  Engineered $Na_{0.75}CoO_2$ is considered a prime candidate to achieve
high-efficiency thermoelectric systems to regenerate electricity from waste
heat. In this work, three elements with outmost electronic configurations, (1)
an open d shell (Ni), (2) a closed d shell (Zn), and (3) a half filled f shell
(Eu) with maximum unpaired electrons, were selected to outline the dopants'
effects on electronic and crystallographic structures of $Na_{0.75}CoO_2$.
Systematic $ab$ $initio$ density functional calculations with $DMOL^3$ package
showed that the Ni and Zn were more stable when substituting Co with formation
energy $-2.35$ eV, $2.08$ eV when Fermi level equals to the valence band
maximum. While Eu is more stable when it substitutes Na having formation energy
of $-2.64$ eV. As these results show great harmony with existing experimental
data, they provide new insights into the fundamental principle of dopant
selection for manipulating the physical properties in the development of
high-performance sodium cobaltate based multifunctional materials.
