Internuclear bond angle

For strained molecules, such as those with small rings, the interorbital bond angle may not be the same as that of the internuclear bond angle. See the discussions of bent bonds later in this chapter. 

Cycloalkanes that do not have internuclear angles of 109.5° cannot have efficient overlap of hybrid orbitals. The internuclear bond angle of cyclopropane is 60°, far less than 109.5°. However, the interorbital angle is larger. As a result, the electron density lies outside the bond axis and is called a bent bond, or sometimes, more whimsically, a banana bond. 

Strong sp -sp a bonds are not possible for cyclopropane, because the 60° bond angles of the ring do not permit the orbitals to be properly aligned for effective overlap (Figure 3.10). The less effective overlap that does occur leads to what chemists refer to as bent bonds. The electron density in the carbon-carbon bonds of cyclopropane does not lie along the internuclear- axis but is distr-ibuted along an arc between the two carbon atoms. The r-ing bonds of cyclopropane are weaker than other carbon-carbon a bonds. 

The structure of the S2O molecule has been determined by rotational spectroscopy. The internuclear distances d and the bond angles a obtained by two groups are as follows ... 

The internuclear distances and bond angles used in this study are the usual experimental equilibrium geometries. The details are given in Table 2. 

Neither interelectronic repulsions nor internuclear repulsions have been considered. To ignore interelectronic repulsions is not serious since the orbitals used in the two forms of the molecule are extremely similar. The internuclear repulsion in the 90° form would be larger than in the linear case, and contributes to the bond angle in the actual water molecule being greater than 90°. The actual state of the molecule, as it normally exists, is that with the lowest total energy and only detailed calculations can reveal the various contributions. At a qualitative level, as carried out so far in this section, the decision from MO theory is that the water molecule should be bent, in preference to being linear. 

We can choose as 37V-6 coordinates any set which are independent of the absolute position and orientation of the nuclei in space. In practice the most convenient coordinates will consist of internuclear distances or bond angles, but there is no unique choice and one must consider the convenience for the particular problem in hand. We will illustrate this in two cases. 

Figure 3. The Mo2(g2-H)(P2-P) plane with appropriate internuclear separations and bond angles and their corresponding standard deviations...

Figure 5. Architecture of the [Cr2(CO)io(M2-H)] monoanion of crystallographic Q-I symmetry showing the approximate D4/, geometry of the metal carbonyl framework and the two centrosym-metrically related (half-weighted) sites of the bridging hydrogen atom in the bent Cr-H-Cr molecular fragment. Internuclear distances and bond angles are given with their estimated standard deviations.

We have shown previously how we can predict bond angles on the assumption that interelectronic (and internuclear) repulsions tend to separate the electron pairs as much as possible. 

First, let us consider what is meant by internuclear coordinates and, in particular, how many of these coordinates are needed in order to specify the electronic energy. We consider a collection of N atomic nuclei, which in this context are considered as point particles. In the following, we will for convenience refer to any collection of nuclei and electrons as a molecule . The atomic nuclei and the electrons may form one or more stable molecules but this is of no relevance to the following argument. The internuclear coordinates are defined as coordinates that are invariant to overall translation and rotation. These coordinates can, for example, be chosen as internuclear distances and bond angles. 

Fig. 3.1.5 A potential energy surface for a direct unimolecular reaction without a saddle point. The surface corresponds to a reaction like H2O — H + OH for dissociation along a fixed bond angle, where only two internuclear coordinates are required in order to specify the configuration. (Note that in this figure all energies above a fixed cut-off value Amax have been replaced by Fmax.)...

This correlation can be described in terms of the geometrical structure of CS3+ just before the Coulomb explosion, which is defined as the geometrical structure that reproduces the observed momentum vectors of the three fragment ions when the internuclear potentials are assumed to be purely Coulombic. The geometrical structures of CS determined from the distribution peaks (marked by a cross) in the three Ap12 — 012 plots in Fig. 1.8b-d show that the S-C-S bond angle becomes smaller (dropping from 162° to 140°) as the two C-S bonds stretch simultaneously from 1.8 A to 3.0 A [23]. 

According to a complete X-ray diffraction analysis, Se6 consists of ring molecules with the molecular symmetry of Dzd the crystal and molecular parameters are listed in Table II (17) and the crystal structure is shown in Fig. 2. Refinement by the least squares method resulted in the following atomic parameters of the single atom in the asymmetric unit x = 0.1602 0.00048, y = 0.20227 0.00047, z = 0.12045 0.00120 calculated density, 4.71 g/cm3. An earlier investigation of selenium vapor by electron diffraction led to an internuclear distance of 234 1 pm and an average bond angle of 102 0.5° for the chairlike cyclic Se6 molecule (23). 

The overall approach to determining the structure of a protein is to use computational power to take into account concurrently (1) the known sequence of the amino acids in the protein (2) the known molecular structure of each of those amino acid residues, including bond distances and angles (3) the known planar structure of the peptide group (4) internuclear distances and interresidue bond angles, as determined from NMR data (5) correlations of chemical shifts and structural features and (6) minimization of energy and avoidance of unreasonable atomic contacts. There are a number of ways to handle the computations and to derive the molecular structure, but all of them depend critically on the data supplied by NMR. 

According to a density functional calculation S15 molecules are of C2 symmetry with internuclear distances ranging from 205.3 to 206.5 pm, bond angles from 104.1° to 109.4°, and absolute torsion angles from 77.1° to 112.3° [102]. 

Table 3 Internuclear distances and bond angles of isothiazoles. 

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