Spin singlet

Figure 28.7 (a) Dinuclear structure of copper(II) acetate, and (b) spin singlet (25 +1 = 1) and spin triplet (25 +1=3) energy levels in dinuclear Cu carboxylates. 

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.B.P. Lever, York University Most model photocatalysts undergo electron transfer reactions via their spin triplet states. You point out that there are advantages to using the spin singlet state for electron transfer as exemplified by chlorophyll. What kind of structural or electronic features should be built into model photocatalysts to favour use of their spin singlet states for electron transfer quenching ... 

Carbenes are electron-deficient two-coordinate carbon compounds that have two nonbonding electrons at one carbon. In the ground state, the two unshared electrons may be either in the same orbital and have antiparallel spins (singlet state S), or in two different orbitals with parallel spins (triplet state T). They can be considered as typical representatives of reactive intermediates and have found a broad range of applications in synthetic chemistry. 

A highly reactive compound containing a neutral divalent carbon with two nonbondmg electrons (ie.,. CR2 or a substitution derivative). The nonbonding electrons can have parallel spins (triplet state) or antiparallel spins (singlet state). The parent species, iCRz, is also known as methylene. A number of carbene derivatives have been used as photoaffinity labels of proteins. Irradiation of 3 -0-(4-benzoyl)benzoyl-ATP will cause 70% inactivation of mitochondrial Fi-ATPase. ... 

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. 

Fig. 1 Molecular orbital diagram showing the electronic configuration for the ground state (So), for the first spin-singlet excited state (Si) and for the first spin-triplet excited state (Ti). The arrows indicate the electron spin, the thin horizontal gray line is a guide to the eye. In this representation, coulomb and exchange energies are explicitly included in the positions of the frontier orbitals...

Figure 2. To the left, quasi-diabatic potential energy surfaces in the B3LYP/cc-pvtz Dunning s basis set. AA represents a cis state (solid line) BB a trans state (solid line) AB is the excited diradical state spin singlet (dashed line) Triplet is the diradical state S=1 (dotted line). To the right, extrapolated diabatic potential energy surfaces for the same states. The angle used to plot energy entries is a = 2 0. All calculations were done with Gaussian 98 [23].

The antiferromagnetic behaviour of (101) and (104) has been correlated with their structures. For (101) all models indicate that /i2 =/34 >/ and that a spin singlet lies lowest with a triplet... 

We can now obtain the result we desire. We can immediately make a unique assignment of multiplicities to the states listed in the lower part of our chart by noting that there is only one yAK state and two yBR states. These must therefore be assigned to the Ag and two Bg states arising from thus establishing that the TXg state is a spin triplet and, hence, that the >4,, Eg. and T2k states are all spin singlets. 

Another study (12) concerns the nominally tetrahedral complex, bis(/V-isopropylsalicylidene)nickel(II) shown in Fig. 14. The principal crystal susceptibilities over the temperature range 20-300°K have been fitted, as shown in Fig. 14, within the complete spin-triplet basis 3F + 3P (further calculations demonstrated the unimportance of including spin-singlet terms in the model) using the parameter set B f k, e (0), eCT(N), e n(N), e i(N), e,m(0), e i(0). 

On the other hand, the product (sym. orb.) - (antisym. spin) is nondegenerate. A state that is nondegenerate in spin is called a spin singlet we have 2S + 1 = 1, and thus S = 0. A singlet state does not have a paramagnetic moment. 

These four wave functions, or linear combinations of them, represent the lowest excited orbital states for the molecule. They can be used both as spin-singlet and spin-triplet functions since the single orbitals are different. 

Focusing now our attention to our set of (t2g )3 states we observe that 2D and S are the MQ = 0 components of a quasi-spin singlet while 2P is the Mc = 0 component of a quasi-spin triplet. The full quantum structure of the (t2g)3 multiplets thus involves seven labels QMQSLTMsMry, albeit the Me label is redundant since all states share the same MQ value. 

Clearly this sum is made up of antisymmetric terms only. It thus corresponds to an irreducible quasi-spin singlet. 

The s.o.c. operator is a one-electron operator which is even under time reversal, and non-totally symmetric in spin and orbit space. The trace of the spin-orbit coupling matrix for the t2g-shell thus vanishes. As a result the s.o.c. operator is found to transform as the MK = 0 component of a pure quasi-spin triplet (Cf. Eq. 26). Application of the selection rule in Eq. 28 shows that allowed matrix elements must involve a change of one unit in quasi-spin character, i.e. AQ = 1. Since 4S and 2D are both quasi-spin singlets while 2P is a quasispin triplet, s.o.c. interactions will be as follows ... 

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