Interatomic distances, in molecules

The determination of values of interatomic distances in molecules has been found to provide much information regarding electronic structure, especially in the case of substances which resonate among two or more valence-bond structures. The interpretation of interatomic distances in terms of the types of bonds involved is made with use of an empirical function formulated originally for single bond-double bond resonance of the carbon-carbon bond.1 There are given in this... 

Molecules in the gas phase provide an electron diffraction pattern which can be analyzed in order to obtain relative interatomic distances in molecules. Some of the distances depend on molecular conformation and, in principle, it is possible to extract conformational data (conformer structure and population). Rough estimates of energy barriers may also be obtained from the peak widths by comparing calculated and experimental distribution functions. Uncertainties on populations are rather high ( 10-15%). 

As a result of the development of the x-ray method of studying the structure of crystals and the band-spectroscopic method and especially the electron-diffraction method of studying gas molecules, a large amount of information about interatomic distances in molecules and crystals has been collected. It has been found that the values of interatomic distances corresponding to covalent bonds can be correlated in a simple way in terms of a set of values of covalent bond radii of atoms, as described below.1... 

Although the angstrom is not recommended, it is still acceptable and is in very common use. Its advantage is that interatomic distances in molecules range from about 1 to 2 A. Use of the nanometer requires fractions for such distances (0.1-0.2 nm), but some workers are now expressing interatomic distances in picometres, such distances ranging from about 100 to 200 pm. 

Classification of composites by the phase inclusion size bears a philosophical aspect how small should a component in the matrix be not to make the term composite material so universal as to include in fact all materials Interatomic distances in molecules and crystals are of 1.5 10 m dimensionality, distances between iterative elements of the crystalline structure are 10 —10 m, while the size of the smallest intermolecular voids in polymers is 10 m. Note that mean nanoparticle size (plastic pigments are 10-8-10 m in size, the diameter of monocrystalline fibers or whiskers is 10 —10 m, glass microspheres are 10 —10 m) is commensurate with parameters of monolithic simple materials. This means that in the totality of engineering materials, nanocomposites occupy a place at the boundary between composite and simple materials. 

Just as bonding atomic radii can be determined from interatomic distances in molecules, ionic radii can be determined from interatomic distances in ionic compounds. Like the size of an atom, the size of an ion depends on its nuclear charge, the number of electrons it possesses, and the orbitals in which the valence electrons reside. When a cation is formed from a neutral atom, electrons are removed from the occupied atomic orbitals that are the most spatially extended from the nucleus. Also, the number of electron—electron repulsions is reduced. Therefore, cations are smaller than their parent atoms ( FIGURE 7.7). The opposite is true of anions. When electrons are added to an atom to form an anion, the increased electron-electron repulsions cause the electrons to spread out more in space. Thus, anions are larger than their parent atoms. 

Sutton, L. E., Interatomic Distances in Molecules and Ions. Chem. Soc. (London),... 

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... 

Linus Pauling, Interatomic Distances in Covalent Molecules and Resonance between... 

In the following discussion use is made of an equation that has been formulated by the method given earlier in a discussion of the equation for resonance between a single bond and a double bond11 and of the interatomic distances in the carbon monoxide molecule and carbon dioxide molecule.13 The potential function for the bond is assumed to have the form... 

In the discussion of metallic radii we may make a choice between two immediate alternative procedures. The first, which I shall adopt, is to consider the dependence of the radius on the type of the bond, defined as the number (which may be fractional) of shared electron pairs involved (corresponding to the single, double, and triple bonds in ordinary covalent molecules and crystals), and then to consider separately the effect of resonance in stabilizing the crystal and decreasing the interatomic distance. This procedure is similar to that which we have used in the discussion of interatomic distances in resonating molecules.7 The alternative procedure would be to assign to each bond a number, the bond order, to represent the strength of the bond with inclusion of the resonance effect as well as of the bond type.8... 

It is pointed out that the radial distribution method is particularly satisfying in that it leads directly to the values of the important interatomic distances in the molecule, thus eliminating many possible models and usually limiting the molecule to the structures represented by small ranges of values of the structural parameters. 

The revision leads to a difference of 0.06 A. between the interatomic distance in the normal oxygen molecule and the sum of the double-bond radii. This may be attributed to the presence of an unusual structure, consisting of a single bond plus two three-electron bonds. We assign this structure both to the normal 2 state, with ro = 1.204 A., and to the excited 2 state, with ro = 1.223 A., the two differing in the relative spin orientations of the odd electrons in the two three-electron bonds. We expect for the double-bonded state the separation n 1.14 A. 

Thus, two values can be evaluated, W+ and W, according to the signs in Eq. (137). If the appropriate integrals are known, these quantities can be calculated for a given interatomic distance in the diatomic molecule. As indicated above the successive substitution of the two values W+ and W- yields... 

Table 5.2 SO Bond Lengths, OSO Bond Angles, and 0---0 Interatomic Distances in Some XYSO2 Molecules...

The interatomic distances in peroxyl radicals were calculated by quantum-chemical methods. The experimental measurements were performed only for the hydroperoxyl radical and the calculated values were close to the experimental measurements (see Table 2.5). The length of the O—O bond in the peroxyl radical lies between that in the dioxygen molecule (r0—o= 1.20 x 10-10m) and in hydrogen peroxide (r0—o= 1-45 x 10-lom). 

Potential energy surface (PES) can be understood by making a plot of energy as a function of various interatomic distances in the complex that is formed during the reaction. For simplicity, let us consider a simplet chemical reaction between an atom A and a diatomic molecule BC to yield another atom C and a diatomic molecule AB as... 

In 1930, R. Wierl and Mark studied N. Davidson and J. Germer s experiments on electron diffraction. Employing their wide experience in instrumentation, they promptly constructed an improved electron scattering apparatus. With this instrument, they determined the interatomic distances in a number of molecules and published a series of papers on the technique and their findings (17, 18, 19). Mark s contributions to the field of crystal structure are discussed in a later chapter of this volume and will not be covered in more detail here (see Pauling, L. "Herman Mark and the Structure of Crystals", this volume.). 

Linus Pauling, "The Nature of the Chemical Bond. III. The Transition from One Extreme Bond Type to Another," JACS 54 (1932) 981003 Linus Pauling, "Interatomic Distances in Covalent Molecules and Resonance between Two or More Lewis Electronic Structures," Proc.NAS 18 (1932) 293297 Linus Pauling, "The Calculation of Matrix Element for the Lewis Electronic Structure of Molecules,"... 

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