Неэмпирический анализ изотопических сдвигов и резонансных эффектов в инфракрасном спектре высокого разрешения фреона-22 (CHF-=SUB=-2-=/SUB=-Cl), обогащенного -=SUP=-13-=/SUP=-C

The IR transmittance spectrum of an isotopic mixture of chlorodifluoromethane (CHF2Cl, Freon-22) with a 33% fraction of 13C and a natural ratio of chlorine isotopes was measured in the frequency range 1400-740 cm–1 with a resolution of 0.001 cm–1 at a temperature of 20C. An ab initio calculation of the structure and sextic potential energy surface and surfaces of the components of the dipole moment has been carried out by the the electronic quantum-mechanical method of Möller-Plesset, MP2/cc-pVTZ. Then the potential was optimized by replacing the harmonic frequencies with the frequencies calculated by the electronic method of coupled clusters, CCSD(T)/aug-cc-pVQZ. The fundamental and combination frequencies were calculated using the operator perturbation theory of Van Vleck (CVPTn) of the second and fourth order (n=2,4). Resonance effects were modeled using an additional variational calculation in the basis up to fourfold VCI excitation (4). The average prediction error for the fundamental frequencies of the 12C isotopologues was ~1.5 cm–1. The achieved accuracy made it possible to reliably predict the isotopic frequency shifts of the 13C isotopologues. It is shown that the strong Fermi resonance ν4/2ν6 dominates in the 12C isotopologues and is practically absent in 13C. The literature assumption [Spectrochim. Acta A, 44: 553] about the splitting of ν1 (CH) due to the resonance ν1/ν2+ν7+ν9 is confirmed. The coefficients of the polyadic quantum number are determined. The analysis made it possible to carry out a preliminary identification of the centers of the vibrational-rotational bands of isotopologues 13CHF235Cl и 13CHF237Cl in the spectrum of the mixture in preparation for individual analyzes of the vibrational-rotational structures of individual vibrational transitions.

Bimodal 1H Double Quantum Build-Up Curves by Fourier and Laplace-like Transforms on Aged Cross-Linked Natural Rubber

The 1H DQ Fourier and Laplace-like spectra for a series of cross-linked natural rubber (NR) samples naturally aged during six years are presented and characterized. The DQ build-up curves of these samples present two peaks which cannot be described by classical functions. The DQ Fourier spectra can be obtained after a numeric procedure which introduces a correction time which depends less on the chosen approximation, spin-½ and isolated CH2 and CH3 functional groups. The DQ Fourier spectra are well described by the distributions of the residual dipolar coupling correlated with the distribution of the end-to-end vector of the polymer network, and with the second and fourth van Vleck moments. The deconvolution of DQ Fourier spectra with a sum of four Gaussian variates show that the center and the width of Gaussian functions increase linearly with the increase in the cross-link density. The Laplace-like spectra for the natural aged NR DQ build-up curves are presented. The centers of four Gaussian distributions obtained via both methods are consistent. The differences between the Fourier and Laplace-like spectra consist mainly of the spectral resolution in the favor of Laplace-like spectra. The last one was used to discuss the effect of natural aging for cross-linked NR.

Travelling Waves for Adaptive Grid Discretizations of Reaction Diffusion Systems I: Well-Posedness

In this paper we consider a spatial discretization scheme with an adaptive grid for the Nagumo PDE. In particular, we consider a commonly used time dependent moving mesh method that aims to equidistribute the arclength of the solution under consideration. We assume that the discrete analogue of this equidistribution is strictly enforced, which allows us to reduce the effective dynamics to a scalar non-local problem with infinite range interactions. We show that this reduced problem is well-posed and obtain useful estimates on the resulting nonlinearities. In the sequel papers (Hupkes and Van Vleck in Travelling waves for adaptive grid discretizations of reaction diffusion systems II: linear theory; Travelling waves for adaptive grid discretizations of reaction diffusion systems III: nonlinear theory) we use these estimates to show that travelling waves persist under these adaptive spatial discretizations.

In Quest of Molecular Materials for Quantum Cellular Automata: Exploration of the Double Exchange in the Two-Mode Vibronic Model of a Dimeric Mixed Valence Cell

In this article, we apply the two-mode vibronic model to the study of the dimeric molecular mixed-valence cell for quantum cellular automata. As such, we consider a multielectron mixed valence binuclear - type cluster, in which the double exchange, as well as the Heisenberg-Dirac-Van Vleck exchange interactions are operative, and also the local (“breathing”) and intercenter vibrational modes are taken into account. The calculations of spin-vibronic energy spectra and the “cell-cell”-response function are carried out using quantum-mechanical two-mode vibronic approach based on the numerical solution of the dynamic vibronic problem. The obtained results demonstrate a possibility of combining the function of molecular QCA with that of spin switching in one electronic device and are expected to be useful from the point of view of the rational design of such multifunctional molecular electronic devices.

Travelling Waves for Adaptive Grid Discretizations of Reaction Diffusion Systems II: Linear Theory

In this paper we consider an adaptive spatial discretization scheme for the Nagumo PDE. The scheme is a commonly used spatial mesh adaptation method based on equidistributing the arclength of the solution under consideration. We assume that this equidistribution is strictly enforced, which leads to the non-local problem with infinite range interactions that we derived in Hupkes and Van Vleck (J Dyn Differ Equ 28:955, 2016). For small spatial grid-sizes, we establish some useful Fredholm properties for the operator that arises after linearizing our system around the travelling wave solutions to the original Nagumo PDE. In particular, we perform a singular perturbation argument to lift these properties from the natural limiting operator. This limiting operator is a spatially stretched and twisted version of the standard second order differential operator that is associated to the PDE waves.

Making Waves

Sixteen-year-old Phil Anderson does not fit in well with the prep school boys at Harvard, but he finds a congenial study group (including future historian of science Thomas Kuhn) and does well academically. The beginning of World War II causes him to change his major to Electronic Physics. His class graduates in three years so they can contribute to the war effort. Anderson does his service as a radar (microwave) engineer at the Naval Research Laboratory where he learns quantum mechanics, learns he is probably not suited for experimental work, and grows up socially. John Van Vleck visits NRL and helps convince Anderson to return to Harvard for graduate school.

Hidden Moments

This chapter traces Anderson’s work from his invention of an impurity model to understand the fate of a magnetic atom immersed in a non-magnetic metal to his solution of the Kondo problem using an early version of the renormalization group invented by him and later generalized by Ken Wilson. Important events on this path are the experimental impetus provided by Bernd Matthias, the Coulomb repulsion model of insulating behavior due to Nevill Mott, and Jacques Friedel’s ideas about treating atoms embedded in metals. Speculation is offered about the award of the 1977 Nobel Prize to Anderson, Mott, and Van Vleck.

Law in Disorder

A formal request by the theorists produces a stand-alone Solid-State Theory Group at Bell Labs. A summer visitor program leads several visiting theorists to conclude that localization occurred in Feher’s samples due to an electrostatic mechanism suggested by Nevill Mott. Anderson develops a theory for localization where the disorder in the positions of the dopants plays a crucial role. Mott champions Anderson’s theory and the Nobel Committee cites it when Anderson wins a share of the 1977 Nobel Prize with Mott and John Van Vleck. David Thouless re-ignites Anderson’s interest in localization and he leads the Gang of Four to develop a novel scaling theory of localization.

A Solid Beginning

Anderson chooses a job at Washington State College over a boring-sounding job at Westinghouse. Van Vleck intervenes to arrange an interview with William Shockley at Bell Telephone Laboratories. Anderson declines Washington and accepts a job offer from Shockley in 1949. A short history of Bell Labs follows, including the creation of a Solid-State Physics group after the war to, among other things, seek a replacement for vacuum tubes. A short description of solid-state physics follows. The team of Shockley, John Bardeen, and William Brattain invent the transistor and Shockley alienates everyone. Shockley tells Anderson to work on ferroelectric materials. Anderson dislikes the work but is personally impressed by Shockley as a physicist.