Atomic Orbitals
Electron waves
The world really is strange. It is stranger than most people realize. Back in your Junior High Science class, you were probably told about the duality of light, where light is both a particle and a wave. This wave/particle duality is not only true about light, but it is true about most of nature. This is the strangeness that we explore in a field called quantum mechanics.
For now, I want us to focus on the wave/particle duality of electrons. One way to think about electrons is that they are little particles orbiting the nucleus. This is a fairly good model that many of us have in our minds, the Bohr planetary model. But, the interesting thing is that electrons are also waves! Let’s focus on two very simple waves. Think of a guitar string. If I pluck a guitar string, it vibrates up and down.
If I combine these, the string vibrates so fast that it looks something like this.
This simple vibrational shape is spherical in nature and leads us to the shape of the simplest electron orbital, the s orbital.
If I put my finger down in the middle of the guitar string and pluck it, I get a wave where when one side is up, the other side is down. A moment later, it switches which side is up and which is down.
When the string vibrates fast, it looks something like this.
There is one spot in the center where there is no wave. We say that it has one node in the center. This vibrational shape has two lobes of equal size. It leads us to the shape of another electron orbital, the p orbital.
These orbital waves can be described with mathematical functions—just like all waves can. We call this mathematical function for the wave the wavefunction which is often represented by the greek letter psi (Ψ). These mathematical functions can be added together or subtracted. Intuitively, you understand this about waves.
For example, a child on a swing set moves forward and backward. This motion is a wave-like motion. When children are learning to swing on a swing set, they are taught to kick their legs out when they are moving forward and bend at the knees and put their feet down when they are moving backward. This motion of their feet is also a wave. They are taught to do this so that their feet wavefunction can be added to the wavefunction of the swing. Constructive interference is when two waves overlap to make a larger wave. When done correctly, the child’s feet motion and the swinging motion constructively interfere to increase the amplitude of the wave, and their swinging, so they go higher and higher.
Photo by GaborfromHungary at Morguefile.com
Many children get confused when learning this, though. If instead, they kicked their feet straight out when they were going backward and bent their knees putting their feet down when they were going forward, their feet wave would be opposite the swing’s wave. Destructive interference is when two waves are out of phase with each other making smaller waves. Children who swing this way will not be swinging for long. When the wavefunctions destructively interfere, they are subtracted from each other and get canceled out.
Two electron orbitals can add constructively or destructively because they are waves. This can happen when orbitals overlap on the same atom (to make hybrid orbitals) or when orbitals on two different atoms overlap when the atoms come close together (to make molecular orbitals or bonds).
Atomic orbitals
A hydrogen atom (atomic number 1) has only one electron surrounding one positive proton in the nucleus. This lone electron is in a round orbital called a 1s orbital and is in the first and only shell of electrons of the hydrogen atom. The outermost electrons of an atom are called its valence electrons. Since this first shell is also the outermost shell of electrons, this 1s electron is the only valence electron for hydrogen.
Hydrogen atom, one shell, 1s orbital
The first shell is small and can only hold two electrons in it. Helium (atomic number 2) fills up this first shell with its two electrons, both in the 1s orbital. Another shell of electrons outside of this first shell is needed for the other important organic chemistry atoms like carbon, nitrogen and oxygen because they contain more than two electrons. Therefore, these other important organic chemistry atoms have two shells of electrons.
The two electron shells of common organic atoms
For these atoms, the first, innermost shell of electrons is made up of two electrons in a round orbital called a 1s orbital. These two electrons are not very interesting because they are tucked inside the atom and don’t interact with other atoms. The second shell is farther away from the positively charged nucleus. It is more interesting because it contains the outermost electrons of the atom. These electrons are the ones that will bump into other atoms to form bonds. This outermost electron shell is called the valence shell and its electrons are the valence electrons. It is also made up of two electrons in a round orbital called a 2s orbital. It is the same shape as the 1s orbital, but just a little bigger as the electrons are a little farther from the nucleus in the second shell.
The round 2s orbital is not the only type of electron orbital in the 2nd shell. There are also three double-lobed 2p orbitals in this valence shell. These three p orbitals are all rotated 90° from each other.
The two electron shells of common organic atoms
The round 2s orbital is not the only type of electron orbital in the 2nd shell. There are also three double-lobed 2p orbitals in this valence shell. These three p orbitals are all rotated 90° from each other.
Showing how 2s and 2p orbitals make the valence (2nd) shell
This is what the atomic orbitals of carbon atom look like. To make bonds between atoms, the outermost valence electrons of one atom must overlap with the outermost valence electrons of another atom to make bonds. If the atomic orbitals described above were the only electron orbitals that atoms contain, we would expect that we could only bond atoms with a carbon atom at 90° and 180° angles. This is not the case. We often see bond angles of 180°, 120°, and 109.5°, but not 90°. Let’s look at methane (CH4) if only atomic orbitals can overlap compared to its true, tetrahedral shape.
CH4 if only atomic orbitals overlap vs. its true shape
Something else must be going on to get these other bond angles. Because all electron orbitals are waves, we can get these other bonding angles when the s and p atomic orbitals that are on the same atom mix together to form new oblong electron orbitals that are called hybrid orbitals. A hybrid is the offspring of two different species. So, hybrid orbitals are the offspring of two different types of orbitals on the same atom. It is important that you realize we are mixing together electron waves on the same atom because mixing together orbitals that are on different atoms is something else entirely, something we call making bonds.