We present an ab initio method using time-dependent density functional theory (TDDFT) to compute the lifetimes of excited adsorbate states at metal surfaces. A modified mid-point and unitary transformation algorithm is used to integrate TDDFT electronic dynamics. As a test, the relaxation of an excited state of a hydrogen atom adsorbed on a lithium atom cluster is investigated. The time evolution of the electronic population at the hydrogen atom site is computed, and the decay of the natural population on the hydrogen gives the energy level width of the excited adsorbate state. (C) 2007 Elsevier B.V. All rights reserved.