Molecular orbital

Tiny parts make up everything.

These parts move in special ways. When tiny bits join, they make a group. This group is called a molecule.

The bits move in special paths. These paths help the parts stick together. Some paths help them stay close. Other paths try to push them apart. This is how things are built. It is a very busy world!

Everything is made of tiny parts.

In a single atom, electrons live in paths called atomic orbitals. When atoms join to make a molecule, these paths change. They combine to form molecular orbitals.

A molecular orbital is a way to show where an electron might be. It shows how an electron moves around a whole molecule.

Scientists use math to find these paths. They often use a method called LCAO. This means they combine the paths from each atom to find the new ones.

There are three main types of these paths. Bonding orbitals have low energy. They help hold the molecule together. Antibonding orbitals have high energy. They work against the bond. Nonbonding orbitals do not change the bond at all.

These paths also have different shapes. We use Greek letters to name them. A sigma orbital is symmetric around the center. A pi orbital is not. These shapes help us understand how molecules are built.

A molecular orbital is a special way to describe electrons. In a single atom, electrons live in paths called atomic orbitals. When atoms join to form a molecule, these paths change. The electrons no longer belong to just one atom. Instead, they belong to the whole molecule. Scientists use a mathematical function to describe this behavior. This function shows the probability of finding an electron in a specific area.

By studying these orbitals, we can learn about the physical properties of a substance.

To understand how they form, we look at how atoms combine. This often uses a method called the Linear Combination of Atomic Orbitals, or LCAO. This method treats molecular orbitals as a sum of the paths from each atom. When two atoms get close, their atomic orbitals overlap. This overlap creates areas where electrons are likely to be found. The number of new molecular orbitals created equals the number of atomic orbitals used.

This process helps us see how atoms hold onto each other.

There are three main types of molecular orbitals. Bonding orbitals have lower energy than the original atomic orbitals. These help create the chemical bonds that hold a molecule together. Antibonding orbitals have higher energy than the atomic orbitals. These actually work to oppose the bonding of the molecule. There are also non-bonding orbitals. These have the same energy as the original orbitals and do not affect the bond.

This balance of energy determines if a molecule stays together.

People have studied these paths for a long time. Friedrich Hund and Robert S. Mulliken first introduced molecular orbitals in 1927 and 1928. Later, in 1929, Sir John Lennard-Jones introduced the LCAO method. His work was very important for modern quantum chemistry. He used these principles to explain the structure of oxygen and fluorine molecules. These discoveries helped scientists understand the tiny world of atoms and energy.

We can also group these orbitals by their shapes using Greek letters. A sigma orbital is symmetric around the axis between the atoms. If you rotate a sigma orbital, it stays the same. A pi orbital is different because it is asymmetric. Rotating a pi orbital causes a change in its mathematical sign. There are even other types like delta and phi orbitals. These shapes depend on which atomic orbitals, like s, p, or d, are interacting.

Knowing these shapes helps chemists build models of how molecules look.

A molecular orbital is a mathematical function used in chemistry. It describes the wave-like behavior and location of an electron within a molecule. These functions help scientists calculate physical and chemical properties. One key property is the probability of finding an electron in a specific region. In an isolated atom, electrons occupy regions called atomic orbitals. When atoms combine to form a molecule through valence chemical bonds, these atomic orbitals merge. The resulting electrons are then governed by the molecule as a whole.

Mathematically, molecular orbitals are approximate solutions to the Schrödinger equation. This equation describes electrons within the electric field of the molecule's atomic nuclei. Because solving this equation directly is often too difficult, scientists use approximations. One common method is the Linear Combination of Atomic Orbitals, or LCAO. This method treats molecular orbitals as a sum or difference of atomic wavefunctions. When two atoms approach each other, their atomic orbitals overlap. This overlap creates new areas of high electron density. The number of molecular orbitals produced must equal the number of atomic orbitals used.

There are three distinct types of molecular orbitals based on their energy levels. Bonding orbitals have energy levels lower than the original atomic orbitals. These orbitals promote the chemical bonds that hold a molecule together. Antibonding orbitals have higher energy than the constituent atomic orbitals. These orbitals actually work to oppose the bonding of the molecule. Finally, non-bonding orbitals have the same energy as the original atomic orbitals. These have no effect on the chemical bonding of the molecule. The balance between these types determines how a molecule behaves.

Scientists also categorize molecular orbitals by their symmetry using Greek letters. These labels describe how the orbital behaves when rotated around the internuclear axis. A sigma (σ) orbital is symmetric with respect to this axis. This means rotating the orbital does not change its mathematical sign. A pi (π) orbital is asymmetric with respect to rotation. Rotating a pi orbital results in a change of its mathematical sign. There are even more complex types like delta (δ), phi (φ), and gamma (γ) orbitals. These labels correspond to the types of atomic orbitals, such as s, p, d, f, or g, that are interacting.

The history of this field began in the late 1920s. Friedrich Hund and Robert S. Mulliken first introduced the concept of molecular orbitals in 1927 and 1928. Later, in 1929, Sir John Lennard-Jones introduced the LCAO approximation. His work was a major step in the start of modern quantum chemistry. He used these principles to derive the electronic structures of fluorine and oxygen. This allowed scientists to understand molecules using quantum principles rather than just simple models.

Molecular orbital theory provides a unique way to look at electron distribution. One major feature is delocalization. This means electrons are spread out over the entire molecule rather than being stuck in one spot. This makes the theory fundamentally different from valence bond theory. In valence bond theory, bonds are seen as localized electron pairs. Molecular orbital theory is essential for modern computational chemistry. Most current methods for studying chemical systems begin by calculating these orbitals.

Understanding these orbitals helps us visualize complex structures like acetylene. In an acetylene molecule, the set of molecular orbitals shows how electrons occupy different energy states. Some orbitals are occupied in the ground state, which is the lowest energy state. Others are virtual orbitals, which are empty in the ground state. These virtual orbitals may become occupied if the molecule enters an excited state. By mapping these mathematical functions, chemists can predict how molecules will react and interact with the world.