Variational transition state theory with multidimensional tunnelling and kinetic isotope effects in the reactions of C2H6, C2H5D and C2D6 with .CCl3 to produce CHCl3 and CDCl3

ABSTRACT

Rate constants for the reactions of C₂H₆, C₂H₅D and C₂D₆ with .CCl₃. for the production of CHCl₃ and CDCl₃ (k₁, k₂, k₃ and k₄) were computed using variational transition state theory coupled with hybrid-meta density functional theory (MPWB1K) over the temperature range of 200–2900 K. The ground-state vibrational adiabatic potential was plotted for all channels. Small- and large-curvature tunnelling were determined to include quantum effects in the calculation of rate constants. Harmonic vibrational frequencies along the reaction path were calculated in curvilinear coordinates with scaled frequencies. Anharmonicity was included in the lowest-frequency torsion. The position of formation and dissociation of bonds was specified using the variation in harmonic vibrational frequencies along the reaction path. Representative tunnelling energy and the thermally averaged transmission probability at 298 K (P(E)exp?( ? ΔE/RT)) were determined for the reactions in which tunnelling is important. The kinetic isotope effect was used to calculate the considerable contributions of tunnelling and vibration. The expressions for rate constants were determined using nonlinear least-square fitting over the temperature range of 200–2900 K.     

Network topology and subgap resonances observed by Fourier transform scanning tunnelling microscopy of cuprate high-temperature superconductors

Fourier transform scanning tunnelling microscopy (STM) on Bi₂Sr₂CaCu₂O_{8+ δ} (BSCCO) subgap resonances has deciphered an octet of ‘quasiparticle’ states that are consistent with the Fermi surface and energy gap observed by angle-resolved photoemission spectroscopy (ARPES), but the origin of the high-intensity k-space octets and the sharply defined r-space chequerboard is unexplained. The filamentary ferroelastic nanodomain model that predicted the r-space chequerboard also explains the k-space octets and the origin of the apparent anisotropic surface d-wave gap by using strong electron–phonon interactions outside the CuO₂ planes. The topological model identifies the factors that stabilize high-intensity k-space octets in the presence of a very high level of irregular r-space chequerboard noise.     

Understanding the reaction between muonium atoms and hydrogen molecules: zero point energy,tunnelling, and vibrational adiabaticity

The advent of very precise measurements of rate coefficients in reactions of muonium (Mu), the lightest hydrogen isotope, with H₂ in its ground and first vibrational state and of kinetic isotope effects with respect to heavier isotopes has triggered a renewed interests in the field of muonic chemistry. The aim of the present article is to review the most recent results about the dynamics and mechanism of the reaction Mu+H₂ to shed light on the importance of quantum effects such as tunnelling, the preservation of the zero point energy, and the vibrational adiabaticity. In addition to accurate quantum mechanical (QM) calculations, quasiclassical trajectories (QCT) have been run in order to check the reliability of this method for this isotopic variant. It has been found that the reaction with H₂(v=0) is dominated by the high zero point energy (ZPE) of the products and that tunnelling is largely irrelevant. Accordingly, both QCT calculations that preserve the products’ ZPE as well as those based on the Ring Polymer Molecular Dynamics methodology can reproduce the QM rate coefficients. However, when the hydrogen molecule is vibrationally excited, QCT calculations fail completely in the prediction of the huge vibrational enhancement of the reactivity. This failure is attributed to tunnelling, which plays a decisive role breaking the vibrational adiabaticity when v=1. By means of the analysis of the results, it can be concluded that the tunnelling takes place through the ν₁=1 collinear barrier. Somehow, the tunnelling that is missing in the Mu+H₂(v=0) reaction is found in Mu+H₂(v=1).     

Rate coefficients and kinetic isotope effects of the abstraction reaction of H atoms from methylsilane

ABSTRACT

Thermal rate constants for chemical reactions using improved canonical variational transition state theory (ICVT) with small-curvature tunnelling (SCT) contributions in a temperature range 180–2000 K are reported. The general procedure is used with high-quality ab initio computations and semi-classical reaction probabilities along the minimum energy path (MEP). The approach is based on a vibrational adiabatic reaction path and is applied to the multiple-channel hydrogen abstraction reaction H + SiH₃CH₃ → products and its isotopically substituted variants. All the degrees of freedom are optimised and harmonic vibrational frequencies and zero-point energies are calculated at the MP2 level with the cc-pVTZ basis set. Single-point energies are calculated at a higher level of theory; CCSD(T)-F12a/VTZ-F12. ICVT/SCT rate constants show that the quantum tunnelling contributions at low temperatures are relatively important and the H-abstraction channel from SiH₃ group of SiH₃CH₃ is the major pathway. The total rate constants are given by the following expression: k_tot(ICVT/SCT) = 2.29 10^?18 T^2.42 exp(?350.9/T) cm³ molec^?1 s^?1. These calculated rates are in agreement with the available experiments. The ICVT/SCT method is further exploited to predict primary and secondary kinetic isotope effects, respectively).     

Non-steady-state tunnelling recombination in insulating solids,controlled by defect diffusion and rotation

Abstract

The experimental data for KCl—Ag, KBr, NaCl—Ag and KCl—SO₄ crystals as well as Na₂O.3SiO₂—Tb³⁺ glass are summarized which demonstrate the delayed increase (decrease) of the intensity of the thermally stimulated tunnelling recombination of radiation defects after step-wise defrosting (frosting) of their mobility. Both theory and experiment presented here allow to distinguish the cases when the recombination kinetics is controlled by the rotation of an anisotropic defects or their diffusion respectively. It can be achieved studying the non-steady-state stages of kinetics. The effect of relative spatial defect distribution upon the kinetics under study is considered; it is argued that the {F, V _k } recombination in KBr occurs within spatially correlated pairs.     

Nanoscopic filters as the origin of d-wave energy gaps

A ferroelastic nanoscopic chequerboard pattern of pseudogaps and superconductive gaps has been resolved by scanning tunnelling microscopy (STM) on Bi₂Sr₂CaCu₂O_{8+ δ} (BSCCO). Using this pattern, one can derive (not assume) a macroscopic anisotropic d-wave superconductive energy gap that agrees well with angle-resolved photoemission spectroscopy and Fourier transform scanning tunnelling microscopy data. The derivation is orbital only (no spins); it explains chemical trends in Raman scattering peak positions and strengths, and it predicts an unexpected reversal of anisotropic Raman gap signatures between BSCCO and La_{2? x} Sr _x CuO₄ (LSCO), in good agreement with experiment.     

Barrier parameters and superconducting gap structure of the etched surface of Y−Ba−Cu−O by scanning tunnelling spectroscopy

Summary Using a scanning tunnelling microscope, the tunnelling currentvs. voltage is measured between a gold tip and the chemically etched (001) surface of YBa₂Cu₃O _x crystals at room temperature. The tunnelling barrier height and thickness are derived by modelling the system in the normal state as a conventional N-I-N junction. TheI(V) andG(V) curves are computed for the same junction in the superconducting state (N-I-S junction). The predicted gap structure for a single BCS-Dynes-like gap is simple and has low zero-bias conductance. The complexG(V) spectra measured belowT _c on the etched junctions with ∼ 50% zero-bias conductance suggest a possible multilayer contribution in the unit cell. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Theory of the thermal magnetocapacitance of multicomponent silicate glasses at low temperature

An explanation is put forward for the early findings of Zeller and Pohl (, Phys. Rev. B, 4, 2029) and, in particular, Stephens (, Phys. Rev. B, 13, 852), and then for the more comprehensive recent findings of Meißner and Strehlow () for the anomalous magnetic-field-dependent behaviour of the heat capacity of some multicomponent glasses at low temperature (0.1?<?T?<?4?K) and in weak-to-moderate fields (0?<?B?<?8T). An essential new ingredient of this theory, together with the standard two-level system approach for cold glasses, is a multi-minima local potential for the quantum motion of metallic ions between near-degenerate wells, separated by relatively shallow barriers. Taking the tunneling entities as independent and assuming a novel probability distribution for the parameters of the multi-welled potential, an expression for the heat capacity C(T,B) is obtained with features that match rather well the reported unusual experimental data for the glasses. The indication coming from this theory for the data available is that the entities involved in tunnelling are nanoclusters of coherent ions.     

Interplay between hybridisation gaps and unusual magnetic orders in Kondo semiconductors CeT2Al10 (T = Ru and Os)

ABSTRACT

Kondo semiconductors based on rare-earth elements possess a narrow gap in the renormalised density of states near the Fermi level. Their ground states remain nonmagnetic due to strong hybridisation of the 4f state with conduction bands. However, in the orthorhombic compounds CeT₂Al₁₀ (T?=?Ru, Os), opening of a hybridisation gap is followed by an antiferromagnetic (AFM) order at a rather high temperature T_N???28?K. Our systematic studies of the effects of electron/hole doping on the magnetic and transport properties, electron tunnelling, and spin-gap formation revealed that the hybridisation gap is indispensable for the unusual AFM order. Under uniaxial pressure, T_N increases linearly as the orthorhombic b-axis parameter is decreased. Our findings support the model that a kind of charge-density wave developing along the b axis in the presence of the hybridisation gap induces the AFM order in these systems.     

Proton N.M.R. study of the dynamics of the ammonium ion in ferroelectric langbeinite, (NH4)2Cd2(SO4)3

The proton N.M.R. lineshape of polycrystalline Langbeinite, (NH₄)₂Cd₂(SO₄)₃, has been studied in the temperature range 300 K to 1·8 K. The resonance line is motionally narrowed over the entire temperature range, and the low temperature proton line shows clear evidence for tunnelling motion of the ammonium ion between spin-symmetry states. From a computer simulation of the lineshape, we obtain an estimate for the tunnelling splitting parameter, J, of the torsional ground state of the ammonium ion, as 375 ± 125 gauss. For an undistorted tetrahedral crystal field this corresponds to a tunnelling splitting Δ = 4J = 6·3 ± 2·1 MHz.

Pulsed proton N.M.R. studies have also been carried out on the above compound at 30·8 MHz and 48·2 MHz and the spin-lattice relaxation time (T ₁) has been measured by the π - t - π/2 pulse sequence as a function of temperature down to 77 K. At 30·8 MHz, a T ₁ minimum of 13 ms occurs at 105·8 K, and is ascribed to random reorientations of the NH₄ ⁺ ion. An activational energy barrier of 0·74 ± 0·1 kcal/mole and an associated pre-exponential factor of 8·0 × 10^-13 s are calculated for the above motional process, and the value of the activation energy is correlated with the tunnelling splitting of the torsional ground state.

An anomaly in T ₁ has been observed at the ferroelectric Curie point (95 K), indicating the order-disorder nature of the transition. This is the first experimental evidence relating to the nature of the transition in Langbeinite.     

Quantum dynamics study of isotope effects of the OD/OH + CH3 reactions

ABSTRACT

A six-degrees-of-freedom, time-dependent quantum dynamics calculation is employed to study the integral cross sections, full-dimensional cumulative reaction probabilities and full-dimensional rate constants for the isotopic reactions of the OD and OH with CH₃ reactions. The full-dimensional cumulative reaction probabilities and full-dimensional rate constants are obtained using the energy and J-K shifting approaches based on the six-degrees-of-freedom calculations. The comparison of integral cross sections shows that the OD?+?CH₃ reaction has a larger energy threshold and a smaller tunnelling effect than the OH?+?CH₃ reaction. The corrected rate constants using the experimental zero-point energy have a very good agreement with the experimental results. The comparison of the rate constants shows that the OD?+?CH₃ has smaller rate constants than the OH?+?CH₃ reaction, which indicates a smaller reactivity due to the isotope substitution.     

Tunnelling through randomly inhomogeneous barriers as a special problem of the scattering theory

The tunnelling of electrons through an inhomogeneous delta barrier is considered. The strength of the barrier is defined as a function oscillating around a constant mean value along a plane. Owing to deviations from this value, the tunnelling through such a delta barrier has to be interpreted as a scattering. A simple model is discussed when circular windows of a given radius b representing themselves delta barriers of a given strength γ₀ are embedded in a homogeneous delta barrier defined with another strength . When the centers of the windows are distributed randomly in the barrier plane, the potential energy of the electrons is a random function of two space coordinates. The perpendicular incidence is discussed with emphasis on the angular probability density of the tunnelled electrons. The derivation of the angular probability density proves that three basic quantum-mechanical phenomena can be described by one simple formula: tunnelling, diffraction and scattering.     

The role of the surface depression of the pair potential on the Josephson and quasi-particle tunnelling in high-T c superconductors

Summary We discuss the influence of the intrinsic surface depression of the order parameter on the temperature dependence of the Josephson critical currentI _c(T) and, tentatively, on the quasi-particle tunnelling conductance in a superconductor with a very short coherence length. The comparison with the experiments shows that the presence of a surface-depressed pair potential can explain the large deviations of theI _c(T) from the ideal BCS behaviour that we recently observed in Bi₂Sr₂CaCu₂O_8+x Josephson break junctions and could mimic the presence of a broadening in the Superconductor-Insulator-Normal tunnelling conductance of the same high-T _c superconductor. Paper presented at the ?VII Congresso SATT?, Torino, 4–7 October 1994.     

Improved Lower Bounds for the Critical Probability of Oriented Bond Percolation in Two Dimensions

We present a coupled decreasing sequence of random walks on Z that dominate the edge process of oriented bond percolation in two dimensions. Using the concept of random walk in a strip, we describe an algorithm that generates an increasing sequence of lower bounds that converges to the critical probability of oriented percolation p_c. From the 7th term on, these lower bounds improve upon 0.6298, the best rigorous lower bound at present, establishing 0.63328 as a rigorous lower bound for p_c. Finally, a Monte Carlo simulation technique is presented; the use thereof establishes 0.64450 as a non-rigorous five-digit-precision (lower) estimate for p_c. Mathematics Subject Classification (1991): 60K35 Supported by CNPq (grant N.301637/91-1). Supported by a grant from CNPq.     

Tunneling conductance in quantum wire/insulator/dx2 -y2 + idxy mixed wave superconductor junctions

Using the extended Blonder-Tinkham-Klapwijk (BTK) theory, this paper calculates the tunnelling conductance in quantum wire/insulator/dx2-y2 + idxy mixed wave superconductor (q/I/dx2-y2 + idxy) junctions. That is different from the case in d- and p-wave superconductor junctions. When the angle α between a-axis of the dx2-y2 wave superconductor and the interface normal is π/4, there follows a rather distinctive tunnelling conductance. The zero-bias conductance peak (ZBCP) may or may not appear in the tunnelling conductance. Both the interface potential z and the quasi-particle lifetime factor Γ are smaller, there is no ZBCP. Otherwise, the ZBCP will appear. The position of bias conductance peak (BCP) depends strongly on the amplitude ratio of two components for dx2-y2 + idxy mixed wave. The low and narrow ZBCP may coexist with the BCP in the tunnelling conductance. Using those features in the tunnelling conductance of q/I/dx2-y2 + idxy junctions, it can distinguish dx2-y2 + idxy mixed wave superconductor from d- and p-wave one.     

Josephson (001) tilt grain boundary junctions of high-temperature superconductors

We calculate the Josephson critical current I_c across in-plane (001) tilt grain boundary junctions of high-temperature superconductors. We solve for the electronic states corresponding to the electron-doped cuprates, two slightly different hole-doped cuprates, and an extremely underdoped hole-doped cuprate in each half-space, and weakly connect the two half-spaces by either specular or random Josephson tunnelling. We treat symmetric, straight, and fully asymmetric junctions with s-, extended-s, or d _{x ²?y ²} -wave order parameters. For symmetric junctions with random grain boundary tunnelling, our results are generally in agreement with the Sigrist–Rice form for ideal junctions that has been used to interpret ‘phase-sensitive’ experiments consisting of such in-plane grain boundary junctions. For specular grain boundary tunnelling across symmetric junctions, our results depend upon the Fermi surface topology, but are usually rather consistent with the random facet model of Tsuei et al. Our results for asymmetric junctions of electron-doped cuprates are in agreement with the Sigrist–Rice form. However, our results for asymmetric junctions of hole-doped cuprates show that the details of the Fermi surface topology and of the tunnelling processes are both very important, so that the ‘phase-sensitive’ experiments based upon in-plane Josephson junctions are less definitive than has generally been thought.     

Tunneling through a disordered potential barrier

Tunnelling through a weakly disordered potential barrier is studied analytically. A perturbative approach is developed to calculate all statistical moments of the tunnelling transmission coefficient, and its probability distribution function. It is shown that on average disorder enhances the tunnelling conductance, resistance, and the coherent component of the transmitted field.On leave from the Institute of Low-Temperature Physics and Engineering, Kharkov 310164, Ukraine.     

Block persistence

We define a block persistence probability p _l (t) as the probability that the order parameter integrated on a block of linear size l has never changed sign since the initial time in a phase-ordering process at finite temperature T<T _c . We argue that in the scaling limit of large blocks, where z is the growth exponent (), is the global (magnetization) persistence exponent and f(x) decays with the local (single spin) exponent for large x. This scaling is demonstrated at zero temperature for the diffusion equation and the large-n model, and generically it can be used to determine easily from simulations of coarsening models. We also argue that and the scaling function do not depend on temperature, leading to a definition of at finite temperature, whereas the local persistence probability decays exponentially due to thermal fluctuations. These ideas are applied to the study of persistence for conserved models. We illustrate our discussions by extensive numerical results. We also comment on the relation between this method and an alternative definition of at finite temperature recently introduced by Derrida [Phys. Rev. E 55, 3705 (1997)]. Received: 25 February 1998 / Revised: 24 July 1998 / Accepted: 27 July 1998     

Limiting Behavior of Eigenvectors of Large Wigner Matrices

A new form of empirical spectral distribution of a Wigner matrix W _n with weights specified by the eigenvectors is defined and it is then shown to converge with probability one to the semicircular law. Moreover, central limit theorem for linear spectral statistics defined by the eigenvectors and eigenvalues is also established under some moment conditions, which suggests that the eigenvector matrix of W _n is close to being Haar distributed.