Pressure-induced Ionization of Hydrogen

When the pressure on an atom is increased to the megapascal region, the electronic energy increases to the point where spontaneous ionization occurs. Thispressure-induced ionization of hydrogen is an important consideration when modeling the atmosphere of the gas giant planets. This paper describes an undergraduate computational chemistry project that models pressure-induced ionization using a hydrogen atom confined at the center of a spherical barrier of finite height. This system is exactly solvable in Kummer’s confluent hypergeometric functions and lends itself to treatment using a computer algebra system. Energy quantization results from matching the wave function and its first derivative at the barrier. When the radius of confinement decreases, the electron energy increases. When the electron energy reaches the height of the confining barrier, pressure-induced ionization occurs. Electronic energies were calculated over a range of confinement radii from 1 a0 (53 pm) to 6 a0 (318 pm). The minimum confinement radius necessary to support a bound 1s ground state was calculated for barrier heights from 0 to 100 Eh (2720 eV).