  We theoretically investigate the properties of a two-electron system confined
in the three-dimensional potential of coupled quantum dots formed in a quantum
wire. For this purpose, we implement a variational Heitler-London method that
minimize the system energies with respect to variational parameters in electron
trial wavefunctions. We find that tunneling and exchange couplings
exponentially decay with increasing inter-dot distance and inter-dot barrier
height. In the quasi-one-dimensional limit achieved by reducing the wire
diameter, we find that the overlap between the dots decreases, which results in
a drop of the exchange coupling. We also discuss the validity of our
variational Heitler-London method with respect to the model potential
parameters, and compare our results with available experimental data to find
good agreement between the two approaches.
