Patterson method was ideal for studying the structures of organometallic and
co-ordination compounds which were studied extensively after the discovery of
ferrocene in 1953. In these compounds, the heavy metals dominate the calculated
Patterson functions, and their co-ordinates in the unit cell can be calculated from the
initial Patterson function. Insertion of these co-ordinates in the Fourier synthesis
calculation leads to an initial set of phases for the electron density map. This set of
phases is applied to the original amplitudes, and an improved electron density map is
derived, which shows the positions of the lighter atoms. This process is repeated
until an error term (usually R free ) has stabilised to a satisfactory value.
This technique was also widely used to determine the structures of organic and
biologically important molecules. Dorothy Hodgkin’s structural analysis of penicillin during World War 2 was made on metal salts of the penicillin anion. Hodgkin
received the first penicillin crystals in autumn 1943 from the US pharmaceutical
company Squibb, who had obtained high-quality crystals of benzylpenicillin (later
known as penicillin G) as the sodium salt. Hodgkin made the potassium and
rubidium salts so that she could compare the three different diffraction patterns. In
the 1950s her determination of the structure of vitamin B 12 was made possible
because it is a co-ordination compound of cobalt which dominates the scattering.
She also pioneered with Perutz and Kendrew the technique which introduced
isomorphous heavy metal salts into protein crystals whilst retaining their isomorphous character in order to solve these complex structures. They were awarded
Nobel Prizes in 1962 and 1964 for these contributions (see Table 1).
The 1953 monograph, “Solution of the Phase Problem I. The Centrosymmetric
Crystal”, by Karle and Hauptman contained the essential ideas necessary for solving
the phase problem by direct methods [62, 63]. They were based on probabilistic
methods and in particular the joint probability distributions of several structure
factors. The direct method estimates the initial phases and expanding phases using
a triple relation (A trio of reflections in which the intensity and phase of one
reflection can be explained by the other two). A number of initial phases are tested
and selected by this method. With the development of computers, the direct method
became the most useful technique for solving the phase problem and is very widely
used. In this monograph they also introduced the concepts of the structure invariants
and semi-invariants, special linear combinations of the phases, and used them to
devise recipes for origin specification in all the centrosymmetric space groups. The
extension to the non-centrosymmetric space groups was made some years later. In
the 1980s the problem of combining the traditional techniques of direct methods
with isomorphous replacement and anomalous dispersion facilitated the solution of
macromolecular crystal structures. For molecules whose crystals provide reflections
in the sub-Ångström range, it is possible to determine phases by brute force methods,
testing a series of phase values until spherical structures are observed in the resultant
electron density map. This works because atoms have a characteristic structure when
viewed in the sub-Ångström range. The technique is limited by processing power
and data quality. For practical purposes, it is limited to “small molecules” because
they consistently provide high-quality diffraction with very few reflections. In
Early History of X-Ray Crystallography
23
co-ordination compounds which were studied extensively after the discovery of
ferrocene in 1953. In these compounds, the heavy metals dominate the calculated
Patterson functions, and their co-ordinates in the unit cell can be calculated from the
initial Patterson function. Insertion of these co-ordinates in the Fourier synthesis
calculation leads to an initial set of phases for the electron density map. This set of
phases is applied to the original amplitudes, and an improved electron density map is
derived, which shows the positions of the lighter atoms. This process is repeated
until an error term (usually R free ) has stabilised to a satisfactory value.
This technique was also widely used to determine the structures of organic and
biologically important molecules. Dorothy Hodgkin’s structural analysis of penicillin during World War 2 was made on metal salts of the penicillin anion. Hodgkin
received the first penicillin crystals in autumn 1943 from the US pharmaceutical
company Squibb, who had obtained high-quality crystals of benzylpenicillin (later
known as penicillin G) as the sodium salt. Hodgkin made the potassium and
rubidium salts so that she could compare the three different diffraction patterns. In
the 1950s her determination of the structure of vitamin B 12 was made possible
because it is a co-ordination compound of cobalt which dominates the scattering.
She also pioneered with Perutz and Kendrew the technique which introduced
isomorphous heavy metal salts into protein crystals whilst retaining their isomorphous character in order to solve these complex structures. They were awarded
Nobel Prizes in 1962 and 1964 for these contributions (see Table 1).
The 1953 monograph, “Solution of the Phase Problem I. The Centrosymmetric
Crystal”, by Karle and Hauptman contained the essential ideas necessary for solving
the phase problem by direct methods [62, 63]. They were based on probabilistic
methods and in particular the joint probability distributions of several structure
factors. The direct method estimates the initial phases and expanding phases using
a triple relation (A trio of reflections in which the intensity and phase of one
reflection can be explained by the other two). A number of initial phases are tested
and selected by this method. With the development of computers, the direct method
became the most useful technique for solving the phase problem and is very widely
used. In this monograph they also introduced the concepts of the structure invariants
and semi-invariants, special linear combinations of the phases, and used them to
devise recipes for origin specification in all the centrosymmetric space groups. The
extension to the non-centrosymmetric space groups was made some years later. In
the 1980s the problem of combining the traditional techniques of direct methods
with isomorphous replacement and anomalous dispersion facilitated the solution of
macromolecular crystal structures. For molecules whose crystals provide reflections
in the sub-Ångström range, it is possible to determine phases by brute force methods,
testing a series of phase values until spherical structures are observed in the resultant
electron density map. This works because atoms have a characteristic structure when
viewed in the sub-Ångström range. The technique is limited by processing power
and data quality. For practical purposes, it is limited to “small molecules” because
they consistently provide high-quality diffraction with very few reflections. In
Early History of X-Ray Crystallography
23