  The gas dynamics in protoplanetary disks (PPDs) is strongly affected by
non-ideal MHD effects. Using a complex chemical reaction network with standard
prescriptions for X-ray and cosmic-ray ionizations, as well as the most
up-to-date results from numerical simulations, we study the non-ideal MHD
effects on the magnetorotational instability (MRI) and angular momentum
transport in PPDs. We first show that no matter grains are included or not, the
recombination time is always shorter than the orbital time in the bulk of PPDs,
justifying the validity of local ionization equilibrium. The full conductivity
tensor at different disk radii and heights is evaluated, with the MRI active
region determined by requiring that (1) the Ohmic Elsasser number be greater
than 1; (2) the ratio of gas to magnetic pressure beta be greater than
beta_min(Am) as identified by Bai & Stone (2011), where Am is the Elsasser
number for ambipolar diffusion. With full flexibility as to the magnetic field
strength, we provide a general framework for estimating the MRI-driven
accretion rate M_dot and the magnetic field strength in the MRI-active layer.
We find that the MRI-active layer always exists at any disk radii as long as
the magnetic field in PPDs is sufficiently weak. However, the optimistically
predicted M_dot in the inner disk (r=1-10 AU) appears insufficient to account
for the observed range of accretion rate in PPDs (around 1e-8M_Sun/yr) even in
the grain-free calculation, and the presence of solar abundance sub-micron
grains further reduces M_dot by one to two orders of magnitude. Our results
suggest that stronger sources of ionization, and/or additional mechanisms such
as magnetized wind are needed to explain the observed accretion rates in PPDs.
In contrast, our predicted M_dot is on the order of 1e-9M_Sun/yr in the outer
disk, consistent with the observed accretion rates in transitional disks.
(Abridged)
