# Re: [ccp4bb]: anisotropic ellipsoids

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Norbert Straeter wrote:
>
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>
> 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

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Eleanor J.Dodson, Chemistry Department, University of York, U.K.
Tel: Home +44 (1904) 42 44 49, work:  +44 (1904) 43 25 65
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