It's basic quantum mechanics and thermodynamics. All molecules with three atoms are greenhouse gases. The information is readily available, I'm not going to repeat it here. Pick up some textbooks.
Wait, what? Why does three atoms make it a greenhouse gas?
Not saying you're wrong, but from the quantum I know (senior level undergrad), that's not "basic". Could you explain the "three atom" bit at an undergrad level?
Molecules with three atoms that are not considered greenhouse gases include:
Ozone (O3): While ozone does absorb some solar radiation, it's primarily involved in blocking ultraviolet light from the Sun, rather than acting as a greenhouse gas in the way that CO2, CH4, or N2O do.
Nitrogen Dioxide (NO2): Although it's a significant air pollutant and plays a role in smog formation, it is not primarily considered a greenhouse gas.
Nitric Oxide (NO): Like NO2, nitric oxide is more involved in air pollution and is not considered a greenhouse gas.
Hydrogen Peroxide (H2O2): This compound is more known for its reactive properties and is not considered a greenhouse gas.
Carbon Monoxide (CO): While carbon monoxide can have indirect effects on global warming by reacting with other substances in the atmosphere, it is not itself considered a significant greenhouse gas.
Iodine Trichloride (ICl3): This is a more exotic example and not commonly found in the atmosphere. It is not a greenhouse gas.
GPT is not a reliable source. Note that 4 out of 6 of these "molecules with three atoms" it offers do not have three atoms. (Carbon monoxide and nitric oxide have two; iodine trichloride and hydrogen peroxide have 4.)
The GP's somewhat cryptic statement about 3 atoms is explained better here:
Monatomic gases and diatomic molecules made of identical atoms (e.g. O2, N2) are not "active" with regard to infrared radiation. They are transparent to it. Almost all other molecules are "IR active," meaning that they can absorb IR radiation in ways that are characteristic of their vibrational modes. This includes the well known greenhouse gases carbon dioxide, methane, and nitrous oxide. Greenhouse gases are those IR active molecules that have a significant residence time in the atmosphere and can thus partially trap IR radiation emitted from the Earth's surface.
Some substances are IR active but are not usually classified as greenhouse gases because they quickly break down in the environment. Other substances are IR active but not counted among greenhouse gases because they have a low vapor pressure and do not significantly make it into the atmosphere.
Tropospheric ozone (O3) is the third most important anthropogenic greenhouse gas after carbon dioxide (CO2) and methane (CH4). Ozone absorbs infrared radiation (heat) from the Earth's surface, reducing the amount of radiation that escapes to space.
Nitrogen dioxide is infrared active and absorbs IR re-radiated from the Earth, as seen in the spectral plots available here:
However, its short atmospheric residence time means that its emissions have little heat-trapping ability, so it is rarely considered as a greenhouse gas: