Carbon, bond lengths

MM2 was, according the web site of the authors, released as MM2 87). The various MM2 flavors are superseded by MM3, with significant improvements in the functional form [10]. It was also extended to handle amides, polypeptides, and proteins [11]. The last release of this series was MM3(%). Further improvements followed by starting the MM4 series, which focuses on hydrocarbons [12], on the description of hyperconjugative effects on carbon-carbon bond lengths [13], and on conjugated hydrocarbons [14] with special emphasis on vibrational frequencies [15]. For applications of MM2 and MM3 in inorganic systems, readers are referred to the literature [16-19]. 

Table 2. Carbon-carbon bond lengths in organic compounds [2J.

The rotational barrier in methylsilane (Table 3.4, entry 5) is significantly smaller than that in ethane (1.7 versus 2.88 kcal/mol). This reflects the decreased electron-electron rqjulsions in the eclipsed conformation resulting from the longer carbon-silicon bond length (1.87 A) compared to the carbon-carbon bond length (1.54 A) in ethane. 

Carbon-carbon bond lengths in hydrocarbons depend both on the formal bond order (single, double, triple) and on the detailed environment. 

Measure and record the carbon-carbon bond lengths in ethane, ethene and ethyne. These will serve as standards for single, double and triple bonds, respectively. 

Measure the carbon-carbon bond length in benzene. Would you describe it as a single bond, a double bond, or somewhere in between Draw whatever resonance contributors are needed to justify your conclusion. 

Compare geometries of the cis and trans cycloalkenes. Are the double bonds incorporated into the trans compounds significantly more distorted than those incorporated into the analogous cis cycloalkenes Consider carbon-carbon bond lengths and the twisting and/ or puckering of the double bond. Are any distortions greater in trans-cycloheptene than in trans-cyclooctene ... 

Another type of correction, which is related to cross terms, is the modification of parameters based on atoms not directly involved in the interaction described by the parameter. Carbon-carbon bond lengths, for example, become shorter if there are electronegative atoms present at either end. Such electronegativity effects may be modelled by adding a correction to the natural bond length based on the atoms which are attached to the A-B bond. 

E Benzene is planar and has the shape of a regular hexagon. All bond angles are 120°, all carbon atoms are sp2-hybndized, and all carbon-carbon bond lengths are 139 pm. 

The electron-lattice interaction is introduced through the dependence of the electron hopping amplitude on the carbon-carbon bond length ... 

In order to mimic the energetic interaction with the aqueous phase, the head groups were restrained by a harmonic force to their average position in each bilayer. The harmonic force constant was chosen such that the head groups could move about one carbon-carbon bond length in or out of the plane determined by the average position of the head groups. The thickness of the layer adjusted itself, under the influence of an external pressure of 1 bar applied to the system. 

Which of two formulas for benzene is correct The answer is neither. The two forms are called resonance structures. The term resonance is a bit misleading because it implies that the two forms are oscillating back and forth. In reality, the carbon-carbon bond lengths in a resonating structure such as benzene are all the same. Resonant structures have only one form, a resonance hybrid somewhere between the two possibilities. 

Symmetrical cyanine dyes, because of the resonance shown in Figure 6.4 (in which the two contributing structures are exactly equivalent), are completely symmetrical molecules. X-ray crystal structure determinations and NMR spectroscopic analysis have demonstrated that the dyes are essentially planar and that the carbon-carbon bond lengths in the polymethine chain are uniform. The colour of cyanine dyes depends mainly on the nature of the terminal groups and on the length of the polymethine chain. The bathochromicity of the dyes is found to increase... 

Support for the above view is provided by the observation that all the carbon-carbon bond lengths in benzene are exactly the same, ... 

Protonation of 12 yields a compound best described as a face-protonated methylidyne complex, the tungsten-carbon bond length lying in the range observed for a triple bond (28). Protonation of the osmium compound 13 yields a true carbene complex, which for R = Ph has been characterized by X-ray crystallography (see Sections IV and VI). 

It is interesting to note that the decrease in metal electron density that accompanies the change from five- to six-coordinate geometry does not have a detectable effect on the metal-carbene carbon bond length in these complexes. The metal-carbyne carbon bond in several osmium carbyne... 

Metal-Carbon Bond Lengths in Osmium Carbene and Related Compounds... 

Compound 72 has been crystallographically characterized. The most striking feature of this structure is how little structural reorganization accompanies this adduct formation. The osmium-carbon bond length at 1.90(2) A is not detectably altered from that of the parent complex 47 and the C—Os—C angle is increased by only 8°. 

The osmium-carbyne carbon bond lengths for the three complexes do not differ significantly, and reference to Table IV indicates that these distances are distinctly shorter than the characterized metal-carbon double bonds of osmium carbene and carbonyl complexes. In both osmium alkylidene and carbyne complexes, then, the metal-carbon multiple bond lengths are largely insensitive to changes in the metal electron density (cf. Section IV,B). 

The X-ray structure determination of 107 reveals that the osmium-carbon bond length is increased by 0.07 A on going from the parent carbyne complex 79 to the silver adduct 107. This may be contrasted with the weaker interaction between the metal-carbon bond and the Aul fragment in Os(CH2AuI)Cl(NO)(PPh3)2 (see Section IV,C,1). 

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