Shapes of orbitals

Only these nine orbital shapes need be memorized. 

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For many reasons, including the Woodward-IIoffm an rules that describe the likelihood of reaction based on arguments about the shapes of orbitals, it is desirable to be able to visualize molecular orbitals. 

Figure 2.3 The shapes of orbitals for the s electron pair, the three pairs of p electrons with obitals mutally at right angles, and the sp orbitals which have the major lobes pointing towards the apices of a regular tetrahedron.

The shapes of orbitals strongly influence chemical interactions. Hence, we need to have detailed pictures of orbital shapes to understand the chemistry of the elements. 

In particular, electron transfer results in that phosphoric acid molecules present in ATP, NADP and NADPN contain oxygen atoms in the form of O". Spatial-energy interactions (including isomorphic) are objectively expressed both at similar and opposite electrostatic charge of atoms-components. Such interactions can also take place between two heterogeneous atoms, if only their PE-parameters are roughly equal, and geometric shapes of orbitals are similar or alike. 

Such approximate equality of PE-parameters and geometric similarity of shapes of orbitals of atoms-components shows that actual degree of their interaction p= ()() %, thus... 

The principal quantum number, n, is related to the size of the orbital. A second quantum number, the angular momentum quantum number, I, is used to represent different shapes of orbital. The orientation of any non-spherical orbital is indicated by a third quantum number, the magnetic quantum number, m. A fourth quantum number, the spin quantum number, s, indicates the spin of an electron within an orbital. 

The tail of j/i in the direction of j/2 becomes much less pronounced at the TS (central column of orbitals). This orbital resembles a distorted carbon 2p AO in the rightmost column, but it begins to attain the form of a distorted sp hybrid at the TS. Orbital /6 is reshaped in a similar fashion and becomes less distorted towards /5 and more towards j/i. The changes in j/i and tj/e are mirrored by identical changes in /4 and /5. All of this indicates that the bonds t /i-t /2, t /5 6 and /3- i/4 are breaking up at the TS, in parallel with the formation of new bonds tj/i-tl/g and tl/4-tl/5. The shapes of orbital /2 and its symmetry-related counterpart, /3, are particularly interesting These orbitals appear to be almost equally distorted towards one another (as the reaction proceeds further, these distortions lead to the formation of the cyclohexene n bond) and towards their former partners in the butadiene tz bonds ( /i and /4, respectively). Consequently, j/2 and j/3 closely resemble in form the SC orbitals for benzene [8-10]. 

The rightmost column of orbitals in Fig. 5 corresponds to the final point along the calculated IRC interval in the direction of hexadiene. The distance between the two terminal carbon atoms is already 2.490A and, as a consequence, the shape of orbital /i is much more jr-like. Together with /2, this orbital forms one of the hexatriene % bonds. The second of these bonds is formed by j/3 and j/4, and the third by /5 and rj/g. 

The orbitals are completely described by specifying three quantum numbers, but only two are used in this hook. The principal quantum number (symbolized n) is a whole number, 1 or greater, that identifies the electron shell of the orbital, where the lower digits denote shells of lower energy that are closer to the atomic nucleus. The second quantum number (symbolized 1) is a whole number from 0 up to n — 1 that defines the type of orbital within a shell (n). For historical reasons, the different shapes of orbitals are represented by letters. (See Table 4-1.)... 

Hie shapes of orbitals are important in theories of chemical bonding. They are less significant in the understanding of atoms themselves than the radial functions discussed below. 

The quantum mechanical model of atomic structure is far too difficult to be explained in detail in an AP Chemistry course. However, some aspects of the theory are appropriate, and you should know them. These include the predicted number and shapes of orbitals in each energy level the number of electrons found in each orbital, sublevel, and energy level and the meaning of the four quantum numbers. 

The orbital angular momentum quantum number, , determines the shape of the orbital. Instead of expressing this as a number, letters are used to label the different shapes of orbitals, s orbitals have f = 0, and p orbitals have - 1. 

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