  A method for highly accurate calculations of atomic electric quadrupole
moments (EQM) is presented, using relativistic general-excitation-rank
configuration interaction wavefunctions based on Dirac spinors. Application to
the clock transition states of the thulium atom employing up to full Quadruple
excitations for the atomic wavefunction yields a final value of
$Q_{zz}({^2F}_{7/2}) = 0.07 \pm 0.07$ a.u., establishing that the thulium
electronic ground state has an exceptionally small EQM. A detailed analysis of
this result is presented which has implications for EQMs of other atoms with
unpaired $f$ electrons.
