As a chemist, I can provide you with a general understanding of how bond length changes as the distance between two hydrogen atoms increases. However, I cannot perform ab initio calculations or provide specific values without access to specialized quantum chemistry software and computational resources.In general, the bond length between two hydrogen atoms in a molecule is determined by the balance between attractive forces electron-nucleus attraction and repulsive forces electron-electron and nucleus-nucleus repulsion . As the distance between two hydrogen atoms increases, the attractive forces decrease, and the repulsive forces become less significant.At a certain distance, called the equilibrium bond length, the attractive and repulsive forces are balanced, resulting in the most stable configuration of the molecule. For hydrogen H2 , the equilibrium bond length is approximately 0.74 .As the distance between two hydrogen atoms increases from 0.5 to 2.0 , the bond length will also increase. However, the bond strength will decrease as the atoms move further apart, and the molecule becomes less stable. At distances significantly greater than the equilibrium bond length, the hydrogen atoms will no longer be bonded, and the molecule will dissociate into individual atoms.To obtain specific values for bond lengths and other molecular properties at different distances, one would need to perform ab initio calculations using a quantum chemical method such as Hartree-Fock, Density Functional Theory DFT , or post-Hartree-Fock methods like Configuration Interaction CI or Coupled Cluster CC theory. These calculations require specialized software and computational resources, and the results will depend on the chosen method and basis set.