  Over the past few years it has been pointed out that direct inversion of
accurate but approximate ground state densities leads to Kohn-Sham
exchange-correlation (xc) potentials that can differ significantly from the
exact xc potential of a given system. On the other hand, the corresponding
wavefunction based construction of exchange-correlation potential as done by
Baerends et al. and Staroverov et al. obviates such problems and leads to
potentials that are very close to the true xc potential. In this paper, we
provide an understanding of why the wavefunction based approach gives the
exchange-correlation potential accurately. Our understanding is based on the
work of Levy, Perdew and Sahni (LPS) who gave an equation for the square root
of density (density amplitude) and the expression for the associated effective
potential in the terms of the corresponding wavefunction. We show that even
with the use of approximate wavefunctions the LPS expression gives accurate
effective and exchange-correlation potentials. Based on this we also identify
the source of difference between the potentials obtained from a wavefunction
and those given by the inversion of the associated density. Finally, we suggest
exploring the possibility of obtaining accurate ground-state density from an
approximate wavefunction for a system by making use of the LPS effective
potential.
