Spin-singlet pairs

At T, the system becomes two-dimensional and will undergo a transition to a spin-Peierls state at lower temperature due to the RG-generated BOW interchain interaction Vcdw- The static uniform magnetic susceptibility vanishes exponentially in this state made of local spin-singlet pairs. The... 

Introductory descriptions of Hartree-Fock calculations [often using Rootaan s self-consistent field (SCF) method] focus on singlet systems for which all electron spins are paired. By assuming that the calculation is restricted to two electrons per occupied orbital, the computation can be done more efficiently. This is often referred to as a spin-restricted Hartree-Fock calculation or RHF. 

At the equilibrium inter-atomic distance R, two paired electrons of occupy the bonding orbital with a closed-shell low-spin singlet (S = 0). When the bond length is further increased, the chemical bond becomes weaker. The dissociation limit of corresponds to a diradical with two unpaired electrons localized at each atom (Fig. 1). In this case, the singlet (S spin-antiparaUel) and triplet (T spin-parallel) states are nearly degenerate. Different from such a pure diradical with... 

The non-bonding electron pair may occupy one orbital with antiparallel spins (singlet, V2), or two different orbitals with antiparallel (singlet, lcrp) or parallel spins (triplet, 3crp). 

A number of cases have been reported in the literature where the exchange between pairs of ions in a lattice is piedominant, i.e., ions aie exchange coupled in pairs because of their proximity. An example of this is copper acetate 168), where the copper ions occur in pairs which are relatively close, so that the spins of pairs of copper ions are coupled together to form a singlet state (paired spins) and a triplet state (unpaired spins). Resonance measurements 158) permit determination of the magnitude and sign of J. 

In the first of the two notations used in this equation, a singlet pair is associated with each combination of an a and a p spin function enclosed within a matching pair of left and right parentheses. The second notation indicates all singlet pairs explicitly. It is easiest to visualize the spin-coupling patterns (3) by means of the familiar five... 

Accordingly, the most important spin function becomes (1 - 2, 3-4, 5-6), which couples the spins associated with the bonded orbitals in singlet pairs (see Fig. 6). The fact that the largest overlaps in Fig. 7 are ( i/i i/2) = (tirsItKe) and ( 3l 4) completes the picture of the now almost completely formed cA-l,3,5-hexatriene chain. 

A molecule containing a neutral nitrogen atom with four nonbonding electrons (R-N ). While two of these nonbonding electrons are paired, the other two may have parallel spins (thus, triplet state) or antiparallel spins (singlet state). Nitrenes are the nitrogen analogues of carbenes. 

The eigenstates of are symmetric spin-free two-electron functions corresponding to singlet pairs, those of F are antisymmetric spin-free two-electron functions corresponding to triplet pairs. Tr(F+) is the probability that two electrons are coupled to a singlet pair, while Tr(F ) is the probability that two electrons are coupled to a triplet pair. 

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