The strength of a hydrogen bond depends on the distance between the atoms involved in the interaction. In general, as the distance between the atoms decreases, the strength of the hydrogen bond increases. This relationship can be explained through quantum chemical calculations.A hydrogen bond is a non-covalent interaction between a hydrogen atom H covalently bonded to an electronegative atom X and another electronegative atom Y . The most common electronegative atoms involved in hydrogen bonding are oxygen, nitrogen, and fluorine. The interaction can be represented as X-HY, where the dotted line represents the hydrogen bond.Quantum chemical calculations, such as ab initio and density functional theory DFT methods, can be used to study the effect of varying the distance between the atoms in a hydrogen bond on the strength of the interaction. These calculations involve solving the Schrödinger equation for the molecular system to obtain the wavefunction and energy of the system.When the distance between the atoms in a hydrogen bond decreases, the overlap between the electron clouds of the atoms increases. This leads to a stronger electrostatic attraction between the positive charge of the hydrogen atom and the negative charge of the electronegative atom Y . As a result, the potential energy of the system decreases, and the hydrogen bond becomes stronger.However, there is a limit to how close the atoms can get before repulsive forces between the electron clouds and nuclei start to dominate, causing the potential energy to increase and the hydrogen bond to weaken. This occurs when the distance between the atoms becomes shorter than the sum of their van der Waals radii.In summary, quantum chemical calculations show that the strength of a hydrogen bond increases as the distance between the atoms decreases, up to a certain limit. Beyond this limit, the repulsive forces between the atoms cause the hydrogen bond to weaken. This relationship between distance and hydrogen bond strength is essential for understanding the structure, stability, and function of many biological molecules, such as proteins and nucleic acids.