Readers who have
arrived at this chapter
in a sequential manner will notice that, apart from the phase
the relationship between the diffraction pattern (reciprocal space) and
the crystal structure (direct space) is mediated by a Fourier
transform represented by the electron density
function: ρ(xyz), (see the figure below).
Readers will also know that the relationship between these two
spaces is "holistic", meaning that the value of this function, at each
point in the unit cell of coordinates (xyz),
is the result of "adding" the contribution of "all" structure factors
[ie diffracted waves in terms of their amplitudes |F(hkl)|
and phases Φ(hkl)]
contained in the diffraction
They will also remember that the diffraction pattern
contains many structural factors (several thousand for a simple structure,
and hundreds of thousands for a protein structure).
The "jump" between direct and reciprocal
spaces, mediated by a Fourier transform represented by the electron
the number of points in the
unit cell, where the ρ function has to be calculated, is very
high. In a cell of about 100 x 100 x 100 Angstrom3,
would be necessary to calculate at least 1000 points in every unit cell
direction to obtain a resolution of 100/1000, which equals 0.1
Angstrom in each
direction. This means calculating at least 1000 x 1000 x 1000 =
1,000,000,000 points (one billion points) and at each point to
structure factors F(hkl).
It should therefore be clear that, regardless of the difficulties of
the phase problem, solving a crystal structure implies the use of
Finally, the analysis of a crystal or molecular structure also implies
calculating many geometric parameters that define interatomic
distances, bond angles, torsional angles, molecular surfaces,
etc., using the atomic coordinates (xyz).
the reasons described above, since the beginning of the use of
Crystallography as a discipline to determine molecular
and crystal structures, crystallographers have devoted special
attention to the development of calculation tools to facilitate
crystallographic work. With this aim, and even before the
computers appeared, the crystallographers introduced the so-called
strips," which were widely used in all Crystallography laboratories.
The Beevers-Lipson strips
Beevers-Lipson strips were strips of paper containing predetermined
values of trigonometric functions of sine and cosine types.
These strips were used in the crystallographic
laboratories to speed up the calculations (by hand)
Fourier transforms (see above: the electron density
function, for example). The
electron density function, among many other periodic functions, can be
broken down into a sum of terms of the sine and cosine type, and hence
the usefulness of these strips.
These strips were
introduced in 1936 by A.H.
Beevers and H. Lipson.
In the 1960s, more than 300 boxes were distributed to nearly
all the laboratories in the world. You can also have a look into
made by the International Union of Crystallography. The nightmare was maintaining upright
box, which had a very narrow base,
otherwise it was impossible to maintain the strips correctly stored!
As expected, the introduction of early computers (or electro-mechanic
calculators) inspired great hope in crystallographers...
Numerical Integrator and Computer, 1945) -- the very first electronic
computer. Some pictures of the rooms where
it was installed.
ENIAC, short for Electronic
was the first general-purpose electronic computer, whose design and
construction were financed by the United States Army during the Second
World War. It was the first digital computer capable of being
reprogrammed to solve a full range of computing problems, especially
calculating artillery firing tables for the U.S. Army's Ballistic
The ENIAC had immediate importance. When it was announced in 1946, it
was heralded in the press as a "Giant Brain". It boasted speeds one
thousand times faster than electro-mechanical machines, a leap in
computing power that no single machine has matched. This mathematical
power, coupled with general-purpose programmability, excited scientists
Besides its speed, the most remarkable thing about ENIAC was its size
and complexity. ENIAC had 17,468 vacuum tubes, 7,200 crystal
diodes, 1,500 relays, 70,000 resistors, 10,000 capacitors and around 5
million hand-soldered joints. It weighed 27 tons, was
roughly 2.6 m by 0.9 m by 26 m, took up 63
consumed 150 kW of power.
Later, with the development of Electronics and Microelectronics, which
introduced integrated circuits, computers became accessible to
crystallographers, who flocked to these facilities with large
boxes of "punched cards" (the only means for data storage at that
time), containing the diffraction intensities and their own
punch card or punched card (or punchcard or Hollerith card or IBM
card), is a piece of stiff paper which contains digital information
represented by the presence or absence of holes in predefined
positions. It was used by crystallographers until the end of the
Punched paper tape (shown in yellow) and
different magnetic tapes (as well as some small disks) used
for data storage during the
1970s and 1980s.
Around the early 1970s, and for over a decade, crystallographers became
nightmare for the managers and operators of the so-called "computing
centers,'' running in some universities and research centers.
In the 1980s the laboratories of Crystallography became "flooded" with
computers, which for the first time gave
crystallographers independence from the large computing centers. The
VAX series of
computers (sold by the company Digital Equipment Corporation) marked
a splendid era for crystallographic calculations.
allowed the use of magnetic tapes and the first hard disk
limited capacity (only a few hundred MB) -- very big and heavy, but
they eliminated the need for the tedious punched cards. Nostalgics should
have a look into this link.!!!
the crystallography applied to macromolecules not only
needs what we could call "hard" computing. The
large electron density maps, which are used to build the molecular
structure of proteins, as well as the subsequent structural
analysis, requires more sophisticated computers with powerful
graphic processors and, if possible, with the capability of displaying
3-dimensional images using specialized glasses...
A Silicon Graphics computer used
to visualize 3-dimensional
maps and structures. The processor and the screen are complemented by
an infrared transmitter (black box on the screen) and the glasses used
by the crystallographer.
The current computing facilities represent a big jump respect to the
capabilities available during the mid-twentieth century, as it is shown
in the representation of the structural model used for the structural
description of penicillin, based on three 2-dimensional electron
And even 3d maps where also used!...
model of the structure of penicillin, based on the
use of three 2-dimensional electron density maps, as used by Dorothy
C. Hodgkin, Nobel laureate in 1964
of 3d electron density maps used until the middle of the
1970's. The contours are lines of electron density and show the
positions of individual atoms in the structure
A typical personal computer commonly used
since 2010 for
crystallographic calculations and also for their graphic capabilities
At present there are
institutional or commercial computer
program developments, or even computing facilities through remote
servers, to fulfill nearly all of the needs for
computing, as well as many sources from which one can download most of
those programs. In this context, it could be useful to check the
Specifically for compounds of small and medium size (molecular
or not) we recommend using the Wingx
package which can be freely downloaded by
courtesy of Louis J. Farrugia, (University of Glasgow, UK). It is
easy to install on a PC and contains an interface which
includes the most important programs for small and medium size
crystallographic problems. Also, for these types of compounds there
is a very useful computer program (Mercury), user-friendly and
free, which includes powerful graphics and some other analytical tools
analyze crystal structures. It can be downloaded
from the Cambridge Crystallographic Data Centre, UK.
crystallographers need more specific programs, and in this context we
recommended using the link offered by CCP4,
Computational Project No.
4, Software for Macromolecular X-Ray Crystallography.
On the other hand,
crystallographic work is
unimaginable without having access to crystallographic
databases, which contain all the structural information that is being
published and which have a clear added value for the
of structure is what determines its inclusion in any of the existing
databases. Thus, metals and intermetallic compounds
available in the database CRYSTMET; inorganic compounds are centralized
in the ICSD database (Inorganic Crystal Structure
Database); organic and organometallic in CSD (Cambridge
Crystallographic Database); and proteins in PDB (Protein Data Bank),
which is a databank (not a database). Other databases, databanks, etc.,
not necessarily contain structural information in the most
but they can also be very helpful for crystallographers. And this is
the case of WebCite
published by the Cambridge Crystallographic Data
containing over 2000 articles with very important
information for structural chemistry research in its broadest sense,
and in particular to pharmaceutical drug discovery, materials design or
drug development, among others.
databases and databanks
As indicated, some of these
databases (or databanks) are
(glycoSCIENCES.de, LipidBank, PDB and NDB), and therefore can be searched online.
However, others (CRYSTMET, ICSD and CSD) require a license or even a
- CRYSTMET: Metals and intermetallic compounds (no longer exists)
- ICSD: Inorganic compounds (license required)
- CSD: Organic and organometallic
- glycoSCIENCES.de: Carbohydrates
- LipidBank: Lipids
- PDB: Proteins, Nucleic
acids and large complexes
- NDB: Nucleic acids
During the period 1990-2012, CRYSTMET, ICSD and CSD have been licensed free of
charge to all CSIC
research institutes (CRYSTMET and ICSD) and
to all academic institutions in Spain and Latin American
(CSD). However, due to economic constraints,
the CSIC's authorities
decided to reduce drastically this program that was
managed through the Department
of Crystallography and Structural Biology (at the Institute of Physical
Chemistry "Rocasolano"). Nowadays this program is maintained
in a reduced manner, only for Spanish institutions, as it
can be seen through this link.