A theoretical perspective of the nature of hydrogen-bond types – the atoms in molecules approach

Hydrogen bonds and their strength were analysed based on their X–H proton–donor bond properties and the parameters of the H–Y distance (Y proton acceptor). Strong, moderate and weak interactions in hydrogen-bond types were verified through the proton affinities of bases (PA), deprotanation enthalpies of acids (DPE) and the chemical shift (σ). The aromaticity and anti-aromaticity were analysed by means of the NICS (0) (nucleus-independent chemical shift), NICS (1) and ΔNICS (0), ΔNICS (1) of hydrogen-bonded molecules. The strength of a hydrogen bond depends on the capacity of hydrogen atom engrossing into the electronegative acceptor atom. The correlation between the above parameters and their relations were discussed through curve fitting. Bader's theory of atoms in molecules has been applied to estimate the occurrence of hydrogen bonds through eight criteria reported by Popelier et al. The lengths and potential energy shifts have been found to have a strong negative linear correlation, whereas the lengths and Laplacian shifts have a strong positive linear correlation. This study illustrates the common factors responsible for strong, moderate and weak interactions in hydrogen-bond types.     

The rate of molecular collisions in gases composed of ‘soft’ molecules

Equations are derived for the number of collisions per unit time in which the centres of the molecules approach to some arbitrary distance, d, or less, for molecules with spherical intermolecular potentials. The collision rates based upon this criterion of closeness-of-approach have a different dependence on temperature from those based upon cross sections determined from the viscosity. It is suggested that the rates calculated in this paper are the more appropriate for the discussion of experiments on the exchange of molecular energy and on the kinetics of chemical reactions.     

An Improved Experiment to Determine the ‘Past of a Particle’ in the Nested Mach-Zehnder Interferometer

We argue that the modification proposed by Li et al. [Chin. Phys. Lett. 32(2015) 050303] to the experiment of Danan et al. [Phys. Rev. Lett. 111(2013) 240402] does not test the past of the photon as characterized by local weak traces. Instead of answering the questions:(ⅰ) were the photons in A?(ⅱ) were the photons in B? and(ⅲ)were the photons in C? the proposed experiment measures a degenerate operator answering the questions:(ⅰ)were the photons in A? and(ⅱ) were the photons in B and C together? A negative answer to the last question does not tell us if photons were present in B or C. On the other hand, a simple variation of the proposal by Li et al. does provide conceptually better evidence for the past of the pre-and post-selected photon, but this evidence will be in agreement with the results of Danan et al.     

The super-heat-kernel expansion and the renormalization of the pion–nucleon interaction

A recently proposed super-heat-kernel technique is applied to heavy baryon chiral perturbation theory. A previous result for the one-loop divergences of the pion–nucleon system to is confirmed, giving at the same time an impressive demonstration of the efficiency of the new method. The cumbersome and tedious calculations of the conventional approach are now reduced to a few simple algebraic manipulations. The present computational scheme is not restricted to chiral perturbation theory, but can easily be applied or extended to any (in general non-renormalizable) theory with boson–fermion interactions. Received: 21 July 1998 / Published online: 5 October 1998     

‘Monte Carlo’ computer simulation of chain molecules III. Simulation of n-alkane molecules

Considering a realistic model for isolated n-alkane molecules, their configurational behaviour has been explored employing a ‘Monte Carlo’ method. The present study shows that the behaviour of the short molecules is unlike that of the longer molecules in regard to the variation with temperature of the mean-square end-to-end distance and radius of gyration. For the short molecules the mean-square end-to-end distance and the radius of gyration are decreasing functions of temperature, but they increase with temperature in the case of the longer molecules. The macromolecules assume random-walk behaviour at approximately 600 K. The computed heat capacity versus temperature curves disclose configurational transitions in the chains.     

Σ- atoms and the ΣN interaction

It is shown that among four models of the Nijmegen baryon-baryon interaction only model F --which leads to a repulsive potential felt by the Σ hyperon inside the nucleus-- is consistent both with the analysis of Σ^- atoms and of the (K ^-,π) reactions. The Nijmegen models are used to determine the strong complex single-particle (s.p.) potential of Σ^-, and to calculate the strong-interaction shifts and widths of the lowest observed levels of Σ^- atoms. The results obtained with model F are in best agreement with the experimental data. Received: 15 January 2002 / Accepted: 14 March 2002     

Atomic resonance behavior in laser-induced Rb atom desorption—the effect of ambient gas atoms and molecules

We report an observation that in a typical optical pumping cell containing Rb metal and 150 Torr N₂ gas, a cw laser beam of a few tens of mW and beam size 5.5 mm² can desorb Rb films on cell surfaces when the laser is tuned to the Rb D₁ line. The frequency dependence of the Rb desorption rate displays atomic resonance behavior. The desorption is suggested to be mediated by the ambient gas atoms (Rb) and molecules (N₂). The phenomenon was used to provide evidence for the existence of thin Rb films on seemingly clear cell surfaces.     

Improved ɛ expansion in the theory of turbulence: summation of nearest singularities by inclusion of an infrared irrelevant operator

A method is put forward to improve the ε expansion in the theory of developed d-dimensional turbulence on the basis of the renormalization of random forcing in the stochastic Navier-Stokes equation. This renormalization takes into account additional divergences, which appear as d →2. In the nth order of the perturbation theory with the extended renormalization the first n terms of the usual ε expansion are correctly reproduced as well as the first n terms of the Laurent expansion in the parameter d-2 of the terms of the rest of the usual ε expansion. The Kolmogorov constant and skewness factor calculated in the one-loop approximation of the improved perturbation theory are in reasonable agreement with their recommended experimental values.     

Direct observation of the optical anisotropy of C70 fullerene molecules in the Shpol’skii spectra

Linear optical absorption and emission spectra of C₇₀ fullerene molecules in single-crystal toluene are investigated. It is established that the lines of purely electronic S ₀-S ₁ transitions are significantly polarized. The degree of linear polarization of the spectral lines depends on the position of the fullerene molecule in the toluene matrix and can be as high as 100%. The polarization characteristics of the lines can be understood in the context of a model in which the S ₀ → S ₁ electronic transition is represented by the excitation of a planar oscillator whose axis is oriented along the principal axis of the C₇₀ molecule. The relationship between the polarization of the spectral lines and the position of the fullerene molecule in the matrix is consistent with the conclusions drawn from a theoretical analysis of different configurations possible upon the embedding of C₇₀ molecules into crystalline toluene.     

Nuclei in the vicinity of ‘island of inversion’ through the fusion reaction

The level structures of N ～ 19 nuclei such as ^32,34P have been investigated using the ¹⁸O(¹⁸O,xnyp) and ¹⁸O(¹⁶O,xnyp) reactions at an incident beam energy of about 34 MeV. The de-exciting γ-transitions were recorded using an array of clover detectors. These detectors have the dual advantage of higher efficiency at E _γ ≥ 2 MeV, and are capable of providing information on the linear polarization of the observed γ-transitions. These polarization measurements when coupled with the angular correlations help us to assign uniquely the spin parity for the observed levels. The experimental results have been compared with the predictions of the spherical shell model. The shell-model calculations are able to reproduce the observed energy levels to a reasonable degree. However, the observed transition probabilities are not reproduced by the calculations. Hence there is a need to re-visit these calculations using more detailed and microscopic effective interactions.     

Effect of strong interaction inpdμ-mesic molecules

It is shown that the inclusion of the exchange interaction between nuclei of a mesic molecule removes the degeneracy of the Coulomb levels and doubles the levels. For the ground state of thepd-molecular ion the splitting is estimated to amount to E10^–2 eV. Possible experiments for detection of this effect are discussed.     

Determination of the sites of Fe atoms in Fe-substituted Mn12

In this paper neutron diffraction experiments were performed for Fe-substituted Mn12 in order to determine the sites of Fe atoms. The results of structure refinements for the sample with our accessed highest Fe content showed that all Fe atoms occupied Mn（3） sites in the Mn12 skeleton. The x-ray absorption fine structure experiments as well as multiple scattering simulations gave the same result. Thus we concluded that Fe atoms only occupied Mn（3） sites. This conclusion also means that Fe-substituted Mn12 series only includes the four single-molecule magnets of [Mn12-xFexO12（CH3COO）16（H2O）4]·2CH3COOH·4H2O （x = 1, 2, 3, and 4）, denoted by Mn11Fe1, Mn10Fe2, MngFe3, and Mn8Fe4, respectively.     

Existence of Hartree–Fock excited states for atoms and molecules

For neutral and positively charged atoms and molecules, we prove the existence of infinitely many Hartree–Fock critical points below the first energy threshold (that is, the lowest energy of the same system with one electron removed). This is the equivalent, in Hartree–Fock theory, of the famous Zhislin–Sigalov theorem which states the existence of infinitely many eigenvalues below the bottom of the essential spectrum of the N-particle linear Schrödinger operator. Our result improves a theorem of Lions in 1987 who already constructed infinitely many Hartree–Fock critical points, but with much higher energy. Our main contribution is the proof that the Hartree–Fock functional satisfies the Palais–Smale property below the first energy threshold. We then use minimax methods in the N-particle space, instead of working in the one-particle space.     

Microscopic theory of dipole–dipole interaction in ensembles of impurity atoms in a Fabry–Perot cavity

We develop a consistent quantum theory of the collective effects that take place when electromagnetic radiation interacts with a dense ensemble of impurity centers embedded in a transparent dielectric and placed in a Fabry–Perot cavity. We have calculated the spontaneous decay dynamics of an excited impurity atom as a specific example of applying the developed general theory. We analyze the dependence of the decay rate on the density of impurity centers and the sample sizes as well as on the characteristic level shifts of impurity atoms caused by the internal fields of the dielectric. We show that a cavity can affect significantly the pattern of collective processes, in particular, the lifetimes of collective states.     

Dynamics of ‘quantumness’ measures in the decohering harmonic oscillator

We studied the behaviour under decoherence of four different measures of the distance between quantum states and classical states for the harmonic oscillator coupled to a linear Markovian bath. Three of these are relative measures, using different definitions of the distance between the given quantum states and the set of all classical states. The fourth measure is an absolute one, the negative volume of the Wigner function of the state. All four measures are found to agree, in general, with each other. When applied to the eigenstates |n〉, all four measures behave non-trivially as a function of time during dynamical decoherence. First, we find that the first set of classical states to which the set of eigenstate evolves is (by all measures used) closest to the initial set. That is, all the states decohere to classicality along the ‘shortest path’. Finding this closest classical set of states helps improve the behaviour of all the relative distance measures. Second, at each point in time before becoming classical, all measures have a state n^? with maximal quantum-classical distance; the value n^? decreases as a function of time. Finally, we explore the dynamics of these non-classicality measures for more general states.     

Investigation of the behaviour of the impurity atoms in Si by μ− SR-method

The dependence of the residual polarization of negative muons in p-type Si on temperature in the 4.2–270 K range has been investigated. Measurements were carried out in external magnetic field of 0.08 T transverse to the muon spin. The impurity concentration in the sample was 2 · 10¹³ cm^–3. Muon spin relaxation was observed at temperatures below 30 K. The relaxation rate atT=30 K is equal to 0.18±0.08s^–1. The relaxation rate grows with the decrease of temperature and at 4.2 K exceeds 30s^–1. The value of the residual polarization at zero timeP(t=0) is constant within the investigated temperature range.In the rangeT<30 K data on the relaxation rate are well described by the dependence =B·T^–q, whereq=2.75. Power dependence of may evidence the essential role of the phonon mechanism in the relaxation of the electron momentum of the acceptor center.The authors express their gratitude to V.B. Brudanin and I.A. Yutlandov for providing the sample, and to Yu.B. Gurov for advices.     

Effects of satellite positioning errors and Earth’s multipole moments in the detection of the gravitomagnetic field with an orbiting gravity gradiometer

The paper deals with a dynamical system analysis related to phantom cosmological model. Here gravity is coupled to phantom scalar field having scalar coupling function and a potential. The field equations are reduced to an autonomous dynamical system by a suitable redefinition of the basic variables and assuming some suitable form of the potential function. Finally, critical points are evaluated, their nature have been analyzed and corresponding cosmological scenario has been discussed.     

Measuring the ‘complexity’ of sound

Sounds in the natural environment form an important class of biologically relevant non-stationary signals. We propose a dynamic spectral measure to characterize the spectral dynamics of such non-stationary sound signals and classify them based on rate of change of spectral dynamics. We categorize sounds with slowly varying spectral dynamics as simple and those with rapidly changing spectral dynamics as complex. We propose rate of spectral dynamics as a possible scheme to categorize sounds in the environment.