Assignment 3 Due Tuesday, March 30, 2010 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) An F center (Farbcentrum) is an electron bound to an anion vacancy and can be introduced into alkali halide and alkali hydride crystals by treating the stoichiometric salt with alkali metal vapor at elevated temperatures. Thus, when NaH is treated with sodium vapor, a doped (Na1H1 x) crystal results. The EPR spectrum shown below is for an F center in NaH. EPR of Na1H1 x. Explain the spectrum (do you see all the lines you would theoretically expect?). (b) According to the table given in Drago s book, for a free Na atom the measured isotropic hyperfine coupling is 886 MHz. Convert this to gauss (G) using the appropriate conversion factor and compare this with the 26.5 G value supplied with this spectrum. What does this seem to imply concerning the location of the unpaired electron? (To what extent is the electron really in the vacancy?) (2) The figure at right is a room-temperature EPR spectrum of a Cr 3+ impurity in MgO (rocksalt structure). Examine the table, Properties of Selected Nuclei, taken from Drago and provide an interpretation of the observed spectral features. (3) The chart below shows various square pyramidal vanadyl, (V IV =O) 2+, complexes for which EPR spectra have been measured and provides a guide to many of the macrocyclic ligand acronyms you see in Table 1. Other ligands are more generally known. For example, salen = N,N - ethylenebis (salicylideneaminato) 2 ; tsalen = N,N - ethylenebis (thiosalicylideneaminato) 2 ; tsalpn = N,N -propane-1,3-diyl (thiosalicylideneaminato) 2. (Thanks to Roxanne Jenkins.) EPR of Cr 3+ impurity in MgO
[(bme-daco)(v=o)] [(bme-dach)(v=o)] salenh2 [(V=O)(CGC)] 2- [(V=O)(ema)] 2- [(V=O)(ema) Table 1. EPR Parameters for Oxovanadium(IV) Complexes. a Complex Donor set gz gx gy Az Ax Ay [(bme-daco)(v=o)], 1 N2S2 1.968 1.991 1.9945 157.40 52.60 42.95 [(bme-dach)(v=o)], 2 N2S2 1.967 1.9915 1.995 153.27 53.67 38 (Et4N)2[(V=O)(ema)], 3 N2S2 1.970 2.001 2.001 153.27 60 33 (K)2[(V=O)(CGC)], 4 N2S2 1.9695 1.999 1.999 156.41 51.60 42 [(V=O)(ema) (CH2)3], 5b N2S2 1.977 2.000 2.000 153.12 49 33 VO(tsalen) c N2S2 1.978 1.986 1.986 148 51 51 [VO(tsatln)] c N2S2 1.966 1.975 1.975 140 37 37 [VO(tsalphen)] c N2S2 1.967 1.987 1.987 145 51 51 [VO(mp)2] 2- d,e O2S2 1.975 2.007 1.999 150 40 40 [VO(mmppt)] f,g O2S2 1.958 1.985 1.981 151 42 52 2 [VO(salen)] h N2O2 1.955 1.986 1.989 166 56 55 [VO(pycac)] i,j N3O 1.9558 1.9777 1.9811 151.43 53.29 42.46 VO(PAIS) k,l N3O 1.961 1.986 1.982 154 45 54 a In frozen DMF. b In frozen MeCN. c Reference 25. d Measured in frozen CH2Cl2/DMF. e Reference 46. f Measured in frozen CH2Cl2/DMF. gf Reference 47. h Reference 48. i Reference 31. j Measured in chloroform at 120 K. k Measured in frozen DMF/ /EtOH. l Reference 32. (a) Are any of these systems rigorously axial? Explain your answer. (b) Give a qualitative discussion of the relative magnitudes of the hyperfine constants (see the malonate radical example from lecture.) (c) Draw a d-orbital splitting diagram for a VOL4 complex; for simplicity, assume L is just a σ donor. (d) Use the g-value information for VO(tsalen) to determine as many of the d-orbital energy splittings as you can from the information given assuming the orbitals have pure d-character (for V 4+, ζ = 248 cm 1 ).
(e) From the trends in the g-values, what can you conclude concerning the donor strengths of the complexes 1 5 versus the other systems in the table? Can you provide a chemical bonding rationalization for your conclusions? (f) Consider the effects of covalence in the calculation of the g-values for VO(tsalen) and discuss how the important ligand bonding effects should influence both g and g. (4) A graduate student (in physics, no doubt) measured EPR spectra of a nitrogen-doped diamond with the applied magnetic field aligned along 3 different directions with respect to the crystallographic axes: the [111], [100], and [110] directions. Unfortunately, the student forgot to label the spectra! Supply the correct H-direction labels to the spectra and fully explain your choices. (Hint: Look at slides 37-9 in the first set of EPR notes and look at the diamond structure using Crystalmaker I suggest that you align each of the directions with the vertical axis in turn and slowly autorotate the structure about the vertical axis. The relative intensities in the spectra are important!) If you cheat and find a literature source for these spectra, you should acknowledge your source and a full explanation for the answer must still be provided.
(5) The following EPR data on a series of high-spin octahedral metal hexafluoride complexes are taken from Proc. Roy. Soc. (London), 236, 535 (1956). Complex g Ametal AF Imetal Temp. 10 4 cm 1 10 4 cm 1 MnF6 4 gx = gy = gz = 2.00 96 17 55 Mn: 5 /2 300 K CoF6 4 gx = 2.6 Ax = 43 Ax = 20 59 Co: 5 /2 20 K gy = 6.05 Ay = 217 Ay = 32 gz = 4.1 Az = 67 Az = 21 CrF6 3 A = 2.00 A = 16.2 A = 3 53 Cr: 3 /2 300 K (a) Explain why the CrF6 3 and MnF6 4 g-values are isotropic and close to ge (2.0023) while the CoF6 4 g-values are highly anisotropic and deviate markedly from ge. (b) Why are the magnitudes of the fluoride hyperfine coupling constants for CoF6 4 and MnF6 4 much larger than those for CrF6 3? (6) A solution of [Rh(py)4Cl2]Cl in acetonitrile and 0.1 M (TBA)Cl was electrochemically reduced and the EPR spectrum measured (Inorg. Chem. 28, 3905 (1989)) for the product is shown below (py = pyridine, TBA = tetrabutylammonium).
(a) The stereochemistry of the complex (cis- or trans-) is not explicitly indicated. What is it? (Why?) Has the symmetry changed in the reduced complex? (b) What are the g-value(s)? (g = 2.0037 ± 0.0002 for DPPH) (c) How do the g-value(s) enable you to predict which orbital the unpaired resides in? (Give a concise, but complete, explanation.) (d) Draw a d-orbital splitting diagram and use the g-value information to determine as many of the d-orbital energy splittings as you can from the information given (for Rh 2+, ζ = 1220 cm 1 ). Indicate whether the value you calculate this way is likely to be correct if not, is it likely to be too large or too small? (Why?) (e) The hyperfine splitting pattern has unusual intensities. Explain what is likely to be responsible for this (Hints: Notice that the outer two lines might best be described as barely split into doublets.) (f) Compute estimates for the relevant hyperfine coupling parameter(s) properly label these as you hopefully did for the g-values.