Day 4: X-Ray Crystallography Analysis
Lab sections will visit the MIT Chemistry Department X-Ray Crystallography Laboratory and the crystal structure of selected (+) and (-) carvone enantiomers will be determined.
Crystal Structure Determination
Crystallography pertains to studying the structure and properties of crystals. More specifically, x-ray crystallography is a method of determining the three-dimensional structure of molecules on the atomic level by means of x-ray diffraction on crystal lattices. The diffraction pattern obtained from the interaction of a monochromatic x-ray beam with the lattice of a single crystal consists of hundreds or thousands of discrete reflections that form a lattice of their own, the reciprocal lattice. The individual reflections in this lattice can be understood as coefficients in a Fourier synthesis where the reflections’ intensities correspond to the magnitudes and their reciprocal coordinates translate into the frequency. The result of the Fourier summation is the three-dimensional electron density function of the entire crystal. The determination of a crystal structure consists of several steps all of which pose their individual challenges.
A high quality single crystal is needed to determine a crystal structure and often, crystal growth is the bottleneck in structure determination. One of the best methods to grow quality crystals is vapor diffusion: an anti-solvent (also called precipitant) with a higher vapor pressure than the solvent is allowed to diffuse into a vial with a solution of the compound of interest and, over time, crystals form. It is important to keep crystals, once obtained, in their mother liquor as often solvent molecules are incorporated into the crystal lattice and drying the crystals might destroy them.
From the first diffraction images, one can usually judge the quality of the crystal and determine the unit cell. Depending on the crystal system, which corresponds to the symmetry group of reciprocal space, a data collection strategy can be devised. A good dataset is complete (>98%) and all data have been collected with a redundancy of 6 or better.
Once all data are collected, correction for polarization and other effects as well as absorption need to me made. This step is called data reduction and the result of it is a file containing a list of all reflections, each with a set of reciprocal coordinates h, k and l, an intensity and a standard uncertainty.
Based on intensity statistics and systematic absences in reciprocal space, the symmetry group of the crystal, the space group, can be reconstructed (not always unequivocally). Knowing the space group is vital for correctly determining the crystal structure, as the entire crystal is to be described by (usually) just one or two molecule(s). The crystal structure, therefore, is the spatial average of the entire crystal and space group symmetry operators plus translation expand the structure to the whole crystal.
For a Fourier synthesis one needs magnitude, frequency and phase. Unfortunately, only the first two can be derived directly from the diffraction experiment. Assigning a (preliminary) phase angle to each reflection is called solving the structure. For chemical crystallography, the phase problem is solved mostly with direct, dual-space, and Patterson methods; in protein crystallography other methods such as MAD/SAD phasing or molecular replacement are also used.
With the trial phases determined during structure solution, a first Fourier summation is performed and a preliminary model of the molecule can be obtained. In this model, some atom types may be assigned incorrectly and other details of the structure may still be missing. The way from the first solution to the final model is called structure refinement. This step can be easy at times (a matter of mere minutes) or difficult in nonroutine cases when refinement may take days or sometimes even weeks.
Müller, P., Crystallography Reviews 2009, 15, 57-83.
Clegg, W., X-Ray Crystallography (Oxford Chemistry Primers) 2nd Edition, Oxford University Press, 2015.