Let's begin by imagining we have a system with just two hydrogen atoms initially apart from each other. As we bring these two hydrogen atoms closer together, the energy from our system begins to decrease because the half-filled 1s orbitals of these two hydrogen atoms begin to overlap. At some point in bringing these nuclei closer together, there will be a minimum energy for our system. The difference in energy between our hydrogen atoms being far apart and the minimum energy is called our bond energy. This is the amount of energy given off when the bond is formed between two hydrogen atoms. If we continued to bring the nuclei closer, the energy of our system will increase as the nuclei repel each other. The distance between the two nuclei at the minimum energy is the bond length. According to valence bond theory, a chemical bond is the overlap of two half-filled atomic orbitals on neighboring atoms and spin pairing of the two valence electrons. The atomic orbitals can be the standard s, p, d, and f atomic orbitals from our quantum mechanical model, or we can create hybridized atomic orbitals. The geometry of the overlapping orbitals determines the shape of the molecule. If we consider the molecule hydrogen sulfide, we want to create single bonds between the two hydrogen atoms and the sulfur atom. Each hydrogen atom initially has a half-filled 1s atomic orbital, and the sulfur initially has two half-filled 3p atomic orbitals. According to valence bond theory, we can create a bond by the overlap of two half-filled atomic orbitals and spin pairing of the two valence electrons. If we overlap the half-filled 1s orbitals of our hydrogen atoms with the half-filled 3p orbitals of our sulfur atom, we would expect the bond angle to be about 90° because the p orbitals in sulfur are 90° apart. Experimental data shows that the bond angle in hydrogen sulfide is indeed about 90°, so we can explain the hydrogen sulfide molecule using the overlap of the standard s and p atomic orbitals. Some molecules, however, have molecular geometries that require hybrid orbitals. Hybridization is the process of combining the standard s, p, d, and f atomic orbitals on an atom to create hybrid atomic orbitals. These hybrid atomic orbitals have a major lobe and a minor lobe. The major lobe will allow for greater overlap in a bond with another atom. When creating hybrid orbitals, we follow some basic guidelines. First, the total number of orbitals is conserved, so if we add together 3 standard atomic orbitals, we'll produce 3 hybrid atomic orbitals. Second, the shapes and energies of the hybrid orbitals produced are determined by the particular combinations of the standard atomic orbitals added together. And third, the type of hybridization that occurs will be the one that yields the lowest overall energy for the molecule. For our purposes, we'll use VSEPR theory to predict what type of hybridization will yield the lowest overall energy. To determine the type of hybridization we need for an interior atom, we'll draw the Lewis structure and count the number of electron groups on the atom in question. The number of electron groups on the atom will match the number of standard atomic orbitals we need to add together to create hybrid orbitals. For example, if there are two electron groups, we will add together two atomic orbitals-- one s orbital and one p orbital--and we'll create two sp hybrid orbitals. If there are three electron groups, we'll add together three atomic orbitals-- one s orbital and two p orbitals--to create three hybrid sp2 orbitals. If there are four electron groups, we'll add together four atomic orbitals-- one s orbital and three p orbitals--to create four hybrid sp3 orbitals. So on and so forth, we'll follow this pattern. Let's look closer at each type of hybridization. We'll start with the methane molecule, CH4. If we draw the Lewis structure for methane, we see that we have four electron groups on our central carbon atom. If we draw the orbital diagram for carbon's valence shell, we see that carbon only has two half-filled p orbitals. This isn't enough to create four bonds in valence bond theory. We need to use hybridization. Since there are four electron groups around carbon, we will use sp3 hybridization. In sp3 hybridization, we're adding together one s atomic orbital and three p atomic orbitals. Since the number of orbitals is conserved, we create four sp3 hybrid orbitals. Hybrid orbitals are degenerate. Their energies are an average of the energies for the atomic orbitals used to create them, so the energies of the sp3 hybrid orbitals are somewhere between the 2s and 2p atomic orbital energies but closer to the 2p since three of them were combined. Remember from the quantum mechanical model that an orbital is the volume that encompasses 90% of the probability of where an electron is likely to be found when modeled as a standing wave around the nucleus. It is derived from solutions to the Schrödinger equation. So in the process of hybridization, we're mathematically adding together the solutions to the Schrödinger equation to create new unique solutions. If we add together an s and three p orbitals in the process of hybridization, our new orbitals will have major lobes going to the four corners of a tetrahedron. This type of hybridization is used for tetrahedral electron geometry. It will allow a greater degree of overlap between the hybrid orbital and the atomic orbital of a neighboring atom. So in methane, our four single bonds are created by the overlap of our half-filled 1s orbitals of each hydrogen atom and the four half-filled sp3 hybrid orbitals on carbon. We can apply the same process to ammonia, NH3. First, we create our Lewis structure. We also have four electron groups around nitrogen in ammonia, so we'll use sp3 hybridization. When we add nitrogen's five valence electrons to the four sp3 hybrid orbitals, one of the hybrid orbitals is filled with a lone pair of electrons. So in ammonia, we see that a lone pair of electrons can occupy a hybrid orbital. Next, let's examine formaldehyde. From the Lewis structure, we see carbon is the central atom with three electron groups. From our orbital diagrams of each atom's valence shell, we see carbon currently has only two unpaired electrons. Since carbon has three electron groups in the Lewis structure, we will want to use three atomic orbitals to create three hybrid orbitals. We'll add together carbon's 2s orbital with two of the 2p orbitals to create three hybrid sp2 orbitals. This leaves one unhybridized p orbital on carbon. In sp2 hybridization, since the energy of our hybrid orbitals is an average of the orbitals used for hybridization, the sp2 orbitals have energies between the 2p and 2s orbitals but slightly closer to the 2p. sp2 hybridization leaves one unhybridized p orbital. If we look at the process of hybridization, adding together the s orbital and two p orbitals produces three hybrid orbitals with major lobes directed toward the corners of a triangle on a single plane. This is used for trigonal planar electron geometry. Let's go back to formaldehyde. Our two single bonds between carbon and hydrogen are the overlap of carbon's half-filled sp2 atomic orbitals and the 1s orbital of each hydrogen atom. That leaves one half-filled hybrid sp2 orbital and one half-filled unhybridized p orbital on carbon. These are used in the double bond with oxygen. The double bond contains two different components. One component of the double bond is the overlap of carbon's sp2 hybridized orbital and oxygen's unhybridized p orbital. The other component is the side by side overlap of carbon's unhybridized p orbital with oxygen's unhybridized p orbital. These components are designated as a sigma component and pi component of the double bond. A pi bond is the side by side overlap of atomic orbitals. In a pi bond, the shared electron density is not on the line that connects the two nuclei: it's either above and below that line or in front and behind of that line. The sigma bond, on the other hand, is the end-to-end overlap of atomic orbitals. In a sigma bond, the shared electron density is on the line that connects the two nuclei. A single bond has one sigma component, and a double bond has one sigma and one pi component. The pi component of the double bond is weaker than the sigma component. This will become important in organic chemistry. Double bonds can be areas of reactivity because it can be energetically favorable to break a single and double bond and form two single bonds. The electrons in the pi bond can also be easier for other molecules to get to: they're not on the line that connects the two nuclei. So in our formaldehyde molecule, the double bond is composed of one sigma component and one pi component, whereas our single bonds just have one sigma component. Next, we'll look at acetylene. According to the Lewis structure, each carbon atom has two electron groups, so we'll use sp hybridization for each of our interior carbon atoms. In the process of sp hybridization, we add together one s and one p atomic orbital to produce two new sp hybrid orbitals. This leaves two p orbitals on carbon unhybridized. The sp hybrid orbitals have an energy directly between the s and the p orbitals used to create them. When adding together one s and one p atomic orbital, we create two hybrid orbitals whose major lobes are 180° apart. This is used for linear electron geometry. The triple bond in acetylene is composed of one sigma component and two pi components. The pi components are formed by the side-by-side overlap of the two unhybridized p orbitals on our carbon atoms. If we have a nonmetal from the third row or below of the periodic table, the atom will have an unfilled d subshell in its valence shell. By using one or more of the d orbitals, we will be able to accommodate more than eight valence electrons around an atom. For example, with sp3d hybridization, we produce five hybrid orbitals with major lobes directed towards the corners of a trigonal bipyramid. So sp3d hybridization is used for trigonal bipyramidal electron geometry. Arsenic pentafluoride uses sp3d hybridization to allow arsenic to create sigma bonds with the five fluorine atoms. And if we add together the s, three of our p, and two of our d orbitals, we'll create six hybrid sp3d2 orbitals, which have major lobes directed toward the corners of an octahedron. sp3d2 hybridization is used for octahedral electron geometry. An example is sulfur hexafluoride. sp3d2 hybridization allows the sulfur atom to create sigma bonds with the six fluorine atoms. So in summary, we will use the Lewis structure to determine how many electron groups are on an interior atom. The number of electron groups determines how many standard atomic orbitals should be added together to form hybrid orbitals.