The Deltan Union was the the Deltan polity and a Federation Member State. (ST reference: Star Charts; ENT - Rise of the Federation novel: Uncertain Logic) Its name was sometimes translated into English using the native term for Delta IV, "Dhei," as the Dhei Union. (ENT - Rise of the Federation novel: Uncertain Logic)
The Deltan Union made first contact with United Earth in 2143 when it encountered the crew of the ECS Horizon. The Horizon crew declined to reveal Delta IV's exact location for fear that Humans were not ready for the Deltans' potent sexuality.
In 2165, the Prime Minister of the Deltan Union was a woman named Mod'hira. That year, contact was established between the Deltan Union and the United Federation of Planets by the crew of the USS Essex. Prime Minister Mod'hira and other Deltan leaders were invited aboard the Essex for a tour of the ship, while several lower-ranking Essex crew toured the capital with Ambhat Mayor Serima.
During this tour, two Essex crew members suffered severe mental illness as a result of exposure to Deltan empathic sexual rituals. This severely strained the new relationship between the Federation and the Deltan Union in spite of the accidental nature of the harm; Essex Captain Bryce Shumar regarded the Deltans as a potential threat to Federation security as a result of what he initially viewed as sexual assault. Relations began to thaw after the consensual nature of the rituals and accidental nature of the harm became clear, prompting the crew of the Essex to respond to Prime Minister Mod'hira's request for assistance after agents of the Orion Syndicate abducted over 30 Deltan citizens. (ENT - Rise of the Federation novel: Uncertain Logic)
When a joint Borg/Cyberman force attack and overwhelmed Delta IV on stardate 45635.2, 2368, the Deltan Prime Minister was hurried away by her aides and taken to an underground command center. She ordered a full planetary evacuation, and she was evacuated on the USS Mattingly. (TNG comic: "Assimilation², Issue 1")
While the ST reference: Star Charts shows the Deltan homeworld in the Alpha Quadrant, the Decipher RPG module: Starfleet Operations Manual states that it is a Beta Quadrant planet. Uncertain Logic establishes Delta IV to be located in the V2292 Ophiuchi system.