Determination Of Molecular Parameters Research Articles

Dipolar relaxation revisited: A complete derivation for the two spin case

Relaxation theory often forms the basis of various studies, like MRI contrast agents and ionic liquids, which require the understanding of the molecular dynamics or determination of molecular parameters (such as correlation times) or both. Such studies compare the explicit expressions of the relaxation times T1 and T2, derived many years ago by quantum physicists, with their experimental findings to understand various aspects of the molecular motion. However, because of the complicated terminology and widely scattered information, the task of understanding or re‐deriving the relaxation theory for even the simplest cases becomes challenging for many students and researchers new to this field. In this article, the dipolar relaxation theory for the basic, yet practical case of a two spin system is presented with a detailed description of the concepts behind it. Aiming at a beginner level and making only modest assumptions on prior knowledge, we have discussed the basics of the quantum mechanics, spherical harmonics, stochastic processes and perturbation theories. It is hoped that this article will enable the reader to understand the general framework of the relaxation theory and will be beneficial in comprehending the relaxation in more complex systems as well, which is not discussed here. © 2015 Wiley Periodicals, Inc. Concepts Magn Reson Part A 44A: 74–113, 2015.

Determination of Molecular Parameters by Fitting Sedimentation Data to Finite-Element Solutions of the Lamm Equation

A method for fitting experimental sedimentation velocity data to finite-element solutions of various models based on the Lamm equation is presented. The method provides initial parameter estimates and guides the user in choosing an appropriate model for the analysis by preprocessing the data with the G( s) method by van Holde and Weischet. For a mixture of multiple solutes in a sample, the method returns the concentrations, the sedimentation ( s) and diffusion coefficients ( D), and thus the molecular weights (MW) for all solutes, provided the partial specific volumes ( v ¯ ) are known. For nonideal samples displaying concentration-dependent solution behavior, concentration dependency parameters for s( σ) and D( δ) can be determined. The finite-element solution of the Lamm equation used for this study provides a numerical solution to the differential equation, and does not require empirically adjusted correction terms or any assumptions such as infinitely long cells. Consequently, experimental data from samples that neither clear the meniscus nor exhibit clearly defined plateau absorbances, as well as data from approach-to-equilibrium experiments, can be analyzed with this method with enhanced accuracy when compared to other available methods. The nonlinear least-squares fitting process was accomplished by the use of an adapted version of the “Doesn’t Use Derivatives” nonlinear least-squares fitting routine. The effectiveness of the approach is illustrated with experimental data obtained from protein and DNA samples. Where applicable, results are compared to methods utilizing analytical solutions of approximated Lamm equations.

Rotational Spectroscopy of the CoH Radical in Its Ground 3Φ State by Far-Infrared Laser Magnetic Resonance: Determination of Molecular Parameters

Five rotational transitions of CoH in its ground 3Φ state have been detected by far-infrared laser magnetic resonance, three in the lowest Ω = 4 component and two in the Ω = 3 component. All the Zeeman transitions show an octet hyperfine pattern due to the 59Co nucleus ( I = 7/2). The much smaller proton doubling was also resolved for most transitions. The data have been fitted to experimental accuracy by an effective Hamiltonian for a molecule in an isolated 3Φ state. The electron orbital and spin g factors determined by the data confirm conclusively that the ground state of CoH is a 3Φ state. The accurate measurement of the rotational constant allows the equilibrium bond length to be determined: r e = 0.15138435(80) nm. A small Λ-type doubling was resolved in the 3Φ 3 component, suggesting the proximity of a 3Σ state among the low-lying electronic states. The cobalt hyperfine splittings have been fitted to determine magnetic dipole and electric quadrupole parameters, which are interpreted in terms of the dominant configuration description for the 3Φ ground state.

Optical ? radio-frequency double resonance spectroscopy with quantum beat detection

A new method is presented for the detection and manipulation of magnetic sublevel coherences in excited molecular states. A radio-frequency field induces coherences between a set of molecular levels which were excited by a short optical pulse. The time evolution of the coherences is directly monitored in the modulated fluorescence decay by quantum beat detection. The system can be brought into particular superposition states with radio-frequency pulses of selected lengths and amplitudes. The method is demonstrated for a Zeeman splitJ=1 state in the electronically excited3A2 triplet of the12CS2 molecule. The interpretation and analysis of the experimental results based on the theoretical description have been further elucidated and corroborated by computer simulations. The presented method extends the quantum beat technique and is applicable for labelling of transitions and determination of molecular parameters in complex level structures such as hyperfine structures.

ℓ-Resonance effects in the νv5, 2ν5←ν5, and ν4 + ν5←ν4 bands of C2H2 and 13C12CH2 near 13.7 μm

Abstract An extension to the previous LSCD (lower state combination difference) determination of molecular parameters involving acetylene's ν 5 fundamental and the strongest one quantum hotbands, 2ν 5 ←ν 5 and ν 4 + ν 5 ←ν 4 [ J. Molec. Spectrosc. 146 , 389 (1991)] has been made. A novel iterative numerical diagonalization procedure was employed to fit the vibrational states involved in the seven one quantum hotbands. This method utilizes the Hellmann—Feynman theorem to calculate first derivatives and singular value decomposition (SVD) in its least-square procedure and permits the simultaneous evaluation of the effective dipole moment responsible for the l-type resonance effect upon IR intensities. A set of molecular parameters describing the rotation—vibration levels of the ground state, ν 5 , ν 4 , 2ν 5 and ν 4 + ν 5 for the major isotope and for 13 C 12 CH 2 are reported based upon FT-spectrometric data taken at the McMath Solar Telescope Observatory. The improved spectroscopic parameters retrieved from this investigation will serve as a database for modelling abundances of acetylene in various astrophysical sources.

Reduction of high-resolution spectroscopic data

Two stages of reduction of high-resolution spectroscopic data are examined: determination of line parameters (positions, intensities) and determination of molecular parameters. Illustrative results obtained recently on vibrational–rotational spectra of tetrahedral molecules are presented. Reliable estimates of the line parameters are obtained by a method of profile fitting, which is improved by introduction of appropriate theoretical constraints (based on covariance calculations).

Modern aspects of measurement technique for excited state spectroscopy

The paper deals with some special kinds of measurement technique useful for the determination of molecular parameters in higher excited energy states. This technique was developed for special purposes of spectroscopy but is very convenient to solve many other problems connected with ultrafast phenomena in physics and technology.

Study on the conformations in poly(p-chlorostyrene)-endothermic solvent (n-propylbenzene) and poly(p-chlorostyrene)-exothermic solvent(tert-butyl acetate) at theta temperatures by X-ray small-angle scattering

Conformations of linear poly(p-chlorostyrene) (PPCS) in an endothermic solvent (n-propylbenzene) and an exothermic solvent (tert-butyl acetate) at theta temperatures have been investigated by X-ray small angle scattering. By analyzing X-ray small-angle scattering data for the two systems, the determination of molecular parameters and the comparison between an angular dependence of experimental scattering curve and that of theoretical one have been made, with the discussion on the asymptotic behavior of the scattering curve.

On the structure and properties of vinyl polymers and their models. IX. The determination of molecular parameters of polyvinyl chloride by sedimentation analysis

On the structure and properties of vinyl polymers and their models. IX. The determination of molecular parameters of polyvinyl chloride by sedimentation analysis

Calculation of the vapour pressure ratio of Ne, A, Kr, and Xe isotopes in the solid state

In order to discuss the validity of the anharmonic Einstein model developed byHenkel, the vapour pressure ratio of neon isotopes is recalculated, following Johns’s method, by making use of a Lennard-Jones (6–12) potential and of different couples of parametersɛ andσ. Results are compared with the recent experimental data byRoth andBigeleisen. The dependence of lnpm/pM from temperature is found to be scarcely sensitive to the choice of molecular parameters and is in good agreement with experimental results. As to the absolute values of lnpm/pM at any given temperature one does not find as good an agreement as claimed byJohns. It is shown how the uncertainty in the determination of molecular parameters cannot explain the whole disagreement between experiments and theory. Calculations for argon are carried on in the same scheme. Results are lower than preliminary experimental results byBoato andScoles. A brief discussion is given to suggest why difference in vapour pressure between two separated isotopes could be slightly different from the same quantity deduced by measuring the fractionation factor of an isotopic mixture. A possible influence of the isotopic composition of an isotopic solid mixture on the fractionation factor is also pointed out. Finally the lnpm/pM for krypton and xenon is calculated by means of the quantum theorem of corresponding states.

Light scattering by linear macromolecules oriented in laminar flow. II. Determination of the main gyration radii

AbstractIn laminar flow, polymer molecules are deformed and oriented. The effect is generally observed by investigating the resulting streaming birefringence. From the measurement of the magnitude of the effect, not only the optical anisotropy of the monomer unit, and its dependence on the solvent, but also the uncoiling of the linear macromolecule in the flow can be determined. From the extinction angle, information about the size and flexibility of the coil can be obtained. Since evaluation of the experimental data depends on the special model and on the statistics of the chain elements, an independent check is highly desireble. Light scattering yields such additional information on the size and shape of the deformed macromolecule, information which is less influenced by the special assumptions of the individual models. The pertinent scattering functions are calculated for the freely draining Gaussian coil and for the optically isotropic monomer unit, which in turn allows the determination of molecular parameters i.e., of the main gyration radii from the measurement of the angular dependence of the scattered light.