automatic gradient between vertex groups

When I apply two different colors to tow adjacent vertex groups, apparently there is a border between the colors. Is there a possibility to let blender calculate the colors of the vertex groups and create a gradient automatically?
Or is the only way to create a third vertex group between the two existing ones and create and adjust a blend texture by myself?

The screenshot shows the two vertex groups where I would like to have a gradient between so I get a smooth change from green to grey.