The platon crystallographic package - səhifə 72
Ca -1.79 In 1.93 Po -2.48 Ti -2.27
Cd 1.58 Ir -2.12 Pr -2.62 Tl 1.96
Ce -2.63 K 2.75 Pt 1.72 Tm -2.52
Cl 1.75 La -2.67 Pu -2.33 U 1.86
Co -2.03 Li 1.82 Ra -2.70 V -2.13
Cr -2.15 Lu -2.52 Rb -2.27 W -2.17
Cs -2.47 Mg 1.73 Re -2.15 Y -2.58
Cu 1.40 Mn -2.15 Rh -2.25 Yb -2.74
D 1.20 Mo -2.27 Ru -2.30 Zn -2.25
Dy -2.55 N 1.55 S 1.80 Zr -2.36
Van der Waals Radii are those of Bondi (1964) or from CCDC Mercury.
Negative entries are estimated as covalent radius + 0.8 Angstrom
APPENDIX V – Algorithms
V-1 – The Calculation of Derived Standard Uncertainties
Appendix VI – The PLATON/CALC Listing Explained
The PLATON/CALC instruction invokes an extensive listing on a file with extension
with information that can be derived from the input data (preferably a
.cif). This file is
suitable to be inspected with an editor. For hardcopy on laser printers both PostScript and
PDF versions are or can be produced with extensions
listing that is obtained for a compound named ambi will be examined. The relevant files
ambi.pdfcan be downloaded from . Not all
features can be illustrated with a single example. Features that are missed in the current
example will be illustrated with the relevant parts of other examples.
Cell Dimensions.The listing starts with info related to the cell dimensions and includes an
orthogonalization matrix that brings the coordinates of the atoms in an orthogonal Angstrom
scale system. Such a system is useful for simple calculations such as distances between
atoms by hand. Orthogonalization is not unique. In the literature at least three versions can
be found. The method used in PLATON is the one described in the excellent book of Dunitz
Space Group Symmetry. The symmetry as provided on input is analyzed and converted
into a standardized list of symmetry operator, Hermann-Mauguin and Hall space group
symbols (Hall, 1981). First comes the set of symmetry operations not including the
inversion or lattice centering operators. This is essentially the group generated from a small
set of so-called generators (for P2
this involves just 2 of the three screw axis). This list
is expanded by inversion where applicable, taking care that translation parts are always in
the range 0 to 1. The resulting list is expanded according to the lattice centering operations.
The resulting list is used in all subsequent calculations.
ADDSYM. A default analysis is carried out to report on possibly missed higher or pseudo
symmetry with ADDSYM (an extended version of the MISSYM algorithm of Le Page
(1987, 1988)). The result of this analysis is not implemented in the rest of the calculations
but might need a more detailed analysis.
Coordinates. The structure is analyzed on the bases of predefined or optionally user-
supplied values associated with the atom types in the structure. The values used are listed.
The structure is analyzed in terms of molecular residues, in this case two, and their
coordinates listed both in terms of fractional coordinates as with Angstrom coordinates. The
atom list is sorted with various properties listed for each atom such as refinement flags and
site-occupation (population) parameter that should be 1.0 unless disordered. This value may
differ from the SHELXL site-occupation parameter value by the site symmetry number for
atoms on special positions. The coordinate list is completed for molecules on special
Summary of of the unit cell contents. The centre-of-gravity for each molecular residue is
listed along with its formula and multiplicity in the unit cell. A moiety and sum formula
with associated Z value is derived from that information. Those values may need a change
by a small integer value in complicated cases where chemistry might point to a better
presentation. In any case, when the Z value is changed also F(000), Z' and the molecular
weight have to be changed accordingly. The calculated Friedif value (Flack & Shmueli,
2007) may be used as a measure for the possibility to determine the absolute structure for
the given structure.
MOLSYM. The point group of each molecular species, within a tolerance, is reported
following an algorithm published by Pilati & Forni (1998, 2000). Hydrogen atoms are
excluded from the analysis.
NONSYM. This is a feature that is under development. It aims at finding local symmetry
relations between two or more chemically identical molecules and their location and
orientation with reference to the unit cell. It is based on a comparison of the inertial systems
of two molecules with at least six non-hydrogen atoms. The current example lists inertial
system data (main axes, Eigenvalues and angles of the main axes with the cell axes) for only
one molecule. The
asymvalue is a measure for the asymmetry of the molecule. Non-
crystallographic symmetry is not uncommon. With more than one chemically identical
molecule in the asymmetric unit there exist often a local symmetry relation that is not
compatible with the space group symmetry elements.
Displacement Parameters. Displacement parameters are listed along with their main axis
values and equivalent isotropic U value (Ueq). The U3/U1 ratio is a measure for the
deviation from spherical. Large values of this ratio may indicate the need to split the atoms
over two positions. Tentative new coordinate sets are given in brackets. Also an average
molecular U3/U1 is calculated. Large values may indicate either a large motion in one
direction or an artifact of unresolved disorder or absorption issues. Also a summary is
given of the Ueq range and average for each atom type.
Rigid Body Analysis. Each molecular residue is analyzed for rigid body motion
(Schomaker & Trueblood, 1968; Dunitz, 1979) expressed in the T, L and S matrices.
Experimental Uij's from the least squares refinement are compared with the Uij's calculated
with the TLS model. The libration tensor is used to calculate corrections for bond lengths of
which their values are shortened due to the effect of libration. In addition, a Hirshfeld Rigid
Bond test is done (Hirshfeld, 1978). The assumption is that the components of the
anisotropic displacement parameters along a bond should have approximately the same
value. Large differences may have many reasons including wrongly assigned atom type's. A
similar test is done for all atoms in the molecule. The result is presented in matrix form. The
upper triangle gives the Hirshfeld differences and the lower triangle the distance between
the atoms involved. Larger values of the Hirshfeld differences for non-bonded atoms may
indicate large flexibility.
Connectivity Table. For each atom those that are bonded to it are listed. The hybridization
(sp, sp2, sp3) is estimated from the geometry around that atom along with the establishment
of whether a chiral atom has to be classified as S or R. The latter assignment has to be
checked when that atom is part of a complicated multi-ring system. 'tnr' is a topology based
number that is calculated for each atom. This number is among others used for automatic
molecule fitting and an automatic numbering scheme.
Bonds, Angles and Torsion Angles. For each molecular residue the bonds, bond angles and
torsion angles are listed. Standard uncertainties are calculated on the basis of the variances
on the coordinates. S.u.'s may deviate slightly from those reported by software that has
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