Binding Energy

The principle use of PE spectroscopy is to determine the binding energies of the atomic and molecular orbits by means of the equation given previously. Ideally, when PE spectra are taken with a monochromatic photon source, one and only one PE peak will occur corresponding to each of the molecular orbitals, since the binding energy is related to the PE energy as expressed in the simple relationship of this equation.

Where y_i are single-electron Hartree-Fock wave functions for the initial ground state, and y_f are single-electron wave functions for the various final states in which an ion can find itself following electron removal from an orbital corresponding to the ionisation potential I_i.

The binding energy of a given molecular orbital is the difference between the total energies of the initial and the final states, the initial state being the neutral molecule, and the final state being the molecular ion in which an electron from the given orbital has been removed. Rather than using calculations of the total energies of the initial and final states in order to compare with experimental binding energies, one usually employs eigenvalues calculated for the molecular orbitals of the neutral molecule based on Koopmans' approximation.

In the approximation calculated eigenvalues e_n, are set equal to the binding energies of the frozen molecular orbitals. In this way, the eigenvalues are related to the adiabatic binding energy by the expression

Where E_R is the relaxation energy. In comparing experimental binding energies with theoretical calculations, it is most proper to use the onset of the vibrational envelope where v' = 0, since the adiabatic binding energy has a well-defined meaning. However, for spectra of more complex molecules it is often most practical to report the peak of the vibrational envelope, which is called the vertical ionization potential.

QUESTION: What is the vertical ionization potential ?
What is the difference of work function between gas and solid?