Molecules interatomic distances

Spectral studies of rotational energy levels have proved most profitable for linear molecules having dipole moments, particularly diatomic molecules (for example, CO, NO, and the hydrogen halides). The moment of inertia of a linear molecule may be readily obtained from its rotation spectrum and for diatomic molecules, interatomic distances may he calculated directly from moments of inertia (Exercise 14d). For a mole-... 

X-ray structure analysis shows that phenazine is a planar molecule of symmetry. Its crystalline form is holohedral with a unit cell of two molecules. Interatomic distances, bond angles and bond orders of phenazine are presented in Table 1. X-ray bond data are also available for substituted phenazine derivatives and phenazine A -oxides. ... 

Molecule Interatomic distance A Molecule Interatomic distance A... 

Molecule Interatomic distance/pm Bond angle Dihedral angle... 

Molecule Interatomic distance A Molecule the single C—O bond a Interatomic constant characteristic distance value of the interatomic distance is obtained for... 

Molecule Interatomic distance A Molecule Inuratomic valence bond structures, distance with a separation oi A charge and a different... 

Bond H—X Molecule Interatomic distance H—X A Half of interatomic distance X—X A Covalent radius of hydrogen A... 

One can thus see that the ratio between real and ideal strengths of solid is determined by the ratio between the size of molecules (interatomic distance), b, and the size of a defect. 

Molecule Interatomic Distance (A) Homopolar Splitting 2V, CeV) Chemical Splitting, 2C (eV) Bond Energy, 2A(eV) Minimum 300 K Energy Gap (eV)... 

If A transforms to B by an antara-type process (a Mdbius four electron reaction), the phase would be preserved in the reaction and in the complete loop (An i p loop), and no conical intersection is possible for this case. In that case, the only way to equalize the energies of the ground and excited states, is along a trajectory that increases the separation between atoms in the molecule. Indeed, the two are computed to meet only at infinite interatomic distances, that is, upon dissociation [89]. 

One way to describe the conformation of a molecule other than by Cartesian or intern coordinates is in terms of the distances between all pairs of atoms. There are N(N - )/ interatomic distances in a molecule, which are most conveniently represented using a N X N S5munetric matrix. In such a matrix, the elements (i, j) and (j, i) contain the distant between atoms i and and the diagonal elements are all zero. Distance geometry explort conformational space by randomly generating many distance matrices, which are the converted into conformations in Cartesian space. The crucial feature about distance geometi (and the reason why it works) is that it is not possible to arbitrarily assign values to ti... 

It is usual to take the centre of the molecule as the origin of the coordinate system. Tl distance of each atom from the centre can be calculated directly from the interatom distances using the following expression ... 

L. E. Sutton, "Tables of Interatomic Distances and Configurations of Molecules, The Chemical Society, London, 1958. 

Dock two different molecules by restraining intermolecular (interatomic) distances. 

Single-Stack Acceptor. Simple charge-transfer salts formed from the planar acceptor TCNQ have a stacked arrangement with the TCNQ units facing each other (intermolecular distances of ca 0.3 nm (- 3). Complex salts of TCNQ such as TEA(TCNQ)2 consist of stacks of parallel TCNQ molecules, with cation sites between the stacks (17). The interatomic distance between TCNQ units is not always uniform in these salts, and formation of TCNQ dimers (as in TEA(TCNQ)2) and trimers (as in Cs2(TCNQ)Q can lead to complex crystal stmctures for the chainlike salts. 

Another area of research ia laser photochemistry is the dissociation of molecular species by absorption of many photons (105). The dissociation energy of many molecules is around 4.8 x 10 J (3 eV). If one uses an iafrared laser with a photon energy around 1.6 x 10 ° J (0.1 eV), about 30 photons would have to be absorbed to produce dissociation (Eig. 17). The curve shows the molecular binding energy for a polyatomic molecule as a function of interatomic distance. The horizontal lines iadicate bound excited states of the molecule. These are the vibrational states of the molecule. Eor... 

A molecular dynamics force field is a convenient compilation of these data (see Chapter 2). The data may be used in a much simplified fonn (e.g., in the case of metric matrix distance geometry, all data are converted into lower and upper bounds on interatomic distances, which all have the same weight). Similar to the use of energy parameters in X-ray crystallography, the parameters need not reflect the dynamic behavior of the molecule. The force constants are chosen to avoid distortions of the molecule when experimental restraints are applied. Thus, the force constants on bond angle and planarity are a factor of 10-100 higher than in standard molecular dynamics force fields. Likewise, a detailed description of electrostatic and van der Waals interactions is not necessary and may not even be beneficial in calculating NMR strucmres. 

The second step concerns distance selection and metrization. Bound smoothing only reduces the possible intervals for interatomic distances from the original bounds. However, the embedding algorithm demands a specific distance for every atom pair in the molecule. These distances are chosen randomly within the interval, from either a uniform or an estimated distribution [48,49], to generate a trial distance matrix. Unifonn distance distributions seem to provide better sampling for very sparse data sets [48]. 

Of the various geometric parameters associated with molecular shape, the one most nearly constant from molecule to molecule and most nearly independent of substituent effects is bond length. Bond lengths to carbon depend strongly on the hybridization of the carbon involved but are little influenced by other factors. Table 1.2 lists the interatomic distances for some of the most common bonds in organic molecules. The near constancy of bond lengths from molecule to molecule reflects the fact that the properties of individual bonds are, to a good approximation, independent of the remainder of the molecule. 

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