Hi all, I would like to ask some questions regarding this thread.. 1) What is exactly meant by "Fourier transformed electron density"?- according to my knowldege performing a fourier transform on the electron density gives you the structure factor back. So, how does it related to what Prof. James H called "non-lattice-convoluted pattern"? It will be really nice if somebody can explain the thing in a " decoded" language?! And also any articles focusing on the concepts discussed in the entire thread will be very helpful
Regards, ARKO On Sat, Jan 14, 2012 at 12:42 AM, Dale Tronrud <det...@uoxray.uoregon.edu>wrote: > I think you have to be a little more clear as to what you mean > by an "electron density map". If you mean our usual maps that we > calculate all the time the Patterson map is just the usual Patterson > map. It also repeats to infinity, with the infinitely long Patterson > vectors (infinitely high frequency components) being required to > create the Bragg peaks. If you mean an electron density map of a > single object with finite bounds your Patterson map will also have > finite bounds, just with twice the radius. > > The Patterson boundary is not a sharp drop-off because there aren't > as many long vectors as short ones, but the distribution depends on > the exact shape of your object. Once you have a Patterson map that > has an isolated edge (no cross-vectors) back calculating the original > object is pretty easy. (Miao, et al, Annu. Rev. Phys. Chem. 2008, > 59:387-410) > > Dale Tronrud > > On 01/13/12 10:54, Jacob Keller wrote: > > I am trying to think, then, what would the Patterson map of a > > Fourier-transformed electron density map look like? Would you get the > > shape/outline of the object, then a sharp drop-off, presumably? Is > > this used to orient molecules in single-particle FEL diffraction > > experiments? > > > > JPK > > > > On Fri, Jan 13, 2012 at 12:33 PM, Dale Tronrud > > <det...@uoxray.uoregon.edu> wrote: > >> > >> > >> On 01/13/12 09:53, Jacob Keller wrote: > >>> No, I meant the non-lattice-convoluted pattern--the pattern arising > >>> from the Fourier-transformed electron density map--which would > >>> necessarily become more complicated with larger molecular size, as > >>> there is more information to encode. I think this will manifest in > >>> what James H called a smaller "grain size." > >> > >> I've been thinking about these matters recently and had a nifty > >> insight about exactly this matter. (While this idea is new to me > >> I doubt it is new for others.) > >> > >> The lower limit to the size of the features in one of these > >> "scattergrams" is indicated by the scattergram's highest frequency > >> Fourier component. Its Fourier transform is the Patterson map. > >> While we usually think of the Patterson map as describing interatomic > >> vectors, it is also the frequency space for the diffraction pattern. > >> For a noncrystalline object the highest frequency component corresponds > >> to the longest Patterson vector or, in other words, the diameter of > >> the object! The bigger the object, the higher the highest frequency > >> of the scattergram, and the smaller its features. > >> > >> Dale Tronrud > >> > >>> > >>> JPK > >>> > >>> On Fri, Jan 13, 2012 at 11:41 AM, Yuri Pompeu <yuri.pom...@ufl.edu> > wrote: > >>>> to echo Tim's question: > >>>> If by pattern you mean the position of the spots on the film, I dont > think they would change based on the complexity of the macromolecule being > studied. As far I know it, the position of the spots are dictated by the > reciprocal lattice points > >>>> (therefore the real crystal lattice) (no?) > >>>> The intensity will, obviously, vary dramatically... > >>>> ps. Very interesting (cool) images James!!! > >>> > >>> > >>> > > > > > > > -- *ARKA CHAKRABORTY* *CAS in Crystallography and Biophysics* *University of Madras* *Chennai,India*
