Interatomic distances electron density

Structural parameters and interatomic distances derived from electron diffraction (7) (77JST(42)l2i) and X-ray diffraction (8) studies (76AX(B)3178) provide unequivocal evidence that pyrazine is planar with >2a symmetry. There is an increased localization of electron density in the carbon-nitrogen bonds, with carbon-carbon bonds being similar in length to those in benzene. ... 

Table 1. Parameters of the interatomic potentials. Distances are given in as, densities in flg, charges in e and energies in Ry. ri4s and Vc have been set to 0.57 and 8.33 ag for iron. The corresponding values for nickel are 0.85 and 8.78 ag ao denotes the equilibrium lattice constant of the elements po is the electron density at equilibrium for the perfect lattices, i.e. 0.002776 ag and 0.003543 ag for iron and nickel respectively.

In order to perform the calculation., of the conductivity shown here we first performed a calculation of the electronic structure of the material using first-principles techniques. The problem of many electrons interacting with each other was treated in a mean field approximation using the Local Spin Density Approximation (LSDA) which has been shown to be quite accurate for determining electronic densities and interatomic distances and forces. It is also known to reliably describe the magnetic structure of transition metal systems. 

The discussions of the structure and the electron density are based on the structure found by a full multipole refinement of the X-ray data with the hydrogen positions fixed at the neutron values and the hydrogen thermal parameters fixed at scaled neutron values (Figure 5).1 The interatomic distances and intramolecular bond angles are given in Table 2. 

Table 2. Heats offormation, H (kcal), magnitude of electron density, Q (Of), displace from the cluster to adsorbed oxygen molecules, equilibrium interatomic distances R (A-B) and bond orders P (A-B), corresponding to them, in PANI-O2 adsorption complexes.

A calculation based on the decrease of the electron density at the surface and on the relaxation of the top lattice plane resulted22 in values such as 190 and 1234 erg/cm2 for the 100 faces of sodium and aluminum, respectively. The above relaxation, that is, the ratio of the interplanar distance in bulk to that in the external region was calculated23, assuming a Morse type interatomic potential. The above ratio appeared to be, e.g., 1.13 for the 100 face of calcium, and 1.016 for the 111 face of lead. The relaxation lowered the energy 7 by 0.5 to 7% for different metals and crystal faces. 

The C—C and C—B interatomic distances in carboranes can also be related to the coordination numbers of the skeletal atoms. Two factors tend to make these distances shorter than the B —B distances in comparable boranes the preference of the carbon atoms for sites of low coordination number and the greater electronegativity of carbon than boron, which increases the electron density in the region of the carbon atoms and so strengthens the bonds that they form. Table IX lists some C—C distances for closo- and wido-carboranes 13, 20, 21, 26, 98,121,168) and metal-acetylene 50, 58,112) complexes, relating them... 

Peripheral contributions become important when short interatomic distances are involved, as, for example, for the EFG at nitrogen nuclei and especially at nuclei of hydrogen atoms. Since hydrogen has only one electron, the electric field gradient is mainly due to the density farther from the nucleus, and has therefore been described as less sensitive to the precise charge distribution (Tegenfeldt and Hermansson 1985). 

If all values of Cy are known, the distribution of flux between the bonds can be calculated by solving eqns (2.7) and (2.11) since they contain only the parameters g, and Cy. Unfortunately, the values of Cy cannot be determined a priori, since they depend on a knowledge of the interatomic distances which are determined by the mutual repulsion of the ions and hence by the electron density distribution. This problem is taken up in Chapter 3 where it is shown that, for a large number of equilibrium structures, the values of Cy can all be set equal. As Cy is common to all the terms in (2.11), it can be cancelled, allowing eqns (2.7) and (2.11) to be solved. 

Every chemist is trained in conceptualizing reactions and rearrangements by pushing arrows to track the movement of electrons in the bonds. This is a depiction that chemists have long found useful. Of course, electron pairs do not really move around like this. In the realm of physical reality, interatomic distances lengthen and shorten, and electron density shifts in the course of a reaction, but no electron pairs hop among the bonds and atoms. Quantum mechanics works. 

Computationally, one first performs a semiempirical all-valence electron calculation (say CNDO/2) to obtain the electron densities P -. One-center epq are constants which were tabulated60 for H, B, C, N, O and F atoms. Two-center Wpq are evaluated by an empirical formula which is a function of the interatomic distance. Computation of the expression (153) is much shorter than a standard CNDO/2 run. It is understandable that such a simple method cannot provide highly accurate estimates of the correlation energy. Actually, this accuracy is claimed61 to be within 0.5 eV. 

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