Single-quantum

After the primary step in a photochemical reaction, the secondary processes may be quite complicated, e.g. when atoms and free radicals are fcrnied. Consequently the quantum yield, i.e. the number of molecules which are caused to react for a single quantum of light absorbed, is only exceptionally equal to exactly unity. E.g. the quantum yield of the decomposition of methyl iodide by u.v. light is only about 10" because some of the free radicals formed re-combine. The quantum yield of the reaction of H2 -f- CI2 is 10 to 10 (and the mixture may explode) because this is a chain reaction. 

For those who are familiar with the statistical mechanical interpretation of entropy, which asserts that at 0 K substances are nonnally restricted to a single quantum state, and hence have zero entropy, it should be pointed out that the conventional thennodynamic zero of entropy is not quite that, since most elements and compounds are mixtures of isotopic species that in principle should separate at 0 K, but of course do not. The thennodynamic entropies reported in tables ignore the entropy of isotopic mixing, and m some cases ignore other complications as well, e.g. ortho- and para-hydrogen. 

For each degree of freedom, classical states within a small volume A/ij Aq- h merge into a single quantum state which cannot be fiirther distinguished on account of the uncertainty principle. For a system with /... 

For a coupled spin system, the matrix of the Liouvillian must be calculated in the basis set for the spin system. Usually this is a simple product basis, often called product operators, since the vectors in Liouville space are spm operators. The matrix elements can be calculated in various ways. The Liouvillian is the conmuitator with the Hamiltonian, so matrix elements can be calculated from the commutation rules of spin operators. Alternatively, the angular momentum properties of Liouville space can be used. In either case, the chemical shift temis are easily calculated, but the coupling temis (since they are products of operators) are more complex. In section B2.4.2.7. the Liouville matrix for the single-quantum transitions for an AB spin system is presented. 

Plakhotnik T, Walser D, Pirotta M, Renn A and Wild U P 1996 Nonlinear spectroscopy on a single quantum system two-photon absorption of a single molecule Science 271 1703-5... 

Most molecular vibrations are well described as hannonic oscillators with small anlrannonic perturbations [5]. Por an hannonic oscillator, all single-quantum transitions have the same frequency, and the intensity of single-quantum transitions increases linearly with quantum number v. Por the usual anhannonic oscillator, the single-quantum transition frequency decreases as v increases. Ultrashort pulses have a non-negligible frequency bandwidth. Por a 1... 

Systems containing symmetric wave function components ate called Bose-Einstein systems (129) those having antisymmetric wave functions are called Fermi-Ditac systems (130,131). Systems in which all components are at a single quantum state are called MaxweU-Boltzmaim systems (122). Further, a boson is a particle obeying Bose-Einstein statistics, a fermion is one obeying Eermi-Ditac statistics (132). 

HC HMQC (heteronuclear multiple quantum coherence) and HC HSQC (heteronuclear single quantum coherence) are the acronyms of the pulse sequences used for inverse carbon-proton shift correlations. These sensitive inverse experiments detect one-bond carbon-proton connectivities within some minutes instead of some hours as required for CH COSY as demonstrated by an HC HSQC experiment with a-pinene in Fig. 2.15. 

HSQC Heteronuclear single quantum coherence, e.g. inverse CH correlation via one-bond coupling providing the same result as HMQC but using an alternative pulse sequence... 

Another strategy reported by Sales links back to the superlattices discussed in Section 7.2.1.4. It was suggested by Mildred Dresselhaus s group at MIT (Hicks et al. 1993) that semiconductor quantum wells would have enhanced figures of merit compared with the same semiconductor in bulk form. PbTe quantum wells were confined by suitable intervening barrier layers. From the results, ZT values of 2 were estimated from single quantum wells. This piece of research shows the intimate links often found nowadays between apparently quite distinct functional features in materials. 

Here we review the properties of the model in the mean field theory [328] of the system with the quantum APR Hamiltonian (41). This consists of considering a single quantum rotator in the mean field of its six nearest neighbors and finding a self-consistent condition for the order parameter. Solving the latter condition, the phase boundary and also the order of the transition can be obtained. The mean-field approximation is similar in spirit to that used in Refs. 340,341 for the case of 3D rotators. 

Bohr s treatment gave spectacularly good agreement with the observed fact that a hydrogen atom is stable, and also with the values of the spectral lines. This theory gave a single quantum number, n. Bohr s treatment failed miserably when it came to predictions of the intensities of the observed spectral lines, and more to the point, the stability (or otherwise) of a many-electron system such as He. 

First of all, the vibrational energy is quantized, and we write the single quantum number v. This quantum number can take values 0, 1, 2,... 

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. 

Figure 1.33 The underlying principle of the Redfield technique. Complex Fourier transformation and single-channel detection gives spectrum (a), which contains both positive and negative frequencies. These are shown separately in (b), corresponding to the positive and negative single-quantum coherences. The overlap disappears when the receiver rotates at a frequency that corresponds to half the sweep width (SW) in the rotating frame, as shown in (c). After a real Fourier transformation (involving folding about n = 0), the spectrum (d) obtained contains only the positive frequencies.

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 1.44 Transitions between various energy levels of an AX spin system. A, and Aj represent the single-quantum relaxations of nucleus A, while Xi and Xj represent the single-quantum relaxations of nucleus X. W2 and are double- and zero-quantum transitions, respectively.

Apparently, all coherence pathways will therefore start at zero coherence levels and end at -t-1 coherence levels since the quadrature receiver is sensitive only to the +1 polarization, only the single-quantum coherence is detected. 

What is the difference between single-quantum coherence and zero-... 

Single-quantum coherence is the type of magnedzadon that induces a voltage in a receiver coil (i.e., Rf signal) when oriented in the xy-plane. This signal is observable, since it can be amplified and Fourier-transformed into a frequency-domain signal. Zero- or multiple-quantum coherences do not obey the normal selection rules and do not... 

No. The vector presentation is suitable for depicting single-quantum magnetizations but is not appropriate when considering zero-, double-, and higher-order quantum coherences. Quantum mechanical treatment can be employed when such magnetizations are considered. 

If only single-quantum transitions (h, I2, S], and S ) were active as relaxation pathways, saturating S would not affect the intensity of I in other words, there will be no nOe at I due to S. This is fairly easy to understand with reference to Fig. 4.2. After saturation of S, the fMjpula-tion difference between levels 1 and 3 and that between levels 2 and 4 will be the same as at thermal equilibrium. At this point or relaxation processes act as the predominant relaxation pathways to restore somewhat the equilibrium population difference between levels 2 and 3 and between levels 1 and 4 leading to a negative or positive nOe respectively. 

In contrast, in a two-spin system the two nuclei coupled with each other by the coupling constant, J, will have four energy levels available for transitions (Fig. 5.56). Such a system not only has single-quantum coher-... 

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