Nuclear quantum numbers

The hfs and quadrupole tensors of one of the nitrogen ligands have been determined with ENDOR by Calvo et al.63). The 14N-ENDOR transition frequencies observed between 11 and 23 MHz were found to depend significantly on the nuclear quantum number mCu of the EPR observer line. These shifts are due to Cu-N crossterms (Sect. 3.2) and amount to more than 1 MHz for certain orientations of B0. ENDOR resonances of... 

Separability between electronic and nuclear states is fundamental to get a description in terms of a hierarchy of electronic and subsidiary nuclear quantum numbers. Physical quantum states, i.e. wavefiinctions 0(q,Q), are non-separable. On the contrary, there is a special base set of functions Pjt(q,Q) that can be separable in a well defined mode, and used to represent quantum states as linear superpositions over the base of separable molecular states. For the electronic part, the symmetric group offers a way to assign quantum numbers in terms of irreducible representations [17]. Space base functions can hence be either symmetric or anti-symmetric to odd label permutations. The spin part can be treated in a similar fashion [17]. The concept of molecular species can be introduced this is done at a later stage [10]. Molecular states and molecular species are not the same things. The latter belong to classical chemistry, the former are base function in molecular Hilbert space. 

The situation with a pair of spins is illustrated in Fig. 1, where the static field B0 is along the z-axis. To first order and neglecting terms in the expansion of Eq. (2) which lead to a change in nuclear quantum numbers of 1 or 2 (i.e. Am — 1 and + 2 transitions), the effect of is to split the Zeeman levels into many closely spaced energy levels, thereby causing a distribution of resonant frequencies and consequently a broad line. Eq. (2) has been simplified by the van Vleck formula 2... 

The different functions (x, ), which may be called the electronic wave functions, correspond to different sets of values of the electronic quantum numbers n only, being independent of the nuclear quantum numbers v. On the other hand, each of these functions is a function of the nuclear coordinates as well as the electronic coordinates x. These functions are... 

There is one such equation for each set of values of the electronic quantum numbers n, and each of these equations possesses an extensive set of solutions, corresponding to the allowed values of the nuclear quantum numbers v. The values of Wn.y are the characteristic energy values for the entire molecule they depend on the electronic and nuclear quantum numbers n and v. 

In this formula, I is the nuclear quantum number, r(Bj) the first derivative lineshape function, B the resonance position and P the transition probability. 0 and i are the Euler angles expressing the orientation of the magnetic field vector B with respect to the principal axes of the tensors. Integration is needed since in powder samples, the crystallites take all possible orientations with respect to the magnetic field. Since the principal tensor axes and the crystal axes are assumed to be coincident, integration can be restricted to one octant of the unit sphere. 

Relative signs of hyperfine and quadrupole coupling constants. In an EPR spectrum with resolved hfs the relative signs of hf and quadrupole coupling constants may be determined from the dependence of the ENDOR intensities on the nuclear quantum number mi of the saturated EPR line . For two magnetically equivalent 1 = 1 nuclei, the signs can be obtained from similar, though more complex, intensity patterns . ... 

The subscripts correspond to the two electron spin quantum numbers, ms = Vi. For each ms value 21 lines with different frequencies occur depending on the value of the nuclear quantum number mi for the transition (ms, mi) (ms, mi -1). 

The powder lineshape is given by the sum of three components, corresponding to the three possible transitions (see Fig. 2, bottom) and each labeled by one value of the nuclear quantum number M (Fig. 6, top). Also in the presence of the hyperfine interaction, the principal values of both the g and A tensors may be measured from the powder lineshape [29]. 

Thus, the nuclei that we will consider have two magnetic quantum numbers, m = +1/2 and m = -1/2. Note that the rules for determining nuclear quantum numbers are similar to those for electronic quantum numbers. 

PARITY Either (1) a nuclear quantum number, or (2) a self checking binary code in which the total number of ones or zeros... 

L, Ml, J, Mj, S, quantum numbers of multielectron atom /, Mj nuclear quantum numbers... 

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