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Is there a physical meaning to the SCF energy of a molecule obtained using pseudopotentials to represent the core electrons of heavy atoms (for example gold)?

I've been running calculations in Gaussian on a system with a number of gold atoms and I became curious whether my use of pseudopotentials for the gold core electrons was skewing the results I obtained. So, I attempted to run a smaller test comparing two identical systems where one used pseudopotentials (specifically the LANL2DZ basis set) for the gold atoms and the other was all-electron with the DZP basis set. When I performed thess calculations, I got very similar orbital energies for the frontier orbitals, but the total energies were completely different, with the total energy of the all-electron calculation approximately 50 times more stable than the pseudopotential calculation (e.g. -100000 vs -2000 au).

Perhaps I've missed some obvious shortfall of pseudopotentials, but I just don't see how the energies obtained could be so different. I would expect an error in the calculation if the orbitals hadn't made sense or there was any unusual messages in the log file, but I didn't notice any such problem. The geometries and route sections used in each case are the same (besides the one having pseudo=read) and the only difference was the basis sets, where LANL2DZ is built in and I found DZP through the basis set exchange.

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  • $\begingroup$ How many electrons are in the all-electron basis set? How many electrons when using pseudopotentials? Knowing this, how might the Hamiltonian between the two calculations differ, and how might this change the total energy? (Remember, for a given method/basis the total energies are seldom meaningful, but differences between energies are.) $\endgroup$ – jjgoings Jul 9 '18 at 20:49
  • $\begingroup$ @jjgoings There are 992 with all electrons and 746 with pseudopotentials. For the Hamiltonian, there should be less electron-electron repulsion terms and less electron kinetic energy in the pseudopotential case, but I assumed the purpose of pseudopotentials was to give a rough estimate of these for the core electrons which are relatively indifferent to the surrounding molecular environment and so should give roughly the same answer. Two different functionals give differences of about .1 au. These are different by about 100000 au. $\endgroup$ – Tyberius Jul 9 '18 at 21:17
  • $\begingroup$ Total enegies in general are not very meaningful. They are very basisset dependent and you cannot compare directly compare calculations using different basis sets, e.g. when calculating binding energies (BSSE). Also ECPs may include scalar relativistic effects. $\endgroup$ – Feodoran Jul 10 '18 at 7:23
  • $\begingroup$ you have to use something like ECPs, or you should use something like DKH to account for relativistic effects etc. Furthermore it seems that your SCF is not converged. $\endgroup$ – Raymond Ghaffarian Shirazi Jul 16 '18 at 22:59

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