A Rydberg-Bohr-de Broglie Algebraic Model of Hydrogen Atoms

Atomic scattering factors for electrons are strongly affected by the charge status of the scattering atoms. The difference in scattering factors for charged and neutral atoms is most pronounced in the resolution range below 5 A. As a result of the negative scattering factors of negatively charged atoms in the low-resolution range, charged glutamate or aspartate residues produce weaker densities in electron crystallographic maps than their neutral forms. Such charge effects were indeed observed in an experimental map of bacteriorhodopsin. Here we present mathematical simulations of this charge effect on electron crystallographic density maps that corroborate the experimental results. For the simulations, we first evaluated the errors introduced by approximating atomic scattering factors for neutral and charged atoms by Gaussians. The simulations then showed that the effect of a polarized pair of oxygen and hydrogen atoms on the density (polarization effect) was much smaller than that expected from the individual charged atoms (charge effect), due to charge compensation. Still, density maps obtained by electron crystallography are expected to show slightly elongated features toward the positively charged atoms.

Helge Kragh. <i>Niels Bohr and the Quantum Atom: The Bohr Model of Atomic Structures, 1913–1925</i>. vi + 410 pp., illus., figs., tables, bibl., index. Oxford: Oxford University Press, 2012. £18.99 (cloth).

Nondispersive wave packets in a fictitious time variable are calculated analytically for the field-free hydrogen atom. As is well known by means of the Kustaanheimo-Stiefel transformation the Coulomb problem can be converted into that of a four-dimensional harmonic oscillator, subject to a constraint. This regularization makes use of a fictitious time variable, but arbitrary Gaussian wave packets in that time variable in general violate that constraint. The set of "restricted Gaussian wave packets" consistent with the constraint is constructed and shown to provide a complete basis for the expansion of states in the original three-dimensional coordinate space. Using that expansion arbitrary localized Gaussian wave packets of the hydrogen atom can be propagated analytically, and exhibit a nondispersive periodic behavior as functions of the fictitious time. Restricted wave packets with and without well defined angular momentum quantum n umbers are constructed. They will be used as trial functions in time-dependent variational computations for the hydrogen atom in static external fields in the subsequent paper [T. Fab\v{c}i\v{c} et al., submitted].

A formula for the mass-energy and the decay of particles is obtained from a model of particles oscillating in the electromagnetic and in the weak fields. For some selected displacements of the particle, important results are obtained. From this formula it is suggested that particles acquire their masses while massless gauge bosons (W ± ) get their masses by Higgs mechanism. Mass-energies and decay of particles are obtained from the decay of a W ± boson coupled to the electromagnetic or the weak fields in which the particles oscillate . In the centre of mass (CM) frame, the spin of a particle is shown as localized circular motion of the centre of charge around the CM

Quantitative structure‐property relation ships (QSPR) were developed with the quantum semiempirical descriptors computed by AM1 Hamiltonian in MOPAC7.0 for phenylthio, phenylsulfinyl and phenylsulfonyl esters. Using step wise regression analysis with a cross‐validation procedure, the most potent and in formative descriptors were screened out from a group of 19 quantum chemical semi‐empirical descriptors, including steric and electronic types, to build QSPR models. Several equations were obtained and used to estimate and predict octanol/water partition coefficients and reversed phase high‐performance liquid chromatography (HPLC) capacity factors for a series of 30 similar sulfur‐containing compounds. The results indicate that molecular descriptors, including average molecular polarizability (α), energy of the lowest unoccupied molecular orbital (ELUMO), net atomic charge on carbon atoms in the carbonyl (QCO), molecular weight (MW), the most positive atomic charge on hydrogen atom (QH+), and net atomic charge on oxygen atoms in the group‐NO2 (QNQ2) are the main factors affecting the octanol/water partition coefficients of the compounds under study. And quantum descriptors, covering the most negative atomic charge on an atom Q−), net atomic charge on carbon atoms in the carboxy (QCOO), molecular weight (MW), heat of formation (HF), the most positive atomic charge on a hydrogen atom (QH+), and total energy (TE), are the main factors affecting HPLC capacity factors of these compounds. Rational mechanisms for the two physico‐chemical proper ties of the sulfur‐containing carboxylates were discussed and interpreted.

Numerical study of models of quantum chaos

The AppA BLUF (blue light sensing using FAD) domain from Rhodobacter sphaeroides serves as a blue light-sensing photoreceptor. The charge separation process between Tyr-21 and flavin plays an important role in the light signaling state by transforming the dark state conformation to the light state one. By solving the linearized Poisson-Boltzmann equation, I calculated E(m) for Tyr-21, flavin, and redox-active Trp-104 and revealed the electron transfer (ET) driving energy. Rotation of the Gln-63 side chain that converts protein conformation from the dark state to the light state is responsible for the decrease of 150 mV in E(m) for Tyr-21, leading to the significantly larger ET driving energy in the light state conformation. The pK(a) values of protonation for flavin anions are essentially the same in both dark and light state crystal structures. In contrast to the ET via Tyr-21, formation of the W state results in generation of only the dark state conformation (even if the initial conformation is in the light state); this could explain why Trp-104-mediated ET deactivates the light-sensing yield and why the activity of W104A mutant is similar to that of the light-adapted native BLUF.

Estimation of gas-phase reaction rate constants of alkylnaphthalenes with chlorine, hydroxyl and nitrate radicals

Atomic charge distribution in 4-isopropylphenol molecule derived from atomic polar tensors

(H(2)O)(17), a cluster with pentagonal water arrangements, squeezed in the sodalite cage of the crystal structure MIL-74 (Zn(6)Al(12)P(24)O(96).[N(CH(2)CH(2)NH(3))(3)](8).(H(2)O)(34)), has its oxygen atoms well located by X-ray powder diffraction. Positioning of hydrogen atoms has been performed by a dynamic partial atomic charges and hardnesses analysis calculation, in which partial charges are recalculated for each hydrogen sub-network modification. Hydrogen atoms are therefore positioned by energy minimization. A quantitative estimation of the hydrogen bonds energy for each H-bond and for the network in the MIL-74 nanoporous compound has been obtained. This result allows a discussion of the effect of imprinting the nanoporous structure onto water or alternatively the templating effect of the cluster onto the inorganic framework.

This paper begins with an examination of the revival structure and long-term evolution of Rydberg wave packets for hydrogen. We show that after the initial cycle of collapse and fractional or full revival, which occurs on the time scale ${\mathit{t}}_{\mathrm{rev}}$, a new sequence of revivals begins. We find that the structure of the new revivals is different from that of the fractional revivals. The new revivals are characterized by periodicities in the motion of the wave packet with periods that are fractions of the revival time scale ${\mathit{t}}_{\mathrm{rev}}$. These long-term periodicities result in the autocorrelation function at times greater than ${\mathit{t}}_{\mathrm{rev}}$ having a self-similar resemblance to its structure for times less than ${\mathit{t}}_{\mathrm{rev}}$. The new sequence of revivals culminates with the formation of a single wave packet that more closely resembles the initial wave packet than does the full revival at time ${\mathit{t}}_{\mathrm{rev}}$, i.e., a superrevival forms. Explicit examples of the superrevival structure for both circular and radial wave packets are given. We then study wave packets in alkali-metal atoms, which are typically used in experiments. The behavior of these packets is affected by the presence of quantum defects that modify the hydrogenic revival time scales and periodicities. Their behavior can be treated analytically using supersymmetry-based quantum-defect theory. We illustrate our results for alkali-metal atoms with explicit examples of the revival structure for radial wave packets in rubidium.

Light emitted from atoms during transitions of electrons from higher to lower discrete states has the form of photons carrying energy and angular momentum. This paper considers the process of emission of a single photon from the hydrogen atom by using quantum theory and Maxwell's equations [W. Gough, Eur. J. Phys. 17, 208, 1996; L. D. Landau and E. M. Lifshitz, Quantum Mechanics (Pergamon Press, Oxford, 1965); J. D. Jackson, Classical Electrodynamics (John Wiley &amp; Son, New York, 1975, 1982); P. M. Morse and H. Feshbach, Methods of Theoretical Physics (McGraw-Hill Book Company, Inc., New York, 1953)]. The electric and magnetic fields of a photon arise from the time-dependent quantum probability densities of the orbit and the spin current. This paper is an extension of the semiclassical description of photon emission published by the author earlier in 1999 [M. Kowalski, Phys. Essays 12, 312 (1999)]. In the semiclassical approach, the Coulomb force and a radiation resistance force have been taken into account to get time-dependent emission of the photon. In both the quantum and semiclassical cases, the transition takes place within a time interval equal to one period of the photon's wave. The creation of a one-wavelength-long photon is supported by the results of experiments using ultrafast (ultrashort) laser pulses to generate excited atoms, which emit light pulses shorter than two photon wavelengths [F. Krausz and M. Ivanov, Rev. Mod. Phys. 81, 163 (2009); H. Kapteyn and M. Murnane, Phys. World 12, 31 (1999)].

We study the time propagation of an initially localized wave packet for a generic one-dimensional time-independent system, using the {open_quote}{open_quote}nonlinear wave-packet dynamics{close_quote}{close_quote} [S. Tomsovic and E. J. Heller, Phys. Rev. Lett. {bold 67}, 664 (1991)], a semiclassical approximation using a local linearization of the wave packet in the vicinity of classical reference trajectories. Several reference trajectories are needed to describe the behavior of the full wave packet. The introduction of action-angle variables allows us to obtain a simple analytic expression for the autocorrelation function, and to show that a universal behavior (quantum collapses, quantum revivals, etc.) is obtained via interferences between the reference trajectories. A connection with the standard WKB approach is established. Finally, we apply the nonlinear wave-packet dynamics to the case of the hydrogen atom in a weak magnetic field, and show that the semiclassical expressions obtained by nonlinear wave-packet dynamics are extremely accurate. {copyright} {ital 1996 The American Physical Society.}

The electronic charge redistribution and the infrared intensities of the two types of intramolecular hydrogen bonds, O-H···O and O-H···π, of o-hydroxy- and o-ethynylphenol, respectively, together with a set of related intermolecular hydrogen bond complexes are described in terms of atomic charges and charge fluxes derived from atomic polar tensors calculated at the B3LYP/cc-pVTZ level of theory. The polarizable continuum model shows that both the atomic charges and charge fluxes are strongly dependent on solvent. It is shown that their values for the OH bond in an intramolecular hydrogen bond are not much different from those for the "free" OH bond, but the changes are toward the values found for an intermolecular hydrogen bond. The intermolecular hydrogen bond is characterized not only by the decreased atomic charge but also by the enlarged charge flux term of the same sign producing thus an enormous increase in IR intensity. The overall behavior of the charges and fluxes of the hydrogen atom in OH and ≡CH bonds agree well with the observed spectroscopic characteristics of inter- and intramolecular hydrogen bonding. The main reason for the differences between the two types of the hydrogen bond lies in the molecular structure because favorable linear proton donor-acceptor arrangement is not possible to achieve within a small molecule. The calculated intensities (in vacuo and in polarizable continuum) are only in qualitative agreement with the measured data.

The atomic polar tensors (APT) of the fluorine and hydrogen atoms for the fluoromethanes are calculated and analyzed with respect to the charge, charge flux, and atomic and homopolar dipole fluxes. Their atomic and bonding contribution are used to discuss the transference of the fluorine and hydrogen APT among these molecules. The contributions of the APT can be written as the sum of a charge and a charge flux tensor leading to a charge-charge flux model. A novel expressive for the atomic charge is obtained on the basis of this proposed charge-charge flux model. The defined atomic charge a calculated for both atoms for this series of molecules. The calculated hydrogen atomic charges vary similarly to the respective equilibrium charges obtained experimentally but in the opposite direction of the Mulliken charges. 15 refs., 1 fig., 8 tabs.