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     

Electric field‐induced birefringence,optical rotatory power and conoscopic measurements of a chiral antiferroelectric smectic liquid crystal

Using a photoelastic modulator‐based novel set‐up, the electric field‐induced in‐plane birefringence and the optical rotatory power (ORP) were measured of an antiferroelectric liquid crystalline compound (12OF1M7) in its various phases using 30 µm homeotropic cells. Some specific signatures of the in‐plane birefringence and of the ORP for the various phases are being established. A relatively small threshold field is needed for the unwinding process of the antiferroelectric phase with a unit cell of four layers [SmC_A*(1/2)] compared with that for two layers [SmC_A*(0)]. On application of the electric field on the high temperature side of the SmC_A*(1/2) phase (80.1–81.5°C), a field‐induced phase transition is shown to occur directly to the SmC* phase, whereas on the lower temperature side (79.4–80.1°C) the transition takes place to SmC* via the SmC_A*(1/3) phase. The in‐plane birefringence exhibits a critical power law dependence for the SmC*–SmA transition. The ORP changes sign within the temperature range of the phase with a unit cell of three layers, reflecting a change in the handedness during this phase. Using tilted conoscopy, the results for the biaxiality and the apparent tilt angle for a smectic liquid crystal with a tilt angle greater than 18° in the ferroelectric phase are reported. The biaxiality implies the difference in the refractive indices between the two minor axes of the refractive index ellipsoid. The optical transmittance at visible and IR wavelengths for free‐standing films reveal characteristic reflection bands for these phases. The modulated structures of the reflected bands appear just above the SmC_A* phase and below SmC_A*(1/3); these are possibly due to an easy deformation of the phase by the surfaces.     

Photosensitivity,substituent and solvent-induced shifts in UV-visible absorption bands of naphthyl-ester liquid crystals: a comparative theoretical approach

The substituent- and solvent-induced shifts in UV-visible absorption bands of naphthyl-ester nematic liquid crystals, viz., 4-octylphenyl-6-octyloxy-2-naphthoate (NAPHE1) and 6-octyloxy-2-naphthylyl-4-octyloxybenzoate (NAPHE2), have been investigated using the DFT, CNDO/S and INDO/S methods. A correlation has been made between molecular charge distribution and phase stability based on Mulliken, Loewdin, AM1, PM3, MNDO, CNDO/S and INDO/S methods. The observed π→π* and n→π* electronic transitions have been reported. The substituent- and solvent-induced shifts in absorption bands, transition energies and energy gaps have been discussed. The photosensitivity of the molecules has been analysed based on these shifts. It has been observed that the substituent has a dominant role on both absorption maxima and energy band gap, whereas the solvent has a dominant role only on absorption maxima, and no effect has been observed on the energy gap. These shifts may provide beneficial consequences in determining the end use of compounds.     

Factorization method and new potentials from the inverted oscillator

In this article we will apply the first- and second-order supersymmetric quantum mechanics to obtain new exactly-solvable real potentials departing from the inverted oscillator potential. This system has some special properties; in particular, only very specific second-order transformations produce non-singular real potentials. It will be shown that these transformations turn out to be the so-called complex ones. Moreover, we will study the factorization method applied to the inverted oscillator and the algebraic structure of the new Hamiltonians.     

The extended Hulburt–Hirschfelder‐long‐range oscillator model for direct‐potential‐fit analysis

In the present work, an extended Hulburt–Hirschfelder oscillator model is proposed as a means of simplifying potential energy functions for direct‐potential‐fit analyses. The new potential energy function is joined smoothly to the long‐range inverse‐power dispersion energy expression. The new model is employed in direct‐potential‐fits using spectroscopic line positions that involve the ground electronic states of the principal isotopologues of hydrogen iodide and carbon monoxide, and the ground and first singlet‐sigma excited states of hydrogen fluoride and hydrogen chloride. The present methodology is found to lead to compact, flexible, and robust representations for the potential energy that compare favorably with the results of past work where more complicated models were employed.