From NuGOwiki

Neurotransmitters are chemicals that are used to relay, amplify and modulate electrical signals between a neuron and another cell. According to the prevailing beliefs of the 1960s, a chemical can be classified as a neurotransmitter if it meets the following conditions:

• It is synthesized endogenously, that is, within the presynaptic neuron
• It is available in sufficient quantity in the presynaptic neuron to exert an effect on the postsynaptic neuron
• Externally administered, it must mimic the endogenously-released substance
• A biochemical mechanism for inactivation must be present

However, there are other materials, such as the zinc ion, that are neither synthesized nor catabolized and are considered neurotransmitters by some.