Six-dimensional quantum dynamics of dissociative chemisorption of H2 on Ru(0001)

Six-dimensional quantum dynamics calculations on dissociative chemisorption of H(2) on Ru(0001) are performed. The six-dimensional potential energy surface is generated using density functional theory. Two different generalized gradient approximations are used, i.e., RPBE and PW91, to allow the results to be compared. The dissociation probability for normally incident H(2) on a clean Ru(0001) surface is calculated. Large differences between the reaction probabilities calculated using the RPBE and PW91 are seen, with the PW91 results showing a much narrower reaction probability curve and a much higher reactivity. Using the reaction probabilities and assuming normal energy scaling reaction rates are generated for temperatures between 300 and 800 K. The rate generated using the PW91 results is higher by about a factor 5 than the rate based on the RPBE results in the range of temperatures relevant to ammonia production.     

Density functional theory calculation of 2p spectra of SiH4, PH3, H2S,HCl, and Ar

The method developed recently for prediction of 1s electron spectra is now extended to the 2p spectra of SiH₄, PH₃, H₂S, HCl, and Ar. The method for X‐ray absorption spectra involves the use of ΔE for the excitation and ionization energies, and application of time‐dependent density functional theory using the exchange‐correlation potential known as statistical average of orbital potentials for the intensities. Additional assumptions and approximations are also made. The best exchange‐correlation functional E_xc for the earlier calculation of ΔE in 1s spectra of C to Ne (namely Perdew–Wang 1986 exchange, combined with Perdew–Wang 1991 correlation) is no longer used in this work on 2p spectra of Si to Ar. Instead, recently tested E_xc good for 2p core‐electron binding energies (known as OPTX) for exchange and LYP for correlation, plus scalar zeroth‐order regular approximation is adopted here for the ΔE calculations. Our calculated X‐ray absorption spectra are generally in good agreement with experiment. Although the predictions for the higher excitations suffer from basis set difficulties, our procedure should be helpful in the interpretation of absorption spectra of 2p electrons of Si to Ar. In addition, we report calculated results for other kinds of electron spectra for SiH₄, PH₃, H₂S, HCl, and Ar, including valence electron ionizations and excitations as well as X‐ray emission. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008     

On the origin dependence of the angle made by the electric and magnetic vibrational transition dipole moment vectors

The concept of robustness of rotational strengths of vibrational modes in a VCD spectrum has been introduced as an aid in assignment of the absolute configuration with the help of the VCD spectrum. The criteria for robustness have been based on the distribution around 90° of the angles ξ(i) between electric and magnetic transition dipoles of all the modes i of a molecule. The angles ξ(i) (not, of course, the rotational strengths) are, however, dependent on the choice of origin. The derived criteria are for the center of mass chosen as the origin of the coordinate system. We stress in this note that application of the derived criteria assumes that excessive translation of the coordinate origin is not applied. Although the ξ(i) angles are not very sensitive to the position of the origin, very small displacements (a few ?) are not a problem, excessive translation of the origin does have considerable effect on the ξ(i) angles. In this note we quantify this effect and demonstrate how the distribution of ξ(i) angles is affected. Although it is possible to recalibrate the robustness criteria for the angles for a specific (large) displacement, we recommend that such displacement simply be avoided. It is to be noted that some modeling software does yield output with excessively displaced coordinate origin; this should be checked and corrected.     

Six-dimensional quantum dynamics of H2 dissociative adsorption on the Pt(211) stepped surface

Results of experimental studies, and theoretical calculations utilizing classical trajectories, have shown that dissociation of H2 on the Pt(211) stepped surface is enhanced at low energies by a molecular trapping mechanism. Because quantum effects can play a large role at the low energies and long lifetimes that characterize molecular trapping, we have undertaken quantum dynamics calculations for this system, the first to treat all molecular degrees of freedom of a gas molecule reacting on a stepped metallic surface. The calculations show that molecular trapping persists in the quantum system, but only at much lower energies than experimentally seen, pointing to possible deficiencies in the potential energy surface. Classical and quasiclassical trajectory calculations on the same potential provide a reasonable picture of reaction overall, but many of the finer details are inaccurate, and certain classical reaction mechanisms are entirely invalid. We conclude that some skepticism should be shown toward any classical study for which long-lived trapping states play a role.     

Kohn-Sham potentials corresponding to Slater and Gaussian basis set densities

A new method based on linear response theory is proposed for the determination of the Kohn-Sham potential corresponding to a given electron density. The method is very precise and affords a comparison between Kohn-Sham potentials calculated from correlated reference densities expressed in Slater-(STO) and Gaussian-type orbitals (GTO). In the latter case the KS potential exhibits large oscillations that are not present in the exact potential. These oscillations are related to similar oscillations in the local error function δ _i (r)=(−ɛ _i )ϕ _i (r) when SCF orbitals (either Kohn-Sham or Hartree-Fock) are expressed in terms of Gaussian basis functions. Even when using very large Gaussian basis sets, the oscillations are such that extreme care has to be exercised in order to distinguish genuine characteristics of the KS potential, such as intershell peaks in atoms, from the spurious oscillations. For a density expressed in GTOs, the Laplacian of the density will exhibit similar spurious oscillations. A previously proposed iterative local updating method for generating the Kohn-Sham potential is evaluated by comparison with the present accurate scheme. For a density expressed in GTOs, it is found to yield a smooth “average” potential after a limited number of cycles. The oscillations that are peculiar to the GTO density are constructed in a slow process requiring very many cycles. Received: 24 February 1997 / Accepted: 18 June 1997     

Orbital localization in transition metal molecules

In multiply bonded, weakly interacting systems the excessive electron repulsion associated with the non-dynamical correlation error can be reduced within the Hartree Fock approximation by localizing the bonding orbitals. The mechanism behind this (unphysical) orbital localization is studied through calculations on a model system, and SCF and CI calculations on the MnO⁺ ion. It is shown, from a pair-population analysis of the two-particle density matrix (which is analogous to a Mulliken population analysis of the one-density) that the orbital localization is a two-electron effect. Transition metal molecules often exhibit this kind of orbital localization which may (or may not) require symmetry breaking. The special characteristics of transition metal molecules that makes them suitable candidates for orbital localization will be discussed.     

Vibronic coupling and double excitations in linear response time-dependent density functional calculations: dipole-allowed states of N2

The present study serves two purposes. First, we evaluate the ability of present time-dependent density functional response theory (TDDFRT) methods to deal with avoided crossings, i.e., vibronic coupling effects. In the second place, taking the vibronic coupling effects into account enables us, by comparison to the configuration analysis in a recent ab initio study [J. Chem. Phys. 115, 6438 (2001)], to identify the neglect of double excitations as the prime cause of limited accuracy of these linear response based TDDFRT calculations for specific states. The "statistical averaging of (model) orbital potentials (SAOP)" Kohn-Sham potential is used together with the standard adiabatic local-density approximation (ALDA) for the exchange-correlation kernel. We use the N2 molecule as prototype, since the TDDFRT/SAOP calculations have already been shown to be accurate for the vertical excitations, while this molecule has a well-studied, intricate vibronic structure as well as significant double excitation nature in the lowest 1Pi(u) state at elongated bond lengths. A simple diabatizing scheme is employed to obtain a diabatic potential energy matrix, from which we obtain the absorption spectrum of N2 including vibronic coupling effects. Considering the six lowest dipole allowed transitions of 1Sigma(u)+ and 1Pi(u) symmetry, we observe a good general agreement and conclude that avoided crossings and vibronic coupling can indeed be treated satisfactorily on the basis of TDDFRT excitation energies. However, there is one state for which the accuracy of TDDFRT/ALDA clearly breaks down. This is the state for which the ab initio calculations find significant double excitation character. To deal with double excitation character is an important challenge for time-dependent density functional theory.     

Perspective on “Self-consistent equations including exchange and correlation effects”

 The paper by Kohn and Sham (KS) is important for at least two reasons. First, it is the basis for practical methods for density functional calculations. Second, it has endowed chemistry and physics with an independent particle model with very appealing features. As expressed in the title of the KS paper, correlation effects are included at the level of one-electron equations, the practical advantages of which have often been stressed. An implication that has been less widely recognized is that the KS molecular orbital model is physically well-founded and has certain advantages over the Hartree–Fock model. It provides an excellent basis for molecular orbital theoretical interpretation and prediction in chemistry. Received: 16 February 1999 / Accepted: 22 June 1999 / Published online: 9 September 1999     

Molecular cluster calculations for the interpretation of CO chemisorption on a Ni(100) surface

Self-consistent Hartree-Fock-Slater molecular cluster calculations for the chemisorption of carbon monoxide on a Ni(100) surface are presented. In earlier calculations of this type the CO molecule has been assumed to be chemisorbed in a hollow position of C_4v symmetry. A recent EELS experiment shows however that in the most stable configuration CO is linearly bonded to the Ni atoms, i.e. a top position of the CO-molecule. This experiment indicates also that there exists an additional bridge bonding of the CO molecule to the two nearest neighbour Ni atoms. The variation of the energy levels, binding energies and charge distribution with the height of the CO molecule above the nickel surface is calculated for the top position using the NiCO and Ni₅CO clusters and for the bridge bonding configuration using the Ni₂CO cluster. The CO 1π level is found to be split by about 0.8 eV in bridge bonding geometry. For both hollow and top positions the 1π and 5σ levels are separated by about 0.5 eV. The energy separation to the 4σ level is about 3 eV, which is in good agreement with experimental data. Theoretical ionization energies relative to the Fermi energy for top position geometry at a bond distance of 3.5 au between the carbon atom and nickel surface were found to be 25.7, 11.7, 8.7 and 8.2 eV for the 3σ, 4σ, 5σ and 1π levels which should be compared with the experimental data of 29.0, 10.8, 8.4 and 7.8 eV, respectively. The corresponding ionization energies for a bond angle of 99° in bridge bonding were 23.7, 12.1, 7.3, 7.0 and 7.9 eV. The two last values represent the 1π level which is split into two levels in this geometry. The variation of the C-O stretch vibrational frequencies with the height of the CO molecule above the surface for the top-position geometry is estimated from the 5σ and 2π gross orbital populations and from the CO σ and π overlap populations.     

Cluster studies of CO adsorption: I. CO on small Li clusters

The various contributions to the adsorption energy of CO such as steric repulsion, σ bonding and π backbonding, are studied as a function of CO-cluster distance, C-O distance, adsorption site and cluster geometry. At the hollow site a double minimum is found in the adsorption energy as a function of CO-cluster distance. The effect of adsorption on the electronic structure of CO is large, in particular at the equilibrium distance close to the surface. Consequences for the C-O stretch frequency, and for the possibility of CO dissociation at the surface, are investigated.