Quantitative Measurement of Transverse and Longitudinal Cross-Correlation betweenC–H Dipolar Interaction andC Chemical Shift Anisotropy: Application to aC-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Conformational Equilibria in Polypeptides. I. Determination of AccurateJHCCoupling Constants in Antamanide by 2D NMR Multiplet Simulation

High-precision heteronuclear three-bond coupling constants including³J(H^N, C′),³J(H^N, C^β),³J(H^α,C^γ), and³J(H^β, C′) are determined for the nonproline residues in uniformly¹³C-enrichedantamanide,cyclo-(-Val¹-Pro²-Pro³-Ala⁴-Phe⁵-Phe⁶-Pro⁷-Pro⁸-Phe⁹- Phe¹⁰-), using quantitative numerical 2D NMR spectrum evaluation based on the product-operator formalism. The experimental basis comprises two-dimensional¹H,¹³C-heteronuclear relayed E.COSY spectra [J. M. Schmidt, R. R. Ernst, S. Aimoto, and M. Kainosho,J. Biomol. NMR6,95 (1995)], the multiplet patterns of which are subjected to iterative least-squares 2D multiplet-simulation procedures. Accuracy and precision of the spectrum fit are assessed byFstatistics and analysis of variances (ANOVA) leading to confidence intervals for the optimized spin-system parameters. The long-range J coupling constants obtained and their standard deviations provide the experimental foundation for a later detailed analysis of φ and χ₁dihedral-angle equilibrium conformations contributing to the flexible peptide structure.     

Nuclear spin–lattice relaxation and complex motion of macromolecules in solution

The NMR spectral densities of a complex motion consisting of a combination of anisotropic overall motion and internal motion have been derived. Two approximations of the equations derived for the cases of slow, J_slow (ω), and fast, J_fast (ω), internal motions are presented. These equations imply that reduction in spectral density of overall motion can be observed if the maxima of internal and overall motions spectral densities versus temperature are well separated, as for fast internal motion. Slow intramolecular motion influences the values of spectral densities of the overall motion if one of the two spins performs a motion, for example a proton in double minimum of the ¹⁵N-H?···?N hydrogen bond. The analysis presented reveals small differences between the temperature dependencies of spectral densities of the isotropic and anisotropic overall motions. The theory is illustrated by the ¹³C protonated carbon spin-lattice relaxation of α-cyclodextrin macromolecule, using the expected motional parameters: D _∥/D _⊥?≈?5 at room temperature and for a fast or slow internal motion.     

Site-specific ϕ- and ψ-torsion angle determination in a uniformly/extensively 13C- and 15N-labeled peptide

A solid-state rotational-echo double resonance (REDOR) NMR method was introduced to identify the ?- and ψ-torsion angle from a ¹H–¹⁵N or ¹H–¹³C′ spin system of alanine-like residues in a selectively, uniformly, or extensively ¹⁵N-/¹³C-labeled peptide. When a C_α(i) or a ¹⁵N peak is site-specifically obtainable in the NMR spectrum of a uniformly ¹⁵N/¹³C-labeled sample system, the ψ- or ?-torsion angle specified by the conformational structure of peptide geometry involving ¹⁵N(i)–¹H_αi–¹⁵N(i + 1) or ¹³C′(i − 1)–¹H^Ni–¹³C′(i) spin system can be identified based on ¹³C_α- or ¹⁵N-detected ¹H_α–¹⁵N or ¹H_N–¹³C REDOR experiment. This method will conveniently be utilized to identify major secondary motifs, such as α-helix, β-sheet, and β-turn, from a uniformly ¹⁵N-/¹³C-labled peptide sample system. When tested on a ¹³C-/¹⁵N-labeled model system of a three amino acid peptide Gly–[U–¹³C, ¹⁵N]Ala–[U–¹³C, ¹⁵N]Leu, the ψ-angle of alanine obtained experimentally, ψ = −40 ± 30°, agreed reasonably well with the X-ray determined angle, ψ = −39°.     

Quantitative Measurement of Transverse and Longitudinal Cross-Correlation between13C–1H Dipolar Interaction and13C Chemical Shift Anisotropy: Application to a13C-Labeled DNA Duplex

Measurement of both longitudinal and transverse relaxation interference (cross-correlation) between¹³C chemical shift anisotropy and¹³C–¹H dipolar interactions is described. The ratio of the transverse to longitudinal cross-correlation rates readily yields the ratio of spectral densitiesJ(0)/J(ω_C), independent of any structural attributes such as internuclear distance or chemical shift tensor. The spectral density at zero frequencyJ(0) is also independent of chemical exchange effects. With limited internal motions, the ratio also enables an accurate evaluation of the correlation time for overall molecular tumbling. Applicability of this approach to investigating dynamics has been demonstrated by measurements made at three temperatures using a DNA decamer duplex with purines randomly enriched to 15% in¹³C.     

Study on ethyl groups with two different orientations in [N(C2H5)4]2CuBr4

The crystal structure and phase transition temperature of [N(C₂H₅)₄]₂CuBr₄ are studied using X-ray diffraction and differential scanning calorimetry (DSC); measurements revealed a tetragonal structure and the two phase transition temperatures T_C of 204 K and 255.5 K. The structural geometry near T_C is discussed in terms of the chemical shifts for ¹H magic angle spinning (MAS) nuclear magnetic resonance (NMR) and ¹³C cross-polarization (CP)/MAS NMR. The two inequivalent ethyl groups are distinguishable by the ¹³C NMR spectrum. The molecular motions are discussed in terms of the spin–lattice relaxation times T_1ρ in the rotating frame for ¹H MAS NMR and ¹³C CP/MAS NMR. The T_1ρ results reveal that the ethyl groups undergo tumbling motion, and furthermore that the ethyl groups are highly mobile.     

Determination of Backbone Angle ψ in Proteins Using a TROSY-Based α/β-HN(CO)CA-J Experiment

Transverse relaxation-optimized NMR experiment (TROSY) for the measurement of three-bond scalar coupling constant between ¹H^α_i−1 and ¹⁵N_i defining the dihedral angle ψ is described. The triple-spin-state-selective experiment allows measurement of ³J_H^αN from ¹³C^α, ¹⁵N, and ¹H^N correlation spectra H₂O with minimum resonance overlap. Transverse relaxation of ¹³C^α spin is minimized by using spin-state-selective filtering and by acquiring a signal longer in ¹⁵N-dimension in a manner of semi-constant-time TROSY evolution. The ³J_H^αN values obtained with the proposed α/β-HN(CO)CA-J TROSY scheme are in good agreement with the values measured earlier from ubiquitin in D₂O using the HCACO[N] experiment.     

C-NOESY-HSQC with Split Carbon Evolution for Increased Resolution with Uniformly Labeled Proteins

Two new pulse sequences are presented for the recording of 2D¹³C-HSQC and 3D¹³C-NOESY-HSQC experiments, containing two consecutive carbon evolution periods. The two periods are separated by az-filter which creates a clean C_xH_z-quantum state for evolution in the second period. Each period is incremented (in anon-constant-time fashion) only to the extent that the defocusing of carbon inphase magnetization throughJ-coupling with neighboring carbons remains insignificant. Therefore,¹³C homonuclearJ-couplings are rendered ineffective, reducing the loss of signal and peak splitting commonly associated with long¹³C evolution times. The two periods are incremented according to a special acquisition protocol employing a¹³C–¹³C gradient echo to yield a data set analogous to one obtained by evolution over the added duration of both periods. The spectra recorded with the new technique on uniformly¹³C-labeled proteins at twice the evolution time of the standard¹³C-HSQC experiment display a nearly twofold enhancement of resolution in the carbon domain, while maintaining a good sensitivity even in the case of large proteins. Applied to the IIA^Manprotein ofE. coli(31 kDa), the¹³C-HSQC experiment recorded with a carbon evolution time of 2 × 8 ms showed a 36% decrease in linewidths compared to the standard¹³C-HSQC experiment, and theS/Nratio of representative cross-peaks was reduced to 40%. This reduction reflects mostly the typical loss of intensity observed when recording with an increased resolution. The¹³C-NOESY-HSQC experiment derived from the¹³C-HSQC experiment yielded additional NOE restraints between resonances which previously had been unresolved.     

A generalized edge of the wedge theorem

The edge of the wedge theorem is generalized to the case where one only assumes the existence and equality of the distribution boundary values off _±(z) and all their derivatives on some analytic curveC inR ⁿ . Heref _±(z) are holomorphic inR ⁿ ±iC, respectively, whereC is a convex cone, andC has its tangent vector inC at every point. Under these assumptions there exists an analytic continuationf(z) holomorphic in some complex neighbourhood of the double cone generated byC. A proof is also given of the connection between the existence of a distribution boundary value and the growth of the holomorphic function near the boundary.     

Torsional splitting and l-doubling in the ν9 R Q 0 infrared band of ethane

A high resolution diode laser absorption spectrum of the ν₉ ^R Q ₀ branch of C₂H₆ at 822 cm^-1 reveals a rotational progression with anomalous spacing and intensity, which is shown to be a result of both l-doubling and torsional splitting of rotational levels, both of which give rise to a J(J+1) energy dependence. From a contour analysis of the spectrum we estimate values for the l-doubling and torsional splitting parameters.     

The anisotropic 3D Ising model

An expression for the free energy of an (001) oriented domain wall of the anisotropic 3D Ising model is derived. The order--disorder transition takes place when the domain wall free energy vanishes. In the anisotropic limit, where two of the three exchange energies (e.g. J_x and J_y ) are small compared to the third exchange energy (J_z ), the following asymptotically exact equation for the critical temperature is derived, sinh(2J_z /k _B T _c)sinh(2(J_x ?+?J_y )/k _B T _c))?=?1. This expression is in perfect agreement with a mathematically rigorous result (k _B T _c/J_z ?=?2[ln(J_z /(J_x ?+?J_y ))?ln(ln(J_z /(J_x ?+?J_y ))?+?O(1)]^?1) derived earlier by Weng, Griffiths and Fisher (Phys. Rev. 162, 475 (1967)) using an approach that relies on a refinement of the Peierls argument. The constant that was left undetermined in the Weng et al. result is estimated to vary from ～0.84 at ((H_x ?+?H_y )/H_z )?=?10^?2 to ～0.76 at ((H_x ?+?H_y )/H_z )?=?10^?20.     

Line Shift Investigations for Different Isotopomers of Carbon Monoxide

Line shift coefficients for five lines of five different isotopomers in the fundamental band of CO in the spectral region near 2058 cm⁻¹were measured using a three channel lead salt diode laser spectrometer. The study includes the linesP(3) of¹³C¹⁷O,R(3) of¹³C¹⁸O,P(9) of¹²C¹⁸O,P(10) of¹³C¹⁶O, andP(21) of¹²C¹⁶O, and covers collisions with N₂, O₂, H₂, D₂, He, Ne, Ar, Kr, and Xe. Line shifts of the isotopomers¹³C¹⁶O,¹²C¹⁸O,¹³C¹⁸O, and¹³C¹⁷O were determined for the first time. Within the experimental uncertainty no significant dependence of the shift effect on the isotopomer was found. TheR-branch line under study shows a smaller line shift coefficient than aP-branch line with a similar rotational quantum number. With increasing mass of the noble gas perturber the absolute size of the shift coefficient increases. Moreover self- and nitrogen-broadening coefficients for the isotopomer lines were determined. Compared to previous measurements no significant deviations between different isotopomers were observed.     

Measurement of C2 and CH temperatures in argon‐acetylene low‐pressure microwave‐induced plasma

The emission spectra of C₂(d³Π_g–a³Π_u), CH(A²Δ–X²Π), and CH(B²Σ–X²Π) bands are analysed to measure rotational T_rot, vibrational T_vib, and gas temperature T_g from Ar/C₂H₂ (5–20% C₂H₂) microwave‐induced plasma (MIP). In case when helium and hydrogen are used in the gas mixture instead of argon, no significant change in T_rot is noticed. Both studied temperatures are insensitive in terms of the C₂H₂ percentage. From CH(0–0, A²Δ–X²Π) band R₂ branch lines, two T_rot (T_rot ～ 520–580 K for J′ = 3–9 and T_rot ～ 1,700–1,800 K for J′ = 10–17) are determined. The lower T_rot equals the T_g (500–700 K) measured from C₂ bands in this study. The H₂ Fulcher‐α diagonal bands are recorded as well in the H₂/C₂H₂ mixtures and T_rot～750–900 K of the H₂ ground state measured. T_vib ～ 6,000 K in Ar/C₂H₂ MIP is calculated from the integral intensity ratio of C₂(2,1) and C₂(3,2) bands.     

Generalized holographic and Ricci dark energy models

In this paper, we consider generalized holographic and Ricci dark energy models where the energy densities are given as ρ _R =3c ² M _pl² Rf(H ²/R) and ρ _h =3c ² M _pl² H ² g(R/H ²), respectively; here f(x), g(y) are positive defined functions of the dimensionless variables H ²/R or R/H ². It is interesting that holographic and Ricci dark energy densities are recovered or recovered interchangeably when the function f(x)=g(y)≡1 or f(x)=Id and g(y)=Id are taken, respectively (for example f(x),g(x)=1−ε(1−x), ε=0or1, respectively). Also, when f(x)≡xg(1/x) is taken, the Ricci and holographic dark energy models are equivalent to a generalized one. When the simple forms f(x)=1−ε(1−x) and g(y)=1−η(1−y) are taken as examples, by using current cosmic observational data, generalized dark energy models are considered. As expected, in these cases, the results show that they are equivalent (ε=1−η=1.312), and Ricci-like dark energy is more favored relative to the holographic one where the Hubble horizon was taken as an IR cut-off. And the suggested combination of holographic and Ricci dark energy components would be 1.312R−0.312H ², which is 2.312H²+1.312[(H)\dot]2.312H^{2}+1.312\dot{H} in terms of H ² and [(H)\dot]\dot{H} .     

Quantitative Investigation of Dipole–CSA Cross-Correlated Relaxation by ZQ/DQ Spectroscopy

A zero-quantum/double-quantum HNCO(H) constant time experiment is presented for the quantitative evaluation of dipole–CSA cross-correlated relaxation involving the¹H^N,¹⁵N, and¹³C′ nuclei of the peptide plane. A simple procedure that allows the extraction of cross-correlated relaxation rate constants from intensity ratios of well-resolved doublet components along ω₁is described. The experiment is demonstrated on fully¹³C,¹⁵N-labeled ubiquitin.     

The vibrational spectrum of thiazole between 600 and 1400 cm revisited: A combined high-resolution infrared and theoretical study

The Fourier transform infrared gas-phase spectrum of thiazole, C₃H₃NS, has been recorded in the 600-1400 cm⁻¹ wavenumber region with a resolution around 0.0030 cm⁻¹. Nine fundamental bands (ν₅(A′) to ν₁₁(A′), ν₁₅(A″), and ν₁₆(A″)) are analysed employing the Watson model. Ground-state rotational and quartic centrifugal distortion constants as well as upper state spectroscopic constants have been obtained from the fits. A detailed analysis of perturbations identified in the ν₁₁(A′) band at 866.5 cm⁻¹ enables a definitive location of the very weak ν₁₀(A′) and ν₁₄(A″) bands at 879.3 and 888.7 cm⁻¹, respectively. The three levels are analysed simultaneously by a model including Coriolis resonance using an ab initio predicted first order c-Coriolis coupling constant; second and higher order Coriolis parameters are determined. Qualitative explanations in terms of Coriolis resonances are given for a number of crossings observed in ν₅(A′), ν₆(A′), and ν₇(A′) at 1383.7, 1325.8, and 1240.5 cm⁻¹, respectively. The rotational constants, anharmonic frequencies, and vibration-rotation constants (alphas, ) calculated by quantum chemical calculations using a cc-pVTZ and TZ2P basis with B3LYP methodology, have been compared with the present experimental data. The rotation constant differences for each vibrational state, from the ground state values, are closer to experiment from the TZ2P calculations relative to those using cc-pVTZ. The values for Δ_J, Δ_JK, Δ_K, δ_J, and δ_K are close to experiment with both basis sets.     

Julia Sets in Parameter Spaces

Given a complex number λ of modulus 1, we show that the bifurcation locus of the one parameter family {f _b (z)=λz+b z ²+z ³} _{b ∈ ℂ} contains quasi-conformal copies of the quadratic Julia set J(λz+z ²). As a corollary, we show that when the Julia set J(λz+z ²) is not locally connected (for example when z↦λz+z ² has a Cremer point at 0), the bifurcation locus is not locally connected. To our knowledge, this is the first example of complex analytic parameter space of dimension 1, with connected but non-locally connected bifurcation locus. We also show that the set of complex numbers λ of modulus 1, for which at least one of the parameter rays has a non-trivial accumulation set, contains a dense G _δ subset of S ¹. Received: 22 September 2000 / Accepted: 16 January 2001     

C<Subscript>60</Subscript> fullerene as an η<Superscript>6</Superscript> ligand in π complexes of transition metals

The possible existence of complexes formed by the C₆₀ fullerene or its derivatives with transition metals interacting with the carbon cage via η⁶−π type bonding is discussed. The derivatives C₆₀ R ₆ of the C₆₀ fullerene (R = −, H, F, Cl, Br, CN) are analyzed using the density functional method within the Perdew-Burke-Ernzerhof approximation. In these molecules, the R groups are attached to carbon atoms located in the α positions with respect to the common hexagon of the C₆₀ fullerene. The structure and electron configuration of complexes formed by these molecules with Cr(C₆H₆), Cr(CO)₃, MoC₆H₆, and Mo(CO)₃ particles are modeled. The “dimer” systems C₆₀R₆-M-R ₆C₆₀ (M = Cr, Mo, R =-, H, F) are investigated in which two fullerene molecules interact via a transition-metal atom. It is found that the introduction of six R groups in the α sites with respect to the common hexagon of C₆₀ favors the formation of complexes of these derivatives of the C₆₀ fullerene with the Cr(C₆H₆), Cr(CO), Mo(C₆H₆), and Mo(CO)₃ particles in which η⁶-π type bonds arise between the metal and the atoms of the hexagon fringed with the R groups. It is also demonstrated that analogous complexes with a “bare” C₆₀ fullerene are possible, but they are significantly less stable. The (C₆H₆) M-R ₆C₆₀ R ₆-M (C₆H₆) complexes of particles M(C₆H₆) (M= Cr, Mo) and derivatives R ₆C₆₀ R ₆ (R =-, H, F, Cl, Br) are studied. In the R ₆C₆₀ R ₆ molecule, six R groups are located in the α sites with respect to the common hexagon of the C₆₀ fullerene and six other groups fringe the opposite hexagon. The obtained results can be applied to planning synthesis of new complexes that C₆₀ fullerene derivatives can form with transition metals. Original Russian Text ￠ E.G. Gal’pern, A.R. Sabirov, I.V. Stankevich, 2007, published in Fizika Tverdogo Tela, 2007, Vol. 49, No. 12, pp. 2220–2223.     

Observation by ICLAS VeCSEL technique, and rotational analysis, of the ΔvGeH=5 stretching vibrational overtone of H3GeD

The fourth GeH stretching overtone band of monoisotopic H₃⁷⁰GeD at 9877 cm⁻¹ has been recorded by ICLAS VeCSEL technique with a path length equivalent to 26 km. The (500 A₁/E) band has been observed and rotationally analyzed up to J^′=18. The band was shown to be essentially unperturbed except some high J states. The assigned transitions were fitted, with σ(Fit) ca. 6.5 × 10⁻³ cm⁻¹. While eight refined parameters were needed up to J^′_max=14, six quartic centrifugal distortion constants were refined in addition for the larger body of 829 data with J^′_max=18. The (500 A₁/E) parameters of H₃⁷⁰GeD perfectly fulfill the theoretical relations valid at the local mode limit, and they fit into the series for other (n00 A₁/E) levels (n=2, 3, 6, 7, and 8). A transition moment ratio M(A₁):M(E)=0.25 was found to be in best agreement with the observed spectrum, only high J (J^′?13) transitions being evidently sensitive to this ratio.     

Reduction of hysteresis loss and large magnetocaloric effects in substituted compounds of itinerant-electron metamagnets La(FexSi1−x)13

The maximum value of hysteresis loss E_h^MAX due to the itinerant-electron metamagnetic (IEM) transition of La(Fe_xSi_1−x)₁₃ and the partially substituted compounds La_1−zCe_z(Fe_0.86Si_0.14)₁₃ and La_1−z′Pr_z′(Fe_0.86Si_0.14)₁₃ increases when the magnetocaloric effects (MCEs) become large. It should be noted that the reduction of E_h^MAX without the decrease of large MCEs is achieved in La_1−zCe_z(Fe_0.86Si_0.14)₁₃ and La_1−z′Pr_z′(Fe_0.86Si_0.14)₁₃. For both the compound systems mentioned above, the critical temperature T₀ for the IEM transition decreases and the difference between T₀ and the Curie temperature T_C becomes larger with decreasing T_C. These results are consistent with the magnetic phase diagram of La(Fe_0.86Si_0.14)₁₃ under hydrostatic pressure. Consequently, the reduction of E_h^MAX in La_1−zCe_z(Fe_0.86Si_0.14)₁₃ and La_1−z′Pr_z′(Fe_0.86Si_0.14)₁₃ is closely related with the magnetovolume effects.