  Vanadium-based materials AV$_3$Sb$_5$ (A=K, Rb, Cs) with layered kagome
lattice structures have drawn great attention recently due to the discoveries
of topologically nontrivial band structures, charge density wave states, giant
anomalous Hall effect, as well as unusual superconducting phase at low
temperatures. In this work, we theoretically study the magnetic and charge
instabilities for this class of materials based on first principles
calculations. We develop a method to calculate the generalized susceptibility
tensor defined in the sublattice-orbital-spin space, with the effects of
Coulomb interactions treated by generalized random phase approximation (RPA).
The RPA susceptibility calculations indicate that there are three leading
ferromagnetic instability modes at $\Gamma$ point, which are further verified
by unrestricted self-consistent Hartree-Fock calculations including both the
on-site and inter-site Coulomb interactions. The inclusion of inter-site
interactions tend to suppress the spin ferromagnetism due to charge transfer
from the V to Sb sites, leading to weak spin magnetic moments $\sim
0.1\mu_{\textrm{B}}$ per V atom with small intrinsic anomalous Hall
conductivity. Current loops can be generated in such weak spin ferromagnetic
states as a result of spin-orbit coupling effects. The electronic structures in
the ferromagnetic states are significantly reconstructed which have nearly
compensated electron and hole carriers from two bands. On the other hand, we do
not find any diverging instability mode at $M$ point driven by
electron-electron Coulomb interactions. First principles phonon calculations
indicate that there are unstable phonon modes which tend to drive the system
into an inverse star-of-David structure. Our results indicate that there may be
separate phase transitions in the magnetic and charge channels in the system.
