An Omega molecule is a highly unstable molecule and the most powerful substance known to exist. The Borg knew it as Particle 010. The molecule could be synthesized with sufficient amounts of boronite ore. However, proper containment methods did not exist to prevent the violent destabilization of the molecule, which destroyed subspace and rendered warp travel impossible. The explosion of one molecule could destroy all subspace within several light years.
Some Federation cosmologists once theorized that Omega existed in nature for an infinitesimal period of time at the instant of the Big Bang. Some claimed Omega itself had been the primal source of energy for the Big Bang. Seven of Nine dismissed this as a creation myth.
Each molecule contained the same energy as a warp core. Theoretically an Omega molecule would be so energetic that a small chain of molecules would be able to power a civilization. (VOY: "The Omega Directive")
The oral history of Species 262, a primitive species, appeared to reference the Omega molecule as a powerful substance which could burn the sky. Another primitive species, Species 263, believed Omega to be a drop of blood from their Creator. (VOY: "The Omega Directive")
The Borg learned of the substance in 2145 through the assimilation of thirteen species. The discovery process started with Species 262, whose oral history referenced a powerful substance which intrigued the Borg. This information led the Borg to Species 263, which was also primitive. After following this trail of myth for many years, they managed to assimilate a species with useful data. They then were able to synthesize a single molecule of Omega that remained stable for one-trillionth of a nanosecond. The experiments the Borg conducted on Omega destroyed a total of twenty-nine Borg vessels and six hundred thousand drones. The Borg, who referred to Omega as Particle 010, regarded Omega with near-reverence as they believed it to exist in a flawless state. Because the Borg saw the Omega molecule as "perfection", all Borg were ordered to assimilate it at any cost. From their data, the Borg designed a harmonic resonance chamber that could theoretically stabilize the molecule, but according to Seven of Nine they didn't have enough boronite left to synthesize more Omega molecules. (VOY: "The Omega Directive")
A single Omega molecule was synthesized in the late 23rd century by the Starfleet physicist Ketteract on board a classified research station in the Lantaru sector. The molecule remained stable for a fraction of a second before it exploded, killing Ketteract and one hundred twenty-six other leading Federation scientists. Additionally, an unexpected secondary effect was the creation of a subspace rupture extending out several light years. This made it impossible to create a stable warp field, complicating rescue efforts.
The accident was covered up and the impassibility of the Lantaru sector was falsely explained as a natural phenomenon. By the late 24th century, Starfleet had come to the conclusion that Omega molecules represented a threat not only to the Federation, but to the entire galaxy. A chain reaction involving a handful of molecules could devastate subspace throughout an entire quadrant. If that were to happen, warp travel would become impossible and conventional space-faring civilization would cease to exist.
Starfleet suppressed all knowledge of Omega and enacted the Omega Directive, on which only starship captains and flag officers were briefed. Specialized teams could be dispatched to deal with Omega-related crises. The prime directive and Starfleet Medical protocols could be suspended during these missions. (VOY: "The Omega Directive")
"Omega destroys subspace. A chain reaction involving a handful of molecules could devastate subspace throughout an entire quadrant; if that were to happen, warp travel would become impossible – space-faring civilization as we know it would cease to exist."
Another civilization in the Delta Quadrant was actually successful in synthesizing some two hundred million Omega molecules in 2374. They were able to keep the molecules stable by using Omega's own resonance frequency (1.68 terahertz) to calibrate their containment field, though eventually an accident devastated their research facility. The starship USS Voyager managed to neutralize the molecules before they could do any further damage to subspace. Seven of Nine adapted the Borg harmonic resonance chamber design to emit an inverse frequency which would dissolve Omega's interatomic bonds. Seconds before the harmonic resonance chamber was jettisoned into space, the molecules started to stabilize spontaneously, and remained stable for at least 3.2 seconds. The remaining Omega molecules were destroyed by a modified gravimetric torpedo, with Voyager escaping to warp before the local subspace was destroyed. (VOY: "The Omega Directive")
When Q Junior visited Voyager's bridge in 2378, he proposed doing something interesting like fighting Species 8472 in fluidic space or detonating a few Omega molecules - to which Captain Janeway replied with a "No". (VOY: "Q2")
Rob Bonchune designed the Omega molecule using Lightwave. He later described it as a bucky ball with a fake electron cloud. The effect of the molecules coming together into the larger structure was one of the first uses of volumetric light in the series. ("Amazing Visual Effects", VOY Season 4 DVD special feature)
In the backstory for the proposed and abandoned animated series Star Trek: Final Frontier, the galaxy would have been devastated by a series of Omega particle detonations, making large areas impassable by warp drive.
In the game Star Trek: Armada, the Borg, led by a clone of Locutus of Borg, led an unsuccessful attack, in 2376, on the Federation and the Klingon and Romulan Empires in an attempt to gain an Omega particle, before being destroyed by the USS Enterprise-E.
In the game Star Trek Online, in a rare star cluster exploration mission, Starfleet Command orders the player's ship to scan a star system for Omega molecules and destroy them. At the end of the mission, the player finds out that there were no Omega molecules in the system and the mission is completed. In the mission "Skirmish", the player is asked to scan a ship for abnormalities. One option is to scan for Omega molecules. After trying this scan (which returns a negative result), the player's science officer says, "Captain, what are Omega molecules?" In the Season 8 update "The Sphere", players enter a Dyson sphere to secure a mysterious factory constantly producing Omega molecules for the Voth, who believe it is their right to have the molecules, as dictated by their Doctrine. It is later revealed that the Omega molecules (and components of them, called "Omega particles") and the sphere itself were created by Solanogen-based lifeforms serving the Iconians. The particles were used as a power source by the systems on board the sphere to conduct near-instantaneous travel through subspace. Also, during some Seasonal events, Q will create Omega molecules at specific locations, which players can stabilize in a minigame for rewards. Unlike other depictions, failing to stabilize the molecules has no destructive or otherwise negative effect, and the Omega Directive is not mentioned or referenced during these events.
In Star Trek: Legacy, the Ketteract incident is found to have been orchestrated by the assimilated Vulcan T'Urell, who actually stabilized the Omega particle and used it to power a sphere that was destroyed by James T. Kirk, leading to the particle's destabilization. In this interpretation of the Ketteract Incident, Kirk recommended the establishment of the Omega Directive. Legacy depicts a stabilized particle, while VOY: "The Omega Directive" mentions that the particle was destabilized fractions of a second after creation – it is possible that even starship captains were only told that the particle exploded upon being created as a cover story to prevent possible classified information about T'Urell from being disseminated.
The Star Trek: Section 31 book Cloak provides a different portrayal of Ketteract's experiment. In the novel, Section 31 actively participated in the disastrous Omega experiment in the 23rd century. The crew of the original USS Enterprise barely escaped when the molecule destabilized.
The Borg fascination with Omega is described in the Star Trek: Destiny novel trilogy. The race the Borg descended from (the Caeliar) utilized it as a power source. Following the degradation of a Caeliar group exiled due to an accident, their connection to Omega (and a power source for their nanoprobes called catoms) was lost. This led the first Borg Queen to focus on recovery of Omega; however, they lost their knowledge of how to control the particles or synthesize them.
In The Eternal Tide, Voyager learns that the Omega molecule did indeed trigger the Big Bang, and is increasingly building power and stability in a sub-dimension, essentially "counting down" to the end of this universe. When a civilian scientific expedition encountered a rift into this dimension, they unintentionally accelerated this decay as their matter provided Omega with additional energy, but the instability caused by this chain reaction also created the Q Continuum, the Q serving as a creative force to 'counter' the destructive potential of the Omega Continuum. Although Q believes that the only way to stop the decay would be to reverse the original incident and thus essentially erase the Q Continuum from existence, Voyager is able to repair the disruption while only shortening the universe's lifespan by a few million years as opposed to the trillions they would have lost previously, thus saving the Q. However this is only achieved through the sacrifice of Captain Afsarah Eden – a "child" of the Omega Continuum, created when the continuum manifested a new entity based on a scientist who discovered it and Q's son, who possessed the potential to channel the power of Omega and contain it once again.
In the crossover miniseries Star Trek: The Q Conflict, when the four captains are recruited to compete against each other to decide a conflict between the Q, Trelane, the Organians and the Metrons, the captains decide that the time is right to oppose Q and try to end the game when he challenges them to collect an Omega molecule, which all three modern captains agree is too dangerous (Kirk alone not sharing their objection, because he doesn't know what an Omega molecule is).
In the cancelled Star Trek: Borg Assimilator game, the main goal is to develop a stable Omega particle, and then go on and assimilate the Alpha Quadrant.