Atomic orbitals boundary surface diagrams

FIGURE 3.8 Atomic orbitals. Boundary surface diagrams for electron densities of Is, 2s. 2p, 3s. 3p, and 3d orbitals. For the p orbitals, the subscript letter on the orbital notation (x, y, z) indicates the cartesian axis along which the orbital lies. 

Figure 7.18 shows boundary surface diagrams for the li, 2s, and 3s hydrogen atomic orbitals. All s orbitals are spherical in shape but differ in size, which increases as the principal quantum number increases. Although the details of electron density variation within each boundary surface are lost, there is no serious disadvantage. For us the most important features of atomic orbitals are their shapes and relative sizes, which are adequately represented by boundary surface diagrams. 

An atomic orbital is a function ip) that defines the distribution of electron density (ip ) in space. Orbitals are represented by electron density diagrams or boundary surface diagrams. 

Actinide series, p. 276 Amplitude, p. 244 Atomic orbital, p. 261 Aufbau principle, p. 274 Boundary surface diagram, p. 264... 

Why is a boundary surface diagram useful in representing an atomic orbital ... 

The quantum state of an electron in a hydrogen atom is given by its wavefunction (or atomic orbital) [ip(r, 0, < )] and the distribution of electron density in space is given by tlfir, 0, tf>). The sizes and shapes of atomic orbitals can be represented by electron density diagrams or boundary surface diagrams. 

Although the details of electron density variation within each boundary surface are lost, the most important features of atomic orbitals are their overall shapes and relative sizes, which are adequately represented by boundary surface diagrams. 

FIGURE 3.10 A (T-bond is formed by the pairing ol electron spins in two 2p7-orbitals on neighboring atoms. At this stage, we are ignoring the interactions of any 2p,-(and 2p -) orbitals that also contain unpaired electrons, because they cannot form electron pair may be found anywhere within the boundary surface shown in the bottom diagram. Notice that the nodal plane of each p7-orbital survives in the tr-bond. 

Boundary surfaces and atomic orbital envelope diagrams... 

Although the formal method of describing orbitals is to use mathematical expressions, much understanding of orbital properties may be gained by the use of pictorial representations. The most useful pictorial representations of atomic orbitals are similar to boundary surfaces (which are based on V /2), but are based upon the distribution of jf values, with the sign of / being indicated in the various parts of the diagram. The shapes of these distributions are based upon the contours of jf within... 

The solutions of the Schrodinger equation show how / is distributed in the space around the nucleus of the hydrogen atom. The solutions for t are characterized by the values of three quantum numbers (essentially there are three because of the three spatial dimensions, x, y and z), and every allowed set of values for the quantum numbers, together with the associated wave function, describes what is termed an atomic orbital. Other representations are used for atomic orbitals, such as the boundary surface and other diagrams described later in the chapter, but the strict definition of an atomic orbital is its mathematical wave function. 

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