The structure of (+)-frondosin B 1 has been the subject of some concern. The compound has been synthesized by a number of research groups with the expected R isomer as the target. However, the Danishefsky¹ and MacMillan² synthesis led to a molecule with [α]_D of about +16°, while Trauner³ reports a value of -16.8° and Ovaska⁴ prepared the S isomer with [α]_D = -17.3°. Something is amiss here.

Joyce and coworkers have looked into this structure problem through a combination of advanced analytical techniques and computational chemistry.⁵ They utilize optical activity, electronic circular dichroism (ECD) and vibrational circular dichroism (VCD) and compare the experiments with computational results. IR and VCD were computed at B3LYP/6-31G** using a Boltzmann-weighted set of low-energy conformations. ECD computations were done at CAM-B3LYP/6-31++G**//B3LYP/6-31G**.

Basically, they found that (+)-frondosin B does have the R stereocenter. The different synthetic schemes did actually all lead to the same isomer, tested by looking at key intermediates along the way. The discrepancy in the optical activity is due to a small impurity, 2, that has the opposite rotation and a magnitude 10 times greater than that of authentic 1.

This paper is another nice example demonstrating the power of modern computational approaches to spectra that can be extremely valuable in structure determination. Organic chemists of all stripes should certainly be aware of how this tool can complement experiments.

My thanks to Derek Lowe who posted on this paper in his In The Pipeline blog.

References

1) Inoue, M.; Carson, M. W.; Frontier, A. J.; Danishefsky, S. J., "Total Synthesis and Determination of the Absolute Configuration of Frondosin B." J. Am. Chem. Soc.
2001, 123, 1878-1889, DOI: 10.1021/ja0021060.

2) Reiter, M.; Torssell, S.; Lee, S.; MacMillan, D. W. C., "The organocatalytic three-step total synthesis of (+)-frondosin B." Chem. Sci. 2010, 1, 37-42, DOI: 10.1039/C0SC00204F.

3) Hughes, C. C.; Trauner, D., "Palladium-catalyzed couplings to nucleophilic heteroarenes: the total synthesis of (−)-frondosin B." Tetrahedron 2004, 60, 9675-9686, DOI: 10.1016/j.tet.2004.07.041.

4) Ovaska, T. V.; Sullivan, J. A.; Ovaska, S. I.; Winegrad, J. B.; Fair, J. D., "Asymmetric Synthesis of Seven-Membered Carbocyclic Rings via a Sequential Oxyanionic 5-Exo-Dig Cyclization/Claisen Rearrangement Process. Total Synthesis of (−)-Frondosin B." Org. Letters 2009, 11, 2715-2718, DOI: 10.1021/ol900967j.

5) Joyce, L. A.; Nawrat, C. C.; Sherer, E. C.; Biba, M.; Brunskill, A.; Martin, G. E.; Cohen, R. D.; Davies, I. W., "Beyond optical rotation: what’s left is not always right in total synthesis." Chem. Sci. 2018, 9, 415-424, DOI: 10.1039/C7SC04249C.

InChIs

1: InChI=1S/C20H24O2/c1-12-6-8-16-14(5-4-10-20(16,2)3)18-15-11-13(21)7-9-17(15)22-19(12)18/h7,9,11-12,21H,4-6,8,10H2,1-3H3/t12-/m1/s1
InChIKey=LSPMJSWSYGOLFD-GFCCVEGCSA-N

2: InChI=1S/C20H24O2/c1-12-5-4-10-20(3)16(12)8-6-13(2)19-18(20)15-11-14(21)7-9-17(15)22-19/h7,9,11,13,21H,4-6,8,10H2,1-3H3/t13-,20-/m1/s1
InChIKey=ZBXZDKMLFIJFHG-ZUOKHONESA-N

Optical activity is a major tool for identifying enantiomers. With recent developments in computational techniques, it is hoped that experiments combined with computations will be a powerful tool for determining absolute configuration. The recent work of Lahiri, et al. demonstrates the scope of theoretical work that is still needed to really make this approach broadly applicable.¹

They prepared (1R,4R)-norbornenone 1 and measured its optical rotation in the gas phase and in dilute solutions of acetonitrile and cyclohexane. The specific rotations at three different wavelengths are listed in Table 1. Of first note is that though there is some small differences in solution, as expected, there really is substantial differences between the gas- and solution phases. Thus cautionary point 1: be very careful of comparing solution phase experimental optical activity with computed gas phase predictions.

1

Table 1. Experimental and computed specific rotation of 1.

For the computations, the geometry of 1 was optimized at B3LYP/aug-cc-pVTZ (see Figure 1. The OR was computed at B3LYP with different basis sets, finding that the difference in the predicted specific rotation at 598.3nm differs only quite little (90.6 deg dm^-1 (g/mL)^-1) between the computations using aug-cc-pVTZ and aug-cc-pVQZ) suggesting that the basis set limit has been reached. The gas –phase computed values at B3LYP and CCSD are also shown in Table 1. Though these computations do get the correct sign of the rotation, they are appreciably off of the experimental values, and the percent error varies with wavelength. Cautionary point 2: it is not obvious what is the appropriate computational method to compute OR, and beware of values that seem reasonable at one wavelength – this does not predict a good agreement at a different wavelength.

Figure 1. Optimized geometry of 1 at B3LYP/aug-cc-pVTZ.

Lastly, computed solution values of the OR were performed with PCM and B3LYP. These values are given in Table 1. Again the agreement is poor. So cautionary point 3: computed (PCM) solution OR
may be in quite poor agreement with experiment.

Often the culprit to poor agreement between computed and experimental OR is attributed to omitted vibrational effects, but in this case, because 1 is so rigid, one might not expect too much error to be caused by the effects of vibrations. So the overall result – we need considerable work towards addressing how to accurately compute optical activity!

References

(1) Lahiri, P.; Wiberg, K. B.; Vaccaro, P. H.; Caricato, M.; Crawford, T. D. "Large Solvation Effect in the Optical Rotatory Dispersion of Norbornenone," Angew. Chem. Int. Ed. 2014, 53, 1386-1389, DOI: 10.1002/anie.201306339.

InChIs

1: InChI=1S/C7H8O/c8-7-4-5-1-2-6(7)3-5/h1-2,5-6H,3-4H2/t5-,6+/m1/s1
InChIKey=HUQXEIFQYCVOPD-RITPCOANSA-N

Computing the optical rotation of simple organic molecules can be a real challenge. One of the classic problems is methyloxirane. DFT typically gets the wrong sign, let alone the wrong value. Cappelli and Barone¹ have developed a QM/MM procedure where methyloxirane is treated with DFT (B3LYP/aug-cc-pVDZ or CAM-B3LYP/aubg-cc-pVDZ). Then 2000 arrangements of water about methyloxirane were obtained from an MD simulation. For each of these configurations, a supermolecule containing methyloxirane and all water molecules with 16 Å was identified. The waters of the supermolecule were treated as a polarized force field. This supermolecule is embedded into bulk water employing a conductor-polarizable continuum model (C-PCM). Lastly, inclusion of vibrational effects, and averaging over the 2000 configurations, gives a predicted optical rotation at 589 nm that is of the correct sign (which is not accomplished with a gas phase or simple PCM computation) and is within 10% of the correct value. The full experimental ORD spectrum is also quite nicely matched using this theoretical approach.

References

(1) Lipparini, F.; Egidi, F.; Cappelli, C.; Barone, V. "The Optical Rotation of Methyloxirane in Aqueous Solution: A Never Ending Story?," J. Chem. Theor. Comput. 2013, 9, 1880-1884, DOI: 10.1021/ct400061z.

InChIs

(R)-Methyloxirane:
InChI=1S/C3H6O/c1-3-2-4-3/h3H,2H2,1H3/t3-/m1/s1
InChIKey=GOOHAUXETOMSMM-GSVOUGTGSA-N

What is the appropriate basis set to use for computing optical rotations? Hedgård, Jensen, and Kongsted examined the optical rotation of 1-6 using B3LYP and CAM-B3LYP at two different wavelengths.¹ They examined a series of different basis sets, including the aug-pCS sets² (developed for NMR computations), the aug-cc-pVXZ series and 6-311++G(3df,3pd). They compared the computed optical rotation with the different basis sets with the value obtained from an extrapolated basis set computation. The mean absolute deviation using either B3LYP or CAM-B3LYP at the two different basis sets are listed in Table 1. The bottom line is that aug-pcS-2 is the preferred method, but this basis set is rather large and computations of big molecules will be difficult. The aug-pcS-1 set is the best choice for large molecules. Errors with the extensive Pople basis set and the aug-cc-pVXZ sets are quite sizable and of concern (especially at the shorter wavelength). It should also be mentioned that even with the largest aug-pcS basis sets extrapolated to the CBS limit, the computed value of the optical rotation of 3 has the wrong sign! Clearly, basis set choice is not the only issue of concern. We remain in need of a robust methodology for computing optical activity.

Table 1. Mean absolute deviation of the optical activities of 1-6 evaluated at two wavelengths.

References

(1) Hedegård, E. D.; Jensen, F.; Kongsted, J. "Basis Set Recommendations for DFT Calculations of Gas-Phase Optical Rotation at Different Wavelengths," J. Chem. Theory Comput. 2012, 8, 4425-4433, DOI: 10.1021/ct300359s

(2) Jensen, F. "Basis Set Convergence of Nuclear Magnetic Shielding Constants Calculated by Density Functional Methods," J. Chem. Theory Comput. 2008, 4, 719-727, DOI: 10.1021/ct800013z

It is striking to me that the absolute configuration of relatively simple compounds remains problematic even today. The structure of two naturally-occurring phytotoxic enantiomers 1, called regiolone and isosclerone, are finally definitively defined using a computational approach.

(R)-1: R = OH, R’ = H
(S)-1: R = H, R’ = OH

Isosclerone is the dextrorotatory isomer, while regiolone is the levorotatory isomer. The question though is which one is R and which one is S? Evidente and co-workers arbitrarily decided to compute the spectral properties of the S isomer.¹ They located four low energy conformers at B3LYP/6-31G* and B3LYP/TZVP. (These conformers are not shown here as the authors did not deposit the coordinates. Reviewers and editors – please insist that this computational data be mandatory for publication!) The conformer relative energies, listed in Table 1, are dependent on the method, however, the two lowest energy structures will dominate the population and both will be present to a significant extent, regardless of which energy set is used. The optical rotation [α]_D was computed at B3LYP/6-31G*//B3LYP/TZVP, and these too are listed in Table 1. The Boltzmann-weighted [α]_D is 21.8. Even though the lowest energy conformer contributes a negative rotation, the much larger positive rotation due to the second-lowest energy conformer, along with the two other conformers, will dominate to dictate the OR value. This suggests that the enantiomers are (S)(+)-1 and (R)(-)-1. Computed ECD spectra confirm this assignment; the computed ECD of the (S) isomer is a near mirror image of the experimental ECD of the (-)-1 compound. Therefore, regiolone is (R)(-)-1 and isosclerone is (S)(+)-1.

Table 1. Relative free energies (kcal mol^-1) and [α]_D of the conformers of (S)-1.^a

^aAll computations performed with B3LYP. ^bAt B3LYP/6-31G*//B3LYP/TZVP

References

(1) Evidente, A.; Superchi, S.; Cimmino, A.; Mazzeo, G.; Mugnai, L.; Rubiales, D.; Andolfi, A.; Villegas-Fernández, A. M., "Regiolone and Isosclerone, Two Enantiomeric Phytotoxic Naphthalenone Pentaketides: Computational Assignment of Absolute Configuration and Its Relationship with Phytotoxic Activity," Eur. J. Org. Chem., 2011, 5564-5570, DOI: 10.1002/ejoc.201100941

InChIs

Regiolone: InChI=1/C10H10O3/c11-7-4-5-9(13)10-6(7)2-1-3-8(10)12/h1-3,7,11-12H,4-5H2/t7-/m1/s1
InChIKey=ZXYYTDCENDYKBR-SSDOTTSWBB

Isosclerone: InChI=1/C10H10O3/c11-7-4-5-9(13)10-6(7)2-1-3-8(10)12/h1-3,7,11-12H,4-5H2/t7-/m0/s1
InChIKey=ZXYYTDCENDYKBR-ZETCQYMHBD

Palau’amine has been of interest since its discovery in the early 1990s. It was just recently synthesized by Baran,¹ to much acclaim. The structure of palau’amine underwent numerous revisions, and though the relative configuration had been settled, the absolute configuration was only determined by Reinscheid and Griesinger using a combination of experimental and computed ECD and ORD spectra.²

3,4-dibromopalau’amine 1 was subjected to careful NMR analysis to set as much of the overall structure as possible. Then two conformations were optimized at B3LYP/6-31G(d), one of which is displayed in Figure 1.

1

Figure 1. B3LYP/6-31G(d) optimized structure of 1.

TD-DFT computations including PCM gave an ECD spectrum that nicely matches with experiment, especially where the positive and negative peaks occur. The computed and experimental ORD spectra also match well, with all the signs matching up and a difference in the absolute value of the rotation of no more that 25%. The resulting absolute configuration is (-)-(6S,10R,11S,12S,16R,17S,18S,20S)-dibromopalau’amine, demonstrating again the power of combining computation and experiment for structure determination!

References

(1) Seiple, I. B.; Su, S.; Young, I. S.; Lewis, C. A.; Yamaguchi, J.; Baran, P. S., "Total Synthesis of Palau’amine," Angew. Chem. Int. Ed., 2010, 49, 1095-1098, DOI: 10.1002/anie.200907112

(2) Reinscheid, U. M.; Köck, M.; Cychon, C.; Schmidts, V.; Thiele, C. M.; Griesinger, C., "The Absolute Configuration of Dibromopalau’amine," Eur. J. Org. Chem., 2010, 6900-6903, DOI: 10.1002/ejoc.201001392

InChI

1: InChI=1/C17H22Br2ClN9O2/c18-6-1-7-11(30)28-3-5-4(2-21)9(20)16(13(31)25-15(23)26-16)8(5)17(28)12(24-14(22)27-17)29(7)10(6)19/h1,4-5,8-9,12-13,24-27,31H,2-3,21-23H2/q+2/p+1/t4-,5-,8+,9+,12+,13+,16+,17-/m1/s1/fC17H23Br2ClN9O2/h21H/q+3
InChIKey=VGQTUXLYZXIYTJ-CAGSSHLPDN

It’s been a while since I blogged about the use of computed spectra to determine the structure or configuration of a compound. Well, here’s a nice example of the use of computed electronic circular dichroism to determine the configuration of a coumarin that displays axial chirality.

Mazzanti and coworkers have synthesized a series of coumarins,¹ obtained their ECD and computed their structures, stero-interconversion barriers (at B3LYP/6-31G(d)) and ECD (at TD-DFT/B3LYP/6-311++G(2d,p)//B3LYP/6-31G(d)). I will mention explicitly here just one example, compound 1, which elutes off a chiral column in two mirror image forms, both of which do not stereomutate over time.

The computed structure of 1 is shown in Figure 1 and the barrier for steromutation is predicted to be quite large, 35.7 kcal mol^-1. This explains the lack of stereomutation. The computed ECD of 1M matches very well with the experimental ECD of the first eluted isomer, making the second eluted isomer 1P.

1

Figure 1. B3LYP/6-31G(d) optimized structure of 1.

References

(1) Lunazzi, L.; Mancinelli, M.; Mazzanti, A.; Pierini, M., "Stereomutation of Axially Chiral Aryl Coumarins," J. Org. Chem., 2010, ASAP, DOI: 10.1021/jo101261k

InChIs

1 (6-isopropyl-4-(2-methyl-1-naphthyl)chromen-2-one):
InChI=1/C23H20O2/c1-14(2)17-10-11-21-19(12-17)20(13-22(24)25-21)23-15(3)8-9-16-6-4-5-7-18(16)23/h4-14H,1-3H3
InChIKey=OEQFRNPVUJVJFO-UHFFFAOYAS

Determination of absolute configuration remains a difficult undertaking, one usually solved by x-ray crystallography. In my book (Chapter 1.6.3) and blog (see these posts) I have noted the use of computations in conjunction with optical rotation or electronic circular dichroism as an alternative: possible configurations are optimized and their optical properties are computed and then matched against experimental spectra.

Neri and coworkers have utilized this approach to determine the absolute configuration of the chiral calix[4]arene 1.¹

Computed optical rotations (TDDFT/B3LYP/6-31G* at 5 frequencies) are compared with experimental values in Table 1. While the magnitude is off (as is typical) the sign of the activity along with the trend matches up very well for the cS configuration shown in Figure 1. It should be noted that a second conformation makes up about 10% of the Boltzmann population, and the contribution of this second configuration is included in the computed values shown in Table 1. In addition, computations at higher levels give very similar results. Lastly, the computed ECD spectrum of the cS isomer also matches up well with experiment.

Table 1. Optical rotation of the cS isomer of 1 compared with experiment

Figure 1. B3LYP/6-31G* optimized structure of the major conformation of 1.

Given the relatively low level of theory employed here, further use of this combined experimental/computational approach to obtaining absolute configurations of large molecules is encouraged.

References

(1) Talotta, C.; Gaeta, C.; Troisi, F.; Monaco, G.; Zanasi, R.; Mazzeo, G.; Rosini, C.; Neri, P., "Absolute Configuration Assignment of Inherently Chiral Calix[4]arenes using DFT Calculations of Chiroptical Properties," Org. Lett., 2010, 12, 2912-2915, DOI: 10.1021/ol101098x

InChIs

1: InChI=1/C59H78O7/c1-16-19-64-53-36-22-35-32-47(59(13,14)15)50(51-48(61)33-45(60)34-49(51)62)46(52(35)63)31-41-30-44(58(10,11)12)29-40(55(41)66-21-18-3)24-39-28-43(57(7,8)9)27-38(54(39)65-20-17-2)23-37(53)26-42(25-36)56(4,5)6/h25-30,32-34,60-63H,16-24,31H2,1-15H3
InChIKey=VGWOVZXMYMCPQO-UHFFFAOYAS

The octaphyrin 1 has been prepared and its crystal structure and electronic circular dichroism (ECD) spectra reported.¹ The x-ray structure identified the compound as having the M,M helical structure. The optical rotation however could not be determined.

Rzepa now reports the computed ECD spectrum and optical activity of 1 and some related compounds.² These computed spectra were obtained using TD0DFT with the B3LYP/6-31G(d) method with the CPCM treatment of the dichloromethane solvent. (The structure of 1 and other computed properties are available from the enhanced web table that Rzepa has deposited with the article (here). Once again this material seems to be available only to subscribers! My repeated discussions with ACS Pubs people that these “web objects” should be treated as data and not as copyrighted materials have fallen on deaf ears.) The computed ECD spectrum matches nicely with the experimental one, except that the signs at 570 and 620 nm are opposite. Rzepa suggests that either the compound is really of P,P configuration or the authors of experimental work have erroneously switched their assignments.

The computed value of [α]_D of 1 is about -4000 °, with the negative sign in agreement with the sign for [α]_D of M-hexahelicene. However, what is truly fantastic is the magnitude of the optical activity of the dication of 1 produced by loss of 2 electrons. This dication should be aromatic and it is predicted to have [α]₁₀₀₀ = -31597°!

References

(1) Werner, A.; Michels, M.; Zander, L.; Lex, J.; Vogel, E., ""Figure Eight" Cyclooctapyrroles: Enantiomeric Separation and Determination of the Absolute Configuration of a Binuclear Metal Complex," Angew. Chem. Int. Ed. 1999, 38, 3650-3653, DOI: 10.1002/(SICI)1521-3773(19991216)38:24<3650::AID-ANIE3650>3.0.CO;2-F

(2) Rzepa, H. S., "The Chiro-optical Properties of a Lemniscular Octaphyrin," Org. Lett. 2009, 11, 3088–3091DOI: 10.1021/ol901172g

I have written a number of blog posts that deal with the computation of optical activity. Trindle and Altun have now reported TD-DFT computations of circular dichroism of high-symmetry molecules.¹ The employ either B3LYP (with a variety of basis sets, the largest being 6-311++G(2d,2p)) and SOAP/ATZP. For a number of the high symmetry molecules (two examples are shown in Figure 1), the two methods differ a bit in their predictions of the first excited state, with SOAP typically predicting a red shift relative to the B3LYP. However, both methods general give the same sign of the CD signals and their line shapes are similar.

1	2

Figure 1. B3LYP/6-31G(d) optimized structures of 1 and 2 (again due to incomplete supporting materials, I reoptimized these structures)

References

(1) Trindle, C.; Altun, Z., "Circular dichroism of some high-symmetry chiral molecules: B3LYP and SAOP calculations " Theor. Chem. Acc. 2009, 122, 145-155, DOI: 10.1007/s00214-008-0494-8.

InChIs

1: InChI=1/C18H14O2/c19-15-7-11-3-1-4-12-8-16(20)10-14-6-2-5-13(9-15)18(14)17(11)12/h1-6H,7-10H2
InChIKey=DYZSIUYFWKNLHS-UHFFFAOYAB

2: InChI=1/C20H24/c1-13-9-18-7-8-20-12-15(3)19(11-16(20)4)6-5-17(13)10-14(18)2/h9-12H,5-8H2,1-4H3
InChIKey=JTMLLDPOLFRPGJ-UHFFFAOYAC

DFT &Optical Rotation Steven Bachrach 27 Jul 2009 No Comments

Next Page »

• Categories

  • Acidity (12)
  • Aromaticity (91)
  • Authors (153)
    • Borden (12)
    • Cramer (11)
    • Grimme (17)
    • Houk (40)
    • Jorgensen (3)
    • Kass (9)
    • Schaefer (13)
    • Schleyer (24)
    • Schreiner (29)
    • Singleton (11)
    • Truhlar (8)
  • Bond Dissociation Energy (6)
  • BSSE (1)
  • cyclophane (0)
  • Dynamics (35)
  • E-publishing (7)
  • Enzyme (4)
  • FEP (1)
  • host-guest (6)
  • Hydrogen bond (5)
  • Ion Pairs (1)
  • Isotope Effects (5)
  • Keto-enol tautomerization (3)
  • Molecules (100)
    • adamantane (3)
    • amino acids (13)
    • annulenes (8)
    • benzynes (4)
    • biphenyl (1)
    • calixarenes (1)
    • carbenes (13)
    • cyclobutadiene (4)
    • dendralenes (1)
    • Dewar benzene (1)
    • diradicals (8)
    • ephedrine (1)
    • ethyl cation (2)
    • fullerene (6)
    • fulvalenes (1)
    • hexacyclinol (2)
    • nanohoops (4)
    • non-classical (4)
    • norbornyl cation (2)
    • nucleic acids (4)
    • oximes (1)
    • phenyloxenium (1)
    • polycyclic aromatics (7)
    • propellane (2)
    • stilbene (1)
    • sugars (5)
    • terpenes (2)
    • twistane (1)
  • NMR (40)
  • Optical Rotation (16)
  • QM Method (96)
    • CASPT2 (1)
    • DFT (71)
    • focal point (7)
    • G3 (3)
    • MP (11)
  • Reactions (83)
    • 1,2-addition (1)
    • aldol (4)
    • Bergman cyclization (6)
    • Claisen rearrangement (2)
    • Cope Rearrangement (5)
    • cycloadditions (12)
    • Diels-Alder (26)
    • electrocyclization (11)
    • electrophilic aromatic substitution (1)
    • ene reaction (1)
    • Hajos-Parrish Reaction (1)
    • Mannich (2)
    • Michael addition (5)
    • ozonolysis (1)
    • proton transfer (1)
    • pseudopericyclic (4)
    • Strecker (1)
    • Substitution (6)
    • Wittig (1)
  • Second Edition (3)
  • Solvation (17)
  • Stereochemistry (2)
  • stereoinduction (4)
  • Tunneling (26)
  • Uncategorized (57)
  • vibrational frequencies (3)

• Monthly

  • June 2019
  • April 2019
  • March 2019
  • February 2019
  • January 2019
  • December 2018
  • November 2018
  • October 2018
  • September 2018
  • August 2018
  • July 2018
  • June 2018
  • May 2018
  • April 2018
  • March 2018
  • February 2018
  • January 2018
  • December 2017
  • November 2017
  • October 2017
  • September 2017
  • August 2017
  • July 2017
  • June 2017
  • May 2017
  • April 2017
  • March 2017
  • February 2017
  • January 2017
  • December 2016
  • November 2016
  • October 2016
  • September 2016
  • August 2016
  • July 2016
  • June 2016
  • May 2016
  • April 2016
  • March 2016
  • February 2016
  • January 2016
  • December 2015
  • November 2015
  • October 2015
  • September 2015
  • August 2015
  • July 2015
  • June 2015
  • May 2015
  • April 2015
  • March 2015
  • February 2015
  • January 2015
  • December 2014
  • November 2014
  • October 2014
  • September 2014
  • August 2014
  • July 2014
  • June 2014
  • May 2014
  • April 2014
  • March 2014
  • February 2014
  • January 2014
  • December 2013
  • November 2013
  • October 2013
  • September 2013
  • August 2013
  • July 2013
  • June 2013
  • May 2013
  • April 2013
  • March 2013
  • February 2013
  • January 2013
  • December 2012
  • November 2012
  • October 2012
  • September 2012
  • August 2012
  • July 2012
  • June 2012
  • May 2012
  • April 2012
  • March 2012
  • February 2012
  • January 2012
  • December 2011
  • November 2011
  • October 2011
  • September 2011
  • August 2011
  • July 2011
  • June 2011
  • May 2011
  • April 2011
  • March 2011
  • February 2011
  • January 2011
  • December 2010
  • November 2010
  • October 2010
  • September 2010
  • August 2010
  • July 2010
  • June 2010
  • May 2010
  • April 2010
  • March 2010
  • February 2010
  • January 2010
  • December 2009
  • November 2009
  • October 2009
  • September 2009
  • August 2009
  • July 2009
  • June 2009
  • May 2009
  • April 2009
  • March 2009
  • February 2009
  • January 2009
  • December 2008
  • November 2008
  • October 2008
  • September 2008
  • August 2008
  • July 2008
  • June 2008
  • May 2008
  • April 2008
  • March 2008
  • February 2008
  • January 2008
  • December 2007
  • November 2007
  • October 2007
  • September 2007
  • August 2007
  • July 2007

This work is licensed under a Creative Commons Attribution-No Derivative Works 3.0 Unported License.