Lanthanide induced shifts of aromatic 1,2,3-trimethoxy compounds: Conformational analysis of tetrahydrofurofuran-lignans in solution

Summary The solution conformations of 1,4-diaryl-tetrahydro-1H,3H-furo[3,4-c]furans were determined by means of the LIS technique using a modified LIS-simulation program specially designed for the requirements of the aromatic 1,2,3-trimethoxy arrangement as a bidentate coordination site for the NMR shift reagent. The resulting geometries were confirmed by force field calculations (MM2-87) and compared with X-ray derived structures. Reliable data for the conformations in solution allowed a quantitative estimation of the circular dichroism based on the coupled oscillator model.

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Lanthanideninduzierte Verschiebungen von aromatischen 1,2,3-Trimethoxy-Verbindungen: Konformationsanalyse von Tetrahydrofurofuran-Lignanen in Lösung

Zusammenfassung Es wurden mittels der LIS-Technik die Konformationen von 1,4-Diaryl-tetrahydro-1H,3H-furo[3,4-c]furanen in Lösung bestimmt. Dazu mußte ein modifiziertes LIS-Simulationsprogramm entworfen werden, das auf die besonderen Verhältnisse der aromatischen 1,2,3-Trimethoxy-Gruppierung eingeht, welche in den untersuchten Verbindungen als zweizähnige Koordinationsstelle für das NMR-Verschiebungsreagens fungiert. Die resultierenden Geometrien wurden mittels Kraftfeldrechnungen (MM2-87) überprüft und soweit vorhanden auch mit Röntgenstrukturdaten verglichen. Für die Lösungskonformationen wurde eine quantitative Abschätzung des Circulardichroismus auf der Basis des Modells für gekoppelte Oszillatoren durchgeführt.

     

Stochastic phase lockings in a relaxation oscillator forced by a periodic input with additive noise: A first-passage-time approach

Noise effects on phase lockings in a system consisting of a piecewise-linear van der Pol relaxation oscillator driven by a periodic input are studied. The problem of finding the period of the oscillator is reduced to the first-passage-time problem of the Ornstein-Uhlenbeck process with time-varying boundary. The probability density functions of the first-passage time are used to define the operator which governs a transition of an input phase density after one cycle of the oscillator. Phase lockings in a stochastic sense are investigated on the basis of the density evolution by the operator.     

The relative importance of temperature and isotope effects on the dipole oscillator strength distribution of H2

Summary The calculation of the effects of temperature and isotopic composition on the energy weighted moments of the dipole oscillator strength distribution of H₂ in the random phase approximation to the polarization propagator are reported. It is seen that the effect of isotopic composition is small, while that of temperature is of an order accessible to experiment. We find that all the mean excitation energiesI , for =–1, 0, 1, decrease with temperature as does the dipole oscillator strength momentS() for >0, while the opposite is true for <0. These effects are interpreted in terms of the bond length dependence of the excitation energies.     

Variation of the ℏω with the particle number and the appearance of “kinks” for atomic clusters

The dependence of the harmonic oscillator (HO) energy level spacing ?ω on the particle number N is studied analytically for atomic (metal) clusters on the basis of their electronic densities, parametrizing Ekardt's results (for sodium clusters) by means of a Fermi distribution. An interesting feature of such an approach is that it leads, under the assumptions made, to “kinks,” that is, to “marked discontinuities in the slope” of ?ω at the closed shells. These discontinuities diminish as N increases. For large N, ?ω becomes simply: ?ω?c₁N^?1/3+c₂N^?1. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Confined systems and the modified virial theorem from semiclassical considerations

We show that two simple semiclassical strategies, one based on the Wilson–Sommerfeld rule and the other on the uncertainty principle, yield the exact modified form of the virial theorem for confined systems. An alternative, easier quantum mechanical route to arrive at this result is also sketched. Pilot calculations on confined oscillators reveal decisive trends. © 2004 Wiley Periodicals, Inc. Int J Quantum Chem, 2005     

Brownian motion of nonlinear oscillators: The projection operator method and its application to a double-well-potential oscillator

A projection operator method is presented, which provides the most efficient way for calculating the stationary behavior of nonlinear Brownian motion. A continued-fraction expansion of the Fourier-Laplace transform of the displacement correlation function or the spectral density is used. This method utilizes a successive optimization procedure on the nonlinear terms and includes the method of statistical linearization as the lowest order approximation. A systematic way to calculate the continued fraction numerically up to sufficient order for convergence is developed, which enables us to obtain the spectral density of a system previously uncomputable.Numerical computations of the spectral density of a nonlinear oscillator with a double-well potential are presented and compared with the results obtained by statistical linearization.This work was supported in part by the National Science Foundation under Grant CHE 75-20624.     

Strong coupling expansion for classical statistical dynamics

We discuss the simple, randomly driven systemdx/dt = –x –x³ +f(t), wheref(t) is a Gaussian random function or stirring force with f(t)f(t) = (t – t). We show how to obtain approximately the coefficients of the expansion of the equal-time Green's functions as power series in (1/R)ⁿ, whereR is the internal Reynolds number ()^1/2/, by using a new expansion for the path integral representation of the generating functional for the correlation functions. Exploiting the fact that the action for the randomly driven system is related to that of a quantum mechanical anharmonic oscillator with Hamiltonianp ²/2 +m ² x ²/2 +vx ⁴ +x ⁶/2, we evaluate the path integral on a lattice by assuming that thex ⁶ term dominates the action. This gives an expansion of the lattice theory Green's functions as power series in 1/(a)^1/3, wherea is the lattice spacing. Using Padé approximants to extrapolate toa = 0, we obtain the desired large-Reynolds-number expansion of the two-point function.Supported financially by the National Science Foundation and the U.S. Department of Energy.     

Oscillatory reduction of bromate by aspirin in acidic aqueous solution

Summary The experimental behavior of the uncatalyzed Belousov - Zhabotinsky reaction between aspirin and bromate in acidic media in the batch reactor has been studied for the first time. Aspirin is an interesting substrate because it is one of the most used medicines. The medical aspirin behaves also in an oscillatory manner with bromate. The oscillating process was investigated under aerobic and anaerobic conditions. The complex dynamic behavior has been observed in the mixed aspirin - vitamin C - _BrO3 - H₂SO₄ system.     

Allowed transitions in silicon isoelectronic ions

Dipole‐allowed transitions have been studied for the first few members of the Si isoelectronic sequence. Transition energies, oscillator strengths, transition probabilities and quantum defect values have been estimated for the low‐ and high‐lying excited states of s and d symmetries up to the principal quantum number n=7 for these 3p open shell ions from P⁺ to Cr¹⁰⁺. Time‐dependent coupled Hartree–Fock (TDCHF) theory has been utilized to calculate such transition properties. Most of the results for transition energies, oscillator strengths, and transition probabilities for higher excited states are new. The transition energies for low‐lying excited states agree well with experimental data wherever available. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

One- and Two-Mode Combination Squeezing Operator for Two Harmonic Oscillators with Coordinate-Momentum Coupling

By virtue of the technique of integration within an ordered product of operators, we derive the normal ordering expansion of a one- and two-mode combination squeezing operator for two harmonic oscillators with coordinatemomentum coupling. It turns out that this squeezing operator just diagonalizes the Hamiltonian H = p21/2m1 m1ω21x21/2 p22/2m2 m2ω22x22/2 - λx2p1, so its ground state is a one- and two-mode combination squeezed state.Quantum fluctuation in the ground state is calculated.