How do you calculate the ionization energy of lithium?
1 Answer
By using a computer... we obtained a value of
Lithium clearly has more than one electron; that makes it so the groundstate energy is not readily able to be calculated by hand, since the electronic coordinates are mutually dependent due to the inherent electronelectron correlation.
Instead, we would have to supply input files to a computer software and calculate the groundstate energies that way, of
Using the socalled FellerPetersonDixon method to get practically perfect accuracy, one would have to calculate (or consider):
#DeltaE_"IE" = DeltaE_("IE",0) + DeltaE_"corr" + DeltaE_"CBS" + DeltaE_"CV" + DeltaE_"QED" + DeltaE_"SR" + DeltaE_"SO" + DeltaE_"Gaunt"# where:
#DeltaE_("IE",0)# is the initial ionization energy calculated from MultiConfigurational SelfConsistent Field (MCSCF) theory.#DeltaE_"corr"# is the dynamic correlation energy contribution not accounted for in MultiConfigurational SelfConsistent Field theory, but recovered in MultiReference Configuration Interaction (MRCI).#DeltaE_"CBS"# is the energy contribution from extrapolating to the limit of an infinite set of basis functions that represent atomic orbitals.#DeltaE_"CV"# is the energy contribution from correlating the core electrons with the valence electron(s).#DeltaE_"QED"# is the energy contribution from the socalled Lamb Shift, a quantum electrodynamics interaction present primarily among#s# orbitals.#DeltaE_"SR"# is the energy contribution from relativistic effects. This is negligible in#"Li"# but is automatically accounted for using the 2nd order DouglasKrollHess (DKH) Hamiltonian for light atoms (3rd order DKH for heavy atoms).#DeltaE_"SO"# is the energy contribution from spinorbit coupling.#DeltaE_"Gaunt"# is the energy contribution from highorder twoelectron correlation in the relativistic scheme.
That WOULD be extremely involved for a heavier atom... Here are some things that save time:
 No electron correlation is present here since only one state is possible (spin up in a
#2s# orbital!).
So we can get by from a simple HartreeFock calculation. There will be a tiny bit of corevalence (
#1s""2s# ) correlation, so#DeltaE_"CV" ne 0# and that can be taken care of with an MRCI using a weightedcore basis set.

The model potentials for QED only are made for
#Z >= 23# (quote: "Fails completely for#Z < 23# "), so there is no point in including the Lamb Shift at all. 
#DeltaE_"SR"# is included by default by the 2nd order DKH Hamiltonian. 
The
#DeltaE_"SO"# contribution can be included but it has been done before... It is#"0.000041 eV"# , or#"0.000945 kcal/mol"# . Gaunt is unimportant here, based on how small the spinorbit value is.
Here are the (not so interesting) results:
From this, we had gotten that:
#color(blue)(DeltaE_"IE") = "123.195465 kcal/mol" + "0.000000 kcal/mol" + "0.000000 kcal/mol" + "1.162450 kcal/mol" + "0.000000 kcal/mol" + "accounted for" + "0.000945 kcal/mol" + "0.000000 kcal/mol"#
#=# #color(blue)(ul"124.358860 kcal/mol")#
#=# #color(blue)(ul"5.39271223 eV")#
whereas the value on NIST is practically the same, at