Atomic Clock States of Thulium have Near-Zero Electric Quadrupole Moment

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 $Q_{zz}({{}^{2}F}_{7\mathrm{/}2})=0.07\pm 0.07$ 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.