Context <p>Coumarin derivatives (CoDe) exhibit significant biological activities, and the positions of different substituents as well as the introduction of methyl groups may influence their biological activity and efficacy. By investigating the relationship between substituent positions, methylation, and hydrogen bond properties, the specific mechanisms and rules governing hydrogen bonds in intermolecular interactions can be further elucidated. This provides a theoretical basis for the synthesis of novel coumarin derivatives with tailored hydrogen bond characteristics and biological activities, as well as a research foundation for the development of new drug molecules. Therefore, the hydrogen bonding interactions between 3-hydroxycoumarin (3-HyCo), 4-hydroxycoumarin (4-HyCo), 7-hydroxycoumarin (7-HyCo), and 7-hydroxy-4-methylcoumarin (4-Me-7-HyCo) with ethanol and water were studied using density functional theory (DFT) and time-dependent density functional theory (TD-DFT). Firstly, the molecular structure of the coumarin (Co) monomer and the charge properties and molecular electrostatic potential extreme value of its four derivatives were analyzed. The stable complex structures of the four derivatives with ethanol and water were obtained through optimization, and the presence of hydrogen bonds in these complexes was confirmed. Secondly, the hydrogen bond lengths, frontier molecular orbitals (FMOs), interaction energies, atoms in molecules (AIM) topological parameters, and hydrogen bond vibration spectra in both the ground and excited states were examined. It was found that among the derivatives with different hydroxyl positions, the hydrogen bond structure of the 4-hydroxycoumarin complex was the most stable, and the introduction of a methyl group further enhanced the stability of the hydrogen bond structure. Finally, the hydrogen bond vibration spectra were found to undergo a red shift in the excited state, rendering the hydrogen bond structure more stable than that in the ground state.</p> Methods <p>All computational studies in this paper were performed using the Gaussian 16 software package (Revision B.01), while GaussView 6.0.16 was employed for the analysis and visualization of compounds. The DFT method was adopted to optimize all compounds, utilizing the B3LYP functional combined with the 6-311++G(d,p) basis set. Multiwfn 3.8 (dev) and VMD 1.9.3 software were used to analyze and create the molecular electrostatic potential extreme value diagrams and frontier molecular orbital (FMO) images. Basis set superposition error (BSSE) correction was introduced during the calculation of interaction energies. Topological analysis was conducted using Multiwfn 3.8 (dev) software, and the excited-state vibration spectra were obtained based on the TD-DFT method.</p>