The process that does not require energy for movement of particles are
Movement of gases through stomata
Absorption of water by the roots
Movement of CO2 for photosynthesis
Certain nutrients, for example ions such as nitrates, sulfates, potassium, zinc, and manganese etc cannot pass through the cell membrane of the root cell easily. This is because the concentration is higher inside the root cells and it is maintained in order to develop osmotic pressure for absorbing water. The movement of nutrients from a region of their lower concentration to the region of their of their higher concentration requires energy in the form of ATP.
Movement of gases in and out of stomata is due to diffusion and the absorption of water in roots is due to osmosis. Osmosis and diffusion are types of passive transport that do not require energy.