From Molecular to Crystal Structure

The ultimate goal in the study of intermolecular geometries and interaction energies is the construction of a conceptual link between molecular and crystal structure. At one extreme, one could think of organic crystal packing as no more than a modulat- 

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Desiraju, G. R., Gavezzotti, A., From molecular to crystal-structure - polynuclear aromatic hydrocarbons. J. Chem. Soc., Chem. Commun. 1989, 621. 

One learns from these molecular complexes that equivalent synthons can lead to virtually identical crystal structures. Synthons in, V and VI are chemically and geometrically equivalent though they originate from different molecules, a nitrile, an N-oxide and a nitro compound. These three synthons are used in crystal design in almost the same way. So, different molecules may yield similar crystal structures if they are capable of forming equivalent synthons. This is a powerful concept because it establishes a many-to-one correspondence between molecular and crystal structures. 

I will show, in a two-dimensional example, how to construct the Patterson map from a simple crystal structure and then how to use a calculated Patterson map to deduce a structure (Fig. 6.10). The simple molecular structure in Fig. 6.10a contains three atoms (dark circles) in each unit cell. To construct the Patterson map, first draw all possible vectors between atoms in one unit cell, including vectors between the same pair of atoms but in opposite directions. (For example, treat 1 —> 2 and 2 — 1 as distinct vectors.) Two of the six vectors (1 — 3 and 3 —> 2) are shown in the figure. Then draw empty unit cells around an origin (Fig. 6.10b), and redraw all vectors with their tails at the origin. The head of each vector is the location of a peak in the Patterson map, sometimes called a Patterson "atom" (light circles). The coordinates (u,v,w)... 

Metalloenzymes pose a particular problem to both experimentalists and modelers. Crystal structures of metalloenzymes typically reveal only one state of the active site and the state obtained frequently depends on the crystallization conditions. In some cases, states probably not relevant to any aspect of the mechanism have been obtained, and in many cases it may not be possible to obtain states of interest, simply because they are too reactive. This is where molecular modeling can make a unique contribution and a recent study of urease provides a good example of what can be achieved119 1. A molecular mechanics study of urease as crystallized revealed that a water molecule was probably missing from the refined crystal structure. A conformational search of the active site geometry with the natural substrate, urea, bound led to the determination of a consensus binding model[I91]. Clearly, the urea complex cannot be crystallized because of the rate at which the urea is broken down to ammonia and, therefore, modeling approaches such as this represent a real contribution to the study of metalloenzymes. 

Bersohn 76) has calculated the crystal field created by the molecular dipoles in the lattice of CH3C1. The static dipole moment of the molecules induces through the polarizability of the molecules an additional dipole moment which increases the dipole moment of the free molecule by a factor of about 1.05. This in turn means that the C—Cl bond has increased in ionic character under the influence of the intermolecular electric fields and therefore (see Eq. (II.9 the quadrupole coupling constant will be lower relative to the gaseous state. Besides the dipole moment induced in the direction of the static dipole, a perpendicular partial moment should be induced, too. Therefore the axial symmetry of the C—Cl bond will be disturbed and the asymmetry parameter 77 may become unequal zero. A small asymmetry parameter 17 = 0.028 has been observed for the nuclear quadrupole interaction in solid CH3I. Bersohn also calculated from the known crystal structure of 1,3,5-trichlorobenzene the induced... 

Vibrational spectra contain information about every aspect of the molecular structure. This information can be evaluated by comparing observed infrared and Raman spectra with those calculated from systematically modified model molecules until the best adjustment is achieved (see Sec. 5.2). However, very simple calculations may help to assign the observed bands to structural features or to predict the effect of a change of the molecular or crystal structure as a result of a chemical reaction or a phase transition. 

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