Internal dynamics of (H<Subscript>2</Subscript>O)<Subscript>2</Subscript> and (D<Subscript>2</Subscript>O)<Subscript>2</Subscript> dimers: III. Description taking into account inversion,exchange and bifurcation motions

Using the symmetry group chain methods, the stationary states of (H₂O)₂ and (D₂O)₂ dimers that correspond to the lowest energy barriers of the inversion, exchange via an intermediate trans configuration, and bifurcation motions are classified taking into account the real geometries of the dimers. A model that rigorously describes the interactions of the motions and leads to a simple algebraic scheme for calculating of both the positions of the levels in the energy spectrum and the intensities of transitions between them is constructed. It is important that the correctness of the model is limited only by the trueness of the choice of symmetry of the internal dynamics.     

A rigorous description of the energy spectrum of the ammonia dimer. II. Taking into account the inversional motion

Using the group chain methods, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with an allowance for both the most important torsional and exchange nonrigid motions and the inversional nonrigid motion also taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

Heteroclinic cycles and modulated travelling waves in systems with O(2) symmetry

We analyze unfoldings of a codimension two, steady-state/steady-state modal interaction possessing O(2) symmetry. At the degenerate bifurcation point there are two zero eigenvalues, each of multiplicity two. The spatial wavenumbers of the critical modes k_i are assumed to satisfy k₂ = 2k₁. We base our analysis on a detailed study of the third order truncation of the resulting equivariant normal form, which is a four-dimensional vector field. We find that heteroclinic cycles and modulated travelling waves exist for open sets of parameter values near the codimension two bifurcation point. We provide conditions on parameters which guarantee existence and uniqueness of such solutions and we investigate their stability types. We argue that such motions will be prevalent in continuum systems having the symmetry of translation and reflection with respect to one (or more) spatial directions.     

A rigorous description of the energy spectrum of the ammonia dimer. I. Taking into account the torsional and exchange motions

Using the methods of a symmetry group chain, a rigorous algebraic model for describing the energy spectrum of the ammonia dimer (NH₃)₂ is constructed with the torsional and exchange nonrigid motions taken into account. The model is rigorous in the sense that its correctness is limited only by the correctness of the chosen symmetry of internal dynamics of the dimer.     

Raman study of (NH4)2CuCl4·2H2O—I: Dynamics and structure in low temperature phase

We report the results of a Raman scattering study of (NH₄)₂CuCl₄2H₂O at 300, 205 and 100°K, in order to elucidate the dynamics and phase transition in this double salt. A group theoretical calculation of the symmetry vectors, in the high temperature phase (D_4h¹⁴), is made and the various modes are identified. The deuterated compound (ND₄)₂CuCl₄·2D₂O has also been investigated to help in identifying the modes involving motion of the ammonium ions and water molecules. Through a careful analysis of the spectra at 100°K, the space group in the low temperature phase has been established as D_2d³. The important consequence of this result is that this leads to parallel spatial ordering of ammonium tetrahedra in this compound in the low temperature phase.     

SU (2N f) ⊗ O(3) light diquark symmetry and current-induced heavy baryon transition form factors

We study the current-induced bottom baryon to charm baryon transitions in the Heavy Quark Symmetry limit as m_q → ∞. Our discussion involves s-wave to s-wave as well as s-wave to p-wave transitions. Using a constituent quark model picture for the light diquark system with an underlying SU (2N_f) ? O(3) symmetry and the heavy quark symmetry we arrive at a number of new predictions for the reduced form factors that describe these transitions.     

Adsorption behavior of H2O on clean and oxygen precovered Ni(s)(111)

Photoelectron spectroscopy (UPS), thermal desorption spectroscopy (TDS), isotope exchange experiments, work function change (δφ) and LEED were used to study the adsorption and dissociation behavior of H₂O on a clean and oxygen precovered stepped Ni(s)[12(111) × (111)] surface. On the clean Ni(111) terraces fractional monolayers of H₂O are adsorbed weakly in a single adsorption state with a desorption peak temperature of 180 K, just above that of the ice multilayer desorption peak (T_m = 155 K). In the angular resolved UPS spectra three H₂O induced emission maxima at 6.2, 8.5 and 12.3 eV below E_F were found for θ ≈ 0.5. Angular and polarization dependent UPS measurements show that the C_2v symmetry of the H₂O gas-phase molecule is not conserved for H₂O(ad) on Ni(s)(111). Although the Δφ suggest a bonding of H₂O to Ni via the negative end of the H₂O dipole, the O atom, no hints for a preferred orientation of the H₂O molecular axes were found in the UPS, neither for the existence of water dimers nor for a long range ordered H₂O bilayer. These results give evidence that the molecular H₂O axis is more or less inclined with respect to the surface normal with an azimuthally random distribution. H₂O adsorption at step sites of the Ni(s)(111) surface leads in TDS to a desorption maximum at T_m = 225 K; the binding energy of H₂O to Ni is enhanced by about 30% compared to H₂O adsorbed on the terraces. Oxygen precoverage causes a significant increase of the H₂O desorption energy from the Ni(111) terraces by about 50%, suggesting a strong interaction between H₂O and O(ad). Work function measurements for H₂O+O demonstrate an increase of the effective H₂O dipole moment which suggests a reorientation of the H₂O dipole in the presence of O(ad), from inclined to a more perpendicular position. Although TDS and Δφ suggest a significant lateral interaction between H₂O+O(ad), no changes in the molecular binding energies in UPS and no “isotope exchange” between ¹⁸O(ad) and H₂¹⁶O(ad) could be observed. Also, dissociation of H₂O could neither be detected on the oxygen precovered Ni(s)(111) nor on the clean terraces.     

An investigation of the phase structure of the two-dimensional O(2) and O(4) symmetric nonlinear sigma-models

We investigate the phase structure of the two-dimensional O(2) and O(4) lattice σ-models by means of a Monte Carlo simulation using Binder's phenomenological renormalization group. For the O(2) model the transition temperature β_c⁻¹ is estimated and the expected line of critical points is found. For the O(4) model no signal of a phase transition is found in the range of couplings considered. This is in contradiction to a recent claim that the O(4) model has a critical point at finite β.     

High-Resolution IR Spectroscopy of the N2O-H2O and N2O-D2O van der Waals Complexes

We report high-resolution infrared vibrational-rotational spectra of the weakly bound complexes N₂O-H₂O and N₂O-D₂O in the higher frequency N₂O stretching mode region (ν₃=2223.756693(124) cm⁻¹). The measurements were carried out using a free jet expansion in combination with a lead salt diode laser spectrometer. Rotational constants, quartic centrifugal distortion constants, and band origins have been derived for both isotopomers. The geometrical structure is determined using isotopic substitution. The deduced structure shows evidence for a second hydrogen bond interaction within the complex. The nonrigidity of the complexes gives rise to an internal rotation of the water molecule around its own C_2v symmetry axis. For N₂O-H₂O, a tunneling splitting arising from this internal motion has been observed in the spectra. According to symmetry considerations, the observed splitting in the spectrum of N₂O-H₂O corresponds to the difference between the tunneling frequencies in the ground and vibrationally excited states.     

Rigorous description of an energy spectrum of the isopropanol molecule taking into account the internal rotation of methyl tops

By using the group chain methods, a rigorous algebraic model is constructed to describe the energy spectrum of the isopropanol molecule (CH₃)₂CHOH with an allowance for the internal motion of hydroxil and two identical methyl tops. The model is rigorous in the sense that its correctness is limited only by the correctness of a symmetry chosen to describe internal dynamics of the molecule.     

Study by X-ray crystallography and Mössbauer spectroscopy of CeFe(CN)6·5H2O and GdFe(CN)6·4H2O

From the X-ray crystallographic point of view, the environment of Fe in CeFe(CN)₆·5H₂O has higher octahedral symmetry than that in GdFe(CN)₆·4H₂O. The single Mössbauer absorption peak for CeFe(CN)₆·5H₂O indicates that the three t_2g levels are close to each other in energy due to a near-perfect octahedral Fe(CN)₆ unit. The doublet peak of of GdFe(CN)₆·4H₂O can be explained by assuming that the three t_2g levels are widely separated as a result of the distortion of the octahedral Fe(CN)₆ unit.     

Geometry of the internal dynamics of C<Subscript>2</Subscript>H<Stack><Subscript>3</Subscript><Superscript>+</Superscript></Stack> carbocation

Using the symmetry group chain methods, the internal dynamics of the simplest carbocation, C₂H ₃ ⁺ , is analyzed under the traditional assumptions that the equilibrium structures of the carbocation are planar and that the nonrigid motion between them is in-plane. This geometry of the internal dynamics is shown to agree with the data of the microwave spectroscopy on the splittings of rotational energy levels caused by the nonrigid motion. Previously, this statement was based on the model that violated the requirement of self-adjointness of operators of physical quantities.     

Chemisorption and dissociation of O2, on Ag(110)

Using an Ag₂₄ cluster, we have calculated the potential energy surface of an O₂ molecule chemisorbing and dissociating on the Ag(110) surface, with its molecular axis parallel to the grooves in the [1&#x0304;10] direction. For molecular chemisorption, we find equilibrium positions and vibrational frequencies in good agreement with experiment and with earlier calculations; the chemisorption energy, ∼ 0.1 eV, may be somewhat too low. Although both our calculated and the experimental vibrational frequencies suggest a chemisorbed O²⁻₂ ion, our calculated charge transfer to the O₂ molecule is a little less than one electron. We can explain the calculated low OO strength frequency by changing occupations of OO bonding and antibonding states with changing OO separation. These results show that one has to be cautious in directly relating observed vibrational frequency lowerings of chemisorbed molecules to their charge states. The dissociation path is completely along the direction of the OO stretch; we find a barrier height of ∼ 0.2 eV. The atomic equilibrium distance, vibrational frequency, and binding energy are in reasonable agreement with experiment. At large OO separation, the energy still decreases with increasing OO distance, indicative of OO Coulomb repulsion.     

Competition of two mechanisms of retardation of domain walls in the molecular ferrimagnet [Mn{(R/S)-pn}]2[Mn{(R/S-pn}2(H2O)][Cr(CN)6]2

The temperature dependence of the magnetization reversal dynamics of the chiral molecular ferrimagnet [Mn{(R/S)-pn}]₂[Mn{(R/S)-pn}₂(H₂O)][Cr(CN)₆]₂ has been studied at low frequencies of 1–1400 Hz, which are characteristic of the domain wall motion. It has been found from the Cole-Cole plots that domain walls undergo relaxation (at temperatures T > 10 K) and creep (at T < 10 K), and the main parameters determining these modes and the transition between them have been determined. It has been shown that the quantitative regularities of the transition between the modes of the domain wall motion correspond to the concepts of the competition between the contributions of two mechanisms to the domain wall retardation (the periodic Peierls relief and random structural defects).     

Quasielastic neutron scattering of hydrated BaZr0.90A0.10O2.95 (A = Y and Sc)

Proton motions in hydrated proton conducting perovskites BaZr_0.90A_0.10O_2.95 (A = Y and Sc) have been investigated using quasielastic neutron scattering. The results reveal a localized motion on the ps time scale and with an activation energy of ~ 10–30 meV, in both materials. The temperature dependence of the total mean square displacement of the protons shows an onset of this motion at a temperature of about 300 K. The low activation energy, much lower than the activation energy for the macroscopic proton conductivity, suggests that this motion is not the rate-limiting process for the long-range proton diffusion, i.e. it is not linked to the two materials significantly different proton conductivities. In fact, a comparison of the QENS results with density functional theory calculations indicates that for both materials the observed motion may be ascribed to intra-octahedral proton transfers occurring close to a dopant atom.     

Analytical potential energy function for the ground state $$ (\tilde X^1 A_1 ) $$ of hydrogen isotopic D2O molecule

The present work is to construct the potential energy function of isotopic molecules. The so-called molecular potential energy function is the electronic energy function under Born-Oppenheimer approximation, in which the nuclear motions (translational, rotational and vibration motions) are not included, therefore, its nuclear vibration motion and isotopic effect need to be considered. Based on group theory and atomic and molecular reactive statics (AMRS), the reasonable dissociation limits of D₂O are determined, its equilibrium geometry and dissociation energy are calculated by density-functional theory (DFT) B3lyp, and then, using the many-body expansion method the potential energy function of D₂O is obtained for the first time. The potential contours are drawn, in which it is found that the reactive channel D + OD→D₂O has no threshold energy, so it is a free radical reaction. But the reactive channel O + DD→D₂O has a saddle point. The study of collision for D₂O is under way. Supported by the National Natural Science Foundation of China (Grant No. NSAF10676022)     

Surface vibrational excitations of O in the p(2 × 2)O and c(2 × 2)O structures on Ni(100)

Surface vibrational excitations of O chemisorbed on the clean Ni(100) surface have been investigated by high-resolution electron energy loss spectroscopy (EELS). The observed vibrational losses in the Ni(100) p(2 × 2)O and Ni(100) c(2 × 2)O surface structures are 53.0 ± 0.5 and 39.5 ± 0.5 meV respectively. The unexpectedly large change in the vibrational excitation energy is attributed to a low potential barrier for oxygen dissolution into the Ni substrate.     

Group theoretical treatment of the planar internal rotation problem in (HF)2

The HF dimer is believed to exhibit an internal rotation tunneling process between two planar but nonlinear equilibrium configurations, during which tunneling the roles of the hydrogen-bonded and the free hydrogen atom are interchanged. This process can be represented schematically with labeled atoms as H_lF_aH₂F_b ? F_aH_lF_bH₂, and gives rise to a permutation-inversion group G₄ containing four operations. In the present work the vibration-rotation-tunneling problem in (HF)₂ is treated group theoretically in three ways: (i) by allowing tunneling only through a trans planar C_2h intermediate, (ii) by allowing tunneling only through a cis planar C_2v intermediate, and (iii) by considering the trans and cis tunneling processes both to occur, though not necessarily with the same probability. The molecular symmetry groups used for these treatments are (i) the point group C_2h, (ii) the point group C_2v, and (iii) a double group, which might be thought of as $\text{G}{}_4{}^2\text{= C}{}_{\mathrm{2h}}{}^2\text{= C}{}_{\mathrm{2v}}{}^2$. Nonplanar tunneling paths are not considered, since the internal axis method (IAM) coordinate system used here cannot easily be adapted to nonplanar internal rotation motions in this molecule. Various-details of energy level diagrams, symmetry species for operators, selection rules for spectroscopic transitions, and statistical weights are presented for the (HF)₂ tunneling problem, as well as some speculation on the general question of when point groups, permutation-inversion groups, or double groups are preferable for treating large-amplitude vibrational motion problems.