Why are the Jaguar energies for the LACVP or LACV3P basis sets so different from those with other basis sets?

The LACVP and LACV3P basis sets include an effective core potential (ECP), which replaces the potential from the core electrons with a parametrized potential. When you use these basis sets, the energy of the core electrons is not included in the total energy, whereas with other basis sets like 6-31G, the core energy is included.

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