It is subjective what constitutes an "intelligent species" so I'm assuming you are talking about an alien species with human-level intelligence. In general it is very difficult to speculate about the biology of an alien species since as of right now there is no scientific evidence for life on other planets. However, what is known is that in humans the brain consumes about 20% of the body's total energy need so it is plausible that a hypothetical species with human-level intelligence would also require large amounts of energy.

On a fundamental level the vast majority of the energy that is potentially available to life on the surface of a planet comes either from a star (the Sun in Earth's case) or from inside the planet (in Earth's case there are geothermal vents at the bottom of the ocean that support life). Notably in Earth's case the amount of energy available from these sources is very sparse though, and any known intelligent organisms cover their energy needs by consuming other organisms. From a thermodynamic standpoint it is however still conceivable that an intelligent organism that directly uses these sparse sources of energy could exist - it's just that evolution has not produced these organisms. Such a hypothetical organism would need to be very large though to cover its energy needs.

If we assume access to advanced technology it may be possible to bio-engineer an intelligent species that does not need to eat in order to survive; it is difficult to envision how such a species would cover its energy needs and what would be counted as "eating". With cybernetic augmentations nutrients could conceivably be synthesized without the need to eat. Finally, it may be possible to discard biology as it exists today entirely and to create an intelligent "species" that uses another medium like silicon-based electronics; the sources of energy would then be constrained to sources of electricity rather than sources of chemical energy.
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