Provided herein are genetically engineered microbes that include at least a portion of a carbon fixation pathway, and in one embodiment, use molecular hydrogen to drive carbon dioxide fixation. In one embodiment, the genetically engineered microbe is modified to convert acetyl CoA, molecular hydrogen, and carbon dioxide to 3-hydroxypropionate, 4-hydroxybutyrate, acetyl CoA, or the combination thereof at levels greater than a control microbe. Other products may also be produced. Also provided herein are cell free compositions that convert acetyl CoA, molecular hydrogen, and carbon dioxide to 3-hydroxypropionate, 4-hydroxybutyrate, acetyl CoA, or the combination thereof. Also provided herein are methods of using the genetically engineered microbes and the cell free compositions.