Assignment 3 Due Tuesday, March 31, 2009 Download and read the Math_techniques.pdf file from the Handouts section of the class web page. Do problems 1, 2, and 4 following section C (for problem 1, you do the S = 1 case). Do problems 1, 2, 6 and 7 after section D. Additional Problems (1) (a) Interpret the EPR spectrum of the catechol anion, shown at right. Determine the hyperfine splittings and show successive splittings of one of the MS states. (b) Determine the hyperfine splittings, draw a stick plot diagram, and interpret the EPR spectrum of (CF3)2N. (Take careful note of the relative intensities.)
(c) The second-derivative EPR solution spectrum is for dithiadazolyl radical is shown at right. The intensity ratios within the multiplets is 1:4:7:7:4:1. Account for the observed pattern and estimate the hyperfine constants. (2) The figure below is a room-temperature EPR spectrum of [Mo(CN) 8 ] 3 in aqueous solution. Examine the table, Properties of Selected Nuclei, taken from Drago and provide an interpretation of all the observed spectral features.
(3) The figure below is a second-derivative EPR spectrum of a mixture of CHD 2 and CH 2 D. Nuclear spin and g-values for protons and deuterons are given in the lecture notes. (a) If deuterium ( 2 H = D) is substituted for protium ( 1 H, light hydrogen ) in a free radical, you should be able to predict the value of a D if a H is known for the undeuterated radical, assuming changes due to vibrational effects are not significant. Derive a general expression for a D /a H. (b) Identify all the lines in the spectrum to CHD 2 or CH 2 D. After you ve sorted out the lines, assign each transition s proton and deuteron nuclear spin values. Is the ratio a D /a H what you predicted from part (a)? (4) Solutions of potassium in ethylamine at concentrations of 10 5 M or higher exhibit an EPR spectrum with four equal intensity resonances with a weaker resonance close to the center of the spectrum. At lower concentrations, the central line becomes the dominant feature. How do you explain these observations? (5) Consider the two square pyramidal Cu(II) complexes shown below. The bidentate ligands are hexafluoroacetylacetonates (i.e., Hfacac ). PPh 3 Cu Cu PPh 3 (a) Discuss these two isomers expected EPR spectra. Describe the general features of the spectra and make it clear how the spectra could be used to distinguish between the two isomers. (For 63 Cu, I = 3 / 2 ; for 31 P, I = 1 / 2.) (b) How would the spectra of both isomers be changed by the use of 17 -labelled Hfacac? (For 17, I = 5 / 2.)
(6) K 6 [Mo 6 Se 8 (CN) 5 ] is a paramagnetic cluster compound with one unpaired electron per Mo 6 Se 8 cluster. The powder EPR spectrum for this compound is shown at right. Two g- values can be obtained from the spectrum, 2.4425(1) and 1.9822(1). (a) The clusters in K 6 [Mo 6 Se 8 (CN) 5 ] are centered at sites of 4/m symmetry. What are the proper labels the two given g-values and how does one obtain these values from the spectrum? (Show an approximate calculation using the figure given.) What is the average g-value? (b) h symmetry Mo 6 Se 8 clusters have a pair of orbitals of e g symmetry into which the one unpaired electron can go. However, the clusters tetragonally distort and the basal Mo-Mo bonds are about 0.04 Å shorter than the other Mo-Mo bonds. (See illustration at right.) This is thought to split the two orbitals in the virtual D 4h environment; the computed energy difference between these two orbitals is ~0.1 ev. Which, if either, of the g-values are affected by this energy difference? (Prove it!) (7) The EPR spectrum of the [V(CN) 5 ] 3 ion in a single crystal of KBr is shown below; the magnetic field is aligned along the [100] axis of the KBr host. (a) What are the values of A and A for the [V(CN) 5 ] 3 ion? (Hint: There are two overlapping spectra shown here! If you think about the way in which the [V(CN) 5 ] 3 ion is likely to substitute for K + and Br ions in the host, the relative intensities of the two spectra should settle which spectrum corresponds to the direction and which corresponds to the direction.)
(b) Give a qualitative discussion of the relative magnitudes of the hyperfine constants (see the malonate radical example from lecture). (c) Identify all the lines in the spectrum. g = 1.9711; what is the value of g? (d) Draw a d-orbital splitting diagram for this ion (π-effects are important too) and use the g-value information to determine as many of the d-orbital energy splittings as you can from the information you have so far (for V 4+, ζ = 248 cm 1 ) assuming the orbitals have pure d-character. (e) Consider the effects of covalence in the calculation of the g-values for this ion and discuss how the important ligand bonding effects should influence both g and g.