Energy level diagram, spin states

C08-0057. The ground state of V has lower spin than that of Cr. Construct energy level diagrams for the valence electrons that show how electron configurations account for this difference. 

Fig. 1. Energy level diagram for an S = 1/2,1 = 1/2 spin system with an isotropic hfs a, > 2 Ng B0 > 0. The steady state populations shown are for the case where the (A, D) (EPR observer) and the (A, B) (rf pump) transitions are saturated...

Figure 12. Energy level diagram for the spin states of Cu + (S-l/2, 1=3/2).

Figure 5.7 A schematic energy-level diagram for an octahedral ABg center within molecular orbital theory. This diagram is constructed from the atomic levels of A and B. The filled and half-filled states (two possible opposite spins for each state) correspond to A = Ti + and B = ions (reproduced with permission from Ballhausen and Gray, 1965).

By inspection of the energy level diagrams it is possible to see directly what sort of spectrum the ion should have in the given environment. For example, it can be seen from Figure 9.3 that a d2 ion in an octahedral complex, say [V(H20)J3+, should have three spin-allowed transitions, from the 37, ground state to the upper states 37, 3T, and 3A2. Experimentally, two absorption bands have been found at —17,000 and —24,000 cm-1, and these may be assigned to the T — 37 and 3T - 3T transitions if A0 is taken as —21,500... 

The procedure we have used would be particularly appropriate in the case of Ag(II), where the two J states are already well separated in the free ion because of a very large spin-orbit coupling. An energy level diagram of the following sort could then be drawn ... 

Figure A1.4 Nuclear spin states for a single proton in a magnetic field. At the top the two spin states, a and j8, are shown in an energy-level diagram with the transition indicated by an arrow. Below is the single-line spectrum. With normal populations, the number of molecules in the lower state is slightly greater than the number in the higher state normal net absorption occurs.

Figure A1.8 Nuclear spin states and spectrum for product 5. At the top the four states are again shown in an energy-level diagram. Heavy lines are the states with enhanced populations. A downward-pointing arrow indicates a net transfer of molecules from an overpopulated higher spin state to a less populated lower one, and corresponds to net emission. The spectrum shows the multiplet effect of type El A. From S. H. Pine, J. Chem. Educ., 49, 664 (1972). Reproduced by permission of the Division of Chemical Education.

For each of the following, (i) give the systematic name of the compound and specify the oxidation state of the transition metal, (ii) draw a crystal field energy-level diagram and assign the d electrons to orbitals, (iii) indicate whether the complex is high-spin or low-spin (for dA-d7 complexes), and (iv) specify the number of unpaired electrons. 

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