We propose the use of the erfgau potential as a smooth alternative to the pure Coulomb potential between nuclei and electrons in simulating the dynamics of electrons within atoms and molecules driven by high-intensity laser pulses. Even without the sophistication of pseudopotentials, by utilizing a well-designed simple approximate potential, it is possible to make the simulations computationally less demanding while keeping accuracy. By employing the erfgau potential designed for the stationary state of hydrogen-like atoms, we demonstrate that it is possible to simulate not only the high harmonic generation from a hydrogen atom but also that of multielectron systems, including molecules.