The pair that is not correctly matched is Option 1: Berlin : Rhine.

The Rhine is a major river in Europe, flowing through several countries including Switzerland, Liechtenstein, Austria, Germany, France, and the Netherlands. However, Berlin is not located on the Rhine River. Berlin is the capital and largest city of Germany, but it is situated in the northeastern part of the country, far away from the Rhine River. Instead, Berlin is situated on the River Spree, which is a smaller river that flows through the city.

Option 2: London : Thames is correctly matched. The Thames is a famous river that flows through London, the capital of the United Kingdom. The river is iconic and has played a significant role in the history and development of the city.

Option 3: New York : Hudson is correctly matched. The Hudson River is a major river located in the eastern United States. It flows through the state of New York, and its estuary forms the harbor for New York City. The Hudson River has great historical and economic importance for New York, and it is often associated with the state and the city.

Option 4: Vienna : Danube is correctly matched. The Danube is one of the longest rivers in Europe, flowing through ten countries, including Germany, Austria, Hungary, and Romania. Vienna, the capital of Austria, is indeed situated on the banks of the Danube. The river plays a significant role in the cultural and historical heritage of Vienna and is an important part of the city`s identity.

To summarize, Option 1 is not correctly matched because Berlin is not located on the Rhine River. The correct match for Berlin would be the River Spree.