Unstrained bond length

Here kb is the force constant or bond strength and r0 is the ideal or unstrained bond length. A first approximation to the force constant can be calculated from the fundamental vibration frequency, v, of the X-Y bond, taken from the infrared spectrum of a representative compound by using Eq. 15.2,... 

Measurements of the bond angles and lengths for typical acyclic and unstrained cyclic sulphones show that the OSO angle is in the range of 116 to 120° (mean, 118°)5, the CSC angle is in the range of 103 to 105°78, and the C—S bond length depends on whether it is to a terminal (i.e., methyl) carbon or to a carbon in a chain. The nature of the substituents on the carbon is also relevant, but if these are nonpolar or not especially bulky, the C—-S... 

As expected, the formal C—C triple bond in benzyne is significantly weaker than in unstrained alkynes, the C=C stretching vibrations of which usually fall in the region 2150 cm. Nevertheless, o-benzyne is better described as a strained alkyne rather than a biradical, which is evident from the large singlet-triplet splitting of 37.5 0.3 kcal/mol as well as the alkyne-like reactivity (e.g., in Diels-Alder reactions). The enthalpy of formation of 4 was determined to be 106.6 3.0 kcal/mol by Wenthold and Squires. For the C=C bond length a value of 124 2 pm was found experimentally, " which comes closer to a typical C C triple bond (120.3 pm in acetylene) rather than a C C double bond (133.9 pm in ethylene). 

In Chapter 2 it was shown that the Madelung field of a crystal is equivalent to a capacitive electric circuit which can be solved using a set of Kirchhoff equations. In Sections 3.1 and 3.2 it was shown that for unstrained structures the capacitances are all equal and that there is a simple relationship between the bond flux (or experimental bond valence) and the bond length. These ideas are brought together here in a summary of the three basic rules of the bond valence model, Rules 3.3, 3.4, and 3.5. 

In many structures, it is possible to change the lengths of unstrained bonds in order to compensate for the stretching and compression required to make the... 

Two MW investigations of iodine-substituted cyclohexane and adamantane apply several geometric constraints in the structure analyses which result in large values for the estimated experimental uncertainties for the C—I bond distances. The bond lengths of ca 216-217 pm correspond to that in ICHMe2 [216.7 (2) pm] and similar observations were made for C—Cl and C—Br bond lengths in monosubstituted unstrained saturated rings. 

Figure 28-7 In force field calculations, different levels of approximations are used to reproduce the stretching and compression of chemical bonds The plot shows a Morse potential energy function siipenmposed with various power series approximations (quadratic, cubic, and quartic functions) Note that the bottoms of the curves, representing the bond length for most chemical bonds of interest to medicinal chemists, almost overlap exactly. This nearly perfect fit in the bonding region is the reason simple harmonic functions can be used to calculate tx>nd lengths for unstrained molecular structures in the force lield method.

One of the fundamental postulates of molecular mechanics is that the steric energy of a molecule can be separated into terms resulting from small, transferable moieties. For all bond lengths and angles, it is assumed that there exists an unstrained state with a steric energy of zero. All deviations from this ideal ... 

A complete force field consists of a functional form, as exemplified in Figure 1, and a set of parameters. For example, for each type of bond in the example force field, two parameters are needed an ideal length k (corresponding to the bond length in a hypothetical unstrained molecule), and a stretching force constant fcj. The latter can be seen as the relative stiffness of the bond, and determines how much the energy increases upon a certain distortion. Some parameters, such as the ideal bond length, correspond closely to observables. However, the optimum set of parameters can rarely be identified by observation. 

An unstrained olefinic double bond in the ground state is described by six atoms lying in a plane with bond angles near 120° and bond lengths of about 134.0 pm. Two classes of deformations can be distinguished in nonplanar or out-of-plane (oop) distortions, substituents move perpendicular to the molecular plane, whereas planarity is maintained with the planar or in-plane (ip) distortions of substituents. For a systematic approach, these static distortions can be derived from the normal vibrations of ethylene. 

The reference value bo in Eqs. [3] and [4] is not the equilibrium bond length in any particular molecule (except by chance).This is a common misconception, and indeed the value of bo is sometimes taken from an experimentally observed value. This is not valid. Rather, bo is the bond length of the particular bond in a virtual, unperturbed state, that is, in a hypothetical state where the bond exists as an isolated entity, outside the molecule, and not affected by any external forces. In any real molecule, there are forces from neighboring atoms and interactions with other internals, which stretch or compress the bond from its unperturbed value. The more strained the molecule, in general, the farther the bond in the equilibrium molecular structure will be from the reference value bo. An obvious example of this is the classic example of the C —C bond in the strained molecule tri-r rt-butylmethane, whose equilibrium value is 1.61 A, far from the typical reference value of 1. .32-1.53 used in standard force fields. Usually, for most unstrained molecules, bo is close to the equilibrium values. 

In Table 8-1 we have listed the lengths of the triple bonds and the angles at the sp centers for cyclic monoalkynes as derived by X-ray and electron diffraction measurements [6, 33, 36-41], It is seen that bending the triple bond even to 150° does not have a significant effect on the bond lengths. The deviation from 1.20 A - the value of the C-C triple bond in unstrained systems - is small. 

Table 1 Typical bond lengths (A) and angles (") in unstrained sulfur-containing rings.

In general, this basis does better at reproducing multiple bonds between first-row atoms than it does for single bonds. Carbon-carbon single bonds in unstrained systems are an exception to this rule. Compensating errors allow the STO-3G Hartree-Fock C—C bond lengths in compounds such as ethane and propane to come within 0.01 A of the experimental values. 

---