Nuclear spin symmetry species

In connection to control in dynamics I would like to take here a general point of view in terms of symmetries (see Scheme 1) We would start with control of some symmetries in an initial state and follow their time dependence. This can be used as a test of fundamental symmetries, such as parity, P, time reversal symmetry, T, CP, and CPT, or else we can use the procedure to discover and analyze certain approximate symmetries of the molecular dynamics such as nuclear spin symmetry species [2], or certain structural vibrational, rotational symmetries [3]. 

Comparison of the results of the previous effort, where it was assumed that excitation and absorption spectrum coincided,7 with the present results shows that there is really not much of a difference. Because of the higher sensitivity, MEs belonging to P(l) are detected over a range of almost 8 GHz instead of 3.5 GHz as found previously, and in accordance with that their number has increased. We now have 35 triplet states over 7.6 GHz, which leads to a density of 140 states per cm-1. The calculated density of pyrazine triplet vibronic states around the singlet energy appears to be around 100 cm-1,13-15 but if we want a comparison, we should take into account that they are triplets (times 3) and that nuclear symmetry permits interaction only between equal symmetry species. Table II gives the nuclear spin symmetry species of pyrazine and their statistical weight. The J = 0, K = 0 has the symmetry At and therefore can only interact with Ae triplet rovibronic states, which constitute th of the triplet manifold. We therefore expect about 3 x 17/48 x 100 a 106 triplet vibronic states per cm-1 to be available for the interaction, which compares favorably to the density of 140 per cm-1 as found from the density of the ME spectrum. 

As discussed in preceding sections, FI and have nuclear spin 5, which may have drastic consequences on the vibrational spectra of the corresponding trimeric species. In fact, the nuclear spin functions can only have A, (quartet state) and E (doublet) symmetries. Since the total wave function must be antisymmetric, Ai rovibronic states are therefore not allowed. Thus, for 7 = 0, only resonance states of A2 and E symmetries exist, with calculated states of Ai symmetry being purely mathematical states. Similarly, only -symmetric pseudobound states are allowed for 7 = 0. Indeed, even when vibronic coupling is taken into account, only A and E vibronic states have physical significance. Table XVII-XIX summarize the symmetry properties of the wave functions for H3 and its isotopomers. 

BalKSO Balasubramanian, K. Graph theoretical characterization of NMR groups, non-rigid nuclear spin species and the construction of symmetry adapted NMR spin functions. J. Chem. Phys. 73 (1980) 3321-3337. 

The hydrogen nucleus is classified as a Eermi particle with nuclear spin I = 1/2. Because of Pauli exclusion principle, hydrogen molecule is classified into two species, ortho and para. Erom the symmetry analysis of the wave functions, para-hydrogen is defined to have even rotational quantum number J with a singlet nuclear spin function, and ortho-hydrogen is defined to have odd J with a triplet nuclear spin function. The interconversion between para and ortho species is extremely slow without the existence of external magnetic perturbation. 

Cu isotopes both with nuclear spin I-3/2. The nucle r g-factors of these two isotopes are sufficiently close that no resolution of the two isotopes is typically seen in zeolite matrices. No Jahn-Teller effects have been observed for Cu2+ in zeolites. The spin-lattice relaxation time of cupric ion is sufficiently long that it can be easily observed by GSR at room temperature and below. Thus cupric ion exchanged zeolites have been extensively studied (5,17-26) by ESR, but ESR alone has not typically given unambiguous information about the water coordination of cupric ion or the specific location of cupric ion in the zeolite lattice. This situation can be substantially improved by using electron spin echo modulation spectrometry. The modulation analysis is carried out as described in the previous sections. The number of coordinated deuterated water molecules is determined from deuterium modulation in three pulse electron spin echo spectra. The location in the zeolite lattice is determined partly from aluminum modulation and more quantitatively from cesium modulation. The symmetry of the various copper species is determined from the water coordination number and the characteristics of the ESR spectra. 

Molybdenum is expected to have oxidation states between 3 and 6 in aqueous solution (3-0 d electrons) and the ESR-active species in these enzymes is believed to be Mo (d )- Molybdenum is a mixture of seven isotopes of which Mo and Mo (combined abundance 25%) both have nuclear spin of 5/2 and give rise to a six line hyperfine spectrum. This interaction is a source of useful information so it is desirable to study isotopically enriched enzymes. ESR measurements can be made at room temperature, frozen solutions generally show axial or lower symmetry, and the principal g-values are close to, or less than, 2.0. 

The origins of symmetry induced nuclear polarization can be summarized as follows as mentioned above molecular dihydrogen is composed of two species, para-H2, which is characterized by the product of a symmetric rotational wave-function and an antisymmetric nuclear spin wave function and ortho-H2, which is characterized by an antisymmetric rotational and one of the symmetric nuclear spin wavefunctions. In thermal equilibrium at room temperature each of the three ortho-states and the single para-state have practically all equal probability. In contrast, at temperatures below liquid nitrogen mainly the energetically lower para-state is populated. Therefore, an enrichment of the para-state and even the separation of the two species can be easily achieved at low temperatures as their interconversion is a rather slow process. Pure para-H2 is stable even in liquid solutions and para-H2 enriched hydrogen can be stored and used subsequently for hydrogenation reactions [54]. 

Figure 11 Effects of nuclear spin on the calculated powder EPR spectrum of a species with orthorhombic symmetry. The spectrum is anisotropic both in gand A (gi is split by A, Q2 is split by A2 and by A ). The value of / varies from 0 to . It should be noted that when / assumes an integer value (as in C), the features of the original /= 0 spectrum (A) are maintained in the centre of the spectrum. When / has half-integer values the hyperfine values are symmetrically disposed about the centre.

Figure 14 The level scheme of a methyl rotor attached to a chromophore. d and d are tunnelling splitting in So and Si, respectively. Ti is the lowest triplet state. E and A label the symmetry species of the rotor states, the subscripts characterize the total nuclear spin of the methyl protons.

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