Ab initio molecular dynamics (AIMD) calculations using the specific reaction parameter approach to density functional theory are presented for the reaction of D 2 on Cu(111) at high surface temperature (T s ¼ 925 K). The focus is on the dependence of reaction on the alignment of the molecule's angular momentum relative to the surface. For the two rovibrational states for which measured energy resolved rotational quadrupole alignment parameters are available, and for the energies for which statistically accurate rotational quadrupole alignment parameters could be computed, statistically significant results of our AIMD calculations are that, on average, (i) including the effect of the experimental surface temperature (925 K) in the AIMD simulations leads to decreased rotational quadrupole alignment parameters, and (ii) including this effect leads to increased agreement with experiment. DOI: 10.1103/PhysRevLett.108.236104 PACS numbers: 68.43.Bc, 34.35.+a, 82.65.+r Experiments on the alignment dependence of moleculesurface reactions yield detailed information on the interaction of molecules with surfaces [1][2][3]. Because the rotational alignment parameter of reacting molecules is connected with the local anisotropy of the potential energy surface (PES), measurements of this parameter in conjunction with theory can lead to the identification of the reaction site [4,5]. Measurement of this parameter as a function of translational energy may also reveal important mechanistic information on, for instance, the importance of orientational steering for reaction [3].The sensitivity of the alignment of reacting molecules to the details of the molecule-surface interaction makes experiments addressing this topic ideal for testing electronic structure theories that attempt to model this interaction. Such tests are highly relevant, and pose huge challenges. About 90% of the chemical manufacturing processes used worldwide employ heterogeneous catalysts [6]. However, the best ab initio theory that can now be used to map out PESs for elementary molecule-surface reactions, density functional theory (DFT) at the generalized gradient approximation (GGA) or meta-GGA level, can provide reaction barriers with an accuracy of no better than 2:2 kcal=mol for gas phase reactions [7]. Even this accuracy has only recently become available [7], and it is therefore not surprising that quantum dynamics calculations using DFT PESs on the rotational quadrupole alignment parameter of H 2 desorbing from metal surfaces such as Pd(100) [8] and Cu(111) [9,10] have not yet been able to quantitatively reproduce the experiments.Dihydrogen-metal surface systems are ideal for testing electronic structure methods as accurate reaction probabilities can be computed within the Born-Oppenheimer (BO) approximation [11]. Making the static surface approximation (neglecting energy transfer involving phonons) should likewise lead to accurate results for low surface temperature (T s ) [12]. Taking advantage of this, it was recently shown that specific reaction pa...