In this paper, simulation study of electron stochastic heating arising from density fluctuation which in turn appears during laser interaction with Hydrogen atoms is considered by use of a massively parallel particle-in-cell (PIC) code. In order to examine the effect of ionization, different mechanisms of electron stochastic heating have been considered and analyzed. Our results reveal that since the ionization affects the pulse scattering process and the medium refractive index, the stochastic heating threshold of the electrons can be changed considerably by the ionization effects. Also, it is shown that when there is a long rise-time laser pulse (here, 80 fs) which induces a weak space charge field, the Raman backscattered radiations are seeded by a strong initial noise at the earlier times. As a result, the Mendonca condition for chaos is happened sooner which in turn causes the electron stochastic heating starts quickly. While, in a short rise-time laser pulse case (here, 40 fs) which produces a stronger electrostatic space charge field, the rapid nonlinear wave breaking because of changes in the density inhomogeneity, leads to early stochastic heating of electron. Moreover, according to our results it turns out that at the boundary between the vacuum and field-ionized plasma, the nonlinear wave breaking occurs sooner and onset of the electron stochastic heating becomes faster.