I believe in some cases a capital was moved to a minor but already-existing city. Amman and Madrid are examples of this, so maybe they don't count as "purpose-built".
Can you explain what you want to tell about Amman? I lived there when I was a kid (and the city a lot smaller) and it is the only major city in Jordan the the only logical choice as a capital. The position is also good for a capital city, there is nothing in the south (I lived in Aqaba first).
Amman is the largest city in Jordan by some distance _now_, but when it was designated as the capital in 1921, it was much smaller. Its growth has come almost exclusively since then, and as a result of its designation as the captial, it became the largest city in the country.
Bonn, Germany’s capital from 49(?) to 1991 would also fit that pattern. There were far larger cities such as Munich, Hamburg, and Frankfurt in West Germany. Nobody wanted a strong German capital.