I have 4-5 plant species picked out that I know are compatible with my setup, but I would LOVE to grow some HC (Dwarf Baby Tears).
I've read HC is difficult to grow without CO2 injection, but I think a lot of people giving this advice maintain aquariums with few fish in them. I plan to have fully stocked fauna as well as flora: shrimp, 3 ottos, 20-25 small schooling fish, and more if the tank can maintain it.
You can absolutely grow HC without injecting CO2 (regardless of how much CO2 your fish may or may not be providing to the water column…. but I agree with Hoppy that it's probably on the low side of zero.) That being said, your success will come down to a few things:
PATIENCE: It will grow very very slowly… It took me four months to carpet the bottom of a non-CO2 10 gal aquarium with HC.
LIGHT: Even though your tank is non-CO2, you're going to have to give the HC moderate lighting. In PAR terms, I've had success when supplying the HC with at least 65 PAR. But you probably don't want to go above 75 PAR to avoid overdriving the Light/CO2/Nutrient balance. In non-PAR terms, the only other way I can express this is: if the new nodal tips of growth aren't growing out horizontally, then you don't have enough light for it to carpet properly.
SUBSTRATE: The two main substrates I use are yard soil and ADA Aquasoil (powder form). Properly chosen yard soil is excellent for HC. If you cap the soil, it must be capped with something that has a 1-2 mm grain size for best results. This is because the roots of HC are very delicate. The powder form of ADA Aquasoil is perfect. But I've also capped my soil with inert 2mm quartz rock that I bought at a LFS. Fluorite, for example, is not a great choice: the pieces range from 3mm to 9mm and are sharp; and that makes planting difficult. Eco-complete is also probably too large.
PLANTING: Because the growth is so slow, you need to give yourself a slight advantage by using a good planting technique that will promote the carpeting effect. Planting in a large clump, or even small clumps, is not the best if a carpet is what you're after. You have to understand that you only need a very small portion of the HC plant to get it growing when you transplant it from the pot or mat or whatever it comes in when you buy it. As long as you have at least one "node" you can cut it and plant it and it will grow new roots and start to add more nodes in the form of a chain. The trick here is that the little "plant-let" needs to be at least big enough to grip the substrate you're planting it in. So, what I do is cut my source plant (pot, mat, etc) into hundreds of plant-lets of 2-3 nodes each. There is usually a root at each node and you keep those. Then, I very painstakingly plant all the plant-lets about 1/4 inch apart from each other, covering the whole fg area of the tank. Don't be afraid to bury some of the nodes if that's what it takes to get them to stay in the substrate. Definitely use planting tweezers… and cover the substrate with only 1/4 inch of water when planting. Don't get me wrong, it is very tedious, but it grows in beautifully and forms a carpet faster. For a 20 gal tank, this will take you about 4 hours to do if you are doing it as I describe. But after the four hours have past, you sit back and wait four months :-) Oh, and after the initial planting, fill the tank very very very carefully and slowly. (The other advantage of this method is that HC is usually grown commercially as emergent. So, when you plant it in your tank it has to grow new submerged leaves. And this particular method of planting spreads that new submerged growth over the entire planting area while the leaves of the original plant-lets die away.)
WATER: One note about water… if you have a water softener in your home/apt and it uses an ion exchange method that leaves you with sodium ions in the water, the high concentration of sodium seems to have an effect on the robustness of the HC. By contrast, when I use a properly mineralized RO water source, the HC is very robust. But lately, I've been experimenting with softened tap water and I have noticed a distinct difference. I can still grow it, but it lacks the zeal that I experience when using a non-softened water source. Other plants in that experimental tank have also responded that way, so it's not just the HC.
WATER MOVEMENT: Make sure you have plenty of cross-tank water movement to keep the plants leaves constantly renewed with fresh water. I have found that the outflow from a canister filter (or HOB) is usually not enough to provide this. Add a powerhead or side mounted impeller.
Here's a tank of mine with HC in the foreground that used the method of planting that I described above. The tank is two months old at the time of the photo. This tank uses the experimental softened water that I mentioned above. I guess the only downside to this photo is that this tank does have CO2 injection…. but I just wanted to illustrate the growth pattern of the HC which I sourced with just two pots of emergent HC. Lighting at the substrate is 75 PAR. Regarding water flow… In the picture you can see the Madagascar Lace plant folding over to the right. This is due to the cross flow created by the Vortech MP-10 which you can see mounted on the back right. This creates a right-->left flow a the back of the tank, but a left-->right flow in the front part of the tank.