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Determining the structure of a
molecule in a crystalline
sample requires knowing both the
amplitude and the phase of the
photon wave being diffracted from
the sample. Although a detector
can measure the intensity of a
wave, which is equal to the square
of its amplitude, there is no
general way to measure its phase.
Thus, when measuring a diffraction
pattern it is common to hear that
one has "lost the phase."
Reconstructing the phase of the
diffracted wave is the crux of the
phase problem.
In
x-ray crystallography, there
are several ways to recover the
lost phases. A powerful solution
is the
multiwavelength anomalous
diffraction (MAD) method.
Partial structural information is
available from the comparison of
the diffraction intensities
obtained by measurements using
different x-ray wavelengths. The
atomic
anomalous dispersion effect
causes these differences, and
every atom has its own
scattering factor. However, it
is necessary to use
synchrotron radiation to
obtain the appropriate wavelengths
when using the MAD method. Other
methods of experimental phase
determination include multiple
isomorphous replacement (MIR) and
single wavelength anomalous
diffraction (SAD). Molecular
replacement can be used to recover
phases if the structure of a
similar molecule has been
previously determined.
There are two major processes
for recovering the phases using
the data obtained by regular
equipment. One is the direct
method, which 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 has a triple relation.)
A number of initial phases are
tested and selected by this
method. The other is the Patterson
method, which determines the
differences of the phases between
heavy atoms by using the
Patterson function, which
gives a large value when the
electron density is large at the
given position. This method can be
applied only when the crystal
contains heavy atoms. Because of
the development of computers, the
direct method is now the most
useful technique for solving the
phase problem.
