Singlets electron spin

The ground state (0 kJ/mol) for the CL molecule is represented by the term symbol 3v . The first excited state (92 kJ/mol above the ground state) is a 1 singlet (electrons spin paired with both electrons in either the n x or the n y level). The 1 v state with paired spin electrons, one each in the 7i v and n y levels, is the next excited level 155 kJ/mol above the ground state. Reduction of 02 by one electron yields the superoxide ion (02), a radical anion. Reduction by two electrons yields the peroxide ion, (02 ). Bond lengths and bond orders for these are given in Table 4.2. As noted in equation 4.2, the reduction potential for 02 in the presence of protons is thermodynamically favorable. Therefore, reversible binding of O2 to a metal can only be achieved if competition with protons and further reduction to superoxide and peroxide are both controlled.8... 

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. 

If all spins ( 1/2) in an atom or molecule are paired (equal numbers of spin +1/2 and -1/2), the total spin must be zero, and that state is described as a singlet (total spin, S = 0 and the state is described by the term 2S + 1 = 1). When a singlet ground-state atom or molecule absorbs a photon, a valence electron of spin 1/2 moves to a higher energy level but maintains the same... 

Derivation of an energy level diagram shows that it consists of two sets of energy levels, one corresponding to the single lines and the other to the double lines, and that no transitions between the two sets of levels are observed. For this reason it was suggested that helium exists in two separate forms. In 1925 it became clear that, when account is taken of electron spin, the two forms are really singlet helium and triplet helium. 

In the limit of infinite atom separations, or if we switch off the Coulomb repui. sion between two electrons, all four wavefunctions have the same energy. But they correspond to different eigenvalues of the electron spin operator the first combination describes the singlet electronic ground state, and the other three combinations give an approximate description of the components of the first triplet excited state. 

The electron densities for a spin electrons and for spin electrons are always equal in a singlet spin state, but in non-singlet spin states the densities may be different, giving a resultant spin density. If we evaluate the spin density function at the position of certain nuclei, it gives a value proportional to the isotropic hyperfine coupling constant that can be measured from electron spin resonance experiments. 

We have to take account of electron spin. It is necessary to write a combination of two Slater determinants in order to correctly describe the excited singlet states. 

Postulate (i) follows from the fact that when two radicals, produced by whatever means, encounter each other, the interaction of the electron spin of one radical with that on the other radical can give rise to two mutually exclusive spin states, triplet and singlet. Random combination of the two possible electron spin states for the two electrons yields the three components of the triplet state, represented as T+i, To, and T i, and the singlet state, S. Throughout this article, S is assumed to be the singlet state of lowest energy. 

In all these cases, the products have three electrons spinning up and the fourth down (as do the starting molecules). However, formation of, say, two triplets (Ti + ii) or two singlets (ti + Ti). whether ground states or excited, would violate the rule. 

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... 

For a triplet to result, two electrons must have different orbitals and the same spin (the Pauli principle forbids having two unpaired electrons in the same orbital since all four quantum numbers would be the same). We saw in Chapter 1 that upon light absorption an electron is promoted from one orbital to a higher orbital. If we were to excite directly from the ground state singlet to the triplet state we would have to simultaneously change orbitals and electronic spins. Since this process is relatively improbable, direct absorption to the triplet state is seldom observed (later in this chapter,... 

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