Atom average

The average cloud is spherically synnnetric with respect to the nucleus, but at any instant of time there may be a polarization of charge givmg rise to an instantaneous dipole moment. This instantaneous dipole induces a corresponding instantaneous dipole in the other atom and there is an interaction between the instantaneous dipoles. The dipole of either atom averages to zero over time, but the interaction energy does not because the instantaneous and induced dipoles are correlated and... 

The resultant viscosity is in centipoise (mPa-sec) if 7 and 7 are given in K and Pa, respectively. This method can also be used for hght nonhydrocarbon gases except for hydrogen where, special N s are required. For hydrocarbons below ten carbon atoms, average errors of about 3 percent can be expected, with errors increasing to 5-10 percent for heavier hydrocarbons. 

Figure 14 Measures of disorder m the acyl chains from an MD simulation of a fluid phase DPPC bilayer, (a) Order parameter profile of the C—H bonds (b) root-mean-square fluctuation of the H atoms averaged over 100 ps.

Subsequent studies provided a wealth of information that appeared to support the hypothesis that the Fepr protein was a genuine [6Fe-6S]-containing protein. In a biochemical study (10) the elemental analysis was meticulously repeated, and, based on an assumed molecular mass of 52 kDa, the prismane protein was found to contain 6.3 Fe atoms, averaged over as many as nine different preparations. Again, no other metals than Fe were detected, suggesting that all... 

An spontaneous assembly of 15 components is reported in the synthesis of [Ag9L6](OTf)9 where L is the hexadentate, tris-chelating 6,6-bis[2-(6-methylpyridine)]-3j3 -bipyrazine. The structure consists of a 3x3 grid of Ag-atoms (average Ag" Ag = 3.72(3)A), sandwiched between two almost perpendicular sets of three parallel L ligands (Figure 10).641... 

All results were obtained from chains of 200 backbone atoms, averaging 100 chains to obtain M2, axial extensions, end-to-end distances, and segmental and chain order parameters and directors. 

Considering other families of similar compounds, the contributions given by Guillermet and Frisk (1992), Guillermet and Grimvall (1991) (cohesive and thermodynamic properties, atomic average volumes, etc. of nitrides, borides, etc. of transition metals) are other examples of systematic descriptions of selected groups of phases and of the use of special interpolation and extrapolation procedures to predict specific properties. 

As in the case of Tripos 5.252, several amino and nitro compounds were retrieved from the CSD and analyzed for their (all) atom movements upon energy minimization. Although the set of 19 amino and nitro compounds calculated with DREIDING is identical to that examined by Tripos 5.2, a direct comparison between the performance of the two force fields is not possible since the former reported RMS movements of all atoms while the latter, of heavy atoms only. The all atom average RMS movement reported by DREIDING for the set of 19 compounds is 0.298 A and the conclusions we derived for the Tripos force field apply also here. Additional results obtained with the DREIDING force field are discussed in Section II.D. 

EtMg(p-L ) 2] or [ EtMg( i-L ) 2] with bridging amido nitrogen atoms (average Mg—N distances of 2.135 and 2.149 A, respectively) only two of four O atoms of the aza-15-crown-5 anion are coordinated to magnesium. 

The molecular structure of the chelate complex was determined by a single-crystal X-ray diffraction study. The Mo distances to the cyclopropene ring carbon atoms, averaging 229... 

Fig. 26. Osl0C(CO)k 21, as in its (PPh )2N+ salt (56). The cluster comprises an octahedral OsgC core, with four additional osmium atoms capping tetrahedrally disposed faces of the octahedron. The overall symmetry is close to Td. Within the Os6C octahedron the Os-Os bondlengths average 2.88(1) A those from the capping metal atoms average 2.79(1) A. The longer meial-metal bonds allow the accommodation of the carbon atom [mean Os-= 2.04(3) A], All the carbonyls are terminal.

Fig. 27. Osl0C(CO)24I, 22, as in its (Ph P)2N+ salt (55). The cluster is related to 21 by the addition of an iodine atom across one of the Os-Os bonds from a capping metal atom to an Os6C core metal atom. The octahedral Os-Os bonds average 2.90(5) A the bonds from the capping atoms to the core metal atoms average 2.80(3) A.

Veith et al.736 have prepared the unique four-membered cyclic phosphenium ion 291. X-ray crystal structure analysis of the tetrachloroaluminate salt clearly indicates the intramolecular backbonding from ring nitrogen atoms (average N—P bond distance = 1.633 A). 

At ambient temperature, it is usually impossible to discern the smearing caused by thermal vibrations (averaged over time) from that caused by static displacements of atoms (averaged over the whole crystal), and the vibrational parameters in fact account for both. Therefore it is now recommended to use the term atomic displacement parameters (ADP) instead. A diffraction study of the same stmcture at different temperatures, however, will show the difference the genuine thermal vibrations diminish on cooling, but the ADP due to static disorder (e.g. in ferrocene ) will remain large. 

The reader may have noted that experi mental spectra of H-bonded species are com monly measured in either the gas phase or in inert gas matrices. Of course, there may be some differences as the molecules of the matrix can interact in various ways with the H-bonded complex. A recent set of measurements provides some estimates as to the perturbations caused by the matrix. Table 3.39 reports in the first row the frequencies of the OH stretches of the free and bridging hydrogens of the proton donor molecule of the water dimer in the gas phase. The next row indicates that a Ne matrix has only a very small effect, perhaps 10 cm . The Ar and Kr matrices produce larger perturbations, reducing the frequencies by about 30 cm . A smaller cluster of Ar atoms, averaging perhaps 50 such atoms yields a result very much like a full Ar matrix. With the single exception of the very small increase for the free OH stretch in the Ne matrix, all matrices and the Ar cluster lower the frequencies of both of the modes studied. 

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