Chemistry Reference
In-Depth Information
Contents
1 Data Processing for X-Ray Diffraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Crystallographic Databases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
3 Crystal Structure Analysis with Geometrical Descriptors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.1 “The Shorter, the Stronger” . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
3.2 Atom-Atom Contact Distribution Functions [
23
] .....................................7
3.3 Molecular Chains, Concatenation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
3.4 Comparing Crystal Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4 Crystal Structure Analysis by Quantum Chemistry . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
4.1 Electron Density Integrals and Atoms-in-Molecules Methods . . . . . . . . . . . . . . . . . . . . . . . . 11
4.2 Ab Initio Quantum Chemical Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
4.3 Perturbation Theory Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
4.4 Semiempirical Methods: The PIXEL Density Sums Approach . . . . . . . . . . . . . . . . . . . . . . . 14
4.5 Empirical Methods: Atom-Atom Force Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
4.6 Chemical Bonds Versus “Approach Preferences” in Crystals . . . . . . . . . . . . . . . . . . . . . . . . 18
4.7 Perspective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
5 Crystal Structure Prediction and Control . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
6 Dynamic Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.1 Principles and Applicability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
6.2 Biased Methods, Ideas, Advantages and Shortcomings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
6.3 What Is the Real Value of a Simulation? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
7 Summary and Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
1 Data Processing for X-Ray Diffraction
About a century ago, a consortium of genial physicists joined their intellectual
power in realizing that periodically symmetric arrays of electron-containing
objects, like atoms in crystals, would have interobject spacings of the same order
of magnitude as the wavelength of the newly discovered Roentgen radiation, whose
nature was at first so mysterious that it was provisionally given the spooky name of
“X-rays”. As we all know, the name stuck. The same intellectual power was then
redirected to the application of the well known concepts of diffraction to an
experiment in which X-rays were shined onto crystalline material [
1
]. The path
from a collection of diffraction fringes (actually black spots on a gray background)
to the shape and size of the diffracting objects is paved in Fourier algebra, and it
soon became evident that computing - dull, heavy, recursive computing - was
indispensable. People below the age of 30 will now find it difficult to understand
that computing in those days did not involve electronic computers.
The next step in the newborn discipline called X-ray crystallography was the
solution of a problem which, in perspective, looks now like minor detail: finding a
way of unraveling the diffraction-
phase
information among what looked like just a
set of diffraction
intensities
. Intensities alone provide at most a set of interobject
vectors, not the absolute positions of the diffracting objects. One clearly needs
phases (the relative timings of the diffracted waves) to reconstruct properly a
diffracting object. After some struggle using astute but scarcely effective methods,
