Abstract: Based on two chemical reactions ① CO₂ + H₂O → H₂CO₃ and ② H₂CO₃ + 3H₂O → H₂CO₃·3H₂O, we optimized and calculated the chemical reactions by quantum chemical method to determine their infrared vibration absorption spectra and intensities, studied and determined the selective absorption and intensity of infrared radiation by these compounds. It’s found that reactions ① and ② can react spontaneously to produce H₂CO₃ and H₂CO₃·3H₂O (carbonic acid trihydrate). H₂CO₃ has strong absorption of infrared radiation (The important absorption frequency is 1919.9 cm⁻¹ and its intensity is 426.7 km/mol etc.), and H₂CO₃·3H₂O possesses very strong absorption of infrared radiation (The important absorption frequency is 3145.9 cm⁻¹ and its intensity is 1124.2 km/mol etc.). Therefore, H₂CO₃ and H₂CO₃·3H₂O can act as the main materials to strongly broad absorb near-infrared and mid-infrared light energy, and emit heat energy to raise the atmospheric temperature, resulting in greenhouse effect. In addition, the infrared radiation absorption spectroscopy of the ionic compounds HCO₃⁻, CO₃²⁻, HCO₃⁻·3H₂O and CO₃²⁻·3H₂O obtained through the hydration reactions of carbonate was also studied in this work. The results show that these ionic compounds also have strong absorption of infrared radiation, convert light energy into heat energy, and enhance the greenhouse effect. Therefore, this research work has found the direct scientific evidence that CO₂ as greenhouse gas leads to greenhouse effect and the mechanism, which is transformed from CO₂ and H₂O to H₂CO₃ and H₂CO₃·3H₂O, thus having strong infrared radiation absorption and causing atmospheric greenhouse effect. According to the importance and sensitive hazards of carbon cycle and carbon emissions in the atmosphere of earth system, this paper proves that CO₂ gas in atmospheric clouds can lead to the greenhouse effect through direct and clear scientific evidence and mechanism, and enhances the urgency to control carbon emission and greenhouse effect.