Odd molecule is a term invented by Gilbert N. Lewis

Gilbert N. Lewis

Gilbert Newton Lewis was an American physical chemist known for the discovery of the covalent bond , his purification of heavy water, his reformulation of chemical thermodynamics in a mathematically rigorous manner accessible to ordinary chemists, his theory of Lewis acids and...

 in 1916 for a molecule

Molecule

A molecule is an electrically neutral group of at least two atoms held together by covalent chemical bonds. Molecules are distinguished from ions by their electrical charge...

 containing an odd number of electron

Electron

The electron is a subatomic particle with a negative elementary electric charge. It has no known components or substructure; in other words, it is generally thought to be an elementary particle. An electron has a mass that is approximately 1/1836 that of the proton...

s.

Taking the p-shell elements, such molecules are rare; they are usually colored and paramagnetic, that is, attracted by a magnet

Magnet

A magnet is a material or object that produces a magnetic field. This magnetic field is invisible but is responsible for the most notable property of a magnet: a force that pulls on other ferromagnetic materials, such as iron, and attracts or repels other magnets.A permanent magnet is an object...

.

Odd molecules are 'radicals

Radical (chemistry)

Radicals are atoms, molecules, or ions with unpaired electrons on an open shell configuration. Free radicals may have positive, negative, or zero charge...

.'

A fine example is nitric oxide

Nitric oxide

Nitric oxide, also known as nitrogen monoxide, is a diatomic molecule with chemical formula NO. It is a free radical and is an important intermediate in the chemical industry...

, q.v.; nitrogen dioxide

Nitrogen dioxide

Nitrogen dioxide is the chemical compound with the formula it is one of several nitrogen oxides. is an intermediate in the industrial synthesis of nitric acid, millions of tons of which are produced each year. This reddish-brown toxic gas has a characteristic sharp, biting odor and is a prominent...

 is another; chlorine dioxide

Chlorine dioxide

Chlorine dioxide is a chemical compound with the formula ClO2. This yellowish-green gas crystallizes as bright orange crystals at −59 °C. As one of several oxides of chlorine, it is a potent and useful oxidizing agent used in water treatment and in bleaching....

is also an example, being a reddish-yellow gas. They are all fairly reactive.

When including d-shell elements, i.e., the transition metals, the concept mostly doesn't apply, and this 'odd' state is not so unusual.