Adiabatic BO Corrections for Hydrogenic Atoms

To give the reader some further appreciation of the adiabatic correction, we next discuss the so-called Rydberg correction of the hydrogenic atom. The kinetic energy of the electron in the hydrogen atom is expressed by Equation 2.5, where mj is set equal to the electron mass, me. It is well known that the Schrodinger equation for the hydrogen atom separates into two equations, one of which deals with the motion of the center of mass of the system and the other with the motion of the electron 

The electronic energy of the ground (Is) state of the hydrogen atom corresponding to infinite nuclear mass is given by 

Equation 2.24 can be thought of as having been derived from Equation 2.25 by adding the third term on the left hand side of Equation 2.24 as a perturbation. In first order quantum mechanical perturbation theory (see any introductory quantum text), the perturbation on the ground state of Equation 2.25 is obtained by averaging the perturbation over the ground state wave function of Equation 2.25. The effect of this 

The meaning of adiabatic correction is that the addition of C to the ground state energy calculated with Roo should yield a value equal to (close to) the exact ground state energy of the hydrogen atom 

It is well known that the exact value of the energy of the ground state of the H atom is 

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