Efficient Two-Step Procedures for Locating Transition States of Surface Reactions.

Using various two-step strategies, we examined how to accurately locate transition states (TS) of reactions using the example of eight reactions at metal surfaces with 14-33 moving atoms. These procedures combined four path-finding methods for locating approximate TS structures (nudged elastic band, standard string, climbing image string, and searching string, using a conjugate gradient or a modified steepest-descent method for optimization and two types of coordinate systems) with subsequent local refinement by two dimer methods. The dimer-Lanczos variant designed for this study required on average 20% fewer gradient calls than the standard dimer method. During the path finding phase, using mixed instead of Cartesian coordinates reduced the numbers of gradient calls on average by an additional 21%, while using a modified steepest-descent method improved that key efficiency criterion on average by 13%. For problematic cases we suggest strategies especially adapted to the problem at hand.

Improving Upon String Methods for Transition State Discovery.

Transition state discovery via application of string methods has been researched on two fronts. The first front involves development of a new string method, named the Searching String method, while the second one aims at estimating transition states from a discretized reaction path. The Searching String method has been benchmarked against a number of previously existing string methods and the Nudged Elastic Band method. The developed methods have led to a reduction in the number of gradient calls required to optimize a transition state, as compared to existing methods. The Searching String method reported here places new beads on a reaction pathway at the midpoint between existing beads, such that the resolution of the path discretization in the region containing the transition state grows exponentially with the number of beads. This approach leads to favorable convergence behavior and generates more accurate estimates of transition states from which convergence to the final transition states occurs more readily. Several techniques for generating improved estimates of transition states from a converged string or nudged elastic band have been developed and benchmarked on 13 chemical test cases. Optimization approaches for string methods, and pitfalls therein, are discussed.

Atomic approximation to the projection on electronic states in the Douglas-Kroll-Hess approach to the relativistic Kohn-Sham method.

We suggest an approximate relativistic model for economical all-electron calculations on molecular systems that exploits an atomic ansatz for the relativistic projection transformation. With such a choice, the projection transformation matrix is by definition both transferable and independent of the geometry. The formulation is flexible with regard to the level at which the projection transformation is approximated; we employ the free-particle Foldy-Wouthuysen and the second-order Douglas-Kroll-Hess variants. The (atomic) infinite-order decoupling scheme shows little effect on structural parameters in scalar-relativistic calculations; also, the use of a screened nuclear potential in the definition of the projection transformation shows hardly any effect in the context of the present work. Applications to structural and energetic parameters of various systems (diatomics AuH, AuCl, and Au(2), two structural isomers of Ir(4), and uranyl dication UO(2) (2+) solvated by 3-6 water ligands) show that the atomic approximation to the conventional second-order Douglas-Kroll-Hess projection (ADKH) transformation yields highly accurate results at substantial computational savings, in particular, when calculating energy derivatives of larger systems. The size-dependence of the intrinsic error of the ADKH method in extended systems of heavy elements is analyzed for the atomization energies of Pd(n) clusters (n

How the C-O bond breaks during methanol decomposition on nanocrystallites of palladium catalysts.

Experimental findings imply that edge sites (and other defects) on Pd nanocrystallites exposing mainly (111) facets in supported model catalysts are crucial for catalyst modification via deposition of CH(x) (x = 0-3) byproducts of methanol decomposition. To explore this problem computationally, we applied our recently developed approach to model realistically metal catalyst particles as moderately large three-dimensional crystallites. We present here the first results of this advanced approach where we comprehensively quantify the reactivity of a metal catalyst in an important chemical process. In particular, to unravel the mechanism of how CH(x) species are formed, we carried out density functional calculations of C-O bond scission in methanol and various dehydrogenated intermediates (CH3O, CH2OH, CH2O, CHO, CO), deposited on the cuboctahedron model particle Pd79. We calculated the lowest activation barriers, approximately 130 kJ mol(-1), of C-O bond breaking and the most favorable thermodynamics for the adsorbed species CH3O and CH2OH which feature a C-O single bond. In contrast, dissociation of adsorbed CO was characterized as negligibly slow. From the computational result that the decomposition products CH3 and CH2 preferentially adsorb at edge sites of nanoparticles, we rationalize experimental data on catalyst poisoning.

Optical spectra of Cu, Ag, and Au monomers and dimers at regular sites and oxygen vacancies of the MgO(001) surface. A systematic time-dependent density functional study using embedded cluster models.

Polarization-resolved optical spectra of coinage metal monomers and dimers Mn (M=Cu, Ag, Au; n=1, 2) at ideal O2- sites of MgO(001) as well as at oxygen vacancies, Fs and Fs+, of that surface were established using a computational approach based on linear response time-dependent density functional theory. Calculations were performed for structures determined by applying a generalized-gradient density functional method to cluster models embedded in an elastic polarizable environment. This embedding scheme provides an accurate description of substrate relaxation and long-range electrostatic interaction. We compared the optical properties of adsorbed atoms and dimers with those of the corresponding gas-phase species and we systematically analyzed trends among congeners.

The heat of formation of gaseous PuO(2)2+ from relativistic density functional calculations.

Using a set of model reactions, we estimated the heat of formation of gaseous PuO2(2+) from quantum-chemical reaction enthalpies and experimental heats of formation of reference species. To this end, we carried out relativistic density functional calculations on the molecules PuO(2)2+, PuO2, PuF6, and PuF4. We used a revised variant (PBEN) of the Perdew-Burke-Ernzerhof gradient-corrected exchange-correlation functional, and we accounted for spin-orbit interaction in a self-consistent fashion. As open-shell Pu species with two or more unpaired 5f electrons are involved, spin-orbit interaction significantly affects the energies of the model reactions. Our theoretical estimate for the heat of formation DeltafH degree 0(PuO2(2+),g), 418+/-15 kcal mol-1, evaluated using plutonium fluorides as references, is in good agreement with a recent experimental result, 413+/-16 kcal mol-1. The theoretical value connected to the experimental heat of formation of PuO2(g) has a notably higher uncertainty and therefore was not included in the final result.

The heat of formation of the uranyl dication: theoretical evaluation based on relativistic density functional calculations.

By using a set of model reactions, we estimated the heat of formation of gaseous UO2(2+) from quantum-chemical reaction enthalpies and experimental heats of formation of reference species. For this purpose, we performed relativistic density functional calculations for the molecules UO2(2+), UO2, UF6, and UF5. We used two gradient-corrected exchange-correlation functionals (revised Perdew-Burke-Ernzerhof (PBEN) and Becke-Perdew (BP)) and we accounted for spin-orbit interaction in a self-consistent fashion. Indeed, spin-orbit interaction notably affects the energies of the model reactions, especially if compounds of U(IV) are involved. Our resulting theoretical estimates for delta fH(o)0 (UO2(2+)), 365+/-10 kcal mol(-1) (PBEN) and 370+/-12 kcal mol(-1) (BP), are in quantitative agreement with a recent experimental result, 364+/-15 kcal mol(-1). Agreement between the results of the two different exchange-correlation functionals PBEN and BP supports the reliability of our approach. The procedure applied offers a general means to derive unknown enthalpies of formation of actinide species based on the available well-established data for other compounds of the element in question.

Efficient treatment of the Hartree interaction in the relativistic Kohn-Sham problem.

We elaborate the two-component Douglas-Kroll reduction of the Dirac-Kohn-Sham problem of relativistic density-functional theory as introduced by Matveev and Rosch [J. Chem. Phys. 118, 3997 (2003)]. That method retains corrections to the Coulomb self-interaction (or Hartree) term of the energy functional that are due to the picture change. Using analytic expressions for the matrix elements, one is able to abandon the resolution of the identity approach for a crucial step of the relativistic transformation. Thus, a major source of uncertainties of the method is eliminated because basis sets no longer have to be extended by functions of higher angular momentum, previously required to ensure kinetic balance. This approach also relies on the electron charge-density fitting scheme via an auxiliary basis set. An efficient approximate implementation results if one restricts the relativistic transformation to the spherically symmetric atom-centered auxiliary functions. It provides accurate results while simplifying greatly the expressions for the matrix elements of the relativistically transformed operators and significantly reducing the computational effort. We demonstrate the performance of the method for the fine structure of one-electron levels of the Hg atom, the g-tensor shifts of NO2, and the properties of the diatomic molecules Bi2, Pb2, PbO, and TlH.

Single d-metal atoms on F(s) and F(s+) defects of MgO(001): a theoretical study across the periodic table.

Single d-metal atoms on oxygen defects F(s) and F(s+) of the MgO(001) surface were studied theoretically. We employed an accurate density functional method combined with cluster models, embedded in an elastic polarizable environment, and we applied two gradient-corrected exchange-correlation functionals. In this way, we quantified how 17 metal atoms from groups 6-11 of the periodic table (Cu, Ag, Au; Ni, Pd, Pt; Co, Rh, Ir; Fe, Ru, Os; Mn, Re; and Cr, Mo, W) interact with terrace sites of MgO. We found bonding with F(s) and F(s+) defects to be in general stronger than that with O2- sites, except for Mn-, Re-, and Fe/F(s) complexes. In M/F(s) systems, electron density is accumulated on the metal center in a notable fashion. The binding energy on both kinds of O defects increases from 3d- to 4d- to 5d-atoms of a given group, at variance with the binding energy trend established earlier for the M/O2- complexes, 4d < 3d < 5d. Regarding the evolution of the binding energy along a period, group 7 atoms are slightly destabilized compared to their group 6 congeners in both the F(s) and F(s+) complexes; for later transition elements, the binding energy increases gradually up to group 10 and finally decreases again in group 11, most strongly on the F(s) site. This trend is governed by the negative charge on the adsorbed atoms. We discuss implications for an experimental detection of metal atoms on oxide supports based on computed core-level energies.