Homonuclear

Alternatively a reaction between a species with a pair of electrons and a species with a vacant orbital to form a covalent bond, heteronuclear molecule See homonuclear molecule. 

Many variations of the basic homonuclear COSY experiment have been devised to extend its range. A brief guide to some classes of experiment follows, along with a few of the connnon acronyms. 

Homonuclear teclmiques such as J-resolved spectroscopy also exist for rotatmg all multiplets tlirough 90°, to resolve overlaps and also give a ID spectrum from which all homonuclear couplings have been removed [26]. 

Aue W P, Kharan J and Ernst R R 1976 Homonuclear broadband decoupling and two-dimensional J-resolved NMR spectroscopy J. Chem. Phys. 64 4226-7... 

In a coupled spin system, the number of observed lines in a spectrum does not match the number of independent z magnetizations and, fiirthennore, the spectra depend on the flip angle of the pulse used to observe them. Because of the complicated spectroscopy of homonuclear coupled spins, it is only recently that selective inversions in simple coupled spin systems [23] have been studied. This means that slow chemical exchange can be studied using proton spectra without the requirement of single characteristic peaks, such as methyl groups. 

The homonuclear rare gas pairs are of special interest as models for intennolecular forces, but they are quite difficult to study spectroscopically. They have no microwave or infrared spectmm. However, their vibration-rotation energy levels can be detennined from their electronic absorjDtion spectra, which he in the vacuum ultraviolet (VUV) region of the spectmm. In the most recent work, Hennan et al [24] have measured vibrational and rotational frequencies to great precision. In the case of Ar-Ar, the results have been incoriDorated into a multiproperty analysis by Aziz [25] to develop a highly accurate pair potential. 

In summary, for a homonuclear diatomic molecule there are generally (2/ + 1) (7+1) symmetric and (27+1)7 antisymmetric nuclear spin functions. For example, from Eqs. (50) and (51), the statistical weights of the symmetric and antisymmetric nuclear spin functions of Li2 will be and respectively. This is also true when one considers Li2 Li and Li2 Li. For the former, the statistical weights of the symmetric and antisymmetiic nuclear spin functions are and, respectively for the latter, they are and in the same order. 

As was shown in the preceding discussion (see also Sections Vin and IX), the rovibronic wave functions for a homonuclear diatomic molecule under the permutation of identical nuclei are symmetric for even J rotational quantum numbers in and E electronic states antisymmeUic for odd J values in and E elecbonic states symmetric for odd J values in E and E electronic states and antisymmeteic for even J values in Ej and E+ electeonic states. Note that the vibrational ground state is symmetric under pemrutation of the two nuclei. The most restrictive result arises therefore when the nuclear spin quantum number of the individual nuclei is 0. In this case, the nuclear spin function is always symmetric with respect to interchange of the identical nuclei, and hence only totally symmeUic rovibronic states are allowed since the total wave function must be symmetric for bosonic systems. For example, the nucleus has zero nuclear spin, and hence the rotational levels with odd values of J do not exist for the ground electronic state f EJ") of Cr. 

H3 (and its isotopomers) and the alkali metal triiners (denoted generally for the homonuclears by X3, where X is an atom) are typical Jahn-Teller systems where the two lowest adiabatic potential energy surfaces conically intersect. Since such manifolds of electronic states have recently been discussed [60] in some detail, we review in this section only the diabatic representation of such surfaces and their major topographical details. The relevant 2x2 diabatic potential matrix W assumes the fomi... 

Here we shall consider a homonuclear diatomic molecule resPicted to a onedimensional x-space (Starzak, 1989) (Eig. 9-5). Although there is only one space coordinate, there are two degrees of freedom. The whole molecule can undergo moPon (Panslation), and it can vibrate. 

For homonuclear molecules (e.g., O2, N2, etc.) the inversion operator i (where inversion of all electrons now takes place through the center of mass of the nuclei rather than through an individual nucleus as in the atomic case) is also a valid symmetry, so wavefunctions F may also be labeled as even or odd. The former functions are referred to as gerade (g) and the latter as ungerade (u) (derived from the German words for even and odd). The g or u character of a term symbol is straightforward to determine. Again one... 

Configuration correlation diagram for homonuclear case in which homolytic bond cleavage is energetically favored. 

For the homonuclear example, the and CSFs undergo Cl coupling to form a pair of states of symmetry (the CSF cannot partake in this Cl mixing because it is of ungerade symmetry the states can not mix because they are of triplet spin symmetry). The Cl mixing of the and 1 CSFs is described in terms of a 2x2 secular problem... 

If the energies of the Sx and Sy orbitals do not differ significantly (compared to the coulombic interactions between electron pairs), it is expected that the essence of the findings described above for homonuclear species will persist even for heteronuclear systems. A decomposition of the six CSFs listed above, using the heteronuclear molecular orbitals introduced earlier yields ... 

Figure 4.11j), for example, and all homonuclear diatomic molecules belong to this point group. 

In general, for a homonuclear diatomic molecule there are (21+ )(/+1) symmetric and (21+ 1)/antisymmetric nuclear spin wave functions therefore... 

All other homonuclear diatomic molecules with / = for each nucleus, such as F2, also have ortho and para forms with odd and even J and nuclear spin statistical weights of 3 and 1, respectively, as shown in Figure 5.18. 

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