In this paper we describe a laser acceleration scheme where an electron is accelerated from rest to GeV energies by the longitudinal electric field of an ultrashort transverse magnetic ( TM01 ) optical pulse. The on-axis longitudinal electric field of the pulse is obtained from the free-space divergence equation beyond the so-called slowly-varying-envelope approximation. The instantaneous electron dynamics is studied; numerical simulations predict net energy gains in the GeV range for laser intensities reaching 10(22) W/ cm(2) .