Raman study of ratational diffusion in methyl iodide

The usefulness of Raman and NMR spin relaxation spectroscopic methods in probing the details of molecular motions in liquids is demonstrated in a study of methyl iodide. Analysis of the lineshape of the ν₃ Raman band of methyl iodide as a function of temperature yields values of the perpendicular component D_⊥ of the diffusion tensor D_i and an activation energy of reorientation perpendicular to the C₃ axis of the molecule of 2.1 kcal/mole. Coupling the Raman data with ²D NMR spin relaxation data yields values of D_| and an activation energy for reorientation about the C₃ axis of 0.4 kcal/mole indicating quasi-free rotation for this motion. Thus the reorientational motions of methyl iodide are shown to be highly anisotropic in the liquid state.     

The Fokker-Planck-Langevin model for rotational brownian motion. IV. Asymmetric top molecules

The general series expansion for the joint angular velocity-orientation conditional probability density for a fluid composed of asymmetric top molecules is derived, and expressions for the reorientational correlation functions, correlation times, spectral densities, and the correlation times relevant to magnetic relaxation via spin-rotation interactions are presented. The reorientational correlation times and spin-rotation functions computed using this Fokker-Planck-Langevin (FPL) model with isotropic friction tensor (τ_x = τ_y = τ_z) are compared with the corresponding times and functions computed with the J-diffusion limit of the extended diffusion (EDJ) model. The models are found to predict significantly different behaviour only in the regime where free rotation and precessional effects become important. The reorientation self- and cross-correlation times are shown to follow Hubbard relations in the limit of short τ_x, τ_y, τ_z. Numerical calculations of the FPL reorientational correlation functions, correlation times and spin-rotation functions show that these properties are sensitive to the anisotropies in the friction tensor in the rotational Langevin equation.     

Nuclear quadrupole and magnetic resonance studies of structure and the molecular motion in SYMC6Cl3F3

³⁵Cl and ¹⁹F relaxation time measurements were carried out on symC₆Cl₃F₃. The analyses of the ¹⁹F high-resolution NMR spectra and the ³⁵Cl spin-lattice relaxation time showed that the crystal belongs to a trigonal or a hexagonal crystal system in which the molecules undergo three-fold reorientation about the molecular figure axis with the correlation time τ_c/s=3.42·10^?7 exp(18.2 kJ mol^?1/RT). Temperature dependences of the ³⁵Cl NQR frequency and ¹⁹F spin-lattice relaxation times are such that only a minor structural change is associated with the phase transition at 296 K.     

Computer simulation of brownian motion of a polyelectrolyte molecule (charged bead-spring model)

A Langevin equation of motion for a charged bead-spring statistical chain is written in difference form and the relaxation and equilibrium behavior of the chain is studied by computer simulation. Results are presented for the behavior of end-to-end length h, principal axes of the polymer ellipsoid L₁, L₂, L₃, and chain contour length c in terms of their averages, root mean square values, root mean square fluctuations, orientations, and relaxation strengths and times. The simulation was made with various sets of parameters, bead number N, charge on the bead q, and radius of ion atmosphere around the bead k^?1. It is found that 〈h²〉^1/2 and 〈L₁²〉^1/2 increase more strongly with increasing q and decreasing κ than 〈L₂²〉^1/2, 〈L₃²〉^1/2, and 〈c₁²〉^1/2, indicating that the chain is expanded in three dimensions and at the same time is extended along the end-to-end direction. The relaxation time τ_rot of rotation of the end-to-end vector, which is proportional to N² at q = 0, increases with increasing q and tends to be proportional to N³ for an extended chain, while the relaxation time τ_conf of the magnitude of h is almost independent of q and is always proportional to N². It is concluded that the extended chain possesses a well-defined end-to-end axis and the chain rotates as a whole with a relaxation time τ_rot which is much longer than τ_conf. The complex viscosity of the chain is calculated from the Fourier transform of the time–correlation function of momentum flux and is found to have a frequency spectrum similar to that observed for aqueous solutions of poly(acrylic acid). The dominant mode appearing in the low-frequency range is evidenced to arise from the rotation of the extended chain.     

Nuclear relaxation and molecular motion of 1,3,5-trifluorobenzene-d3 in liquid solutions

The ²D and ¹⁹F spin-lattice relaxation times of 1,3,5-trifluorobenzene-d₃ in 0.15 mol fraction solutions in various solvents have been measured over the temperature range 270–400 K. The relationship between the reorientational correlation times, τ_θ, and the angular momentum correlation times, τ_J, obtained from the nuclear relaxation data has been compared with the theoretical relationships predicted by the J-diffusion limit of the extended diffusion (EDJ) model and the Fokker-Planck-Langevin (FPL) model for symmetric top molecules. It was found that the rotational motion of 1,3,5-trifluorobenzene-d₃ in most solutions was better described by the FPL model with frictional anisotropy τ₆/τ_· in the range 1–2. (τ₆ and τ_· are the correlation times for the angular velocity components along the axes parallel and perpendicular to the molecular symmetry axis.) The viscosity and temperature dependence of τ_θ has been analyzed in terms of a modified Debye equation and values for the anisotropic interaction parameter, κ, in each solvent are reported. The variation in κ with solvent is attributed mainly to the variation in the dipole moment of the solvent molecules. The frictional anisotropy (τ₆/τ_·) is found to decrease as κ increases. This is interpreted in terms of the effects of molecular shape and electrostatic interactions between CF bond dipole moment and solvent dipole moments.     

Rotational correlation times of adenosine 5′-monophosphate in solution as deduced from 1H and 13C spin-lattice relaxation times

Rotational correlation times (τ_T) of the 5′-AMP molecule deduced from spin-lattice relaxation times (T₁) of different protons in the molecule agree fairly well with each other in the temperature range of 3.5–74°C. The same is true with τ_T values deduced from ¹³CT₁ values. These results indicate that the internal motions are slow as compared to the overall rotation of the 5′-AMP molecule.     

Temperature dependence of rotational correlation times in tribromobenzene

The ¹³C relaxation times and nuclear Overhauser enhancements of the protonated carbons in 1,3,5-tribromobenzene were measured as a function of temperature in the solvent benzene-d₆. Rotational correlation times, τ_C(CH), calculated by the Microviscosity/Free Rotor and Hu-Zwanzig “slip” models are substantially below the measured values. In contrast, correlation times predicted by the Hynes—Kapral—Weinberg model are in near quantitative agreement with experiment at all temperatures studied.     

Dynamic viscosity of dilute aqueous solutions of poly(acrylic acid) at frequencies of 2–500 kHz

The dynamic viscosity of aqueous solutions of poly(acrylic acid) at a polymer concentration of ca. 0.15 g/100 ml has been measured at frequencies from 2 to 500 kHz as a function of degree of polymerization P, degree of neutralization α, and salt (NaCl) concentration C_s. Relaxation spectra have been obtained from the dynamic viscosity. The spectra in the short relaxation time region can be approximated by the Zimm theory for the conformational relaxation of nonionic polymers. The maximum relaxation time τ₁ of the Zimm spectra is proportional to P² and depends rather moderately on α and C_s. Increased deviation is found, however, in the long relaxation time region, in particular for high values of P and α and low values of C_s. The major part of the deviation is interpreted in terms of rotational relaxation of a molecule as a whole. The rotational relaxation time τ_R is proportional to P³ and increases with increasing α and decreasing C_s. The remaining part of the excess spectra located between τ₁ and τ_R is ascribed to the deviation of the conformational relaxation from the Zimm theory arising from ionization of the polymer.     

Exponential gap relation and the rotational inelasticity of H2M systems

Previously published values of state-to-state integral inelastic cross sections for the H₂(J_i)—M (M  H, He, Li, Li⁺, H₂, CO₂) systems are fitted to the exponential gap relation for the rotational inelastic process to obtain the C value that reflects the magnitudes of relative cross sections. While the vibration of the rotor seems to have little influence, the C value is shown to decrease dramatically with increase in initial collision energy T_i, ΔC/ΔT_i being larger at lower T_i for all systems analysed, in accord with the prediction of the surprisal synthesis of Procaccia and Levine. For the only case of H₂(J_i)-Li⁺ for which results are available for several J_i, C decreases with increase in J_i or J_i(J_i + 1)). The C value predicted by Procaccia and Levine for H₂M systems falls within the range of C values calculated for the various collision partners. However, there is a noticeable change in C (albeit within a factor of two) with change in M, indicating that dynamical factors do play an important role in rotational inelastic processes.     

Synthese und reaktivität des diphenylacetyleniridium-komplexes C5H5Ir(C2Ph2)PPr3i und bildung einer isomeren iridainden-verbindung

trans-[IrCl(C₂R₂)(PPr₃ⁱ)₂] complexes are prepared from [(C₈H₁₄)₂IrCl]₂, PPr₃ⁱ and C₂R₂ (R = H, Me, Ph) via the intermediate [IrCl(PPr₃ⁱ)₂]. With phenylacetylene, a mixture of two isomers, trans-[IrCl(PhC₂H)(PPr₃ⁱ)₂] and IrHCl(C₂Ph)(PPr₃ⁱ)₂ is formed which reacts with pyridine to give IrHCl(C₂Ph)(py)(PP₃ⁱ)₂. Reaction of trans-[IrCl(C₂Ph₂)(PPr₃ⁱ)₂] with NaC₅H₅ yields the compound C₅H₅Ir(C₂Ph₂)PPr₃ⁱ (VI) which is transformed via the vinyl complex C₅H₅Ir(CPhCHPh)(OCOCF₃)PPr₃ⁱ (VII) into the iridaindene derivative IX. Using VII as the starting material, C₅H₅Ir(OCOCF₃)₂PPr₃ⁱ, C₅H₅Ir(CPhCHPh)(I)PPr₃ⁱ and C₅H₅Ir(CPhCHPh)(CH₃)PPr₃ⁱ are also obtained. Treatment of VI with Br₂ and I₂ respectively yields the complexes C₅H₅IrX₂PPr₃ⁱ) (XII, X = Br; XIII, X = I), of which XIII reacts with CH₃MgI to give C₅H₅Ir(CH₃)₂PPr₃ⁱ.     

An EPR line shape study of anisotropic rotational reorientation and slow tumbling in liquid and frozen jojoba oil

Spin probe investigation of jojoba oil was carried out by electron paramagnetic rresonance (EPR) spectroscopy. The spin probe used was 2,2,6,6-tetramethyl-4-piperidone-N-oxide. The EPR line shape studies were carried out in the lower temperature range of 192 to 275 K to test the applicability of the stochastic Liouville theory in the simulation of EPR line shapes where earlier relaxation theories do not apply. In an earlier study, this system was analysed by employing rotational diffusion at the fast-motional region. The results show that PD-Tempone exhibits asymmetric rotational diffusion with N = 3.3 at an axis z′= Y in the plane of the molecule and perpendicular to the NO bond direction. In this investigation we have extended the temperature range to lower temperatures and observed slow tumbling EPR spectra. It is shown that the stochastic Liouville method can be used to simulate all but two of the experimentally observed EPR spectra in the slow-motional region and details of the slow-motional line shape are sensitive to the anisotropy of rotation and showed good agreement for a moderate jump model. From the computer simulation of EPR line shapes it is found that the information obtained on τ_R, and N in the motional-narrowing region can be extrapolated into the slow-tumbling region. It is also found that ln (τ_R) is linear in 1/T in the temperature range studied and the resulting activation energy for rotation is 51 kJ/mol. The two EPR spectra at 240 and 231 K were found to exhibit the effects of anisotropic viscosity observed by Birell for nitroxides oriented in tubular cavities in inclusion crystals in which the molecule is free to rotate about the long axis but with its rotation hindered about the other two axes because of the cavity geometry. These results proved that the slow-tumbling spectra were very sensitive to the effects of anisotropy in the viscosity.     

Anisotropy of local relaxation properties of macromolecules. Spin-lattice relaxation of 13C nuclei,the nuclear overhauser effect and the estimation of parameters of an equivalent ellipsoid for kinetic segments of polymer chains

The expressions for the functions of spectral density at different orientations of the components of the internuclear vector with respect to the chain backbone, the frequency dependences of the spin-lattice relaxation time of ¹³C nuclei (T_1C) and the values of the nuclear Overhauser effect (NOE) were obtained for the tetrahedral lattice model of a polymer chain with three-unit kinetic elements. It was shown that peculiar features of the behavior of T_1C and NOE reflect the characteristic properties of the spectra of relaxation (correlation) times for “longitudinal” and “transverse” components of the internuclear vector. It was established that in the range of relatively short times of the relaxation spectrum the dynamics of an anisotropic kinetic segment of the chain may be described with the aid of a simple model of an elongated ellipsoid of rotation with an axial ratio of about 10. It is shown that the equivalent-ellipsoid model leads to significant differences from a more specific model of chain dynamics when a broad frequency range is considered.     

Molecular mobility of counterion functional groups in ionic liquid 1-ethyl-3-methylimidazolium acetate according to 1H and 13C NMR relaxation data

1-Ethyl-3-methylimidazolium acetate was studied by NMR relaxation. The temperature dependences of the spin-lattice relaxation rates (1/T ₁) for ¹H and ¹³C were obtained. The curves with maxima were observed for the majority of the temperature dependences 1/T ₁, which provided a reliable temperature dependence of the correlation times (τ_c). In the low-temperature range, the proton relaxation rates tend to an asymptotic value, which is related, most likely, to spin diffusion manifested in the studied samples. The values of correlation times τ_c calculated for ¹H and ¹³C of the same functional group almost coincide at high temperatures, which confirms that the used approach is adequate for the determination of characteristic times of rotational reorientation of counterions in the studied ionic liquid.     

INTRINSIC POLARIZATION AND ROTATIONAL DEPOLARIZATION OF FLUORESCENCE OF DNA BASES IN AQUEOUS SOLUTION AT ROOM TEMPERATURE*

Abstract— A counting procedure is described for determining the polarization characteristics of very weak emission. The degree of polarization of weak emission of DNA bases in aqueous solution at room temperature is found to he high and positive, and shows an inverse correlation with their emission quantum yields which can be understood in terms of a competition between emission lifetimes and rotational relaxation times. For 5-methylcytosine the emission quantum yield can be changed by varying the acidity and the corresponding degrees of polarization show the behavior expected from Perrin's relation. The ratio τ_o/τ_rot is discussed in terms of anisotropic relaxation and calculations of τ₀.     

Laser-induced-fluorescence study of A Na/Na2 free jet. II. State-dependent effective inelastic cross sections for rotational and vibrational relaxation

Laser-induced-fluorescence measurements along the jet axis are used to study the relaxation of Na₂ molecules in a Na/Na₂ expansion. From the fluorescence intensity, the evolution of the occupancies of several vibration—rotation levels of the Na₂ ground state is obtained. The whole relevant region along the jet axis is covered: from the equilibrium region close to the nozzle down to the downstream part of the jet, where the internal-state distribution is non-Boltzmann and “frozen”. The relaxation of Na₂ molecules is analysed using first-order relaxation equations. Vibrational and rotational relaxation are treated separately by means of similar equations but with different inelastic cross sections determining the relaxation rates. The evolution of the vibrational levels can be described by means of a single effective cross section of = 100 Ų; the rotational cross sections are strongly J-state dependent and range from = 250 to 15 Ų, for J = 13-55.     

Orientation dependence in collision induced electronic relaxation studied through van der Waals complexes with isomeric structures

Weakly bound molecular complexes with more than one well-defined structures provide us with an unique opportunity to investigate dynamic processes induced by intermolecular interactions with specific orientations. The relative orientation of the two interacting molecules or atoms is defined by the complex structure. The effect of the orientation in the spin changing collisions glyoxal(S₁)+Ar → glyoxal(T₁)+Ar and acetylene (S₁)+Ar → acetylene(T)+Ar have been studied by measuring the intersystem crossing (ISC) rates of the glyoxal(S₁)·Ar and acetylene(S₁)·Ar complexes with different isomeric structures. Results show that there is a strong orientation dependence in the ISC of glyoxal(S₁) induced by interaction with the Ar atom: the Ar atom positioned in the molecular plane is much more effective than in the out-of-plane position in inducing the S₁ → T₁ transition of glyoxal. On the other hand, studies of acetylene(S₁)·Ar complexes indicate that the Ar-induced ISC rates are nearly identical for the in-plane and out-of-plane positions. Orientation dependence in the collision induced vibrational relaxation process C₂H₂(S₁,v _i )+Ar → C₂H₂(S₁,v _f <v _i )+Ar is also studied by measuring the vibrational predissociation rates of the acetylene(S₁)·Ar complex isomers. The results indicate that collisions of C₂H₂(S₁,v ₃=3, 4) with Ar at two orthogonal orientations are equally effective in causing vibrational relaxation of C₂H₂.     

Investigation of the rotational dynamics in liquids by time-resolved cars

The asymptotic decay time τ_an of the anisotropic vibrational excitation in liquids has been measured for the first time in time-resolved CARS. The use of different polarization geometries also allows us to determine the orientational relaxation time τ_R. Experimental data are presented for totally symmetric modes of liquid CS₂ and CH₃I, where τ_R describes the “tumbling” motion of the symmetry axis.     

Effects of polymer chain disentanglement on NMR properties. II. 13C magnetic relaxation in polystyrene

The transverse magnetic relaxation of ¹³C_α nuclei has been studied in concentrated solutions of polystyrene. The magnetic relaxation rate was measured as a function of molecular weight at several temperatures (313,318, and 323 K) and at several concentrations (0.53, 0.43, and 0.34 g/cm³). The spin-system response of these nuclei in natural abundance exhibits a characteristic evolution from pseudosolid properties to liquidlike one, induced by decreasing the molecular weight of polymer molecules. This evolution is analogous to that already observed in protons attached to polyisobutylene or polydimethylsiloxane chains; it is assumed to be induced by an increase of the disentanglement rate of polymer chains. The spin-system response may be considered as reflecting single-chain magnetic properties, because of the low concentration of ¹³CC_α nuclei, although all chains are in dynamic interaction with one another. The NMR disentanglement transition is interpreted in terms of a two-step motional averaging effect involving submolecules. A numerical analysis of NMR properties is given using a model of polymer chain relaxation based on a multiple-mode relaxation process, characterized by (i)a terminal relaxation time τ^v₁ depending upon M³, the molecular weight, and approximately proportional to the polymer concentration C (like the reptation time); (ii)a relaxation-time spectrum analogous to a Rouse spectrum; (iii)a terminal relaxation time τ^v₁ = 2.5 × 10^?2s for M = 2.5 × 10⁵, C = 0.53 g/cm³ in carbon tetrachloride at 313 K.     

Hartree-Fock theory for negative ions

It is shown that HF computations which yield ?_i > 0 for an occupied MO do not minimize the HF energy. If ?_i > 0, which frequently occurs in the RHF treatment of negative ions, one can reduce ?_i to zero and simultaneously lower E_HF by an appropriate admixture of a continuum function to the corresponding MO ?. We propose a modification of the HF model that takes these facts into account. Applications to the systems O^2?, N^3?, C^4?, S^2?, O₂^2?, C₂^2? are reported and discussed.