Total bond orders

Molecular orbital calculations at various levels of approximation have been applied to both furazans and furoxans. Ab initio procedures using minimal (STO-3G) and split valence (3-2IG) basis ets have been used to determine bond orders, total energies, ionization potentials, and dipole moments for the parent furazan and furoxan, and several derivatives <88JCS(P2)66l> the calculated molecular geometries (3-21G) are compared in Table 1 with those obtained experimentally. 

Table 7.2 Effective bond order, total bond order, Tc-Tc and Tc-X bond distances (A) for the TcjXg (X = Cl, Br) calculated at the CASPT2/VTZP level of theory.

P is the total spinless density matrix (P = P + P ) and P is the spin density matrix (P = p" + P ). For a closed-shell system Mayer s definition of the bond order reduces to ... 

The total it electron energy is the sum of occupied orbital energies multiplied by two if. as is usually the ease, the orbital is doubly occupied. The charge densities and free valency indices were treated in separate sections above. The bond order output should be read as a lower triangular serni matrix. The bond order semi matrix for the butadiene output is shown in Fig. 7-7. 

Indazoles have been subjected to certain theoretical calculations. Kamiya (70BCJ3344) has used the semiempirical Pariser-Parr-Pople method with configuration interaction for calculation of the electronic spectrum, ionization energy, tt-electron distribution and total 7T-energy of indazole (36) and isoindazole (37). The tt-densities and bond orders are collected in Figure 5 the molecular diagrams for the lowest (77,77 ) singlet and (77,77 ) triplet states have also been calculated they show that the isomerization (36) -> (37) is easier in the excited state. 

The molecular orbital description of the bonding in NO is similar to that in N2 or CO (p. 927) but with an extra electron in one of the tt antibonding orbitals. This effectively reduces the bond order from 3 to 2.5 and accounts for the fact that the interatomic N 0 distance (115 pm) is intermediate between that in the triple-bonded NO+ (106 pm) and values typical of double-bonded NO species ( 120 pm). It also interprets the very low ionization energy of the molecule (9.25 eV, compared with 15.6 eV for N2, 14.0 eV for CO, and 12.1 eV for O2). Similarly, the notable reluctance of NO to dimerize can be related both to the geometrical distribution of the unpaired electron over the entire molecule and to the fact that dimerization to 0=N—N=0 leaves the total bond order unchanged (2 x 2.5 = 5). When NO condenses to a liquid, partial dimerization occurs, the cis-form being more stable than the trans-. The pure liquid is colourless, not blue as sometimes stated blue samples owe their colour to traces of the intensely coloured N2O3.6O ) Crystalline nitric oxide is also colourless (not blue) when pure, ° and X-ray diffraction data are best interpreted in terms of weak association into... 

These methods can give us useful information on radicals in a manner similar to that for closed-shell systems, provided the exploitation is correct. Of course, in expressions for total energy, bond orders, etc., a singly occupied orbital must be taken into account. One should be aware of areas where the simple methods give qualitatively incorrect pictures. The HMO method, for example, cannot estimate negative spin densities or disproportionation equilibria. On the other hand, esr spectra of thousands of radicals and radical ions have been interpreted successfully with HMO. On the basis of HMO orbital energies and MO symmetry... 

In principle, a total of 4 electrons may be progressively added to the oxygen molecule, eventually resulting in zero bond order — hence the ultimate reduction product is oxide. 

Dipole moments of azolides have been reviewed, with emphasis on the conformation of the acyl group. 441 Unfortunately, structural and conformational studies on azolides by X-ray structure analysis are almost totally lacking, although they would be of great interest with regard to the conformations and to the bond lengths and bond orders in these systems. Only an X-ray analysis of V-acetyl-4-bromopyrazole 451 has been reported. 

Typical Ni—L bond lengths have been extracted from the Cambridge Structure Database (CSD) and listed in tabular form.321 Also, Ni11—L bond lengths from the CSD have been analyzed by the BDBO technique, which is related to the bond valence model (BVM) where the total bond order is equal to the oxidation state of any atom.322 Selected mean Ni—L distances from the CSD source are collected in Table 2. 

In order to complete its octet, each carbon atom must share a total of four electron pairs. The order of a bond is the number of electron pairs shared in that bond. The total number of shared pairs is called the total bond order of an atom. Thus, carbon must have a total bond order of four (except in CO). A single bond is a sharing of one pair a double bond, two and a triple bond, three. Therefore, in organic compounds, each carbon atom forms either four single bonds, a double bond and two single bonds, a triple bond and a single bond, or two double bonds. As shown in the table below, each of these possibilities corresponds to a total bond order of 4. 

Number and Types of Bonds Total Bond Order... 

Table 21-1 Total Bond Orders in Organic Compounds...

Each element in this example is characterized by a total bond order corresponding to that listed in Table 21 -1. 

Electron dot formulas are useful for deducing the structures of organic molecules, but it is more convenient to use simpler representations—structural or graphic formulas—in which a line is used to denote a shared pair of electrons. Because each pair of electrons shared between two atoms is equivalent to a total bond order of 1, each shared pair can be represented by a line between the symbols of the elements. Unshared electrons on the atoms are usually not shown in this kind of representation. The resulting representations of molecules are called graphic formulas or structural formulas. The structural formulas for the compounds (a) to (e) described in Example 21.1 may be written as follows ... 

For even more convenience in representing the structures of organic compounds, particularly in printed material, line formulas are used, so-called because they are printed on one line. In line formulas, each carbon atom is written on a line adjacent to the symbols for the other elements to which it is bonded. Line formulas show the general sequence in which the carbon atoms are attached, but in order to interpret them properly, the permitted total bond orders of all the respective atoms must be kept in mind. Again referring to the compounds (a) to (e) described above, the line formulas are as follows ... 

If the permitted total bond orders of the respective atoms are remembered, it is apparent that the line formula CH4 cannot represent such structures as... 

The aromatic hydrocarbons are characterized by molecules containing six-membered rings of carbon atoms with each carbon atom attached to a maximum of one hydrogen atom. The simplest member of the series is benzene, ChH6. Using the total bond order rules discussed above, the structural formula of benzene can be written as follows ... 

What is the total bond order of sulfur in CH3SCH3 ... 

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