A study of information-theoretic properties of molecular bond on the example of the ground (bound) and the lowest excited (unbound) states of H was conducted. Data about general information-theoretic measures, information products (Cramér-Rao, Fisher-Shannon information, and LMC complexity) and their inequalities in position and momentum spaces as a function of internuclear distance –20 a.u. were obtained by an exact numerical calculation of the wave function. A systematic correlation between these information products was established. It was found that LMC complexity is most sensitive and detailed among these information products. A clear correlation between accuracy of determination of energy and information products in the simplest LCAO model compared to results of the exact calculation was observed.