Orbital Shapes
General Orbital Shape Properties
General Orbital Shape Properties
It is not precisely correct to refer to atomic orbitals as having a specific “shape.” The regions of highest electron density appear to describe shapes in space, and it is useful for us to remember those shapes when thinking about atomic properties and chemical bonding. The pictures you have drawn or seen in previous Chemistry classes (such as Figure 1) are important shorthand ways to describe and conceptualize atomic orbitals.
Figure L25.1 Typical shape-representations of a) an s-type orbital and b) a p-type orbital.
The following cloud plots are more accurate representations of the atomic orbitals, and familiarity with the actual electron distribution patterns is invaluable to understanding the resulting chemical behaviors.
Usually, the shapes of atomic
orbitals are collections of rounded lobes that are arranged in symmetric
patterns around the nucleus of the atom. The number of lobes increases as the
quantum numbers of the orbitals increase. Regions of zero electron density,
called nodes, separate the lobes. The number of nodes present in an orbital is
equal to the value of n+ -1. Only the s-type orbitals have nonzero
electron density at the nucleus; all other orbital types have at least one node
through the nucleus.
Important properties of commonly-encountered orbitals are discussed below. In the mathematical forms of the orbitals, the substitution ρ = Zr is used to simplify the appearance of the equations.
The 1s Orbital
The mathematical form of the 1s orbital is a simple exponential decay as the radius increases. The greatest electron density is at the nucleus and smoothly decreases as distance from the nucleus increases.
{0-1}
Figure L25.2 Cloud plot of the 1s orbital.
The 2s Orbital
The 2s orbital strongly resembles the 1s in being spherically-symmetric, but does not smoothly decay in density with distance from the nucleus. As demonstrated in Figure 4, the 2s has a region of high density near the nucleus and a spherical shell of electron density farther out, but a region between them of low density. There is a node, or region of precisely zero electron density, between the two regions.
Figure L25.3 Cloud plot of the 2s orbital.
Figure L25.4 A thin section of the cloud plot for the 2s orbital, showing the distribution of electron density near the yz plane.
The 2p Orbitals
The 2p orbital does not have the spherical symmetry of the s-type orbitals. In the case of the 2pz orbital, Figure 5, a planar node bisects the orbital and causes the orbital to have two separate lobes. The electron density is exactly zero at the nucleus. The orbital is oriented along the z axis.
Unlike the unique 2s orbital, there are three 2p orbitals. Along with the 2pz is a 2py orbital (Figure 6), oriented along the y axis, and a 2px orbital, oriented along the x axis.
{0-3}
{0-4}
{0-5}
Figure L25.5 Cloud plot of the 2pz orbital.
Figure L25.6 Cloud plot of the 2py orbital.
The 3s Orbital
The 3s orbital, like the 1s and 2s, is spherically-symmetric. It follows the trend set by the previous s-type orbitals. The 1s has one shell; the 2s has two shells and the 3s has three shells. The three regions of high electron density are evident in Figure 8.
{0-6}
Figure L25.7 Cloud plot of the 3s orbital.
Figure L25.8 A thin section of the cloud plot for the 3s orbital, showing the distribution of electron density near the yz plane.
The 3p Orbitals
There are three 3p orbitals, as there were three 2p orbitals. The shapes of the 3p orbitals are similar to those of the 2p orbitals, except that the 3p orbitals have a spherical node that cuts each lobe into two distinct sections. The node is apparent in Figure 10.
{0-7}
{0-8}
{0-9}
Figure L25.9 Cloud plot of the 3pz orbital.
Figure L25.10 A thin section of the cloud plot for the 3pz orbital, showing the distribution of electron density near the yz plane.
Figure L25.11 Cloud plot of the 3py orbital.
The 3d Orbitals
There are five 3d orbitals, with rather complicated three-dimensional shapes. The 3dz2 (Figures 12 and 13) has three regions of high electron density. The 3dz2 resembles a 2pz orbital with a “doughnut” of electron density in the xy plane surrounding the nucleus.
{0-10}
Figure L25.12 Cloud plot of the 3dz2 orbital.
Figure L25.13 A thin section of the cloud plot for the 3dz2 orbital, showing the distribution of electron density near the yz plane.
The remaining four 3d orbitals each have four lobes, caused by two perpendicular planar nodes. They are best viewed in 3D, using the Mathcad-based Orbital Reader. A picture of the 3dyz (Figures 14 and ) shows the general appearance of these orbitals. All have four nodes, but their orientations relative to the Cartesian axes differ.
{0-11}
{0-12}
{0-13}
{0-14}
Figure L25.14 Cloud plot of the 3dyz orbital.
Figure L25.15 Rotating cloud plot of the 3dyz orbital. Click the image to view the motion.
The 4s Orbital
Following the previous trends for s-type orbitals, the 4s is spherically symmetric (Figure 16), with four shells of high electron density and three spherical nodes (Figure 17).
{0-15}
Figure L25.16 Cloud plot of the 4s orbital.
Figure L25.17 A thin section of the cloud plot for the 4s orbital, showing the distribution of electron density near the yz plane.
The 4p Orbitals
The three 4p orbitals resemble the previous p-type orbitals, with the addition of another spherical node, as evident in Figure 19.
{0-16}
{0-17}
{0-18}
Figure L25.18 Cloud plot of the 4pz orbital.
Figure L25.19 A thin section of the cloud plot for the 4pz orbital, showing the distribution of electron density near the yz plane.
The 4d Orbitals
The 4d orbitals resemble the 3d orbitals in their general shapes. The addition of a spherical node near the nucleus forces the 4d orbitals to concentrate their electron density further from the nucleus than the 3d orbitals. For a direct comparison, contrast Figures 13 and 21, or Figures 14 and 22.
{0-19}
{0-20}
{0-21}
{0-22}
{0-23}
Figure L25.20 Cloud plot of the 4dz2 orbital.
Figure L25.21 A thin section of the cloud plot for the 4dz2 orbital, showing the distribution of electron density near the yz plane.
Figure L25.22 Cloud plot of the 4dyz orbital.
The 4f Orbitals
The seven 4f orbitals continue the trend of increasing complexity. The simplest 4f to visualize, the 4fz3 (Figures 23 and 24), resembles a p-type orbital with two “doughnuts” of electron density ringing the nucleus.
{0-24}
Figure L25.23 Cloud plot of the 4fz3 orbital.
Figure L25.24 A thin section of the cloud plot for the 4fz3 orbital, showing the distribution of electron density near the yz plane.
The remaining six 4f orbitals contain either six lobes (as the 4fyz2 orbital, Figure 25) or eight lobes. These orbitals cannot be adequately demonstrated in two-dimensional images, and should be viewed using the Orbital Reader.
{0-25}
{0-26}
{0-27}
{0-28}
{0-29}
{0-30}
Figure L25.25 Cloud plot of the 4fyz2 orbital.
The 5s Orbital
The 5s orbital, continuing previous trends, is spherically-symmetric and consists of five concentric shells of electron density. The smallest region, located near the nucleus, is not easily seen on the scale of Figure 27 but is discernable in the expanded view of Figure 28.
{0-31}
Figure L25.26 Cloud plot of the 5s orbital.
Figure L25.27 A thin section of the cloud plot for the 5s orbital, showing the distribution of electron density near the yz plane.
Figure L25.28 An expansion of the inner region of Figure 27. The large, outer ring of electron density in Figure 27 is outside the scope of this image.