  The recently established existence of spherical harmonic functions,
$Y_\ell^{m}(\theta,\phi)$ for half-odd-integer values of $\ell$ and $m$, allows
for the introduction into quantum chemistry of explicit electron
spin-coordinates; i.e. spherical polar angles $\theta_s, \phi_s$, that specify
the orientation of the spin angular momentum vector in space. In this
coordinate representation the spin angular momentum operators, $S^2, S_z$, are
represented by the usual differential operators in spherical polar coordinates
(commonly used for $L^2, L_z$), and their electron-spin eigenfunctions are
$\sqrt{\sin\theta_s} \exp(\pm\phi_s/2)$. This eigenfunction representation has
the pedagogical advantage over the abstract spin eigenfunctions, $\alpha,
\beta,$ that ``integration over spin coordinates'' is a true integration (over
the angles $\theta_s, \phi_s$). In addition they facilitate construction of
many electron wavefunctions in which the electron spins are neither parallel
nor antiparallel, but inclined at an intermediate angle. In particular this may
have application to the description of EPR correlation experiments.
