Most flowers produce "nectar" of some kind...it is one of the things what attracts bees, pollen is the other.
Most ant control is done with "sticky" traps
I use pieces of double side tape to trap ants have to change it out quite often because they will make a sacrifical bridge.
Another reason ants would find your clematis interesting is because of the presence of aphids. Take a good look under the leaves.
I'm with you Douglas!! Aphids! Look at the new growth on your plant for little green Aphids.
Aphids produce a sticky, sweet substance called honeydew. The ants milk them like cows. You may also see some curling of the new growth from the aphid damage. Aphids are soft-bodied and easy to kill with soapy water, just don't do it in the sunshine! Good luck!
I have a question, Please tell me what the purple leaf plant is. I have some growing in my bed around my bird bath.