XPS of oxygen atoms on Ag(111) and Ag(110) surfaces: Accurate study with SAC/SAC‐CI combined with dipped adcluster model

O1s core‐electron binding energies (CEBE) of the atomic oxygens on different Ag surfaces were investigated by the symmetry adapted cluster‐configuration interaction (SAC‐CI) method combined with the dipped adcluster model, in which the electron exchange between bulk metal and adsorbate is taken into account properly. Electrophilic and nucleophilic oxygens (O_elec and O_nuc) that might be important for olefin epoxidation in a low‐oxygen coverage condition were focused here. We consider the O1s CEBE as a key property to distinguish the surface oxygen states, and series of calculation was carried out by the Hartree–Fock, Density functional theory, and SAC/SAC‐CI methods. The experimental information and our SAC/SAC‐CI results indicate that O_elec is the atomic oxygen adsorbed on the fcc site of Ag(111) and that O_nuc is the one on the reconstructed added‐row site of Ag(110) and that one‐ and two‐electron transfers occur, respectively, to the O_elec and O_nuc adclusters from the silver surface. © 2013 Wiley Periodicals, Inc.     

Q‐symmetry and conditional Q‐symmetries for Drinfel'd–Sokolov–Wilson system

We study in this paper the Q‐symmetry and conditional Q‐symmetries of Drinfel'd–Sokolov–Wilson equations. The solutions which we obtain in this paper take the form of convergent power series with easily computable components. Copyright © 2014 John Wiley & Sons, Ltd.     

Dirac reduction for nonholonomic mechanical systems and semidirect products

This paper develops the theory of Dirac reduction by symmetry for nonholonomic systems on Lie groups with broken symmetry. The reduction is carried out for the Dirac structures, as well as for the associated Lagrange–Dirac and Hamilton–Dirac dynamical systems. This reduction procedure is accompanied by reduction of the associated variational structures on both Lagrangian and Hamiltonian sides. The reduced dynamical systems obtained are called the implicit Euler–Poincaré–Suslov equations with advected parameters and the implicit Lie–Poisson–Suslov equations with advected parameters. The theory is illustrated with the help of finite and infinite dimensional examples. It is shown that equations of motion for second order Rivlin–Ericksen fluids can be formulated as an infinite dimensional nonholonomic system in the framework of the present paper.     

Quantum McKay Correspondence for Disc Invariants of Toric Calabi–Yau 3-orbifolds

We announce a result on quantum McK ay correspondence for disc invariants of outer legs in toric Calabi–Yau 3-orbifolds, and illustrate our method in a special example [C3/Z5(1, 1, 3)].     

Exploiting space‐group symmetry in fragment‐based molecular crystal calculations

Recent developments in fragment‐based methods make it increasingly feasible to use high‐level ab initio electronic structure techniques to molecular crystals. Such studies remain computationally demanding, however. Here, we describe a straightforward algorithm for exploiting space‐group symmetry in fragment‐based methods which often provides computational speed‐ups of several fold or more. This algorithm does not require a priori specification of the space group or symmetry operators. Rather, the symmetrically equivalent fragments are identified automatically by aligning the individual fragments along their principle axes of inertia and testing for equivalence with other fragments. The symmetry operators relating equivalent fragments can then be worked out easily. Implementation of this algorithm for computing energies, nuclear gradients with respect to both atomic coordinates and lattice parameters, and the nuclear hessian is described. © 2014 Wiley Periodicals, Inc.     

Characterization of the potential energy surfaces of two small but challenging noncovalent dimers: (P2)2 and (PCCP)2

This work characterizes eight stationary points of the P₂ dimer and six stationary points of the PCCP dimer, including a newly identified minimum on both potential energy surfaces. Full geometry optimizations and corresponding harmonic vibrational frequencies were computed with the second‐order Møller–Plesset (MP2) electronic structure method and six different basis sets: aug‐cc‐pVXZ, aug‐cc‐pV(X+d)Z, and aug‐cc‐pCVXZ where X = T, Q. A new L‐shaped structure with C₂ symmetry is the only minimum for the P₂ dimer at the MP2 level of theory with these basis sets. The previously reported parallel‐slipped structure with C_2h symmetry and a newly identified cross configuration with D₂ symmetry are the only minima for the PCCP dimer. Single point energies were also computed using the canonical MP2 and CCSD(T) methods as well as the explicitly correlated MP2‐F12 and CCSD(T)‐F12 methods and the aug‐cc‐pVXZ (X = D, T, Q, 5) basis sets. The energetics obtained with the explicitly correlated methods were very similar to the canonical results for the larger basis sets. Extrapolations were performed to estimate the complete basis set (CBS) limit MP2 and CCSD(T) binding energies. MP2 and MP2‐F12 significantly overbind the P₂ and PCCP dimers relative to the CCSD(T) and CCSD(T)‐F12 binding energies by as much as 1.5 kcal mol^?1 for the former and 5.0 kcal mol^?1 for the latter at the CBS limit. The dominant attractive component of the interaction energy for each dimer configuration was dispersion according to several symmetry‐adapted perturbation theory analyses. © 2014 Wiley Periodicals, Inc.     

Residual symmetry reductions and interaction solutions of the (2+1)-dimensional Burgers equation

In nonlinear physics,it is very difficult to study interactions among different types of nonlinear waves.In this paper,the nonlocal symmetry related to the truncated Painleve′expansion of the(2+1)-dimensional Burgers equation is localized after introducing multiple new variables to extend the original equation into a new system.Then the corresponding group invariant solutions are found,from which interaction solutions among different types of nonlinear waves can be found.Furthermore,the Burgers equation is also studied by using the generalized tanh expansion method and a new Ba¨cklund transformation(BT)is obtained.From this BT,novel interactive solutions among different nonlinear excitations are found.     

Is Electrostatics Sufficient to Describe Hydrogen‐Bonding Interactions?

The stability and geometry of a hydrogen‐bonded dimer is traditionally attributed mainly to the central moiety A?H???B, and is often discussed only in terms of electrostatic interactions. The influence of substituents and of interactions other than electrostatic ones on the stability and geometry of hydrogen‐bonded complexes has seldom been addressed. An analysis of the interaction energy in the water dimer and several alcohol dimers—performed in the present work by using symmetry‐adapted perturbation theory—shows that the size and shape of substituents strongly influence the stabilization of hydrogen‐bonded complexes. The larger and bulkier the substituents are, the more important the attractive dispersion interaction is, which eventually becomes of the same magnitude as the total stabilization energy. Electrostatics alone are a poor predictor of the hydrogen‐bond stability trends in the sequence of dimers investigated, and in fact, dispersion interactions predict these trends better.     

Spin‐State Ordering on One Sub‐lattice of a Mononuclear Iron(III) Spin Crossover Complex Exhibiting LIESST and TIESST

The two‐step spin crossover in mononuclear iron(III) complex [Fe(salpm)₂]ClO₄ ? 0.5 EtOH ( 1 ) is shown to be accompanied by a structural phase transition as concluded from ⁵⁷Fe Mössbauer spectroscopy and single crystal X‐ray diffraction, with spin‐state ordering on just one of two sub‐lattices in the intermediate magnetic and structural phase. The complex also exhibits thermal‐ and light‐induced spin‐state trapping (TIESST and LIESST), and relaxation from the LIESST and TIESST excited states occurs via the broken symmetry intermediate phase. Two relaxation events are evident in both experiments, that is, two T(LIESST) and two T(TIESST) values are recorded. The change in symmetry which accompanies the TIESST effect was followed in real time using single crystal diffraction. After flash freezing at 15 K the crystal was warmed to 40 K at which temperature superstructure reflections were observed to appear and disappear within a 10 000 s time range. In the frame of the international year of crystallography, these results illustrate how X‐ray diffraction makes it possible to understand complex ordering phenomena.