it seems it is much easier to first split the water and then combine the hydrogen with CO2. a simple copper or zinc catalyst with the two gases will produce methanol. I don't know the precise details of the process but it will probably be heated. nobel prize winner George Olah wrote a book called Beyond gas and oil: the methanol economy where he mentions several specific processes for making methanol from hydrogen and CO2. it has been done industrially since 1920
there are even ways of capturing CO2 from the air so we can make fuel for cars and power plants with only water and air and power from windmills or the sun
