Singlet coupling

Addition is even more facile in radical -b radical reactions due to the usually barrierless formation (on the singlet-coupled surface) of a chemical bond... 

I if the spins associated with orbitals and ( )y are exactly singlet coupled... 

We show again the traditional five covalent Rumer diagrams for six electrons and six orbitals in a singlet coupling and emphasize that the similarity between the ring of orbitals and the shape of the molecule considerably simplifies the understanding of the S5mimetry for benzene. 

This allows one to interpret the combination of two CSFs which differ from one another by a double excitation from one orbital (< )) to another (< ) ) as equivalent to a singlet coupling of... 

Figure 3.9b portrays homolytic bond formation by the recombination of radicals and is accompanied by charge transfer from A to B. The radicals must be singlet coupled. The interaction of triplet-coupled electron pairs is repulsive and does not lead to bond formation. The reverse process describes homolytic bond cleavage and results in singlet-coupled free radicals. 

The electronic states of the CN radical have been fully characterized by Schaefer and Heil (90). Ground state CN(X2E+) has a triple bond between the carbon and nitrogen atoms, and an unpaired electron localized on the carbon atom. Collinear approach of two CN(X E+) singlet-coupled radicals leads to the... 

We find that the only important Rumer structures are R4 and R5, which correspond to singlet coupling of the two electrons on nitrogen. In a description based on orbitals... 

The weights of the different Rumer structures are collected in Table 2. Structure Rl5 which corresponds to singlet coupling of the spins of the two electrons in the orbitals associated with each N or O atom, is dominant in both cases. The contributions from the other structures are very small, and we find that the resonance energies are negligible. 

Denoting the tt AOs of the C1-C4 carbons by a,b,c, and d, respectively, the fully covalent VB wave function for the tt system of butadiene displays two singlet couplings one between a and b, and one between c and d. It follows that the wave function can be expressed in the form of Equation 3.8, as a product of the bond wave functions. 

The product of bond wave functions in Equation 3.8, involves so-called perfect pairing, whereby we take the Lewis structure of the molecule, represent each bond by a HL bond, and finally express the full wave function as a product of all these pair-bond wave functions. As a rule, such a perfectly paired polyelectronic VB wave function having n bond pairs will be described by 2" determinants, displaying all the possible 2x2 spin permutations between the orbitals that are singlet coupled. 

Since the A B — C structure displays a singlet coupling between orbitals b and c, Equation 3.50 gives its wave function ... 

As shown above in Scheme 4.2, the Rumer basis for butadiene is made of the VB structures 6 and 7. From Section 3.1.4, the VB function corresponding to a given bonding scheme is the one that involves singlet coupling between the AOs that are paired in this scheme. This, however, can be done in two ways. In the first way, the AOs are kept in the same order in the various determinants, and the determinants display all the possible 2x2 spin permutations between the orbitals that are singlet coupled. This is the convention used in Equation 4.16, which is similar to Equation 3.9. In this case, the determinant has a positive or... 

All the VB methods that deal with semilocalized orbitals use a generalization of the Coulson—Fischer idea (12), whereby a bond is described as a singlet coupling between two electrons in nonorthogonal orbitals that possess small delocalization tails resulting from the variational orbital optimization. Albeit formally covalent, this description implicitly involves some optimal contributions of ionic terms, as a decomposition of the wave function in terms of pure AO determinants would show (see Eqs. 3.5 and 3.6). For a polyatomic... 

Each geminal function is a singlet-coupled GVB pair (

associated with a particular bond or lone pair in the molecule. For example, CH4 will have the familiar Lewis structure and its wave function will involve a product of four geminal functions, each corresponding to a C-H bond. 

The VB structures are specified in section struct . In the first line, the VB orbitals 1-6 are doubly occupied, while 7 and 8 are singly occupied and singlet coupled. As 7 and 8 are VB orbitals of a type, each localized on their respective fragments, this line designates the covalent VB structure — . The two following lines correspond to the ionic structures F F+ and F+F, respectively. 

Slater s bond eigenfunctions constitute one choice (out of an infinite number) of a particular sort of basis function to use in the evaluation of the Hamiltonian and overlap matrix elements. They have come to be called the Heitler-London-Slater-Pauling (HLSP) functions. Physically, they treat each chemical bond as a singlet-coupled pair of electrons. This is the natural extension of the original Heitler-London approach. In addition to Slater, Pauling[12] and Eyring and Kimbal[13] have contributed to the method. Our following description does not follow exactly the discussions of the early workers, but the final results are the same. 

Analysis of the total spin function reveals that the spins associated with the pairs (v /2,V /4), (v3,V6) and (v / V /6) remain essentially singlet coupled throughout the course of the reaction, with no evidence for any aromatic structure along the IRC. As such, the spin-coupled description corresponds to a mechanism that involves the simultaneous relocation of three orbital pairs, as might be represented by the following simplistic scheme ... 

---