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*To*: Norbert Straeter <strater@chemie.fu-berlin.de>*Subject*: Re: [ccp4bb]: anisotropic ellipsoids*From*: "Eleanor J. Dodson" <ccp4@ysbl.york.ac.uk>*Date*: Thu, 08 Mar 2001 17:36:11 +0000*CC*: ccp4bb@dl.ac.uk*Organization*: Structural Biology Lab. , Dep. Of Chemistry, University of York*References*: <Pine.LNX.4.21.0103081739350.19298-100000@gloria.chemie.fu-berlin.de>*Reply-To*: E.Dodson@ysbl.york.ac.uk*Sender*: owner-ccp4bb@dl.ac.uk

*** For details on how to be removed from this list visit the *** *** CCP4 home page http://www.dl.ac.uk/CCP/CCP4/main.html *** Norbert Straeter wrote: > > *** For details on how to be removed from this list visit the *** > *** CCP4 home page http://www.dl.ac.uk/CCP/CCP4/main.html *** > > According to many textbooks the first three of the thermal parameters > U11 U22 U33 U12 U13 and U23 describe the displacements along the > perpendicular principal axis of the ellipsoid and the latter three give > the orientation of the principal axes with respect to the unit cell axes. > However, I can't find anywhere how U12 U13 and U23 (apparently as > direction cosini) exactly describe the orientation of the ellipsoid, say > in a cartesian system. > > Any hint is appreciated (but don't suggest to try to follow the ortep > code)... > > Thanks, Norbert Is this any help? Taken from $CLIBS/rwbrook.f C PDB files contain cartesian anisotropic temperature factors as orthogonal Us. C Stored as U11 U22 U33 U12 U13 U23 C The anisotropic temperature factors can be input/output to this routine C as orthogonal or as crystallographic Us. C C Shelx defines Uf to calculate temperature factor as: C T(aniso_Uf) = exp (-2PI**2 ( (h*ast)**2 Uf_11 + (k*bst)**2 Uf_22 + ... C + 2hk*ast*bst*Uf_12 +..) C C Note: Uo_ji == Uo_ij and Uf_ji == Uf_ij. C C [Uo_ij] listed on ANISOU card satisfy the relationship: C [Uo_ij] = [RFu]-1 [Uf_ij] {[RFu]-1}T C C where [Rfu] is the normalised [Rf] matrix read from the SCALEi cards. C see code. [ROu] == [RFu]-1 C C T(aniso_Uo) = U(11)*H**2 + U(22)*K**2 + 2*U(12)*H*K + ... C where H,K,L are orthogonal reciprocal lattice indecies. ( EJD: I think????) C C Biso = 8*PI**2 (Uo_11 + Uo_22 + Uo_33) / 3.0 C C [Uf(symm_j)] = [Symm_j] [Uf] [Symm_j]T C -- ------------------------------------------------------------------ Eleanor J.Dodson, Chemistry Department, University of York, U.K. Tel: Home +44 (1904) 42 44 49, work: +44 (1904) 43 25 65 ------------------------------------------------------------------

**References**:**[ccp4bb]: anisotropic ellipsoids***From:*Norbert Straeter <strater@chemie.fu-berlin.de>

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