Molecules and Crystals

A description of Pasteur s work, as part of a broader discussion concerning crystal structure, can be found in the article "Molecules, Crystals, and Chirality" in the July 1997 issue of theJourna/ of Chemical Education, pp. 800-806. 

Calculations of the electronic structure of molecules, crystals and surfaces are often performed in atomic units. They are defined by setting the most important constants equal to unity h — eo — me — 1, where me is the electronic mass. The Coulomb law is written in electrostatic units V(r) = q/r, so that the time-independent Schrodinger equation for the hydrogen atom takes on the simple form ... 

We have used x-ray diffraction in our laboratory to probe transient structures of laser-excited liquids, small-molecule crystals and protein crystals. The diffraction patterns are recorded on a CCD detector that makes efficient use of most of the diffracted x-rays. Several experimental protocols have been developed Laue diffraction from proteins [6-8], small-molecule diffraction [9,10] and diffraction from liquids [2,11,12]. In proteins, the... 

The size-and-shape factor is of special importance with respect to electron confinement in atoms, molecules, crystals and interfaces. This confinement, empirically characterised by parameters such as electronegativity is the decisive fundamental factor that decides chemical reactivity. The demonstration that atomic electronegativity is equivalent to the chemical quantum potential of the valence state [108] holds the key to molecule formation by electron pairing and space-like delocalization. It opens a new angle on the nature of chemical binding, molecular structure, chemical equilibrium and surfaces. 

It may not be obvious how we would locate the x, y, z coordinates of the heavy atom in the unit cell. Indeed it is sometimes not a simple matter to find those coordinates, but as for the heavy atom method described above, it can be achieved using Patterson methods (described in Chapter 9). As we will see later, Patterson maps were used for many years to deduce the positions of heavy atoms in small molecule crystals, and with only some modest modification they can be used to locate heavy atoms substituted into macromolecular crystals as well. Another point. It is not necessary to have only a single heavy atom in the unit cell. In fact, because of symmetry, there will almost always be several. This, however, is not a major concern. Because of the structure factor equation, even if there are many heavy atoms, we can still calculate Juki, the amplitude and phase of the ensemble. This provides just as good a reference wave as a single atom. The only complication may lie in finding the positions of multiple heavy atoms, as this becomes increasingly difficult as their number increases. 

Atoms, Molecules, Crystals and Nanotubes in Laser Fields From Dynamical Symmetry to Selective High-Order Harmonic Generation of Soft X-Rays... 

Atoms, Molecules, Crystals and Nanotubes in Laser Fields... 

The addition of a reflecting microscope to the IR spectrometer permits to obtain IR spectra of small molecules, crystals and tissues cells, thus we can apply the IR spectroscopy to biological systems, such as connective tissues, blood samples and bones, in pathology in medicine [15, 26-27]. In Fig. 7 is shown the microscope imaging of cancerous breast tissues... 

There are two subjects that I am deeply interested in— structure, the det ed nature of molecules, crystals, and cells, described in terms of their constituent atoms, with interatomic distances determined to within 0.01 A, an interest that began in my youth and has received most of my attention until recent years and the basis of the physiological activity of substances, an interest that is more recent but just as keen. It is with a deep feeling of satisfaction that I have reached the firm conclusion in recent years that these two fields are most intimately related. 

The concept of symmetry is equally important for understanding properties of individual molecules, crystals and liquid crystals [1]. The symmetry is of special importance in physics of liquid crystal because it allows us to distinguish numerous liquid crystalline phases from each other. In fact, all properties of mesophases are determined by their symmetry [2], In the first section we consider the so-called point group symmetry very often used for discussion of the most important hquid crystalline phases. A brief discussion of the space group symmetry will be presented in Section 2.2. 

Glasser L, von Szentpaly L (2006) Born-Haber-Fajans cycle genertilized linear eneigy relation between molecules, crystals and metals. J Am Chem Soc 128 12314-12321 Dimitrov V, Sakka S (1996) Electronic oxide polarizability and optictil basicity of simple oxides. J Appl Phys 79 1736-1740... 

The lattice energies of the single-molecule crystals and co-crystal are assumed to be those for the most stable forms of each. To predict the stability of a given co-crystal it is therefore necessary to perform crystal structure prediction on each molecule independently and on the co-crystal itself. If it is necessary to predict which stoichiometry of co-crystal is the most stable, it is also necessary to perform crystal structure prediction on crystals with each possible stoichiometry. Since the cost and difficulty of a crystal structure prediction calculation increases considerably with the number of independent molecules in the asymmetric unit, this becomes a very hard problem which few have ventured to tackle. The role of crystal structure prediction is to identify the lowest energy structures that are possible for both co-crystal and its single-molecule crystalline components. The prediction of stoichiometry for a co-crystal requires consideration of all dissociation processes available for a given number of molecules in the asymmetric unit, for example ... 

Much of the analysis of plastics microstructures is fairly straightforward. It is easy to tell whether you are dealing with a crystalline or an amorphous material by observing the sample using polarized light. Amorphous areas appear black, but crystalline areas can be clearly examined. The explanation for this effect is that in the case of crystalline polymers the molecules crystallize and fold together in a uniformly ordered manner,... 

At Nikko, presentations and ensuing discussions centered on the refinement of approximations used in molecular problems, the extension of methods to deal with larger molecules, crystals, and solids, and the assessment of the state of calculations of molecular integrals after the Shelter Island Conference. 

Multidimensional nuclear magnetic resonance (NMR) techniques, since their inception in the 1970s, have turned into a powerful tool that provides structures and dynamics of very complex molecules, crystals, and proteins. By extending these ideas to the optical regime, it is possible to come up with novel classes of spectroscopies that can probe complex vibrational motions. Its realization, however, has to wait for the recent breakthrough in femtosecond laser techniques, which has provided necessary impulsive excitation to overcome tremendous line broad-... 

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