Equilibrium structures crystallization

Burton, W.K., Cabrera, N. and Frank, F.C., 1951. The growth of crystals and the equilibrium structure of their surfaces. Philosophical Transactions, A243, 299-358. 

The reactions of mercury(II) salts with oligo-amines afford informative examples for the fact that counterions induce the formation of a distinct complex or select a distinct complex in an equilibrium to crystallize with. Thus, Hg11 acetate with dien under exactly the same reaction conditions, in the presence of C104- or PF6-, yields the dinuclear complex [Hg2(dien)3](C104)4 or the mononuclear species [Hg(dien)(H20)](PF6)2, respectively, both characterized by IR, H, and 13C NMR spectrometries, by fast-atom bombardment (FAB) MS, cyclovoltammetry, and X-ray structure analyses.209 In the first compound Pna2, Z = 4), one Hg adopts five-coordination with one tridentate and one bidentate dien ligand, which with the remaining N-donor binds to the... 

The conformations of the furanose ring in 250 nucleoside and nucleotide structures were analysed by Bartenev et al. (1987). These authors made the assumption, referred to above, that intermolecular interactions have a random effect on the structure in the crystal, and that the probability JVg of a structure crystallizing in a non-ground-state conformation is the same as the probability of it arising in thermal equilibrium at ambient temperature T in solution (6). (A difficulty arises immediately with the definition of the temperature, because structural parameters for molecules in crystals are... 

Burton, W. K., N. Carbrera, and F. C. Frank (1951), The Growth of Crystals and the Equilibrium Structure of Their Surfaces", Phil Trans. Roy. Soc. A243, 299-358. 

In their pioneering work on crystal growth Burton, Cabrera and Frank predicted that on an atomic length scale the equilibrium structure of a crystal surface should exhibit a transition from a smooth state at low temperatures to... 

In reply to Dr. Hess I may add that, although energy is admittedly required to construct the bacteriorhodopsin molecules in the first place, the proteins are not assembled inside the membrane. They enter the membrane and form an equilibrium structure. On another point, ordering inside the membrane is analogous to crystallization. 

The temporally and spatially resolved transient structures elucidated by UED include structures in radiationless transitions, structures in non-concerted organic reactions, structures in non-concerted organometallic reactions, structures of carbene intermediates, dynamic pseudorotary structures, non-equilibrium structures and conformational structures on complex energy landscapes, transient structures of surfaces and bulk crystals, and solid-to-... 

Nitromethane, CH -NOf. The equilibrium structure of singlet nitromethane has been studied at several levels of theory [3,60,64-71]. Two conformations are possible for nitromethane, staggered (Is) and eclipsed (le), but the eclipsed form has been characterized as a transition structure at MP2/6-31G with an imaginary frequency of 30 cm 1 [3]. Rotation around the H3C-NO2 bond occurs essentially without barrier the estimated value is only 0.01 kcal/mol. This is in accordance with a microwave study, which reports a C-N rotation barrier of only 6 cal/mol [72,73]. The C-N bond length of nitromethane has been estimated with X-ray single crystal diffraction [74], neutron diffraction [46,75], microwave spectroscopy [72,73], MP2/6-31G [3], and B3LYP/6-31+G [71] at respectively 1.449, 1.486, 1.489, 1.485, and 1.491 A, showing that the theoretical estimates compare very well with those determined by experimental methods. The experimentally reported vibrational frequencies of nitromethane... 

There are two types of macroscopic structures equilibrium and dissipative ones. A perfect crystal, for example, represents an equilibrium structure, which is stable and does not exchange matter and energy with the environment. On the other hand, dissipative structures maintain their state by exchanging energy and matter constantly with environment. This continuous interaction enables the system to establish an ordered structure with lower entropy than that of equilibrium structure. For some time, it is believed that thermodynamics precludes the appearance of dissipative structures, such as spontaneous rhythms. However, thermodynamics can describe the possible state of a structure through the study of instabilities in nonequilibrium stationary states. 

Cohen, A. J., and R. G. Gordon (1975). Theory of the lattice energy, equilibrium structure, elastic constants, and pressure-induced phase transitions in alkali-halide crystals. Phys. Rev. B12, 3228 1. 

Contribution of the Nearest Surroundings of the Central Atom to the Vector Equilibrium of Crystal Structures... 

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