Sigma bond

Tiny bits use a strong hold to stay together.

This hold happens when they meet head-on. They overlap in a straight line. This makes the bond very strong.

Most single bonds use this kind of hold. A double bond has one of these. A triple bond has one too. These holds help make rings and long chains. They keep all the tiny parts in place.

It is a very sturdy way to stick.

Atoms use special holds to stick together. These are called sigma bonds. They are the strongest type of covalent bond.

These bonds form when parts of atoms overlap head-on. The atoms meet along a straight line. This direct overlap makes the bond very strong. The electrons in these bonds are called sigma electrons.

When you look down the bond, it looks like a circle. This is why it looks like an "s" orbital. A single bond is always a sigma bond. A double bond has one sigma bond and one pi bond. A triple bond has one sigma bond and two pi bonds.

There is a rule to find how many sigma bonds are in a molecule. You take the number of atoms and add the number of rings. Then, you subtract one. For example, a molecule with no rings follows this rule. A molecule with two hydrogen atoms has one sigma bond. Ammonia has three sigma bonds. This rule works for many shapes, but not all. Some shapes, like nanotubes, follow a different rule.

A sigma bond is a special way atoms stick together. It is the strongest kind of covalent bond. These bonds help build the world around us. Scientists use the Greek letter sigma, or σ, to name them.

They are very important for making different shapes. Most single bonds are made of one sigma bond. Even bigger bonds use them as a base. A double bond has one sigma bond and one pi bond. A triple bond has one sigma bond and two pi bonds.

These bonds work through a head-on overlap. Atoms have areas called orbitals where electrons live. When these orbitals overlap directly along a straight line, a sigma bond forms. This line is called the internuclear axis.

Looking down this axis shows a circular shape. This shape looks like a simple "s" orbital. Because the overlap is so direct, the bond is very strong. The electrons inside are called sigma electrons.

Scientists use math to understand how these orbitals mix. This mixing is called hybridization. It happens when orbitals with the same symmetry blend together. For example, s and p orbitals can mix. The amount of mixing depends on their energy levels.

In some cases, an antibonding orbital forms. This is called a sigma star orbital, or σ*. These have a nodal plane between the atoms. A nodal plane is a place where the wavefunction is zero.

There is a rule to count sigma bonds in many molecules. You take the number of atoms and add the number of rings. Then, you subtract one. This is written as Nσ = Natoms + Nrings − 1. For example, ammonia (NH3) has three sigma bonds. The anthracene molecule (C14H10) has three rings. The rule says it should have 26 sigma bonds. These include 16 C−C bonds and 10 C−H bonds.

This rule does not work for every single shape. It can fail for molecules like Buckminsterfullerene (C60). C60 has 60 atoms and 32 rings. The rule would predict 91 bonds, but it actually has 90. Other shapes like nanotubes follow different rules. For nanotubes, the number of bonds is atoms plus rings. This happens because of how their faces are shaped.

A sigma bond, or σ bond, is the strongest type of covalent chemical bond. These bonds form when atomic orbitals overlap in a head-on fashion. This specific type of overlap occurs along the internuclear axis, which is the straight line connecting two nuclei. Because the overlap is so direct, sigma bonds are very stable. The electrons involved in these bonds are often called sigma electrons.

To understand how they form, we must look at atomic orbitals. These are the regions where electrons exist around an atom. In a sigma bond, orbitals overlap directly along the axis between the atoms. When you look down this bond axis, the molecular orbital has circular symmetry. This symmetry makes it look similar to an "s" atomic orbital. Common ways these bonds form include s+s, pz+pz, s+pz, and dz2+dz2 overlaps. In these examples, "z" represents the internuclear axis.

Quantum theory adds another layer of complexity to how these bonds behave. It shows that molecular orbitals with identical symmetry can undergo a process called hybridization. This means the orbitals mix or blend together. For instance, the wavefunctions for s+s and pz+pz molecular orbitals can become blended. The extent of this hybridization depends on the relative energies of the molecular orbitals involved.

There is also a distinction between bonding and antibonding orbitals. For homonuclear diatomic molecules, bonding sigma orbitals have no nodal planes. A nodal plane is a location where the wavefunction is zero. However, an antibonding orbital, known as a sigma star orbital (σ*), is defined by having one nodal plane between the two bonded atoms.

Sigma bonds serve as the foundation for many different types of chemical structures. In a single bond, there is typically only one sigma bond. Multiple bonds are built using a sigma bond as a base combined with other bonds. A double bond consists of one sigma bond and one pi bond. A triple bond consists of one sigma bond and two pi bonds.

In complex organic molecules like propane, the structure is held together by many sigma bonds. Propane contains ten sigma bonds: two C−C bonds and eight C−H bonds.

Chemists use a specific formula to predict the number of sigma bonds in many molecules. This is known as the sigma bond rule. The formula is Nσ = Natoms + Nrings − 1. This rule is a special application of the Euler characteristic from graph theory. For a molecule with no rings, like ammonia (NH3), the number of bonds is simply the number of atoms minus one. For a molecule like anthracene (C14H10), which has three rings, the rule predicts 26 sigma bonds. This total includes 16 C−C bonds and 10 C−H bonds.

However, the sigma bond rule does not work for every molecular shape. It can fail for certain structures like Buckminsterfullerene (C60). While C60 has 60 atoms and 32 rings, it actually has 90 sigma bonds. The rule would incorrectly predict 91 bonds. This happens because the rule treats each ring as a face in a graph. In C60, the way the molecule is drawn can change how faces are counted. Other shapes, such as nanotubes or toroidal fullerenes, follow different mathematical patterns. For nanotubes, the number of sigma bonds is equal to the number of atoms plus the number of rings.