Intra- and intermolecular forces competition was investigated in the 9,10-anthraquinone (1) and its derivatives both in vacuo and in the crystalline phase. The 1,8-dihydroxy-9,10-anthraquinone (2) and 1,8-dinitro-4,5-dihydroxy-anthraquinone (3) contain Resonance-Assisted Hydrogen Bonds (RAHBs). The intramolecular hydrogen bonds properties were studied in the electronic ground and excited states employing Møller-Plesset second-order perturbation theory (MP2), Density Functional Theory (DFT) method in its classical formulation as well as its time-dependent extension (TD-DFT). The proton potential functions were obtained via scanning the OH distance and the dihedral angle related to the OH group rotation. The topological analysis was carried out on the basis of theories of Atoms in Molecules (AIM—molecular topology, properties of critical points, AIM charges) and Electron Localization Function (ELF—2D maps showing bonding patterns, calculation of electron populations in the hydrogen bonds). The Symmetry-Adapted Perturbation Theory (SAPT) was applied for the energy decomposition in the dimers. Finally, Car–Parrinello molecular dynamics (CPMD) simulations were performed to shed light onto bridge protons dynamics upon environmental influence. The vibrational features of the OH stretching were revealed using Fourier transformation of the autocorrelation function of atomic velocity. It was found that the presence of OH and NO2 substituents influenced the geometric and electronic structure of the anthraquinone moiety. The AIM and ELF analyses showed that the quantitative differences between hydrogen bonds properties could be neglected. The bridged protons are localized on the donor side in the electronic ground state, but the Excited-State Intramolecular Proton Transfer (ESIPT) was noticed as a result of the TD-DFT calculations. The hierarchy of interactions determined by SAPT method indicated that weak hydrogen bonds play modifying role in the organization of these crystal structures, but primary ordering factor is dispersion. The CPMD crystalline phase results indicated bridged proton-sharing in the compound 2.