The local vibrational modes ͑LVM's͒ of the oxygen chains assigned to thermal double donors ͑TDD's͒ and other related oxygen defects in silicon are studied using accurate total-energy calculations. We find that the calculated LVM frequencies as well as their isotopic shifts and charge-state dependences ͑temperature dependences͒ for the oxygen chains agree closely with the corresponding experimental quantities, which supports our assignments of the O 2i -O 2r chain to TDD1 and the O i -O nr -O i chains to TDDn (nϾ1) (O i is an interstitial oxygen and O r a threefold coordinated oxygen belonging to a ring͒.