  We extend our previous work on symplectic semiclassical Gaussian wave packet
dynamics to incorporate electromagnetic interactions by including a vector
potential. The main advantage of our formulation is that the equations of
motion derived are naturally Hamiltonian. We obtain an asymptotic expansion of
our equations in terms of $\hbar$ and show that our equations have
$\mathcal{O}(\hbar)$ corrections to those presented by Zhou, whereas ours also
recover the equations of Zhou in the case of a linear vector potential and
quadratic scalar potential. One and two dimensional examples of a particle in a
magnetic field are given and numerical solutions are presented and compared
with the classical solutions and the expectation values of the corresponding
observables as calculated by the Egorov or Initial Value Representation (IVR)
method. We numerically demonstrate that the $\mathcal{O}(\hbar)$ correction
terms improve the accuracy of the classical or Zhou's equations for short times
in the sense that our solutions converge to the expectation values calculated
using the Egorov/IVR method faster than the classical solutions or those of
Zhou as $\hbar \to 0$.
