Hydrogen molecular ion and molecule in two dimensions

摘要

We discuss some general properties of the wave functions of H_2~+ in two dimension, when the electron is close to the nucles, and when it is far away from the nucles. Based on these properties, some simple, parameter-free wave functions are developed for some of the states. They lead to quite accurate energies and give an insight into the structure of H_2~+ in two dimensions. These wave functions and appropriate correlation functions, are then used to develop reliable wave functions for H_2 in two dimensions. They provide a clear and interesting comparison with the corresponding results in three dimensions.