Molecules, large discrete

Yoshikawa, K., Takahashi, M., Vasilevskaya, V.V. and Khokhlov, A.R. (1996a) Large discrete transition in a single DNA molecule appears continuous in the ensemble. Phys. Rev. Lett., 76, 3029-3031. 

Nonmetals that form more than one covalent bond can give crystals based on three-dimensional frameworks such as a diamond, or they give large discrete molecules. Boron, carbon, and sulfur are interesting examples of the latter. 

Small dendritic molecules are discrete structures but may be less effective if larger aoss-linking agents are required for multivalent effects to be realized. Large dendrimers have low polydispersities relative to other polymeric systems but are not as homogeneous as the smaller dendrimers. 

The synthesis and eharacterization of large, discrete molecules having mononuclear coordinated metal ions have been growing at a rapid pace. A few years... 

There lays a coexistence region of coil and globule in the diagram of the phase transition. In other words, the transition is largely discrete individual DNA molecules, whereas it appears continuous in the ensemble average of DNA chains. 

It should be noted that a straightaway interpretation of scattering curves is possible only in the case of large discrete molecules-that is, in the case of monodisperse systems such as certain proteins (see below), when all scattering particles are identical in size and shape. In the case of polydisperse systems, only average parameters concerning the size and shape of macromolecules in solution can be deduced from X-ray scattering curves [37]. 

Many molecular mechanics potentials were developed at a time when it was computationally impractical to add large numbers of discrete water molecules to the calculation to simulate the effect of aqueous media. As such, techniques came into place that were intended to take into account the effect of solvent in some fashion. These techniques were difficult to justify physically but they were used nevertheless. 

A final comment on the interpretation of stochastic simulations We are so accustomed to writing continuous functions—differential and integrated rate equations, commonly called deterministic rate equations—that our first impulse on viewing these stochastic calculations is to interpret them as approximations to the familiar continuous functions. However, we have got this the wrong way around. On a molecular level, events are discrete, not continuous. The continuous functions work so well for us only because we do experiments on veiy large numbers of molecules (typically 10 -10 ). If we could experiment with very much smaller numbers of molecules, we would find that it is the continuous functions that are approximations to the stochastic results. Gillespie has developed the stochastic theory of chemical kinetics without dependence on the deterministic rate equations. 

The most usual type of coordination in compounds of Hg with other donor atoms is a distorted octahedron with 2 bonds much shorter than the other 4. In the extreme, this results in linear 2-coordination in which case the bonds are largely covalent. Hg(CN)2 is actually composed of discrete linear molecules (C-bonded CN ), whereas crystalline Hg(SCN)2 is built up of distorted octahedral units, all SCN groups being bridging ... 

Because carbon stands at the head of its group, we expect it to differ from the other members of the group. In fact, the differences between the element at the head of the group and the other elements are more pronounced in Group 14/IV than anywhere else in the periodic table. Some of the differences between carbon and silicon stem from the smaller atomic radius of carbon, which explains the wide occurrence of C=C and G=Q double bonds relative to the rarity of Si=Si and Si=0 double bonds. Silicon atoms are too large for the side-by-side overlap of p-orbitals necessary for -it-bonds to form between them. Carbon dioxide, which consists of discrete 0=C=0 molecules, is a gas that we exhale. Silicon dioxide (silica), which consists of networks of —O—Si- O - groups, is a mineral that we stand on. 

MD simulations also provide an opportunity to detect the structure of molecularly thin films. The most commonly known ordering structure induced by the confinement, the layering, has been revealed that the molecules are packed layer by layer within the film and the atoms would concentrate on several discrete positions. This has been confirmed in the simulations of liquid decane [29]. The density profile of unite atoms obtained from the simulations is given in Fig. 12 where two sharp density peaks appear at the locations near the walls, as a result of adsorption, while in the middle of the film smaller but obvious peaks can be observed on the density profile. The distance between the layers is largely identical to the thickness of the linear chain of decane molecules, which manifests the layered packing of molecules. 

A large number of discrete, highly conserved, and small stable RNA species are found in eukaryotic cells. The majority of these molecules are complexed with proteins to form ribonucleoproteins and are distributed in the nucleus, in the cytoplasm, or in both. They range in... 

---