# Organic Chemistry/Foundational concepts of organic chemistry/Atomic structure/Shells and orbitals

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### Electron orbitals

Electrons orbit atoms in clouds of distinct shapes and sizes. The electron clouds are layered one inside the other into units called shells (think nested Russian dolls), with the electrons occupying the smallest, innermost shell having the lowest energy state and the electrons in the largest, outermost shell having the highest energy state. The higher the energy state, the more potential energy the electron has, just like a rock at the top of a hill has more potential energy than a rock at the bottom of a valley. These concepts will be important in understanding later concepts like optical activity of chiral compounds as well as many interesting things outside the realm of organic chemistry (like how lasers work).

### Wave nature of electrons

Electrons behave as particles but also as waves. (Work by Albert Einstein and others revealed that in fact, light and all matter behaves with this dual nature, and it is most clearly observed in the tiniest particles.) One of the results of this observation is that electrons are not just in simple orbit around the nucleus as we imagine the moon to circle the earth, but instead occupy space as if they were a wave on the surface of a sphere.
If you jump a jumprope you could imagine that the wave in the rope is in its fundamental frequency. The high and low points fall right in the middle, and the places where the rope doesn't move much (the nodes) occur only at the two ends. If you shake the rope fast enough in a rythmic way, using more energy than you would just jumping rope, you might be able to make the rope vibrate with a wavelength shorter than the fundamental. You them might see that the rope has more than one place along its length where it vibrates from its highest spot to its lowest spot. Furthermore, you'll see that there is one or more places (or nodes) along its length where the rope seems to move very little, if at all.
Or consider stringed musical instruments. The sound made by these instruments comes from the different ways, or modes the strings can vibrate. We can refer to these different patterns or modes of vibrations as linear harmonics. Going from there, we can recognize that a drum makes sound by vibrations that occur across the 2-dimensional surface of the drumhead. Extending this now into three dimensions, we think of the electron as vibrating across a 3-dimensional sphere, and the patterns or modes of vibration are referred to as spherical harmonics. The mathematical analysis of spherical harmonics were worked out by the French mathematician Legendre long before anyone started to think about the shapes of electron orbitals. The algebraic expressions he developed, known as Legendre polynomials, describe the three dimension shapes of electron orbitals in much the same way that the expression x$^2$+y$^2$ = z describes a circle (or, for that matter, a drumhead). Many organic chemists need never actually work with these equations, but it helps to understand where the pictures we use to think about the shapes of these orbitals come from.

### Electron shells

Each different shell is subdivided into one or more orbitals, which also have different energy levels, although the energy difference between orbitals is less than the energy difference between shells.
Longer wavelengths have less energy; the s orbital has the longest wavelength allowed for an electron orbiting a nucleus and this orbital is observed to have the lowest energy.
Each sub-shell in the main electron shell has a characteristic shape, and are named by a letter. The sub-shells are: s, p, d, and f.
As one progresses up through the shells (represented by the principle quantum number n) more types of orbitals become possible.

### S orbital

The s orbital is the orbital lowest in energy and is spherical in shape. Electrons in this orbital are in their fundamental frequency.

### P orbital

The next lowest-energy orbital is the p orbital. Its shape is often described as like that of a dumbbell. There are three p-orbitals each oriented along one of the 3-dimensional coordinates x, y or z.
These three different p orbitals can be referred to as the p$_x$, p$_y$, and p$_z$.
The s and p orbitals are important for understanding most of organic chemistry as these are the orbitals that are occupied by the type of atoms that are most common in organic compounds.

### D orbital

[[Image
configuration species excited states Ca+2, Ti+4, Sc+3 0 Ti+3 1 V+3 3 Cr+3 3 Mn+3 1 Mn+2, Fe+3 0 Fe+2 1 Co+2 3 Ni+2 3 Cu+2 1 Zn+2 0
* Jahn-Teller distortion breaks the expected degeneracy. :]]
There are 5 types of d orbitals. Three of them are roughly X-shaped, as shown here, and might be viewed as being shaped like a crossed pair of dumbbells . They are referred to as d$_{xy}$, d$_{xz}$, and d$_{yz}$. Like the p-orbitals, these three d orbitals have a node at the origin of the coordinate system where the three axes all come together. Unlike the p orbitals, however, these three d orbitals are not oriented along the x, y, or z axes, but instead are oriented in between them. The d$_{xy}$ orbital, for instance, lies in the xy plane, but the lobes of the orbital point out in between the x and y axes.

### F orbital and beyond

There are 7 kinds of F orbitals, but we will not discuss their shapes here. F orbitals are filled in the elements of the lanthanide and actinide series, although electrons in these orbitals rarely come into play in organometallic reactions involving these elements.