape quantum number I determines the shape of the atomic orbital. When / = 1, the atomic orbital is called an s orbital there are two s orbitals for each value of n, and they are spherically symmetric in space around the nucleus. When I = 2, the orbitals are called the p orbitals there are six p orbitals, and they have a dumbbell shape of two lobes that are diametrically opposed. When I = 3 and 4, we have 10 d orbitals and 14 f orbitals. The orbital orientation quantum number m controls the orientation of the orbitals. For the simplest system of a single electron in a hydrogen atom, the most stable wave function Is has the following form ... 

The trick is to make two equivalent orbitals in Be out of the atomic orbitals so that each hydrogen will see essentially the same electronic environment. We can accomplish this by mixing the 2s orbital and one of the empty 2p orbitals (say, the 2p ) to form two equivalent orbitals we call sp" hybrids, since they have both s and p characteristics. As with molecular orbital theory, we have to end up with the same number of orbitals we started with. The bonding lobes on the new spa and spb orbitals on Be are 180° apart, just as we need to form BeH2. In this manner, we can mix any type of orbitals we wish to come up with specific bond angles and numbers of equivalent orbitals. The most common combinations are sp, sp, and sp hybrids. In sp hybrids, one and one p orbital are mixed to get two sp orbitals, both of which... 

Problem 8.55 (a) Apply the MO theory to the C==C—C=C—C carbocation, considering the signs of the upper lobes of adjacent p atomic orbitals (f>) Indicate the relative energies of the molecular orbitals and state if they are bonding, nonbonding, or antibonding, (c) Show the distribution of the n electrons. ... 

Fig. 2. Contour plots of (Hike bonding orbitals of Zeise s anion. The contour values increase in absolute magnitude with increasing absolute values of the contour labels. The sign of the labels gives the sign of the orbital lobes. The set of contour values plotted is the same for each of the three orbitals. The interior nodes at the various atoms are not shown for clarity of presentation (a) the 5a, orbital, (b) the 6at orbital, and (c) the 7ot orbital showing significant interaction between the ethylene 7r-orbital and the Pt dx, yi orbital. [Reproduced from Rosch et at. (193), by permission of the American Chemical Society.]...

The Schrodinger equation is a differential equation, which means that solutions of it are themselves equations. The solutions, however, are not differential equations, but simple equations for which graphs can be drawn. Such graphs, which are three-dimensional pictures that show the electron density, are called orbitals or electron clouds. Most students are familiar with the shapes of the s and p atomic orbitals (Figure 1.1). Note that each p orbital has a node—a region in space where the probability of finding the electron is extremely small.2 Also note that in Figure 1.1 some lobes of the orbitals are labeled + and others -. ... 

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