  We present an analysis of constraints on two types of CP-odd electron-gluonic
operators $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$ and
$(\bar{e}e)G_{\mu\nu}^a \tilde{G}^{a\mu\nu}$ from current and future electric
dipole moment (EDM) experiments. The recent result from the ACME experiment
using ThO molecules is used to derive an impressive lower bound on the
effective scale for $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$ at 8 TeV,
assuming a QCD one-loop factor and no helicity suppression from new physics.
One interesting aspect is that $(\bar{e}i\gamma^5 e)G_{\mu\nu}^a G^{a\mu\nu}$
contributes to the observable EDM in ThO experiment mainly through CP-odd
electron-nucleon interaction rather than direct electron EDM which arises from
three-loop running and matching. For $(\bar{e}e)G_{\mu\nu}^a
\tilde{G}^{a\mu\nu}$ the current bound is much weaker and suffers from large
uncertainties. We also discuss the QCD running and matching for the CP-odd
electron-gluonic operators and give an estimate of the relevant nucleon matrix
elements and uncertainties that are needed in the calculation.
