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Lesson 19

Lesson 19. Logging on to the X-ray Lab computer Running xprep on your structure Theory of refinement and structure solution. Logging on to the X-ray Lab. Start → All programs →Standard Software →Telecommunications → NCD PC-Xware Select PC Xware connection

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Lesson 19

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  1. Lesson 19 • Logging on to the X-ray Lab computer • Running xprep on your structure • Theory of refinement and structure solution

  2. Logging on to the X-ray Lab • Start → All programs →Standard Software →Telecommunications → NCD PC-Xware • Select PC Xware connection • Select “Begin an X session managed ...” • Next • Name: csd • Click on csd • There should be a icon for an x screen in the lower right

  3. Go back a window and click on Secure CRT • Secure CRT • File → New Session(3rd icon top left) • Next • Hostname: “csd.chem.purdue.edu” • Username: “chem696” • Next • Session name: csd • Connect • Login • The program will remember the session csd.

  4. Running XPREP • Change the directory to your structure –cd # where # is your structure number • Start solve • Select the xprep button. • Basically use defaults in the program studying the output. • If when you go to save there is no default file name use “xll”

  5. Electron Density in Crystals • Since the crystal is made up of repeating unit cells, the electron density in the cell must be periodic! • This is called the Charge Density Wave. • In 1-dimension, the length of the charge density wave is the cell length.

  6. One-Dimensional Crystal

  7. Charge Density Wave

  8. Fourier Series

  9. Wave Components One wavelength/cell h=1 ten wavelengths/cell h=10

  10. Correct Phasing

  11. Incorrect Phasing

  12. Diffraction in 1-D • is the electron density at any point x F(h) is called the structure factor and is indexed by the value h F is related to the square root of the intensity of the diffracted beam. Fo is the observed structure factorFc calculated

  13. A Comparison • The Charge Density Wave (CDW) can be decomposed into Fourier components which when summed give the CDW. • The CDW can also be calculated from a Fourier sum of the diffracted waves. • The structure factors F represent the Fourier components of the CDW • The amplitude F is the Fourier coeffcient!

  14. Shift of Origin

  15. Shift of Origin • Clearly this shift does nothing to change the Fourier Coefficients since the shape of the wave is unchanged. • All that is needed is to change the phase of each wave by ½ wavelength. • The location of the atoms is in the phases and not the coefficients!! • Cannot tell positions from diffraction data

  16. Duck Intensity Cat Phases

  17. Cat Intensity Duck Phases

  18. Fourier Domains • In the crystal the electron density makes up real space. • Real space has the symmetry of the space group • The Fourier Transfer generates reciprocal space • Reciprocal Space is the diffraction space • Reciprocal space has the same symmetry as real space.

  19. The structure factor F and the electron density  Ihkℓis proportional to |Fhkℓ|2 Fhkℓ = V xyz exp[+2i(hx+ky+ℓz)] dV xyz = (1/V) hkℓ Fhkℓ exp[–2i(hx+ky+ℓz)] Fhkℓand xyz are related to each other by means of these Fourier transformations. The electron density  is real and positive, but the struktur factor F is a complex number: to calculate the electron density from the structure factors, we also need the phase () of F. Under normal conditions we can only measure the diffracted intensitiesI and not the phase  of a reflection h,k,ℓ, so it appears that we are faced with an insoluble problem, the crystallographic phase problem.

  20. The phase problem • In order to calculate an electron density map, we need both the intensities (|F| is proportional to the square root of I) and the phases  of the X-ray reflections hkl. • The information content of the phases is significantly greater than that of the intensities. • It is unfortunately not normally possible to determine the phases experimentally. This is known as the crystallographic phase problem and would appear to be impossible to solve! In spite of this, small molecule structure are solved routinely these days, usually without serious problems, with the help of thePatterson function and the heavy atom method, or (more commonly) by so-called direct methods based on probability relations involving phases.

  21. What are phases (1)? The electron density is obtained by Fourier transformation of the structure factors Fhkl. Fhkl are complex numbers with amplitudes and phases. The reciprocal transformation to calculate Fhkl from xyz: can also be represented as a sum over the n atoms in one unit-cell: where fjis the scattering factor of atom j (including thermal motion). If the structure is centrosymmetric, the sine terms for x,y,z and –x,–y,–z cancel, with the result that the phase of Fhkl must be 0º or 180º. In the special case of one atom on the origin, all phases must be 0º. xyz = (1/V) hkl Fhkl exp[-2i(hx+ky+lz)] Fhkl = Vxyz exp[+2i(hx+ky+lz)] dV Fhkl = j=1fj exp[+2i(hxj+kyj+lzj)] or n Fhkl = j=1fj { cos[2(hxj+kyj+lzj)]+i·sin[2(hxj+kyj+lzj)] } n

  22. Exercises b 1 0 • Find the 11 enantiomorphic pairs of space groups (hint: all are of course chiral and possess 3N, 4N or 6N axes). • The incomplete picture should show the space group I41. Why is there no space group I43? .. + ¾+ .. a .. ¼+ ½+ .. 1 3. Assign the space group of a tetragonal crystal with the systematic absences: hkℓ, h+k+ℓ = 2n; hk0, h = 2n or k = 2n;hhℓ, 2h+ℓ = 4n

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