Formal bond

In ub initio calculations all elements of the Fock matrix are calculated using Equation (2.226), ii re peifive of whether the basis functions ip, cp, semi-empirical melh ids it is useful to consider the Fock matrix elements in three groups (the diagonal... 

The silicon surface contains chains of atoms that are formally bonded to just three other atoms. These atoms compensate for the lack of a full valence complement of bonds by tt... 

The single-bond covalent radius of C can be taken as half the interatomic distance in diamond, i.e. r(C) = 77.2pm. The corresponding values for doubly-bonded and triply-bonded carbon atoms are usually taken to be 66.7 and 60.3 pm respectively though variations occur, depending on details of the bonding and the nature of the attached atom (see also p. 292). Despite these smaller perturbations the underlying trend is clear the covalent radius of the carbon atom becomes smaller the lower the coordination number and the higher the formal bond order. 

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

For bonded atoms, the off-diagonal terms (where i j) are taken to depend on tjje type and length of the bond joining the atoms on which the basis functions y- and Xj 0 centred. The entire integral is written as a constant, 0ij, which is not the same as the fixY in Hiickel 7r-electron theory. The are taken to be parameters, fixed by calibration against experiment. It is usual to set Pij to zero when the pair of atoms are not formally bonded. 

In both compounds the hydratemolecules form hydrogen bridges, in which as in the difluorophosphates, only the 0-atoms of the [POgF] ions participate in (NH4)2[P03F] H2O there are additional N—H 0 bridges (26). In the P03F ion the formal bond order po decreases from 1.83 to 1.67 (95) in comparison to... 

Additional insight is obtained if these results are compared with the related absorption experiments in which an electron from the delta-bonding orbital is excited to the delta-antibonding orbital (2). The pertinent data is summarized in the Table. The state obtained by 6 ionization has a greater formal bond order than the state obtained by 6-h5 excitation, but has a weaker metal-metal force constant and a longer metal-metal bond. It is... 

Through an interaction of the two singly occupied ji orbitals, a transannular six-center four-electron 71 -ji bond with a formal bond order of 0.67 results... 

It is generally known that phosphorus is capable not only of forming species with five formal bonds to the phosphorus atom, but also that such compounds can be stable under ordinary conditions. We are concerned here with those pentacoordinate phosphorus compounds that have at least one formal carbon-phosphorus bond. We will focus primarily on the processes that generate such a bond. 

In conclusion, sp-hybrid character differs strongly between dialkali neutrals and cations, in sharp distinction to the rather constant s character in H2 versus H2+. A comparison of bonding in Li2 and Li2+ therefore does not merely depend on the number of electrons in the bonding NBO (change in formal bond order), but rather reflects deep differences in the bonding hybrids themselves, particularly with regard to directional p character. 

The final cu-bonded formulas (3.213), (3.214), and (3.219)-(3.221) bear an obvious resemblance to the usual VSEPR representations of these hypervalent species. Indeed, each cu-bonded structure has the same number of formal bond pairs (bp) and lone pairs (lp) as the VSEPR representation. Furthermore, the predicted angular geometries of the two models are essentially identical, with the linear (or near-linear) cu-bonded ligands occupying axial positions in the SN2-like trigonal bipyramidal motif. 

Figure 4.23 graphically displays the metal-metal bond lengths (cf. Table 4.15) and their dependences on the formal bond order of the Lewis-like formula. These plots all show the expected decrease of mm with increasing bond order, but with somewhat different rates of decrease for different metal atoms. Thus, the multiplebonding of the Lewis-like picture readily accounts for the variations of metal-metal bond length in these hydrides. 

Figure 4.23 Variations of metal-metal bond length with nominal formal bond order (the number of bonds in the natural Lewis structure) in duodectet-rule-conforming dinuclear hydrides H MMH (see Table 4.15).

Intermolecular interactions only operate over relatively short distances, so we assume that, under normal conditions, each molecule in a gas is wholly unaffected by all the others. By contrast, when the gas is compressed and the particles come to within two or three molecular diameters of each other, they start to notice each other. We say the outer-shell electrons on an atom are perturbed by the charges of the electrons on adjacent atoms, causing an interaction. We call these interactions bonds, even though they may be too weak to be formal bonds such as those permanently connecting the atoms or ions in a molecule. 

A formal bond involves the permanent involvement of electrons in covalent or ionic bonds see p. 64. Interactions between molecules in a compressed gas are temporary. 

The great American scientist G. N. Lewis coined the word covalent, early in the 20th century. He wanted to express the way that a bond formed by means of electron sharing. Each covalent bond comprises a pair of electrons. This pairing is permanent, so we sometimes say a covalent bond is a formal bond, to distinguish it from weak and temporary interactions such as induced dipoles. 

The content of The Forces Between Molecules, by Maurice Rigby, E. Brian Smith, William A. Wakeham and Geoffrey C. Maitland, Oxford University Press, Oxford, 1986, is more explicitly about interactions than formal bonds. Again, it will be a fairly austere and mathematical read. In the Oxford Primer series, try Energy Levels in Atoms and Molecules by W. G. Richards and P. R. Scott, Oxford University Press, Oxford, 1994. It s easier than the two books above, and again helps provide some of the background material to the subject. It is still mathematically based. 

Other electron-poor clusters include the 44-electron Pt3(CO)3(PPh3)4 and the 42-electron species Pd3(CO)3(PPh3)3 and [Re3Cl12p. For the 44-electron system, the 18-electron rule predicts two double bonds within the M3 triangle and for the 42-electron complexes, three double bonds. The structures of the platinum and palladium complexes are unknown, but the Re-Re distances of 2.47-2.49 A in the anion [Re l ]3- are regarded (20) as short and consistent with a formal bond order of two. 

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