According to the second law of thermodynamics, all human activities cause exergy destructions, adding to additional root causes for carbon dioxide emissions responsibility. It means that current carbon dioxide concentrations are accurately observed, but the root causes and their potential solutions against global warming fall short of achieving the goals of the Paris agreement by almost 45% in terms of decarbonization efforts, as shown in this paper. This result applies to all activities, including the green facility concept. In this respect, the primary aim of this paper is to raise awareness about the essence of the Second Law of Thermodynamics in expanding the green facility concept to reach more effective and sustainable rating methodologies concerning the climate crisis. A new evaluating and rating model with a set of exergy-based green building metrics that relate additional carbon dioxide emissions to irreversible exergy destructions has been developed. Examples about apparently green buildings according to the First Law of Thermodynamics are given by showing that these buildings are not green due to additional carbon dioxide emissions responsibility due to exergy destructions. An airport terminal building case is elaborated. It has been shown that although part of the electricity comes from a third-party wind energy provider, it ends up with carbon dioxide emissions responsibility because it is not entirely used in exergy-rational demand points and compares less favorably with an on-site cogeneration system using natural gas by about 30% more emissions responsibility. The results and derivations of new metrics are discussed, which shed light on adding new criteria to existing green building certification programs.