Analytical expressions are derived for the evaluation of energy gradients in the zeroth order regular approximation ͑ZORA͒ to the Dirac equation. The electrostatic shift approximation is used to avoid gauge dependence problems. Comparison is made to the quasirelativistic Pauli method, the limitations of which are highlighted. The structures and first metal-carbonyl bond dissociation energies for the transition metal complexes W͑CO͒ 6 , Os͑CO͒ 5 , and Pt͑CO͒ 4 are calculated, and basis set effects are investigated.

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DFT schemes based on conventional exchange-correlation (XC) functionals have been employed to determine the dipole moment (μ), polarizability (α), and first (β) and second (γ) hyperpolarizabilities of push−pull π-conjugated systems. In addition to the failures already pointed out for α and γ in a recent study on polyacetylene chains [J. Chem. Phys. 1998, 109, 10489; Phys. Rev. Lett. 1999, 83, 694], these functionals are also unsuitable for the evaluation of μ and β. In the case of β, in particular, an almost catastrophic behavior with respect to increasing chain length is found. We show that the C functional has a negligible effect on the calculated μ, α, β, and γ whereas the X-part is responsible for the large property overestimations when the size of the system increases. The overly large μ values are associated with an overestimation of the charge transfer between the donor and the acceptor whereas for α, β, and γ, incomplete screening of the external electric field is responsible for the large discrepancies with respect to accurate values. Our results show that current XC functionals incorrectly describe the polarization of conjugated systems when the polarization is due to donor/acceptor substitution or an external field or both.

Shape corrections to the standard approximate Kohn-Sham exchange-correlation ͑xc͒ potentials are considered with the aim to improve the excitation energies ͑especially for higher excitations͒ calculated with time-dependent density functional perturbation theory. A scheme of gradient-regulated connection ͑GRAC͒ of inner to outer parts of a model potential is developed. Asymptotic corrections based either on the potential of Fermi and Amaldi or van Leeuwen and Baerends ͑LB͒ are seamlessly connected to the ͑shifted͒ xc potential of Becke and Perdew ͑BP͒ with the GRAC procedure, and are employed to calculate the vertical excitation energies of the prototype molecules N 2 , CO, CH 2 O, C 2 H 4 , C 5 NH 5 , C 6 H 6 , Li 2 , Na 2 , K 2 . The results are compared with those of the alternative interpolation scheme of Tozer and Handy as well as with the results of the potential obtained with the statistical averaging of ͑model͒ orbital potentials. Various asymptotically corrected potentials produce high quality excitation energies, which in quite a few cases approach the benchmark accuracy of 0.1 eV for the electronic spectra. Based on these results, the potential BP-GRAC-LB is proposed for molecular response calculations, which is a smooth potential and a genuine ''local'' density functional with an analytical representation.

The Born-Oppenheimer approximation of uncoupled electronic and nuclear motion is a standard tool of the computational chemist. However, its validity for molecule-metal surface reactions, which are important to heterogeneous catalysis, has been questioned because of the possibility of electron-hole pair excitations. We have performed experiments and calculations on the scattering of molecular hydrogen from a catalytically relevant metal surface, obtaining absolute probabilities for changes in the molecule's velocity parallel to the representative Pt(111) surface. The comparison for in-plane and out-of-plane scattering and results for dissociative chemisorption in the same system show that for hydrogen-metal systems, reaction and diffractive scattering can be accurately described using the Born-Oppenheimer approximation.

atom upon formation of the base pair from the separate bases.

Here, we give a full account of a large collaborative effort toward an atomic-scale understanding of modern industrial ammonia production over ruthenium catalysts. We show that overall rates of ammonia production can be determined by applying various levels of theory (including transition state theory with or without tunneling corrections, and quantum dynamics) to a range of relevant elementary reaction steps, such as N 2 dissociation, H 2 dissociation, and hydrogenation of the intermediate reactants. A complete kinetic model based on the most relevant elementary steps can be established for any given point along an industrial reactor, and the kinetic results can be integrated over the catalyst bed to determine the industrial reactor yield. We find that, given the present uncertainties, the rate of ammonia production is well-determined directly from our atomic-scale calculations. Furthermore, our studies provide new insight into several related fields, for instance, gas-phase and electrochemical ammonia synthesis. The success of predicting the outcome of a catalytic reaction from first-principles calculations supports our point of view that, in the future, theory will be a fully integrated tool in the search for the next generation of catalysts.