V - MSpace at the University of Manitoba

computational costs. Almlöf et al. [41] were first to recognize the benefit of separating
the calculation of the two-electron interaction into both a Coulomb and an exchange part.
The theory behind the RI approximation method has been well reviewed by both Whitten
[42] and Dunlap et al. [43], and has been implemented in numerous density functional
codes.
Dmitri N. Laikov, author of the Priroda code, takes this expansion method a step
further by not only expanding the Coulomb energy term but also the exchange–
correlation energy term with auxiliary basis sets. Such an approach has been shown to be
about an order of magnitude faster than the usual approximation to the Coulomb energy.
Though there is some loss in accuracy, tests have shown that basis sets of moderate size,
such as the ones we use, are sufficient to yield good accuracy for geometries and energies
[44].
2.2 Relativistic Effects
In molecules containing heavy atoms the motion of the electrons must be treated
relativistically because the effective velocity of the electrons, especially the inner core
ones that penetrate closer to the nucleus, is non-negligible relative to the speed of light.
Relativistic corrections are often found to be quite substantial. A primary relativistic
stabilization effect, as a consequence of orbital orthogonality requirements, leads to the
contraction of the 1s and higher s functions. The same effect is also seen, to a lesser
degree, for the p electrons. A secondary effect arises from an increased shielding of the
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