V - MSpace at the University of Manitoba

Spin-orbit effects accounted for in the second term of equation (2–14), where ��
is the spin operator, can be either included or neglected depending on the circumstances.
A key benefit of this method is that the mentioned singularities of the Breit-Pauli
Hamiltonian, equation (2–13), are avoided.
2.2.3 Relativistic Effective Core Potentials (RECPs)
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In the Schrödinger equation for a valence orbital the one-electron Hamiltonian,
equation (2–15), includes the kinetic energy of the electron, the interactions of the
nucleus, and the core electrons, as well as the interactions with the other valence
electrons and the relativistic operator [27].
H �
� T �Vcore
�Vnuc
�Vrel
Vval
(2–15)
With the RECP, the Schrödinger equation (2–16) serves to replace the Coulomb
effects of the inner core electrons, as well as the direct relativistic effects on the valence
electrons. In general, RECPs can be used with either ab initio methods, including HF, or
with DFT methods, to study molecules containing heavy elements. For the purposes of
this research RECPs were used only with the density functional method.
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