Double-quantum

Although the natural abundance of nitrogen-15 [14390-96-6] leads to lower sensitivity than for carbon-13, this nucleus has attracted considerable interest in the area of polypeptide and protein stmcture deterrnination. Uniform enrichment of is achieved by growing protein synthesi2ing cells in media where is the only nitrogen source. reverse shift correlation via double quantum coherence permits the... 

Suppression of the tme diagonal peaks by double-quantum filtering (DQF-COSY) may resolve such problems. Finally, quantitative measurements of the magnitude of the coupling constants is possible using the Z-COSY modification, These experiments ate restricted to systems of abundant spins such as H, and which have reasonably narrow linewidths. 

INADEQUATE Incredible natural abundance double quantum transfer experiment, segregates AB or AX systems due to homonuclear one-bond couplings of less abundant nuclei, e.g. 

The purpose of this work is to demonstrate that the techniques of quantum control, which were developed originally to study atoms and molecules, can be applied to the solid state. Previous work considered a simple example, the asymmetric double quantum well (ADQW). Results for this system showed that both the wave paeket dynamics and the THz emission can be controlled with simple, experimentally feasible laser pulses. This work extends the previous results to superlattices and chirped superlattices. These systems are considerably more complicated, because their dynamic phase space is much larger. They also have potential applications as solid-state devices, such as ultrafast switches or detectors. 

Figure 1. Pulse sequences of some typical 2D-NMR experiments. COSY = correlation SpectroscopY, DQFCOSY = Double Quantum Filtered COSY, RELAY = RELAYed Magnetization Spectroscopy, and NOESY = Nuclear Overhauser Effect SpectroscopY.

A single-quantum transition involves one spin only, whereas the zero- and doublequantum transitions involve two spins at the same time. The zero- and double-quantum transitions give rise to cross-relaxation pathways, which provide an efficient mechanism for dipole-dipole relaxation. 

The transitions between energy levels in an AX spin system are shown in Fig. 1.44. There are four single-quantum transitions (these are the normal transitions A, A, Xi, and X2 in which changes in quantum number of 1 occur), one double-quantum transition 1% between the aa and j8 8 states involving a change in quantum number of 2, and a zero-quantum transition 1% between the a)3 and fia states in which no change in quantum number occurs. The double-quantum and zero-quantum transitions are not allowed as excitation processes under the quantum mechanical selection rules, but their involvement may be considered in relaxation processes. 

Figure 1.45 Coherence transfer pathways in 2D NMR experiments. (A) Pathways in homonuclear 2D correlation spectroscopy. The first 90° pulse excites singlequantum coherence of order p= . The second mixing pulse of angle /3 converts the coherence into detectable magnetization (p= —1). (Bra) Coherence transfer pathways in NOESY/2D exchange spectroscopy (B b) relayed COSY (B c) doublequantum spectroscopy (B d) 2D COSY with double-quantum filter (t = 0). The pathways shown in (B a,b, and d) involve a fixed mixing interval (t ). (Reprinted from G. Bodenhausen et al, J. Magn. Resonance, 58, 370, copyright 1984, Rights and Permission Department, Academic Press Inc., 6277 Sea Harbor Drive, Orlando, Florida 32887.)...

An interesting feature of the energy diagram is that there are two transitions that involve the simultaneous flip of both spins. These are the transitions aa )3j8 (a double-quantum process, Wf) and a/3 )8a (a zero-... 

Since the equilibrium state has been disturbed, the system tries to restore equilibrium. For this it can use as the predominant relaxation pathways the double-quantum process (in fast-tumbling, smaller molecules), leading to a positive nOe, or the zero-quantum process 1% (in slower-tumbling macromolecules), leading to a negative nOe. 

Is it possible to predict the predominant mode of relaxation (zero-quantum or double-quantum) by observing the sign of nOe (negative or positive) ... 

Why do we need to involve zero-quantum (VI()) or double-quantum Wi) processes to explain the origin of the nuclear Overhauser enhancement ... 

The positive nOe observed in small molecules in nonviscous solution is mainly due to double-quantum relaxation, whereas the negative nOe observed for macromolecules in viscous solution is due to the predominance of the zero-quantum 1% cross-relaxation pathway. 

When the zero-quantum 1% transition is greater than double-quantum Wi, the nOe enhancements will be negative. Similarly, when is greater than 1%, the resultant nOe will have a positive sign. The predominance of Wi and over one another depends on the molecular motion. It is known that the Wo transition is maximal when the molecule tumbles at a rate of about 1 KHz, while the Wi transition is fastest at a tumbling rate of about 800 MHz. On this basis, a rough idea of the sign of nOe can be obtained. For example, small molecules in nonviscous... 

One problem associated with COSY spectra is the dispersive character of the diagonal peaks, which can obliterate the cross-peaks lying near the diagonal. Moreover, if the multiplets are resolved incompletely in the crosspeaks, then because of their alternating phases an overlap can weaken their intensity or even cause them to disappear. In double-quantum filtered COSY spectra, both the diagonal and the cross-peaks possess antiphase character, so they can be phased simultaneously to produce pure 2D absorption line... 

Figure 5.37 (a) Conventional phase-sensitive COSY spectrum of basic pancreatic trypsin inhibitor, (b) Double-quantum filtered (DQF) phase-sensitive COSY spectrum of the same trypsin inhibitor, in which singlet resonances and solvent signal are largely suppressed. Notice how clean the spectrum is, especially in the region near the diagonal line. (Reprinted from Biochem. Biophys. Res. Comm. 117, M. Ranee, et al., 479, copyright (1983) with permission from Academic Press, Inc.)... 

The NMR techniques discussed so far provide information about proton-proton interactions (e.g., COSY, NOESY, SECSY, 2D y-resolved), or they allow the correlation of protons with carbons or other hetero atoms (e.g., hetero COSY, COLOC, hetero /resolved). The resulting information is very useful for structure elucidation, but it does not reveal the carbon framework of the organic molecule directly. One interesting 2D NMR experiment, INADEQUATE (Incredible Natural Abundance Double Quantum Transfer Experiment), allows the entire carbon skeleton to be deduced directly via the measurement of C- C couplings. 

Thus, if the vertical axis representing the double-quantum frequencies is defined by v, and the horizontal axis representing the chemical shifts of the two carbons A and X is defined by V2, then both pairs of C satellites of nuclei A and X will lie on the same row (at + Vx), equidistant from the diagonal. This greatly facilitates identification. The advantage is that no overlap can occur, even when fir.c values are identical, since each pair of coupled C nuclei appear on different horizontal rows. 

The delay is generally kept at Vi x> The coupling constant Jcc for direcdy attached carbons is usually between 30 and 70 Hz. The first two pulses and delays (90J -t-180 2-t) create a spin echo, which is subjected to a second 90J pulse (i.e., the second pulse in the pulse sequence), which then creates a double-quantum coherence for all directly attached C nuclei. Following this is an incremented evolution period tu during which the double quantum-coherence evolves. The double-quantum coherence is then converted to detectable magnetization by a third pulse 0,, 2, and the resulting FID is collected. The most efficient conversion of double-quantum coherence can... 

The DQF (double-quantum filtered)-COSY spectrum of an isoprenyl coumarin along with H-NMR data are shown. Determine the H/ H homonuclear interactions in the DQF-COSY spectrum. 

SELINQUATE (Berger, 1988) is the selective ID counterpart of the 2D INADEQUATE experiment (Bax et al., 1980). The pulse sequence is shown in Fig. 7.4. Double-quantum coherences (DQC) are first excited in the usual manner, and then a selective pulse is applied to only one nucleus. This converts the DQC related to this nucleus into antiphase magnetization, which is refocused during the detection period. The experiment has not been used widely because of its low sensitivity, but it can be employed to solve a specific problem from the connectivity information. 

The SELINCOR experiment is a selective ID inverse heteronuclear shift-correlation experiment i.e., ID H,C-COSYinverse experiment) (Berger, 1989). The last C pulse of the HMQC experiment is in this case substituted by a selective 90° Gaussian pulse. Thus the soft pulse is used for coherence transfer and not for excitation at the beginning of the sequence, as is usual for other pulse sequences. The BIRD pulse and the A-i delay are optimized to suppress protons bound to nuclei As is adjusted to correspond to the direct H,C couplings. The soft pulse at the end of the pulse sequence (Fig. 7.8) serves to transfer the heteronuclear double-quantum coherence into the antiphase magnetization of the protons attached to the selectively excited C nuclei. 

Figure 7.25 illustrates the power of magnetic field gradient pulses to eliminate unwanted coherences. The double-quantum filtered COSY spec-... 

Figure 7.25 Homoniiclear double-quantum filtered COSY spectrum (400 MHz) of 8-mMangiotensin II in H,0 recorded without phase cycling. Magnetic field gradient pulses have been used to select coherence transfer pathways. (Reprinted from J. Mag. Reson. 87, R. Hurd, 422, copyright (1990), with permission from Academic Press, Inc.)...

Coherence A condition in which nuclei precess with a given phase relationship and can exchange spin states via transitions between two eigenstates. Coherence may be zero-quantum, single-quantum, double-quantum, etc., depending on the AM of the transition corresponding to the coherence. Only single-quantum coherence can be detected directly. 

Double-quantum coherence Coherence between states that are separated by magnetic quantum numbers of 2. This coherence cannot be detected directly, but must be converted to single-quantum coherence before detection. 

---