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Automated X-Ray Structure Determination as an Analytical Method.

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Automated X-Ray Structure Determination as an Analytical Method
By Carl Kriiger[*]
1. Introduction
The last few years have seen such rapid advances in X-ray
structure analysis, even of complicated chemical compounds, that the method now appears able to provide the
preparative chemist with a valuable service as a modern
analytical technique. The main reason for this development
is technological progress. Firstly, large, third-generation
computers, which are necessary for the time-consuming
evaluation of extensive data sets, have become available ;
secondly, the manufacturers of analytical instruments offer
fast automatic diffractometers that are necessary for the
collection of these data. The working schedule for the
elucidation of the exact structure of a chemical compound
by three-dimensional X-ray structural analysis is therefore
divided into two parts:
1.Measurement ofposition and intensity for a large number
of diffraction data from a single crystal
2. Evaluation of these data for subsequent solution of the
structure and representation of the molecule and the
contents of the unit cell of the crystal.
The first part of this report describes the operational
features of our diffractometer system, while the second
part deals with our computational approach to the solution
of structural problems. Problems that have not yet been
satisfactorily solved are indicated. It should be pointed out
that ours is not the only system possible, but an optimal
one for our computational and operational facilities.
tapes. Any changes in the measuring parameters during
data collection (e.g. crystal misalignment) were tedious
and necessitated preparation of a new controlling tape.
This and other similar tasks may be more flexibly performed
automatically by a process-control computer.
In principle this control could also be accomplished by a
time-sharing computer in on-line operation. The advantages
of such a mode would include the programming facilities
available in a higher-level language (FORTRAN etc.), fast
program change, and direct data transfer to external data
storage devices of the computer. An alternative would be
the utilization of a small process-control computer or
“dedicated computer” (see ref. [’I for the advantages and
disadvantages of these two systems).
In lengthy experiments, where a relatively large computer
effort is required for control, the use of a small computer
appears more suitable. A small computer is independent of
servicing and breakdown periods of a naturally more
sensitive, large computer system. It is useful, however, to
link the small computer to a large computer for rapid
transfer of programs and data. Thus the external storage
capacities of a large computer become accessible, while
still preserving a certain independence in the data collection
system. The arrangement of our diffractometer system is
shown in Figure 1.
2. Fully Automatic Single-Crystal Diffractometers
Construction and operation of modern single-crystal
diffractometers have already been described in detail“].
As a common feature, crystals having approximate dimensions of 0.1 to 0.6 mm are mounted on a carrier and oriented
in a homogeneous,monochromaticx-ray beam in reflecting
positions according to Bragg. The integrated intensity of a
reflection is measured with a scintillation counter. During
the course of one analysis of average difficulty, there are
more than a thousand reflecting positions for a crystal and
a corresponding number of intensity measurements must
be performed.
Most of the available instruments orient the crystal into
reflecting positions using the so-called “Eulerian cradle”
which allows the crystal to be rotated about three or four
axes into any position. Control of these movements in early
instruments was accomplished using stepping motors
driven by paper tape. This technique relies heavily on the
availability of a computer for preparing the controlling
Dr. C. Kruger
Max-Planck-Institut fur Kohlenforschung
433 Mulheim/Ruhr, Kaiser-Wilhelm-PIatz 1 (Germany)
Angew. Chem. internat. Edit. 1 Vol. I I (1972) 1 N o . 5
Fig. 1. Arrangement of our diffractometer system, consisting of an
automatic, four-circle X-ray diffractometer, Kristalloflex 4 AED
(Hoppe-Siemens), an interface, and a small computer ( P D P 8) connected to a large computer ( P D P 10).For further details see text.
A fully automatic four-circle diffractometer[*l (AED Siemen~-Hoppe)[~’
is controlled by a small PDP 8 computer
(12-bit word length, 4 K memory and 32 s cycle time) using
an interface linked to an IBM 026 card punch. An ASR 35
[*] In principle, all commercially available computer-controlled
diffractometers can be used in the manner described here.
teletype is also connected uia an additional link and can
be used to communicate with the large computer. The connection between large and small computers is very important. For several technical reasons we chose to connect
the small computer in the simplest possible manner, i. e. as
a pseudo-teletype, which allows for selection of various
data transfer
data can be transferred ten times faster if desired. The
experimentalist therefore enjoys the advantages of both
Storage of data collection programs for a process-control
computer in binary form on external devices of a large
computer and loading them when needed has proved to
be an optimal mode of operation. The time required for
loading programs is ordinarily about two minutes. Programs which may be needed at the diffractometer in the
course of the experiment may also be initialized on the
large computer from the same teletype (e.g., least-squares
programs for cell dimensions or programs for generation
of Miller indices with the corresponding angular values
for the instrument).
This type of connection can be made without altering the
operating system of the large computer. The normal data
transfer rate permits operation of the teletype as a normal
time-sharing terminal, but data-collection programs or
Selection and
mounting of the crystal
Figure 2 gives the scheme of a routine X-ray analysi~‘~!
Photographic investigation
(Weissenberg and precession
Cell data and space group
Transfer to diffractometer
and alignment
1 Search f o r positions I
of reflection maxima
\Accurate cell data
Determination of the
orientation matrix
Successive intensity measurements
of all reflections
Output of these data on
punched c a r d s
1 Data reduction
direct methods
Patterson methods (vector)
the method of least squares
Molecular geometry and drawings
Fig. 2. Scheme of a routine automatic X-ray structural analysis.
Alternatively, the diffractorneter could be controlled by a small
computer with an expanded memory (8 K) OJ a fast disk unit. These
systems are relatively economical, but not in comparison to our
Crystal quality is again checked (Q-scans, @-scans)before
data collection. Accurate diffracting angles of several (ca.
50) high-angle reflections are then determined from the
positions of the maxima obtained by computer controlled
step-scan profiles using a receiving slit in front of the scintillation counter. These measured data are treated by the
method of least squares and yield accurate unit cell parameters (+O.OOl A) that are subsequently used for exact
positioning of the crystal and counter for the determination
of the intensities of the reflections.
Various programs for these operations are available for
the small as we11 as the large computer and are accessible
from the teletype. Experience has shown the availability
of more than one computer system to be especially timesaving in such cases.
Data correction (Lorentz- and
polarization effects, absorption,
extinction, misalignment) and
calculation of structure factor
4 F
amplitudes I
1 Structural model
After selection with the aid of a polarizing microscope, the
crystal may be mounted on a goniometer head, if necessary
under an inert gas atmosphere in a Lindemann glass
capillary, centered, and adjusted optically. Determination
of cell data and space group is performed by Weissenberg
and precession photographic techniques,which also furnish
information about the crystal quality and crystal symmetry.
Crystal and goniometer head are transferred to the automatic diffractometer where the operations of centering and
adjusting the crystal are computer controlled.
A possible alternative to the point-to-point search for
reflections lies in the use of computer programs that determine optimum angular positions of accessible reflections
within specified limits and record these values. From our
experience we prefer the former method.
The actual data collection program of the controlling
computer subsequently generates Miller indices of desired
reflections within defined limits and excludes those that are
systematically absent due to molecular arrangement (space
Every reflection is centered on the counter by movement of
the “Eulerian cradle” and the integral intensity is determined by scanning in one angle. Each reflection has five
measured values of which two are background measurements on each side of the peak (five-value measurement[61).
There are also data collection programs employing difference filter measurement. Every reflection is scanned twice :
once with a filter screening out the white radiation and a
Angew. Chem. internat. Edit. 1 Vol. I1 (1972) 1 No. 5
second time with another filter screening out the primary
peak as well as the white radiation.
Additional characteristics of our measuring programs
include the following : The scan-width for each reflection
can be controlled as a function of the diffracting angle
by the computer, thus reducing the overall measuring time.
Furthermore, very strong reflections are scanned with
attenuating filters automatically introduced into the
primary beam and are marked accordingly. The intensity
of a monitoring reflection is determined with a slit system
at the end of a cycle (about 20 to 40 reflections) and indicates
possible misalignment or decomposition of the crystal.
Misalignment errors are reported. Output of the measured
intensity as well as the diffractometer parameters for each
reflection are printed out on the teletype and punched on
cards. The remainder of the calculations for the structural
analysis is done off-line on the large computer.
3. Determination of the Structure
After data collection the measured intensities are prepared
for evaluation. The relevant program[71utilizes the five
measurements of each reflection, determines probable
errors and indicates possible reasons, scales the data with
respect to the initial monitoring reflection, and then writes
the results onto a magnetic tape that is used for the actual
data reduction. Most of our programs write data onto
magnetic tapes that are subsequently read by other programs. Data reduction first corrects themeasured intensities
( I ) for Lorentz and polarization effects and for absorption,
and then converts them into the required amplitudes
(structure factor amplitudes, F)[81.
The crucial and remaining problem of an X-ray crystal
structure analysis is to derive the electron density distribution of the unit cell, which means computing the parameters
that define the geometry and vibrational characteristics of
the molecule. Given the measured amplitudes (structure
factor amplitudes (IFI))and the corresponding phases, this
computation is relatively simple. However, the necessary
phase angles (zero and 71 for centrosymmetric space groups)
are neither known nor measurable.
The subsequent mathematical treatment of the structural
analysis is divided into three parts :
1. Solution of the phase problem by finding parts of the
2. Construction of the complete molecule
ficient number of phases are then known so that a Fourier
synthesis will establish the remainder of the molecule more
or less completely.
Similar results are obtained by the convolution method[’].
The geometry of a known molecular fragment (e.9. one
or more benzene rings) generates a vector set which is
optimally adjusted to the observed vector set. Phases
obtained from the located molecular fragment are then
applied as a pseudo heavy atom.
3.2. Direct Methods
Direct methods[101are structural solving processes which
furnish structural models directly from structure factor
amplitudes and not from information about heavy atoms
etc. These methods employ statistical relationships between
the phases ofcertain reflections (triple-product relationship).
For centrosymmetric space groups there are computer
programs that yield probable solutions by iterative techniques. This method is best applied to molecules with
atoms of similar atomic number. The program set (FAMEMAG1C)‘”l which we use works automatically in most
centrosymmetric problems. Structures in acentric space
groups require considerably more mathematical treatment,
but computer programs for these situations are in an
advanced testing stage in several laboratories.
Apart from these principal methods, crystal structures can
also be solved by anomalous dispersion effects or by isomorphous replacement of heavy atoms where the space
group symmetry remains the same. Another, “trial and
error” method which adjusts a given model to the unit cell
has received only limited attention.
4. Structural Refinement
After a sufficient part of the molecule has been ascertained,
the complete construction of the unit cell is determined by
successive Fourier and difference Fourier syntheses. Proposals have also been made for automation of this timeconsuming part of structural analysis” ’]. One method
which appears very promising refines the occupancy factors
of all atoms according to a third order polynomial equation
(phase refinement). Also included in this refinement are
positions which may eventually prove to be false. The
method works in reciprocal space as well as real space[’31
and is being automated.
3.1. Heavy Atom Method
The last step, which requires the most computer time,
adjusts the atomic positions and vibrational parameters to
the observed data by the method of least squares[*! The
subsequent calculation of inter- and intramolecular distances and planes or drawing of the molecule, as shown in
several examples, requires comparatively less computing
In this method the larger electron density of a heavy atom
is utilized to ascertain the spatial position of the heavy atom
by Patterson methods with the squared amplitudes (IF’/)
and does not require any knowledge of the phases. A suf-
The program system which we apply to structural determinations has been developed around the operational mode
of the available computer. All of the necessary programs
are stored on a disk unit and are individually accessible
from a teletype at any time. Input data for these programs
3. Adjusting the molecular parameters to the measured data.
For practical solutions to the phase problem the methods
described in Sections 3.1 and 3.2 have been applied successfully.
Angew. Chem. internal. Edit. [ Vol. I I (19721 / N o . 5
can also be given from the teletype, while all other information is stored on mini-magnetic tapes or on disk units
and are retrievable when needed. Systems for other computers work similarly, but input control for programs is
generally by punched card^['^^[*^.
5. Examples
The following typical examples illustrate how efficient these
present methods are in application to routine operations.
In this analysis 5977 reflections were measured with the
following cell data: P2,/n, a=21.83, b=16.54,c=21.24
p= 102.7°,Z=4,d(X-ray)=1.12,d(observed)=1.13 gcn-3.
The positions of the heavy atoms were determined by direct
methods; all subsequent C and N atom positions were
established through ten cycles of phase refinement in direct
space. The following refinement of the molecular parameters had to be divided into several parts, because the size
of the problem far exceeded the capacities of the computer.
In view of this situation, the resulting computing time for
the anisotropic refinement of the vibrational parameters
The drawings were prepared with a local modification of
the program ORTEPrlS1on an x-y plotter.
Fig. 5. Illustration of the group P,Ni-NrN-NiPZ
in the nitrogen
adduct to bis(!ricyclohexylphosphane)nickel(O) shown in Fig. 4.
Fig. 3. Structure of a pyridine adduct to cyclooctatetraenechlorotitanium.
Figure 3 shows the geometrical arrangement of a pyridine
adduct to a cyclooctatetraenechlorotitanium. The gross
features of the structure were obtained by direct methods,
even though the cyclooctatetraene fragment was disordered
about the transition metal atom and the pyridine rings
occupy two statistically disordered orientations. Several
examples of similar disorder are known[161.
A further example indicates the present limits of our
operation with respect to molecular size and is depicted in
the stereoscopic drawing of Figure 4. This structure is a
nitrogen adduct to bis(tricyclohexylphosphane)nickel(O)
and is a molecule with 80 atoms[”1.
Fig. 6. Structure of the nitrogen adduct to bis(tricyclohexy1phosphane)nickel(0) depicting the enclosure of the nitrogen molecule by the
cyclohexyl rings.
Fig. 4. Structure of a nitrogen adduct to bis(tricyclohexylphosphane)nickel(O) illustrated by a stereoscopic drawing.
[*] The system described in [Ida], which contains all necessary
programs, is available from Deutsches Rechenzentrum Darmstadt.
An expanded version is in use at the Max-Planck-Institut for Eiweissund Lederforschung, Abteilung fur Kun~gen-Strukturforschung,Munchen.
indicated termination of the refinement at the agreement
value of ~ = 0 . 1 1 .~i~~~~ 5 shows the geometry for an
important section Of the molecular grouping
Angew. Chem. internat. Edit.
VoI. 11 (1972) No. 5
Fig. 9. Structure of bis(s-pineny1)nickel and structural formula.
symmetry axis can be seen parallel to the c axis. The
molecular structure is also illustrated stereoscopically in
Figure 9 and Figure 10.
Fig. 7. Structure of di-~-hydridobis[l,3-trimethylenebis(dicyclohexylphosphane)nickel] ( N i - N i ) and structural formula.
The last example, the structure determination of a compound prepared by the displacement of one carbonyl from
Ni(CO), by the ylide tricyclohexylethylidenephosphorane,
will also illustrate the costs incurred by a three-dimensional
structural analysis. The molecular arrangement is shown
in Figure 11[201.
Fig. 10. Stereoscopic drawing of bis(n-pineny1)nickel.
From Figure 6 it is evident that the effective stability of this
compound is primarily dependent on the molecular nitrogen
being enclosed by the cyclohexyl rings. This steric arrangement is also evident in the dihedral angle of 96.7" between
planes (see also Fig. 4).
A similar torsion (116.7") between opposite P-Ni-P
groups can also be observed in di-p-hydridobis[ 1,3-trimethylenebis(dicyclohexylphosphane)nickel] (Ni-Ni) (Fig.
711']). The bond distance of the complexed nitrogen is
slightly lengthened (0.01 A) compared to that in the free
Another form used to illustrate the molecular parameters
with the plotter program ORTEP is shown in Figure 8 for
the unit cell of bis(a-pinenyl)nickel"9! A two-fold screw
Fig. 11. Structure of the compound (CO),N1-CH-P(C6H,,),
Fig. 8. Stereoscopic drawing of the unit cell of bisfx-pineny1)nickel. a axis horizontal, b axis vertical
Angew. Chem. internal. Edit. 1 Vol. I1 (1972) 1 No. 5
The formation of a sigma Ni-C bond between the sp3
carbon (C4) of the ylide and the transition metal is of
interest. This bond is noticeably longer than several other
o-Ni-C bonds117*
”I which we have recently investigated
(Figs. 12 and 13). The phosphorus-carbon distance is
relatively short, although longer than that found in free
ylides1”1, but is similar to the P-C distance found in
phosphonium compounds1231.
According to our present experience three-dimensional
structural analyses of average difficulty (approximately 50
atoms per molecule maximum) can be completed in a
minimum of four weeks. Certain unforeseen difficultiesthat
may occur during the analysis can increase this time to
two or three months. Of course the minimal time is based
on the availability of a large computer and an automatic
data collection system. Approximately a week for each part
of the analysis-preliminary investigation, data collection,
structure determination, and refinement (kO.01 A)-has
been assumed.
The cost of such an analysis is largely dependent on the
expenditures for computer time and man-hours required.
Depending upon the problem this may be between
Fig. 12. Structure of 2,4-pentanedionatomethyltricyclohexylphosphanenickel(ir) and structural formula.
Fig. 13. Structure of methyldiisopropyfphenylphosphane-x-pentenylnickel and structural formula.
DM 20000 and DM 200000. It clearly follows that routine
X-ray structural analyses should be applied only in situations where less expensivemethods do not provide sufficient
I would like to thank my co-workers Dr. B. L. Barnett,
B. Boleslawsky, K . H . Claus, M . Eckhardt, and Dr. I!-€€. B a y
for their enthusiastic support.
Received: November 18, 1972 [A 872IEI
German version: Angew. Chem. 84,412 (1972)
Transiated by Dr. B. L. Barnett, Mulheim/Ruhr
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Angew. Chem. internat. Edit. / Vol. 1 1 (1972) / N o . 5
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