Introduction

Radicals are some of the most reactive species you'll encounter in organic chemistry. What makes them special isn't a positive charge or a negative charge. Instead, it's the presence of a single unpaired electron. That one electron dramatically changes how molecules behave and explains why radicals are often short-lived reaction intermediates.

In this lesson, we'll look at the three possible states of an orbital, compare radicals to cations and anions, and learn why radicals are often neutral even though they are extremely reactive. Understanding radicals now will make it much easier to understand radical reaction mechanisms later in your organic chemistry course.

The Three Possible States of an Orbital

An orbital can exist in one of three states:

• Empty (0 electrons)
• Filled (2 electrons)
• Half-filled (1 electron)

Understanding these three possibilities helps explain many of the important reactive species encountered in organic chemistry.

Empty Orbitals

An empty orbital contains zero electrons.

Systems with empty orbitals are often cations, although they do not have to be.

Examples include:

• The hydrogen cation (H⁺), often called a proton
• A methyl cation (CH₃⁺)
• Borane (BH₃)

In the methyl cation, carbon is bonded to three hydrogens and contains an empty orbital. The molecule is positively charged because it lacks sufficient electron density around the carbon.

Borane is an interesting exception. Boron also possesses an empty orbital, but the molecule remains neutral.

The important idea is that an empty orbital creates an electron-deficient system.

Filled Orbitals

A filled orbital contains two electrons.

These electrons may be:

• Shared in a bond
• Present as a lone pair

Filled orbitals are generally more stable than empty or half-filled orbitals.

Examples include:

• Hydride ion (H⁻)
• Hydrogen gas (H₂)
• Methyl anion (CH₃⁻)
• Water (H₂O)

For example, oxygen in water has:

• Two bonding orbitals
• Two lone-pair orbitals

All four orbitals contain electron pairs, making them fully occupied.

Filled orbitals can sometimes create anions when extra electrons are present, but they also occur in many neutral molecules.

Half-Filled Orbitals: Radicals

The main focus of this lesson is the half-filled orbital.

A half-filled orbital contains only one electron.

When a molecule contains an orbital with a single unpaired electron, we call it a radical.

The atom bearing the unpaired electron is often referred to as a radical center.

Examples of Radicals

Hydrogen Radical

A hydrogen radical contains one electron in its 1s orbital.

Unlike:

• H⁺, which has zero electrons
• H⁻, which has two electrons

the hydrogen radical contains exactly one electron.

Methyl Radical

The methyl radical (CH₃•) consists of a carbon attached to three hydrogens with one unpaired electron.

This is one of the most common radical examples discussed in organic chemistry.

Hydroxyl Radical

The hydroxyl radical (HO•) contains:

• One oxygen-hydrogen bond
• Two lone pairs
• One unpaired electron

The unpaired electron occupies a half-filled orbital on the oxygen atom.

Bromine Radical

A bromine radical (Br•) contains:

• Three filled lone-pair orbitals
• One half-filled orbital containing a single electron

That single unpaired electron is what makes bromine a radical.

The Carbon Radical

For carbon, radicals are commonly represented as sp²-hybridized species.

The carbon forms three sigma bonds using sp² hybridized orbitals arranged in a trigonal planar geometry.

One unhybridized p orbital remains perpendicular to that plane.

That p orbital contains a single unpaired electron.

As a result:

• The carbon is sp² hybridized.
• The geometry is trigonal planar.
• The unpaired electron occupies the p orbital.

Why Are Radicals So Reactive?

An unpaired electron is inherently unstable.

Electrons generally prefer to exist in pairs, so molecules with unpaired electrons tend to seek reaction partners that allow them to achieve a more stable electronic arrangement.

Because of this, radicals are typically:

• Highly reactive
• Short-lived
• Important reaction intermediates

While your organic chemistry course may not cover a large number of radical reactions, the radical intermediates that do appear are almost always extremely reactive.

The Surprising Thing About Radicals

One of the most interesting features of radicals is that they are often neutral.

At first, this seems strange.

Many students expect highly reactive species to carry a charge, but radicals show that reactivity and charge are not the same thing.

Hydrogen Radical

Hydrogen wants one valence electron.

The hydrogen radical owns one electron.

1 − 1 = 0

The species is neutral.

Methyl Radical

Carbon wants four valence electrons.

In the methyl radical, carbon owns:

• One electron from each of three bonds
• One electron from the radical orbital

That gives carbon four electrons.

4 − 4 = 0

The methyl radical is also neutral.

Other Radical Examples

The same logic applies to:

• Hydroxyl radicals
• Bromine radicals

Although they contain unpaired electrons and are highly reactive, their formal charges remain zero.

Why One Electron Changes Everything

The defining feature of a radical is not a charge.

The defining feature is a single unpaired electron occupying a half-filled orbital.

That one electron makes radicals fundamentally different from:

• Cations with empty orbitals
• Anions with extra electron pairs
• Stable molecules containing only filled orbitals

Even though radicals are often neutral, they are among the most reactive species encountered in organic chemistry because they contain an electron that is not paired.

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