We perform first principles density functional calculations to investigate the adsorption of Te on the Si(0 0 1) surface from low coverage up to a monolayer coverage. At low coverage, a Te atom is adsorbed on top of the Si surface dimer bond. At higher coverages, Te atoms adsorption causes the Si-Si dimer bond to break, lifting the (2 Â 1) reconstruction. We find no evidence of the Te-Te dimer bond formation as a possible source of the (2 Â 1) reconstruction at a monolayer coverage. Finite temperature ab initio molecular dynamics calculations show that Te covered Si(0 0 1) surfaces do not have any definitive reconstruction. Vibrations of the bridged Te atoms in the strongly anharmonic potentials prevent the reconstruction structure from attaining any permanent, two-dimensional periodic geometry. This explains why experiments attempting to find a definite model for the reconstruction reached conflicting conclusions.