Terpene-based natural deep eutectic solvents (NADES) formed by using carvone as the hydrogen bond acceptor and a series of organic acids including tartaric, succinic, malic, and lactic acids as hydrogen bond donors are studied using a combination of molecular simulation methods. Density functional theory was used to study small molecular clusters and the topological characterization of the intermolecular forces using the atoms-in-a-molecule approach. Close-range interactions between the optimized carvone bases eutectic solvents between carbon dioxide have been studied for potential utilization of these solvents for gas capture purposes. Furthermore, COSMO-RS calculations have been carried out for the carbon dioxide solubilization performance of NADES compounds and to obtain s-profiles to infer the polarity and H-bond forming ability of the studied solvents. On the other hand, molecular dynamics simulations were carried out to analyze the bulk liquid properties and their relationship with relevant macroscopic properties (e.g., density or thermal expansion). Last but not least, relevant toxicity properties of the studied systems were predicted and reported in this work. The reported results provide the characterization of environmentally friendly NADES and show the suitability of carvone for advanced applications as carbon dioxide solubilizers.