Embedded cluster methods for surface and chemisorption studies

Cluster methods for studying chemisorption and also for studies of surface defect states have been most useful in extending our ability to predict surface properties and behaviors. Such methods while seeming accurate, are problematic in that they often ignore, or at best intuit, the interaction of the cluster with the remainder of the system. The author along with his associates has proposed a series of rigorous steps to permit the inclusion of such interactions in ionic insulator and semiconductors. This formal development neglects molecular solids and also metals. In this paper, the systematics devised are extended to molecular solids in a practical way.     

Dimer statistics on a Bethe lattice

We discuss the exact solutions of various models of the statistics of dimer coverings of a Bethe lattice. We reproduce the well-known exact result for noninteracting hard-core dimers by both a very simple geometrical argument and a general algebraic formulation for lattice statistical problems. The algebraic formulation enables us to discuss loop corrections for finite dimensional lattices. For the Bethe lattice we also obtain the exact solution when either (a) the dimers interact via a short-range interaction or (b) the underlying lattice is anisotropic. We give the exact solution for a special limit of dimers on a Bethe lattice in a quenched random potential in which we consider the maximal covering of dimers on random clusters at site occupation probability p. Surprisingly the partition function for "maximal coverage" on the Bethe lattice is identical to that for the statistics of branched polymers when the activity for a monomer unit is set equal to -p. Finally we give an exact solution for the number of residual vacancies when hard-core dimers are randomly deposited on a one dimensional lattice.     

Differential correlation effects in chemisorption cluster model calculations: an FCI study

The interaction of atomic hydrogen with Cu₅ and Ag₅ cluster models simulating the Cu(100) and Ag(100) surfaces has been studied at the full configuration interaction (FCI) level in order to establish the transferability of differential correlation arising from the valence shell. It is shown that pseudopotentials that deal explicitly with one electron or eleven electrons lead to differential correlation effects which agree to within 1–2 mhartree when a localization procedure is used to separate d-shell MOs from the valence ones.     

Tree pruning and lattice statistics on Bethe lattices

The method of tree pruning is employed to obtain generating functions for lattice statistics on Bethe lattices. It is shown that tree pruning significantly simplifies the evaluation of the generating function for the number of ways of placing disjoint dimers on a Bethe lattice. Analytical expressions are derived for several Bethe lattices. An iterative algorithm is outlined for obtaining generating functions for placing dimers on a Bethe lattice of any valence and with lengthn. It is further shown that the method could also be applied to weighted or anisotropic lattices.Alfred P. Sloan fellow; Camille and Henry Dreyfus Teacher-scholar.     

Entropy of polydisperse chains: solution on the Bethe lattice

We consider the entropy of polydisperse chains placed on a lattice. In particular, we study a model for equilibrium polymerization, where the polydispersivity is determined by two activities, for internal and endpoint monomers of a chain. We solve the problem exactly on a Bethe lattice with arbitrary coordination number, obtaining an expression for the entropy as a function of the density of monomers and mean molecular weight of the chains. We compare this entropy with the one for the monodisperse case and find that the excess of entropy due to polydispersivity is identical to the one obtained for the one-dimensional case. Finally, we obtain an exponential distribution of molecular weights.     

Basis-Modified hydrogen atoms as embedding atoms in ab initio chemisorption cluster model calculations on Si surfaces

A comparative and systematic ab initio study of different models simulating the Si (111) surface has been carried out for a variety of embedding hydrogen atoms including unmodified hydrogen atoms and modified hydrogen atoms described with a STO-4G basis set and a Slater exponent optimized to have the cluster atoms as neutral as possible. The study has been extended to some chemisorption processes as Ag and Al on Si (111). The main conclusion of the present work is that neither the electronic structure of the isolated cluster models nor the nature of the chemisorption bond depend on the kind of embedding hydrogen atoms used to saturate the free valences of the cluster edge atoms. © John Wiley & Sons, Inc.     

Dissociative chemisorption of D2 on a Ni13 cluster

Selected characteristic results of a quasiclassical trajectory study of dissociative adsorption of a D₂ molecule on a Ni₁₃ cluster are presented. These include detailed probabilities as functions of the impact parameter and of the relative translational energy of D₂, and cross sections as functions of this energy. The roles of the initial rovibrational state of the D₂ molecule and of the initial temperature of the cluster are examined. The effect of freezing the cluster into a rigid geometry is tested.     

Embedded cluster model studies of impurities at metal surfaces

A knowledge of the electronic properties of impurities at metal surfaces is of great value in the understanding of such important phenomena as chemisorption and surface segregation in alloys. We have adopted here a unified approach based on an Embedded Cluster model to study the properties of surface impurities. We have mainly concentrated on hydrogen impurities either adsorbed above the surface or incorporated into the bulk of metals. We have also considered the case of substitutional metal impurities at the surface of host metals.For hydrogen chemisorption we have considered such substrates as free-electron, transition and noble metals as well as bimetallic substrates composed of a single metal impurity in a host matrix or a metallic overlayer on a metal support. The electronic structure of the chemisorbed system is compared to photoemission data when available, from which interpretation of the details of the experimental spectra may be made. It is found that hydrogen adsorption on transition and noble metals results in the formation of a pair of bonding/antibonding resonances on either side of the metal d-band, while for hydrogen on free-electron metals a single hydrogen induced resonance is observed. One-electron energy differences between the H on jellium and H on metal systems are estimated and trends in such energies across the 3d and 4d transition series are compared to the trends in experimental chemisorption energies for H on these metals. The change in hydrogen chemisorption capacity of an inert substrate due to the introduction of chemically active impurities is investigated. The different properties of Pd overlayers with respect to Pd surfaces are also investigated. Interaction energies between adatoms on surfaces are estimated in order to predict the geometry of ordered structures on surfaces.One-electron heats of segregation for binary alloys are calculated. These show a strong solute surface segregation for noble metal impurities in group VIII metals, which is due to the higher d-band occupancy of the noble metal.     

紧束缚模型方法及其在DNA分子中的应用

近年来,紧束缚模型方法被广泛应用于计算生物大分子体系.本文从第一性原理出发,根据紧束缚近似的思想,推导出生物大分子体系中的单电子运动方程.在此基础上给出了紧束缚模型方法中所涉及参数(在位能和迁移积分)的计算公式,在理论上完善了紧束缚模型方法.我们将所提出的参数化方法应用于理想B型DNA分子,给出了各种序列组合下的在位能和迁移积分.此外,我们还计算了周期性DNA分子poly(A)-poly(T)和poly(G)-poly(C)中空穴在位能和迁移积分随格点间距离的变化,为改进现有的SSH极化子模型提供了新的思路,有助于DNA中电荷输运的极化子机理的研究.     

Kinetics of phase transformation on a Bethe lattice in the presence of spin exchange

Kinetics of phase transformation on a Bethe lattice governed by single-spin-flip Glauber and spin-exchange Kawasaki dynamics is examined. For a general Glauber dynamics for which all processes (splitting and coagulation, growth and decay of clusters, as well as creation and annihilation of single-spin clusters) take place, the addition of the Kawasaki dynamics accelerates the transformation process without changing the qualitative behavior. In the growth-decay regime of the Glauber dynamics, regime in which the splitting and coagulation, and creation and annihilation processes due to single-spin flips are negligible, the Kawasaki dynamics strongly increases the fraction of transformed phase because of the splitting and coagulation of clusters induced by the spin-exchange processes. Acting alone, the Kawasaki dynamics leads to the growth of the clusters of each of the phases after the quenching of the temperature to a lower value. When the final temperature T(f) is smaller than a certain temperature T(f0), the average cluster radius grows linearly with time during both the initial and intermediate stages of the kinetic process, and diverges as log(2)(t(d)-t)(-1) when the time t approaches the value t(d) at which infinite clusters arise. It is shown that, among the various spin-exchange processes involved in Kawasaki dynamics, the main contribution is provided by those which decrease or increase the number of clusters by unity.     

Exact phase boundary of an amphiphile-rich phase in a ternary solution on a Bethe lattice

A model ternary solution is considered in which the bonds of a three-coordinate Bethe lattice are covered by rodlike molecules of types AA, BB, and AB, the AB-type molecule representing an amphiphile. The phase boundary in temperature-composition space of an ordered amphiphile-rich phase is calculated exactly.     

Coupled cluster and density functional theory calculations of atomic hydrogen chemisorption on pyrene and coronene as model systems for graphene hydrogenation

Ab initio coupled cluster and density functional theory studies of atomic hydrogen addition to the central region of pyrene and coronene as molecular models for graphene hydrogenation were performed. Fully relaxed potential energy curves (PECs) were computed at the spin-unrestricted B3LYP/cc-pVDZ level of theory for the atomic hydrogen attack of a center carbon atom (site A), the midpoint of a neighboring carbon bond (site B), and the center of a central hexagon (site C). Using the B3LYP/cc-pVDZ PEC geometries, we evaluated energies at the PBE density functional, as well as ab initio restricted open-shell ROMP2, ROCCSD, and ROCCSD(T) levels of theory, employing cc-pVDZ and cc-pVTZ basis sets, and performed a G2MS extrapolation to the ROCCSD(T)/cc-pVTZ level of theory. In agreement with earlier studies, we find that only site A attack leads to chemisorption. The G2MS entrance channel barrier heights, binding energies, and PEC profiles are found to agree well with a recent ab initio multireference wave function theory study (Bonfanti et al. J. Chem. Phys.2011, 135, 164701), indicating that single-reference open-shell methods including B3LYP are sufficient for the theoretical treatment of the interaction of graphene with a single hydrogen atom.     

Solution on the Bethe lattice of a hard core athermal gas with two kinds of particles

Athermal lattice gases of particles with first neighbor exclusion have been studied for a long time as simple models exhibiting a fluid-solid transition. At low concentration the particles occupy randomly both sublattices, but as the concentration is increased one of the sublattices is occupied preferentially. Here, we study a mixed lattice gas with excluded volume interactions only in the grand-canonical formalism with two kinds of particles: small ones, which occupy a single lattice site and large ones, which, when placed on a site, do not allow other particles to occupy its first neighbors also. We solve the model on a Bethe lattice of arbitrary coordination number q. In the parameter space defined by the activities of both particles, at low values of the activity of small particles (z(1)) we find a continuous transition from the fluid to the solid phase as the activity of large particles (z(2)) is increased. At higher values of z(1) the transition becomes discontinuous, both regimes are separated by a tricritical point. The critical line has a negative slope at z(1) = 0 and displays a minimum before reaching the tricritical point, so that a re-entrant behavior is observed for constant values of z(2) in the region of low density of small particles. The isobaric curves of the total density of particles as a function of the density or the activity of small particles show a minimum in the fluid phase.     

Island formation in chemisorption 1. Chemisorption model

A model of dissociative chemisorption on a surface with a square lattice was studied using the Monte Carlo method. The model is based on two chemisorption pathways: “direct”—nucleation of adsorption islands, and “indirect”—their growth. The development of the surface distribution picture of chemisorbed particles was found to depend significantly on the contribution of these two pathways (S_indir/S_dir).     

DFT and MO calculations of atomic and molecular chemisorption energies on surface cluster models

Summary Density functional theory (DFT) (including gradient corrections) and MCPF calculations have been performed for atomic (H, C, N, O) and molecular CH _x (x = 1–3) chemisorption on cluster models of different sites of the Cu(100) surface. The DFT and MCPF results are in good agreement once the important effects of core-valence correlation have been accounted for in the MCPF calculations by including contributions from a core polarization potential (CPP); in the DFT approach the core-valence correlation is obtained directly from the total density using the functional. Very large effects on the four-fold hollow site binding energy from core-valence correlation are found for C, N and CH. Several different DFT functionals were employed and compared in the calculations.     

Model studies of the chemisorption of hydrogen and oxygen on nickel surfaces

Atomic chemisorption of hydrogen and oxygen on the Ni(100) surface has been studied using an Effective Core Potential (ECP) approach described in a previous paper. Clusters of up to 50 nickel atoms have been used to model the surface. The computed chemisorption energies are 62 kcal/mol (exp. 63 kcal/mol) for hydrogen and 106 kcal/mol (exp. 115–130 kcal/mol) for oxygen. Correlating the adsorbate and the cluster-adsorbate bonds is extremely important for obtaining accceptable results, particularly for oxygen. Reasonable convergence of chemisorption energies is obtained with 40–50 cluster atoms for both hydrogen and oxygen. For hydrogen the addition of a third cluster layer stabilizes the results considerably. Both hydrogen and oxygen are adsorbed at (or close to) the four-fold hollow site. The calculated barriers for surface migration are also in good agreement with the experimental estimates. The calculated equilibrium heights above the surface are on the other hand too high compared with experiments. This disagreement is believed to be due to core-valence correlation effects, which are not incorporated in the present ECP. The cluster convergence for the height above the surface is much slower than for the chemisorption energy.