  We calculate the ground state energies of a system of two dipolar fermions
trapped in a harmonic oscillator potential. The dipoles are assumed to be
aligned parallel to each other. We perform the calculations of ground state
energy as a function of strength of interaction between two fermions by
employing variational method with Hylleraas-like explicitly correlated wave
function. Furthermore, we perform calculations of ground state energy within
Hartree-Fock approximation and the magnitude of correlation energy is estimated
by subtracting these results from the corresponding wave function based
results. We also carry out calculations of ground state energies within the
realm of density functional theory by using recently reported expressions for
exchange and correlation energies under local density approximation. By
comparing correlated wave function based results with those obtained using
density functional theory approach we examine the role of fermion-fermion
correlation and assess the accuracy of local density approximation based
expression for the correlation energy functional.
