The platon crystallographic package - səhifə 62
( -1 1 0 ) X ( 1 0 1 ) = ( 1 0 2 ) =
( -1 -1 0 ) ( -1/2 -1/2 0 ) ( -1 0 0 ) 2.000
Cell Lattice a b c alpha beta gamma Volume CrystalSystem Laue
Input mC 6.626 41.080 6.600 90.00 120.11 90.00 1554 Monoclinic 2/m
Reduced P 6.600 6.602 20.806 94.59 94.58 119.75 777
Convent oF 41.080 11.419 6.626 90.02 90.00 90.00 3108 Orthorhombic mmm
:: Cell Angles differ 0.02 Deg. from (90/120)
Conventional, New or Pseudo Symmetry
Space Group Fdd2 No: 43, Laue: mmm [Hall: F 2 -2d ]
Lattice Type oF, Acentric, Orthorhombic, Order 16( 4) [Shoenflies: C2v^19 ]
CHIRAL - See P.G. Jones, Acta Cryst. (1986), A42, 57.
Nr ***** Symmetry Operation(s) *****
1 X , Y , Z
2 - X , - Y , Z
3 3/4 - X , 3/4 + Y , 1/4 + Z
4 1/4 + X , 1/4 - Y , 1/4 + Z
5 X , 1/2 + Y , 1/2 + Z
6 - X , 1/2 - Y , 1/2 + Z
7 3/4 - X , 1/4 + Y , 3/4 + Z
8 1/4 + X , 3/4 - Y , 3/4 + Z
9 1/2 + X , Y , 1/2 + Z
10 1/2 - X , - Y , 1/2 + Z
11 1/4 - X , 3/4 + Y , 3/4 + Z
12 3/4 + X , 1/4 - Y , 3/4 + Z
13 1/2 + X , 1/2 + Y , Z
14 1/2 - X , 1/2 - Y , Z
15 1/4 - X , 1/4 + Y , 1/4 + Z
16 3/4 + X , 3/4 - Y , 1/4 + Z
:: Origin shifted to:-0.125, 0.269, 0.000 after transformation
:: * Symmetry Elements preceded by an Asterisk are New and indicate
:: Missed/Pseudosymmetry Summary
:: M/P CcToFdd2 Cc (Anonymous ExamC => oF 0.000 0.02 0.026 100% Fdd2
:: note: glide plane codes are with reference to input cell !!
:: An SPF-style file is written to be used for the cell transformation.
:: Change of Crystal System indicated. (Maxdev. = 0.026 Ang.)
Chapter 5 - VOID and SQUEEZE Calculations
5.1 - Introduction
Crystal structures frequently include solvents of crystallization filling voids in the packing
pattern of the molecule of interest. Often crystals can be obtained only after multiple
crystallization attempts from many different solvents and solvent mixtures. The successful
solvent has obviously just the spacial and interaction characteristics to fill the the void. In
chemical crystallography solvents often occupy voids at special positions such as n-fold
axes, mirror planes and their combinations. Those symmetry elements are poor 'packers' as
opposed to twofold screw axes and glide planes which allow close contacts of convex and
concave regions of the molecules. Voids can have both finite and infinite volumes (e.g.
channels along n-fold screw axes with n =3, 4 or 6). Since the site symmetry of finite voids
is often higher than the symmetry of the solvent molecules the result will be disorder.
Similarly, the stacking of solvent molecules in infinite channels will usually be
incommensurate with the translation period of the ordered part of the structure, resulting in
ridges of constant density. Our interest in solvent accessible voids in a crystal structure
stems from a problem that we encountered with the refinement of the crystal structure of the
drug Salazopyrin that appeared to include such continuous solvent channels (van der Sluis
& Spek, 1990a). The residual electron density in those channels (shown in
Fig. 5.1-1) could
not be modeled satisfactorily with a disorder model. The difference Fourier map showed no
isolated peaks but rather a continuous density tube filled with unknown solvent. After
having surmounted the problems to obtain suitable crystals for data collection we got
subsequently stuck with an unsatisfactorily high and un-publishable R-value. This problem
was the start of the development of a technique now named SQUEEZE and available in the
program package PLATON. A description of a prototype implementation of the current
method, at that time named BYPASS, can be found in van der Sluis & Spek (1990b). The
underlying concept of SQUEEZE is to split the total scattering factor F
(calc) into two
contributions: the contribution of the ordered part F
(Model) and the contribution of the
disordered solvent F
(solvent). The latter contribution is obtained by back-Fourier
transformation of the electron density that is found in the solvent region in the difference
Fourier map. This recovery procedure is repeated until conversion is reached.
Judging from the number of structures that are flagged in the CSD for the fact that
SQUEEZE was used it can be estimated that the procedure was used at least 1000 times and
probably many more.
Fig. 5.1-1.Views down and perpendicular to the solvent accessible channels (green) in the
crystal structure of the drug Salazopyrin.
5.2 - The Algorithm
All structures contain void space in small regions and cusps between atoms. In the order of
35% of the space in a crystal structure lies outside the van der Waals volume of the atoms in
the structure. In the current context, we are not interested in those voids but rather in voids
that can at least accommodate a sphere with minimum radius R(min). A good default choice
for R(min) = 1.2 Angstrom, being the van der Waals radius of the hydrogen atom. Most
structures exhibit no voids in the last sense.
In this section, we will first give an ‘analog’ graphical introduction to the concept of
‘solvent accessible volume’ and then more details on its numerical implementation.
5.2.1 - The analog model
Solvent accessible voids are determined in three steps as illustrated in
Step #1: A van der Waals radius is assigned to all atoms in the unit cell. In this way, we have
divided the total volume V into two parts: V(inside) and V(outside). Note that as a
byproduct, we can determine the so called Kitajgorodskii packing index (Kitaigorodskii,
1961) defined as: Packing Index = V(inside) / V.
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