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The coupling of Fe magnetic moments in LaFeAsO$_{1-x}$F$_{x}$ with the As$A_{1g}$ phonon is calculated. We present first principles calculations of theatomic and electronic structure of LaFeAsO as a function of electron doping. Weperform calculations using the virtual crystal approximation as well assupercell calculations with F substitutional impurity atoms. The resultsvalidate the virtual crystal approximation for the electronic structure nearthe Fermi level. Its is found that the electronic density of states at theFermi level is maximum for x=0.125, enhancing the electron-phonon interaction.An additional increase of the electron-phonon parameter $\lambda$ is obtainedif the coupling between the $A_{1g}$ phonon and the Fe magnetic moment isincluded. It is found that the electron-phonon interaction can be one order ofmagnitude larger than its value if no spin resolution is included in thecalculation. The implications of these results on the superconductingtransition are discussed

Electron-phonon interaction in Fe-based superconductors: Coupling of magnetic moments with phonons in LaFeAsO$_{1-x}$F$_{x}$