  We report on a study of the electronic and magnetic properties of the
triangular antiferromagnetic $\{Cu_3\}$ single-molecule magnet, based on spin
density functional theory. Our calculations show that the low-energy magnetic
properties are correctly described by an effective three-site spin $s=1/2$
Heisenberg model, with an antiferromagnetic exchange coupling $J \approx 5$
meV. The ground state manifold of the model is composed of two degenerate spin
$S=1/2$ doublets of opposite chirality. Due to lack of inversion symmetry in
the molecule these two states are coupled by an external electric field, even
when spin-orbit interaction is absent. The spin-electric coupling can be viewed
as originating from a modified exchange constant $\delta J$ induced by the
electric field. We find that the calculated transition rate between the chiral
states yields an effective electric dipole moment $d = 3.38\times 10^{-33} {\rm
C\ m} \approx e 10^{-4}a$, where $a$ is the Cu separation. For external
electric fields ${{\varepsilon}} \approx 10^8$ V/m this value corresponds to a
Rabi time $\tau \approx 1$ ns and to a $\delta J$ of the order of a few
$\mu$eV.
