Bonding electrostatic

The belief that electrostatic (Coulomb) interactions exhibit little directionality (i.e., that their energy hardly depends on the bond angle) is widespread. This is because the concept of net atomic charges (atom-centered monopoles) has become ingrained in chemists thinking, so that Coulomb interactions with a polar atom are believed to be necessarily isotropic and directionahty of Coulomb interactions only to be the result of secondary interactions with more distant atoms. Neither of these assumptions is correct and the reasons have been known for decades. Nonetheless, directionality in noncovalent interactions is still often attributed to covalent contributions or donor-acceptor interactions because the Coulomb interaction is believed not to be able to give rise to significant directionality. The purpose of this chapter is to discuss Coulomb interactions with special emphasis on directionality and anisotropy of the molecular electrostatic potential (MEP) [1] around atoms. 

The Chemical Bond Chemical Bonding Across the Periodic Table, First Edition. 

Anisotropic Moiecuiar Eiectrostatic Potential Distribution Around Atoms 

The MEP defines the Coulomb interaction of an unperturbed molecule with its surroundings. It represents the sum of the contributions from the nuclei (positive) and the electron cloud (negative) and is a measurable quantity. It is commonly visualized by color coding a van der Waals-like isodensity surface [8] according to the MEP. As the point at which the MEP is measured moves from outside the molecule toward its center, the effect of the electron cloud diminishes and that of the nuclei takes over. This means that the MEP becomes more positive as we approach the nuclei within the molecule. This is demonstrated for a slice through ethanol in figure 18.1. 

Lone pairs can also lead to anisotropic MEP patterns on molecular surfaces. In this case, two factors play a role the position of the element concerned in the periodic table and the coordination geometry. Kutzelnigg [28] pointed out that lone pairs for elements of the third period (Na-Kr) and higher exhibit an 

The third group in the classification mentioned above corresponds to a vast number of solid compounds which can be considered as aggregates of positive and negative particles interacting in an electrostatic manner. 

Most ionic solids are formed by a combination of elements with very different electronegativities, for instance, between halide or oxide ions and cations from electropositive metals as those of the groups 1, 2, or from the transition series. 

By considering perfectly ionic materials and determining the arrangements of the ions in the lattice it is possible to calculate in a relatively simple way the potential energy of the system. 

The formation of ions, involving the ionization energy (IP) and the electroaffinity (EA) of the electropositive and electronegative atoms respectively, is an 

In the energy calculations for ionic solids at least three factors should be considered 1. The electrostatic energy determined mainly by the charge of the ions and the interatomic distances, 2. the arrangement of the ions in the solids, and 3. the interelectronic repulsive interactions between the ions at the bonding distances. 

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The rearranging entity has been shown to be the bivalent cation the adjacent charges may so weaken the N—N link that charges of nearly integral size may be built up in the 4 and 4 positions. In the bent, but strainless, cation the minimum separation of the two p-positions would suffice for the establishment of a lai ely electrostatic bond, which could pass smoothly into the covalent rearrangement product (benzidine). 

Several different kinds of noncovalent interactions are of vital importance in protein structure. Hydrogen bonds, hydrophobic interactions, electrostatic bonds, and van der Waals forces are all noncovalent in nature, yet are extremely important influences on protein conformations. The stabilization free energies afforded by each of these interactions may be highly dependent on the local environment within the protein, but certain generalizations can still be made. 

Ion Radius ratio Predicted coordination number Observed coordination number Strength of electrostatic bonds... 

Primary structures are stabilized by covalent peptide bonds. Higher orders of structure are stabilized by weak forces—multiple hydrogen bonds, salt (electrostatic) bonds, and association of hydrophobic R groups. 

In a stable ionic structure the valence (ionic charge) of each anion with changed sign is exactly or nearly equal to the sum of the electrostatic bond strengths to it from adjacent cations. The electrostatic bond strength is defined as the ratio of the charge on a cation to its coordination number. 

Let a be the coordination number of an anion. Of the set of its a adjacent cations, let nt be the charge on the i-th cation and kl its coordination number. The electrostatic bond strength of this cation is ... 

Let the cation M2+ in a compound MX2 have coordination number 6. Its electrostatic bond strength is s = 2/6 = The correct charge for the anion, z = -1, can only be obtained when the anion has the coordination number a = 3. 

Let the cation M4+ in a compound MX4 also have coordination number 6 its electrostatic bond strength is s = 4/6 = . For an anion X- having coordination number a = 2 we obtain = + = for an anion with a = 1 the sum is = . For other values of a the resulting p deviate even more from the expected value z = -1. The most favorable structure will have anions with a = 2 and with a = 1, and these in a ratio of 1 1, so that the correct value for z results in the mean. 

The electrostatic valence rule usually is met rather well by polar compounds, even when considerable covalent bonding is present. For instance, in calcite (CaC03) the Ca2+ ion has coordination number 6 and thus an electrostatic bond strength of s(Ca2+) =. For the C atom, taken as C4+ ion, it is s(C4+) =. We obtain the correct value of z for the oxygen atoms, considering them as O2- ions, if every one of them is surrounded by one C and two Ca particles, z = -[2s(Ca2+) + s(C4+)] = -[2 j + ] = -2. This corresponds to the actual structure. NaN03 and YBOs have the same structure in these cases the rule also is fulfilled when the ions are taken to be Na+, N5+, Y3+, B3+ and 02. For the numerous silicates no or only marginal deviations result when the calculation is performed with metal ions, Si4+ and 02 ions. 

The electrostatic valence rule has turned out to be a valuable tool for the distinction of the particles O2-, OH- and OH2. Because H atoms often cannot be localized reliably by X-ray diffraction, which is the most common method for structure determination, O2-, OH- and OH2 cannot be distinguished unequivocally at first. However, their charges must harmonize with the sums pj of the electrostatic bond strengths of the adjacent cations. 

Kaolinite, Al2Si205(0H)4 or Al203-2Si02-2H20 , is a sheet silicate with A1 atoms in octahedral and Si atoms in tetrahedral coordination the corresponding electrostatic bond strengths are ... 

Calculate the electrostatic bond strengths of the cations and determine how well the electrostatic valence rule is fulfilled. Calculate the expected individual V-O bond lengths using data from Table 7.2 and the values d(V4+0) = 189 pm and b(V4+0) = 36 pm. 

The coordination of an O2- ion is three Al3+ ions within an A1404 cube and one Mg2+ ion outside of this cube. This way it fulfills the electrostatic valence rule (Pauling s second rule, cf p. 58), i.e. the sum of the electrostatic bond strengths of the cations corresponds exactly to the charge on an O2- ion ... 

The most successful sensitizers so far tested are complexes of Ru(II) with various derivatives of 2,2 bipyridine, e.g. 2,2 -bipyridine 4,4 -dicarboxylic acid (L). The Ru(II)L3 complex is adsorbed from an aqueous solution of suitable pH value to oxidic semiconductors via electrostatic bonds between —COO- groups of the ligands and the positively charged (protonized) semiconductor surface. 

Recently, Rumpf (R5) has considered the forces of attraction between a plate and a sphere and between irregular shape particles. His conclusions are that the capillary bonds are relatively insensitive to the particle shape, but the van der Waals force of attraction is extremely sensitive. Although weaker in magnitude than the two aforementioned bonds, the electrostatic bonds may persist over long separation distances. 

Procedure of pollen preparation Pollen can be washed off stigmas with an acetone solution as water or other polar solutions often fail to sufficiently break electrostatic bonds holding heterospecific pollen to stigma. However, this means the acetone must be evaporated in an air drying oven (48 h) because a Coulter Counter requires a saline solution of standard volume (usually 10-20 ml) be used to prepare pollen samples. If the solutions are mixed and the volumes are inconsistent, there is a risk that differences in conductivity will create errors. 

A different pH-triggered deshielding concept with hydrophilic polymers is based on reversing noncovalent electrostatic bonds [78, 195, 197]. For example, a pH-responsive sulfonamide/PEl system was developed for tumor-specific pDNA delivery [195]. At pH 7.4, the pH-sensitive diblock copolymer, poly(methacryloyl sulfadimethoxine) (PSD)-hZocA -PEG (PSD-b-PEG), binds to DNA/PEI polyplexes and shields against cell interaction. At pH 6.6 (such as in a hypoxic extracellular tumor environment or in endosomes), PSD-b-PEG becomes uncharged due to sulfonamide protonation and detaches from the nanoparticles, permitting PEI to interact with cells. In this fashion PSD-b-PEG is able to discern the small difference in pH between normal and tumor tissues. 

For the NaCl crystal, the radius ratio is 0.54, which is well within the range for an octahedral arrangement of anions around each cation (0.414 - 0.732). However, because this is a 1 1 compound, there are equal numbers of cations and anions. This means that there must be an identical arrangement of cations around each anion. In fact, for 1 1 compounds, the environment around each type of ion must be identical. We can see that this is so from a very important concept known as the electrostatic bond character. If we predict (and find) that six Cl- ions surround each Na+, each "bond" between a sodium ion and a chloride ion must have a bond character of 1/6 because the sodium has a unit valence, and... 

Rutile, Ti02, which has the structure shown in Figure 7.8, is an important chemical that is used in enormous quantities as the opaque white material to provide covering ability in paints. Because the Ti4+ ion is quite small (56 pm), the structure of Ti02 has only six O2- ions surrounding each Ti4+, as predicted by the radius ratio of 0.39. Therefore, each Ti-O bond has an electrostatic bond character of 2/3 because the six bonds to (ions total the valence of 4 for Ti. There can be only three bonds from Ti4+ to each ()2 ion because three such bonds would give the total valence of 2 for oxygen (3 X 2/3 = 2). 

Consider now the bonds to each O2- ion in the perovskite structure. First, there are two bonds to Ti4+ ions that have a character of 4/6 each, which gives a total of 4/3. However, there are four Ca2+ ions on the corners of the face of the cube where an oxide ion resides. These four bonds must add up to a valence of 2/3 so that the total valence of 2 for oxygen is satisfied. If each Ca-O bond amounts to a bond character of 1/6, four such bonds would give the required 2/3 bond to complete the valence of oxygen. From this it follows that each Ca2+ must be surrounded by 12 oxide ions so that 12(1/6) = 2, the valence of calcium. It should be apparent that the concept of electrostatic bond character is a very important tool for understanding crystal structures. 

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