DescriptionShort hydrogen bonds (SHBs), which have the donor and acceptor separations below 2.7 Å, occur widely in condensed phase system and exhibit prominent quantum mechanical characters. SHBs have been associated with crucial functions in biological macromolecules, and hence I first conduct a statistical analysis on atomic-resolution biomolecular structures from the Protein Data Bank and demonstrate the structural and chemical features of biological SHBs. The exact determination of the geometry and functional roles of SHBs is often subject to the limited sources of high-resolution protein structures. As such, I collaborate with the group of Professor Sijian Wang to develop boosting based machine learning models to predict the presence of biological SHBs in a protein structure with moderate or low resolution. Using electronic structure calculations, I further elucidate how the interplay of the structural and chemical features determines the proton potential energy surfaces and the proton sharing conditions, and how the competition of intermolecular interactions results in different preference to form SHBs between amino acid side chains. As one of the spectral signatures of SHBs is their highly downfield (> 14 ppm) ¹H NMR chemical shift, I carry out first principles simulations on a set of model molecules to assess how quantum effects determine the symmetry and chemical shift of their SHBs. From these simulations, I reveal a universal relation between the instantaneous chemical shift and the position of the proton in a SHB and develop a metric that allows one to determine the proton position directly from its ¹H chemical shift. Besides biological systems, SHBs have been observed in protic ionic liquids and aqueous solutions. I apply first principles simulations and IR spectra calculations to the mixture of 1-methylimidazole and acetic acid and the aqueous solutions of bifluoride ions to demonstrate how quantum effects promote the delocalization of the hydrogen atom between acid and base in protic ionic liquids and how SHBs disturb the hydrogen bond structures of liquid water.