Exploring the Spin Structure of the Neutron by the Measurement of g$_2$ and d$_2$

The experiment E12-06-121 at Jefferson Lab aims to do a precision measurement of the neutron spin structure function g$_2$ using the inelastic scattering of electrons over the kinematic range 0.20 $<$ x$_{Bj} <$ 0.95 and 2.5 $<$ Q$^{2} <$ 6.0 (GeV/c)$^2$. The large kinematic coverage will allow for the precision determination of d$_2$, the third moment of the linear combination of the spin structure functions g$_1$ and g$_2$. As one of the cleanest higher twist observables, g$_2$ contains information on quark-gluon correlations, and d$_2$ is connected to the ``color polarizability" of the nucleon. The experiment was performed and successfully completed in Hall C using a longitudinally polarized 10.4 GeV electron beam and a polarized helium-3 gas target. The combination of Super High Momentum Spectrometer (SHMS) and High Momentum Spectrometer (HMS) allowed us to run the experiment for three constant Q$^2$ values over a wide range of x$_{Bj}$ for the first time. The extraction of d$_2^n$(Q$^2$) will serve as a benchmark to the predictions from Lattice QCD. An overview of the experiment and the present status of the experimental data analysis will be presented.