Effects of strong coupling in homonuclear correlation spectroscopy

A calculation of the complex signals in homonuclear correlation spectra (HOMCOR) of strongly coupled ABX three-spin systems is presented. It is shown that the presence of strong coupling causes the behavior of the cross-peaks to differ significantly from that found in the case of weak coupling. Two classes of connectivity patterns, namely weak and strong connectivity pairs of transitions are distinguished. Closed expressions for the real amplitudes are given. The dependence of the real amplitude on the flip angle of the mixing pulse and on the coupling strength is analyzed.     

Fast and accurate algorithm for the simulation of NMR spectra of large spin systems

The computational cost for the simulation of NMR spectra grows exponentially with the number of nuclei. Today, the memory available to store the Hamiltonian limits the size of the system that can be studied. Modern computers enable to tackle systems containing up to 13 spins [1], which obviously does not allow to study most molecules of interest in research. This issue can be addressed by identifying groups of spins or fragments that are not or only weakly interacting together, i.e., that only share weakly coupled spin pairs. Such a fragmentation is only permitted in the weak coupling regime, i.e., when the coupling interaction is weak compared to the difference in chemical shift of the coupled spins. Here, we propose a procedure that removes weak coupling interactions in order to split the spin system efficiently and to correct a posteriori for the effect of the neglected couplings. This approach yields accurate spectra when the adequate interactions are removed, i.e., between spins only involved in weak coupling interactions, but fails otherwise. As a result, the computational time for the simulation of 1D spectra grows linearly with the size of the spin system.     

描述自旋体系密度算符演化的新方法

提出一种描述自旋体系密度算符演化的新方法,可统一处理核磁共振波谱学中强、弱偶合自旋体系及弱射频场存在下密度算符的演化。具体分析一些核磁共振实验:自旋轻扰、自旋锁定、偶极耦合作用、强耦合AB和ABX自旋体系的演化。     

超材料谐振子间的电耦合谐振理论与实验研究

通过将两个金属开口环谐振器口对口地放置, 实现了超材料谐振子间的电耦合谐振. 对电耦合谐振的微波等效电路进行了理论分析和数值计算, 结果表明耦合后的超材料谐振子能产生两个谐振频率, 其中一个随耦合强度的增加逐渐向低频方向移动, 而另一个固定在单谐振子的谐振频率处不变. 微波透射谱的实验测试和电磁仿真结果表明, 两个谐振峰随耦合强度的增加分别向低频和高频方向移动. 分析表明: 低频谐振峰的位置主要是由超材料谐振子间的电耦合强度决定的; 高频谐振偏离单谐振子的谐振频率主要是由不可避免的磁耦合引起的, 而且在耦合间距越小时磁耦合影响越大. 提出的基于超材料谐振子间的电磁耦合实现的双频谐振及其可调性极大地增加了超材料的设计与应用空间.     

关于核磁共振中ABX体系的各种跃迁与体系耦合常数符号之间的关系

本文用ABC体系理论分析了ABX体系各特定跃迁的位置与强度,弄清它们与耦合常数之大小及其符号的一般变化规律,从而沟通了实测谱图与能级关联图、能级简图及耦合常数符号之间的关系.提出了只对体系作出初略强度分析以及通过双共振方法可容易地判断体系的耦合常数的相对符号的方法.     

Analysis of longitudinal multispin orders in strongly coupled spin systems

Longitudinal multispin orders provide an effective way for measurement of scalar couplings and also to probe molecular interactions and dynamics. Analysis of longitudinal orders has been made in strongly coupled AB and ABX spin systems to determine the dependence of strong coupling parameter on these orders. Experimental and simulated spectra of various longitudinal orders are illustrated for these spin systems. This general procedure can be extended to broad range of spin systems to understand the influence of strong coupling on longitudinal orders.     

The relative signs of N.M.R. spin coupling constants from double irradiation experiments

The method of double irradiation in high resolution proton magnetic resonance has been used to confirm that the spin coupling constant between the methyl group and the proton in the cis position in both trans-crotonaldehyde and trans-crotonic acid differs in sign from the other coupling constants. Since this is a particularly searching test of the double irradiation method, it is suggested that relative signs of coupling constants could be determined in this way for most molecules containing three coupled hydrogen nuclei provided that the chemical shifts are large compared with the coupling constants.     

High resolution hydrogen resonance spectra of some substituted ethylenes

The olefinic proton resonance spectra of a number of mono- and 1, 2 di-substituted ethylenes have been analysed as AB, ABC or ABX systems to obtain the coupling constants and chemical shifts. The values of J _trans (range observed 13·7 to 18·0 c/s in 14 compounds) were significantly larger than J _cis in similar molecules. The values of J _cis (range observed 6·5 to 12·3 c/s in 8 compounds) are abnormally large when the olefinic bond is conjugated to an aromatic ring. Coupling between adjacent protons in an olefinic methylene group (J _gem) is much smaller, and sometimes negative. The shielding of the lone vinyl proton in mono-substituted ethylenes is smaller than that of the methylene group and in two cases (the vinyl group directly bonded to an oxygen atom) the difference is so great as to give an approximation to the ABX condition, so that the methylene protons appear to be shielded to an unusually large extent.     

Proton magnetic resonance of non-planar condensed benzenoid hydrocarbons

The spectra of the title compounds have been analysed iteratively by computer, and chemical shifts and coupling constants have been determined at infinite dilution (or very low concentration) in carbon tetrachloride. The ortho coupling constants are compared with an empirical equation. The effect of concentration on chemical shifts is qualitatively related to inter-molecular ‘ring current’ effects. The chemical shifts at infinite dilution are to be compared with a new theory in the next paper [7].     

Synchronization transition of limit-cycle system with homogeneous phase shifts

The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated when phase shifts are considered. In the system of coupled oscillators, phase shifts are the same between different oscillators. Synchronization and synchronization transition are revealed with different phase shifts. Phase shifts play an important role for this kind of system. When the phase shift α<0.5π, the synchronization state can be attained by increasing the coupling, and the system cannot reach the synchronization state while α≥q0.5π. A clear scaling between complete synchronization critical coupling strength K_pc and α-0.5π is found.     

Chemisorption and surfaces studied by nuclear magnetic resonance spectroscopy

This paper presents an introduction to the study of surfaces and chemically adsorbed species with nuclear magnetic resonance (NMR) spectroscopy. The analysis is based on nuclear magnetic interactions in the solid state: dipole-dipole couplings, chemical shift anisotropy, Knight shifts, and quadrupolar splitting. The physical origins and characteristics of each interaction, as well as relative intensities for different nuclei, are discussed. In particular, emphasis is placed on the relation of these interactions to quantities of interest to studies in adsorption and catalysis: motional properties of the adsorbate, the distribution of adsorption sites, the chemical state of atoms adsorbed at the surface, electrostatic field gradients, and the metallic character of surface atoms. Techniques to observe these interactions are described; subdivided by the type of nucleus: strongly coupled nuclei (e.g. ¹H, ¹⁹F), weakly coupled nuclei (e.g. ¹³C, ¹⁵N, ²⁹Si, ¹⁹⁵Pt), and quadrupolar nuclei (e.g. ²H, ¹⁴N, ²⁷Al). The techniques described to isolate and identify the overlapping effects in the spectra include multiple-pulse spin echoing and decoupling, double-resonance irradiation, multiple-quantum excitation, and mechanical sample spinning. A review of the recent application of these techniques to studies of adsorption and surfaces illustrates the potentials and limitations. Finally, a procedure for formulating a NMR study of surface samples is proposed, with respect to sample composition and character, and the type of information desired.     

Quantum key distribution with multi letter alphabets

We present a new protocol for continuous variable quantum key distribution (CV QKD). The novelty of the protocol is a multi letter alphabet represented by coherent states of light with a fixed amplitude and variable phase. Information is encoded in the phase of a coherent state which can be chosen from a regular discrete set consisting, however, of an arbitrary number of letters. We evaluate the security of the protocol against the beam splitting attack. As a result we show the proposed protocol has advantages over the standard two letter coherent state QKD protocol, especially in the case when losses in the communication channel are low.     

Determination of signs of hyperfine coupling constants for an S = ½ system through E.P.R., ENDOR and double ENDOR

A systematic method of obtaining relative signs of hyperfine coupling constants is described. It applies to systems consisting of (a) a set of one or more nuclei coupled fairly strongly to the electron spin, and possessing a two-fold (or higher) axis of symmetry, together with (b) a set of weakly coupled nuclei defining superhyperfine transitions. ENDOR measurements for several E.P.R. hyperfine transitions, with the field oriented along the symmetry axis, give relative signs of hyperfine components for this direction. Signs for the other directions can then be obtained through ENDOR measurements on a single hyperfine transition at various field orientations. Additional double ENDOR measurements may be necessary for very weakly coupled nuclei. This method can complement double ENDOR studies in favourable cases. It is illustrated by the determination of signs of coupling constants of protons and of ⁷⁵As in the AsO₄ ^4- radical in KH₂AsO₄.     

Unusual "AB" Spectra in High-Resolution Magic-Angle-Spinning NMR-Studies of Solids

Phosphorus-31CP-MAS spectra of Cd(NO₃)₂(PPh₃)₂ have been obtained as a function of spinning frequency. Although the two ³¹P nuclei are crystallographically equivalent and have the same isotropic chemical shifts in the solid state, they exhibit spinning-rate-dependent MAS spectra which have been analyzed to obtain the value of ²J(P, P). At high spinning rates, the spectra are analogous to "A₂" spectra in isotropic solutions, while at slower spinning rates, the spectra are more characteristic of strongly coupled "AB" solution spectra. The AB spectra are unusual in that δ_A = δ_B and J(A, B) is given by the splitting between the alternate peaks in the four-peak multiplet as opposed to the splitting between the outer and adjacent inner lines. This assignment was confirmed by a 2D CP-MAS J-resolved experiment. The unusual spinning-rate-dependent MAS lineshapes result from recoupling of the J interaction between the two crystallographically equivalent nuclei via anisotropic interactions, i.e., weak homonuclear dipolar coupling and differences in the orientation dependence of the chemical-shift tensors. Such spinning-rate-dependent MAS lineshapes are predicted to be a more frequent observation at higher applied magnetic fields.     

On Diastereotopic Carbon Atoms in Natural Abundance Carbon-13 Magnetic Resonance Spectra

Diastereotopic nuclei are intrinsically nonequivalent both chemically and magnetically.¹ Magnetic nonequivalence is either isochronous or anisochronous depending upon whether the two nuclei in question are magnetically nonequivalent in the spin-coupling sense (unequally coupled to a third nucleus) or in the chemical-shift sense (different nuclear) shieldings).² While both isochronous and anisochronous magnetic non-equivalence have been thoroughly documented in ¹H- and ¹⁹F-nuclear magnetic resonance studies,^{1, 2} reported examples from natural abundance ¹³C-magnetic resonance (cmr) spectra are conspicuously rare.³     

Two-dimensional ENDOR-ESEEM correlation spectroscopy

A two-dimensional (2D) experiment that correlates electron-nuclear double resonance (ENDOR) and electron spin-echo envelope modulation (ESEEM) frequencies, useful for unraveling and assigning ENDOR and ESEEM spectra from different paramagnetic centers with overlapping EPR spectra, is presented. The pulse sequence employed is similar to the Davies ENDOR experiment with the exception that the two-pulse echo detection is replaced by a stimulated echo detection in order to enhance the resolution in the ESEEM dimension. The two-dimensional data set is acquired by measuring the ENDOR spectrum as a function of the time interval T between the last two microwave pulses of the stimulated echo detection scheme. This produces a series of ENDOR spectra with amplitudes that are modulated with T. Fourier transformation (FT) with respect to T then generates a 2D spectrum with cross peaks connecting spectral lines of the ESEEM and ENDOR spectra that belong to the same paramagnetic center. Projections along the vertical and horizontal axes give the three-pulse FT-ESEEM and ENDOR spectra, respectively. The feasibility of the experiment was tested by simulating 2D ENDOR-ESEEM correlation spectra of a system consisting of an electron spin (S = (1/2)) coupled to two nuclei (I(1) = I(2) = (1/2)), taking into account experimental conditions such as pulse durations and off-resonance irradiation frequencies. The experiment is demonstrated on a single crystal of Cu(2+) doped l-histidine (Cu-His), containing two symmetrically related Cu(2+) sites that at an arbitrary orientation exhibit overlapping ESEEM and ENDOR spectra. While the ESEEM spectrum is relatively simple and arises primarily from one weakly coupled (14)N, the ENDOR spectrum is very crowded due to contributions from two nonequivalent nitrogens, two chlorides, and a relatively large number of protons. The simple ESEEM projection of the 2D ENDOR-ESEEM correlation spectrum is then used to disentangle the ENDOR spectrum and resolve two sets of lines corresponding to the different sites. Copyright 2000 Academic Press.     

Enhanced double quantum signals in nuclear magnetic resonance

A suggestion by Yatsiv for enhancing the strength of double quantum signals in high resolution nuclear magnetic resonance by use of radio-frequency sidebands is examined and shown to be practical. The theory shows that double quantum techniques can be extended to weakly coupled systems of nuclei (including systems of nuclei of different isotopic species). The AX part (with J _AX=5·4 c/s, δ_AX/2π=99·2 c/s) of the proton magnetic resonance spectrum of maltol (3-hydroxy-2-methyl-γ-pyrone) serves to confirm experimentally the quantitative theoretical treatment for weakly coupled systems. An enhancement factor of eight was observed as can be seen in figure 2.     

Synchronization in networks of limit cycle oscillators

We investigate the synchronization behaviour of three different networks of nonlinearly coupled oscillators. Each network consists of several clusters of oscillators, and the clusters themselves consist of any number of oscillators. In each cluster the eigenfrequencies scatter around the cluster frequency (mean frequency). The coupling strength varies in each cluster, too. We analyze the synchronized states by means of the center manifold theorem. This enables us to calculate these states explicitly, and to prove their stability. Moreover we are able to determine frequency shifts caused by different coupling mechanisms. In a number of cases we calculate the synchronisation threshold explicitely. Numerical simulations illustrate our analytical results. In one of the three networks we have additionally analyzed a single cluster consisting of infinitely many oscillators, that is an oscillatory field. Again, the center manifold theorem enabled us to calculate the synchronized state explicitly and to prove its stability. Our results concerning the oscillatory field are in contradiction to Ermentrout's analysis [6].