Molecules linear structure

Rigid linear molecules are a special case in which an extended MS group, rather than the MS group, is isomorphic to the point group of the equilibrium structure see chapter 17 of [1]. 

An N-atom molecular system may he described by dX Cartesian coordinates. Six independent coordinates (five for linear molecules, three fora single atom) describe translation and rotation of the system as a whole. The remaining coordinates describe the nioleciiUir configuration and the internal structure. Whether you use molecular mechanics, quantum mechanics, or a specific computational method (AMBER, CXDO. etc.), yon can ask for the energy of the system at a specified configuration. This is called a single poin t calculation. ... 

FIGURE 2 18 Acetylene is a linear molecule as indicated in (a) the structural formula and (b) a space filling model... 

Each of the lasing vibrational transitions has associated rotational fine structure, discussed for linear molecules in Section 6.2.4.1. The Sgli transition is — Ig with associated P and R branches, for which AJ = — 1 and +1, respectively, similar to the 3q band of HCN in Figure 6.25. The 3q22 band is, again, with a P and R branch. 

Fig. 6.1. A spectral exchange scheme between components of the rotational structure of an anisotropic Raman spectrum of linear molecules. The adiabatic part of the spectrum is shadowed. For the remaining part the various spectral exchange channels are shown ( - — ) between branches (<— ) within branches.

Now consider the alkynes, hydrocarbons with carbon-carbon triple bonds. The Lewis structure of the linear molecule ethyne (acetylene) is H—O C- H. To describe the bonding in a linear molecule, we need a hybridization scheme that produces two equivalent orbitals at 180° from each other this is sp hybridization. Each C atom has one electron in each of its two sp hybrid orbitals and one electron in each of its two perpendicular unhybridized 2p-orbitals (43). The electrons in the sp hybrid orbitals on the two carbon atoms pair and form a carbon—carbon tr-bond. The electrons in the remaining sp hybrid orbitals pair with hydrogen Ls-elec-trons to form two carbon—hydrogen o-bonds. The electrons in the two perpendicular sets of 2/z-orbitals pair with a side-by-side overlap, forming two ir-honds at 90° to each other. As in the N2 molecule, the electron density in the o-bonds forms a cylinder about the C—C bond axis. The resulting bonding pattern is shown in Fig. 3.23. 

This treatment could be applied to anthracene and phenanthrene, with 429 linearly independent structures, and to still larger condensed systems, though not without considerable labor. It is probable that the empirical rule6 of approximate proportionality between the resonance energy and the number of benzene rings in the molecule would be substantiated. 

There is evidence that the reactions can take place by all three mechanisms, depending on the structure of the reactants. A thermal [ 2, + 2s] mechanism is ruled out for most of these substrates by the orbital symmetry rules, but a [ 2s + mechanism is allowed (p. 1072), and there is much evidence that ketenes and certain other linear molecules in which the steric hindrance to such an approach is... 

The TCNQ molecule in [TR(bzim)]2-TCNQ is sandwiched between two units of [ J,-N, C -bzimAu]3 in a face-to-face manner so that it is best represented by the formula (7t-[ J,-N, C -bzimAu]3)( j,-TCNQ)(7t-[p-N, C -bzimAu]3). The cyanide groups clearly are not coordinated to the gold atoms. The distance between the centroid of TCNQ to the centroid of the AU3 unit is 3.964 A. The packing of [TR(bzim)]2-TCNQ shows a stacked linear-chain structure with a repeat pattern of-(Au3)(Au3)(p-TCNQ) (Au3)(Au3)(p-TCNQ)- an ABBABB repeat The complex [TR(bzim)]2-TCNQ contains two very short intermolecular Au Au distances of 3.152 A (identical for the two aurophilic bonds). The intermolecular Au Au distance is even shorter than the intramolecular distances in the starting compound, which are 3.475, 3.471, and 3.534 A. The adjacent AU3 units in [TR(bzim)]2-TCNQ form a chair-type structure rather than the face-to-face (nearly eclipsed) pattern reported in Balch s studies of the nitro-9-fluorenones adducts with the trinuclear Au(I) alkyl-substituted carbeniate complexes. 

The crystal structure of the complex [PhCH2PPh3][Au(C6F5)Cl] has been determined by X-ray diffraction it consists of an anion-cation pair where the anion shows a two coordinate Au(I) atom bonded to a Cl atom and a C Fs ring and the coordination is almost linear (molecules with two different angles were found but the differences between the two molecules in the asymmetric unit are not significant 177.8(5) and 179.8(4) A) [78]. 

Macromolecules differ from small molecules in a number of critical properties. First, the linear chain structure confers elasticity, toughness, and strength on the solid state system. This is a consequence of the reorientational freedom of the skeletal bonds and of their ability to absorb impact or undergo elastic deformation by means of conformational changes rather than bond cleavage. 

Hg(CN)2 in the solid state has a structure (I42d neutron diffraction), completely different from that of Cd(CN)2 Almost-linear molecules (r(Hg—C) 201.9, r(C—N) 116.0pm (corrected for thermal motion) a(C—Hg—C) 175.0°) are arranged such that four secondary bonds N" Hg (274.2 pm) yield the often-occurring 2 + 4 coordination around Hg.103 Analysis of the 199Hg MAS NMR spectrum of Hg(CN)2 has yielded the chemical shift and shielding tensor parameters.104... 

Linnett used the concept that an octet of valence shell electrons consists of two sets of four opposite-spin electrons to show that in diatomic and other linear molecules the two tetrahedra are not in general formed into four pairs as we have discussed for F2 and the CC triple bond in C2H2. This idea is the basis of the double-quartet model, which Linnett applied to describe the bonding in a variety of molecules. It is particularly useful for the description of the bonding in radicals, including in particular the oxygen molecule, which has two unpaired electrons and is therefore paramagnetic This unusual property is not explained by the Lewis structure... 

Various types of power law relaxation have been observed experimentally or predicted from models of molecular motion. Each of them is defined in its specific time window and for specific molecular structure and composition. Examples are dynamically induced glass transition [90,161], phase separated block copolymers [162,163], polymer melts with highly entangled linear molecules of uniform length [61,62], and many others. A comprehensive review on power law relaxation has been recently given by Winter [164],... 

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