Is there no garden space near the downspout or elsewhere? It won't grow up a downspout without some support such as a downspout trellis. To my mind it's a lot more work to grow in a planter - special mix that won't break down over time, regular fertilizer and water, and winter protection if you live in a cold area, even if they would be fine when grown in the ground. If you don't have an alternative in-ground planting spot, I'd choose something at least the size of a half whiskey barrel - they have fairly large root systems.

Hmm, I was hoping it would wrap around a downspout (there is room between the downspout and the house). I will investigate a trellis or some sort of support structure.

There is no garden space or dirt at all near it--just poured concrete. Thanks!

Henri clematis grows fairly large. So the root system is fairly large too. If the container is not big enough, it will not thrive. Further, from my experience, if you live in a cold area, either the planter will have to be moved into your unheated garage or should be further insulated to protect the plant in winter. I have lost a couple of clematis that were in planters, which I was opted to leave outside during the winter time. I am in zone 6 ( New York).

The OP said she lives in zone 7b, so winter temps shouldn't be a problem. I overwintered several clems in 1-5 gallon pots with no protection in zone 7a last winter and the winter before.

That said -- use the biggest container you can afford and that you have space for. I do a lot of container gardening, because my property is basically on solid rock. I try to use mostly half-barrel sized planters. If you're going to put the planter on the concrete, though, you may have problems with excess heat in the summer -- and clems don't really appreciate that. And I have not yet tried the large clems in planters over a long term, so a container may not be a long-term solution for you. But give it a try -- you never know until you try!

I grow about 14 Clematis in pots ----- and only 4 in the ground. My Pots/Urns/Container are all 18+" wide and I prefer even wider, and they are all 18+" Deep to accommodate the roots. I grow both Group 2 and Group 3 Clematis in containers. It really depends on the material the pot is constructed of. I grow mine in Stone Urns and containers made of "Ceramix" which will protect the roots over the winters here.

Sorry for the comments about over wintering. I missed or forgot the zone of OP. I deleted the overwintering comments.

I have had 2 type 3 clems "Hagley Hybrid" and "Warsaw Nike" together in one giant pot for about 4 years now. Conventional wisdom says not to do this, but I have considerably limited space. They have gotten huge and overwinter just fine. The pot is about 56cm high and 45cm wide. It is pretty large and they are doing great. You most certainly can grow them in pots! I haven't had to do any root pruning yet but that might be something to consider down the line.

Your Pot is 21-Inches High and 18-Inches Wide. Yes, I imagine those 2 Clematis have gotten quite large. What is your Giant Pot made of ?