How many hydrogen atoms will a single carbon atom bond with to form a stable molecule?

9.11 Coordinate covalent bonds

A single covalent bond in which both electrons in the shared pair come from the same atom is called a coordinate covalent bond. To indicate a coordinate covalent bond an arrow is sometimes drawn from the atom that donates the electron pair toward the atom with which the pair is shared.

The donor atom provides both electrons to a coordinate covalent bond and the acceptor atom accepts an electron pair for sharing in a coordinate covalent bond. For coordinate covalent bonds, as for any other kind of bond, it is impossible to distinguish among the electrons once the bond has formed. For example, a hydrogen ion unites with an ammonia molecule by a coordinate covalent bond to form the ammonium ion

but all four hydrogens in the ammonium ion are alike.

Covalent Bonds

Covalent bonds are much more common in organic chemistry than ionic bonds. A covalent bond consists of the simultaneous attraction of two nuclei for one or more pairs of electrons. The electrons located between the two nuclei are bonding electrons. Covalent bonds occur between identical atoms or between different atoms whose difference in electronegativity is insufficient to allow transfer of electrons to form ions.

Let’s consider the covalent bond in the hydrogen molecule. A hydrogen molecule forms from two hydrogen atoms, each with one electron in a 1 s orbital. The two hydrogen atoms are attracted to the same pair of electrons in the covalent bond. The bond is represented either as a pair of “dots” or as a solid line. Each hydrogen atom acquires a helium-like electron configuration.

H•+H•→H••HorH─H

Energy is released when the electrons associated with the two hydrogen atoms form a covalent bond. The process releases heat; therefore, it is exothermic. The heat released when one molecule of a compound forms at 298 K is the standard enthalpy change (ΔH°) for the process. ΔH° for forming a mole of hydrogen from two hydrogen atoms is − 435 kJ mole−1. Since energy is released in the reaction, the hydrogen molecule is more stable than the two hydrogen atoms. The reverse process, pulling the two bonded hydrogen atoms apart, requires 435 kJ mole−1, a quantity called the bond strength of the H─H bond.

The two hydrogen nuclei are separated by a distance called the bond length. This distance results from a balance between attractive and repulsive forces. There is an attraction between the nuclei and the bonding electrons, but there is also a repulsion between the two nuclei as well as between the two electrons. Figure 1.5 is a schematic diagram of these attractive and repulsive forces. It provides a starting point for our discussion of bonding.

When a covalent bond forms between two hydrogen atoms, there are two sets of electrostatic repulsions (nuclear–nuclear and electron–electron, red), but four sets of electrostatic attractions (green). The attractive forces are equal in magnitude, but opposite in sign. Each hydrogen nucleus attracts both electrons. The net result is that the energy of the system decreases when the bond forms. This simple electrostatic model for bonding does not adequately describe chemical bonds. For that we will need to expand our analysis, and we will do that in the following sections.

A covalent bond also occurs in Cl2. In the chlorine molecule, the two chlorine atoms are attracted to the same pair of electrons. Each chlorine atom has seven valence electrons in the third energy level and requires one more electron to form an electron core with an argon electron configuration. Each chlorine atom contributes one electron to the bonded pair shared by the two atoms. The remaining six valence electrons of each chlorine atom are not involved in bonding. They are variously called nonbonding electrons, lone pair electrons, or unshared electron pairs.

As we noted earlier, a covalent bond is drawn as a dash in a Lewis structure. Also, in a Lewis structure, nonbonding electron pairs are shown as “dots.” The Lewis structures of four simple organic compounds: methane, aminomethane, methanol, and chloromethane are shown below with both bonding and nonbonding electrons.

The hydrogen atom and the halogen atoms form only one covalent bond to other atoms in stable neutral compounds. However, the carbon, oxygen, and nitrogen atoms can bond to more than one atom. The number of covalent bonds an atom can form is called the valence of the atom. The valence of a given atom is the same in most stable neutral organic compounds. Table 1.2 lists the valences of some common elements contained in organic compounds.

Table 1.2. Valences of Common Elements1

3.2.3 Covalent Bonds

Covalent bonds are the most important means of bonding in organic chemistry. The formation of a covalent bond is the result of atoms sharing some electrons. The bond is created by the overlapping of two atomic orbitals [1]. This process is illustrated in Figure 3-4. In this type of bond, each shared electron will be counted toward both atoms’ valence shells for the purpose of satisfying the octet rule. In a single bond one pair of electrons is shared, with one electron being contributed from each of the atoms. Double bonds share two pairs of electrons and triple bonds share three pairs of electrons. Bonds sharing more than one pair of electrons are called multiple covalent bonds.

In a single covalent bond, when the electrons are shared between two s orbitals, the resulting bond is a sigma (σ) bond as shown in Figure 3-4. Sigma bonds are the strongest covalent chemical bonds. Sigma bonds also occur when an s and a p orbital share a pair of electrons or when two p orbitals that are parallel to the internuclear axis share a pair of electrons (see Figure 3-4). A pi (π) bond is the result of the sharing of a pair of electrons between two p orbitals that are perpendicular to the internuclear axis (see Figure 3-5). In double and triple bonds, the first bond is a σ bond and the second and third ones are π bonds. Pi bonds are weaker than sigma bonds, however a double bond has the combined strength of the σ and π bonds. Analogously, a triple bond has the combined strength of a σ and two π bonds. As an example, each of the hydrogen atoms in water (H2O) is bonded to the oxygen via a single bond (σ bond) whereas the oxygen atoms in carbon dioxide (CO2) are bound to the carbon atom via double bonds, each consisting of a σ bond and a π bond.

Covalent Binding

A covalent bond can be represented as a linkage between electron pair and two atoms. Different molecules such as hydrogen, nitrogen, chlorine, water, ammonia have a covalent bond, and other ligands with sulfate, amide, silane, carboxyl, hydroxyl groups are covalently bound the MONPs and act as a linker between the biomolecules and NPs. For example, Varache et al. conjugated carboxyl groups to mesoporous SiO2 NPs (covalently attached) to bind with PEG or PEI (Varache et al., 2019). Further, cisplatin was conjugated with PEG or PEI coated SiO2 NPs and studied the drug release pattern after surface functionalization. The results revealed that PEI-coated SiO2 NPs were more efficient in delivering cisplatin than PEG-coated SiO2 NPs. Jaramillo et al. (2017) attempted to surface functionalized ZnO NPs with APTES using the direct mixing method, where ZnO NPs and APTES were mixed for 24 hrs under constant stirring. The surface functionalization was confirmed using FTIR and Raman spectroscopy. The results suggested that APTES was attached on the surface of ZnO NP via one or two Si-O-Zn (covalent bond) bonds.

Covalent Bonds

A covalent bond consists of the mutual sharing of one or more pairs of electrons between two atoms. These electrons are simultaneously attracted by the two atomic nuclei. A covalent bond forms when the difference between the electronegativities of two atoms is too small for an electron transfer to occur to form ions. Shared electrons located in the space between the two nuclei are called bonding electrons. The bonded pair is the “glue” that holds the atoms together in molecular units.

The hydrogen molecule is the simplest substance having a covalent bond. It forms from two hydrogen atoms, each with one electron in a 1s orbital. Both hydrogen atoms share the two electrons in the covalent bond, and each acquires a helium-like electron configuration.

H•+H•→H—H

A similar bond forms in Cl2. The two chlorine atoms in the chlorine molecule are joined by a shared pair of electrons. Each chlorine atom has seven valence electrons in the third energy level and requires one more electron to form an argon-like electron configuration. Each chlorine atom contributes one electron to the bonding pair shared by the two atoms. The remaining six valence electrons of each chlorine atom are not involved in bonding and are concentrated around their respective atoms. These valence electrons, customarily shown as pairs of electrons, are variously called nonbonding electrons, lone pair electrons, or unshared electron pairs.

The covalent bond is drawn as a dash in a Lewis structure to distinguish the bonding pair from the lone pair electrons. Lewis structures show the nonbonding electrons as pairs of dots located about the atomic symbols for the atoms. The Lewis structures of four simple organic compounds—methane, methylamine, methanol, and chloromethane—are drawn here to show both bonding and nonbonding electrons. In these compounds carbon, nitrogen, oxygen, and chlorine atoms have four, three, two, and one bonds, respectively.

The hydrogen atom and the halogen atoms form only one covalent bond to other atoms in most stable neutral compounds. However, the carbon, oxygen, and nitrogen atoms can simultaneously bond to more than one atom. The number of such bonds is the valence of the atom. The valences of carbon, nitrogen, and oxygen are four, three, and two, respectively.

4.2.1 Dipole–Dipole Forces

Covalent bonds can have appreciable polarity due to the unequal sharing of electrons by atoms that have different electronegativities. For most types of bonds, this charge separation amounts to only a small percentage of an electron charge. For example, in HI it is about 5%, but in HF where the difference in electronegativity is about 1.8 units, it is about 44%.

In order to show how dipole–dipole forces arise, let us consider a polar molecule that can be represented as

where δ+ and δ− represent the fraction of an electronic charge residing on the positive and negative ends, respectively. When polar molecules are allowed to approach each other, there will be an electrostatic interaction between them. The actual energy of the interaction will depend on the orientation of the dipoles with respect to each other. Two limiting cases can be visualized as shown in Figure 4.9.

By assuming an averaging of all possible orientations, the energy of interaction, ED can be shown to be

(4.13)ED=−2μ43kTR6

where μ is the dipole moment, R is the average distance of separation, k is Boltzmann's constant, and T is the temperature (K). On the basis of this interaction, it is expected that polar molecules should associate to some extent, either in the vapor state or in solvents of low dielectric constant. Dipole association in a solvent having a low dielectric constant leads to an abnormal relationship between the dielectric constant of the solution and the concentration of the polar species. Although the procedure will not be shown, it is possible to calculate the association constants for such systems from the dielectric constants of the solutions. If the solvent has a high dielectric constant and is polar, it may solvate the polar solute dipoles thus preventing association which forms aggregates. Consequently, the association constants for polar species in solution are always dependent on the solvent used.

1 Introduction

The coordination compounds found their applications long before the establishment of coordination chemistry. Bright red coloured alizarin dyes were under applications even before the fifteenth century. This bright red dye, now characterized as a chelated complex of hydroxyanthraquinone with calcium and aluminium metal ions, is shown in Figure 1.

Later, in the sixteenth century, the formation of a well-known member of today's coordination chemistry family, the tetraamminecupric ion [Cu(NH3)4]+2, was recorded upon contact between brass alloy and ammonium chloride. Addition of Prussian blue Fe4[Fe(CN)6]3·xH2O increased the use of coordination compounds in dyes and pigments. A platinum complex K2[PtCl6] offered an application for the refinement of platinum metal. Thus, before the coordination chemistry was structured, the coordination compounds, complexes and chelates found their applications.

A systematic investigation of structure and bonding in coordination chemistry began with the inquisitiveness of Tassaert (1798), which was extended by distinguished chemists like Wilhelm Blomstrand, Jorgensen and Alfred Werner [1] until the end of the nineteenth century. In the events, Werner's coordination theory (1893) became the base of the modern coordination chemistry. It is worth noting that the electron was discovered subsequent to Werner's theory.

The bonding in compounds like CoCl3 and NH3 were easily understood and explained and hence such compounds were regarded as simple compounds. For instance, the +3 formal oxidation of cobalt in cobalt chloride is balanced by three uni-negative chloride ions and the coexistence of these ionic moieties to form a molecule is understood and explained. Similarly, the valence shell (n = 2) of nitrogen (N = 7) contains five electrons and four orbitals (2s, 2px, 2py and 2pz). Keeping an electron pair in one of these orbitals while the other three remains half filled, an opportunity for three hydrogen atoms to contribute one electron each for the formation of a covalent bond with nitrogen, can also be explained. Thus an ammonia molecule has three N

A ‘complex’ situation arises when one comes to know that the molecule CoCl3 can encompass six ammonia molecules, resulting into a third independent entity. This situation was fully understood and explained by Werner's coordination theory, followed by naming the entity as ‘complex’.

1.1 Definitions

Coordination compounds are the compounds containing one or more coordinate covalent bonds.

Coordinate covalent bonds are the covalent bonds in which both the bonding electrons are contributed by one of the bond partners. Figure 2 distinguishes the covalent bonds from the coordinate covalent bond in NH3BF3. While the three B

F covalent bonds are formed due to the sharing of electron pairs resulting from contributions of both boron and fluorine atoms, an N

B bond is formed due to the donation of a lone pair of electrons from nitrogen into the empty orbitals of boron. The coordinate covalent bond is shown by an arrow with its head pointing towards the direction of the donation of an electron pair, as shown in Figure 2.

Figure 2. Bonding in NH3BF3.

A complex is a molecule/ion containing a central metal atom/ion surrounded by a definite number of ligands held by secondary valences or coordinate covalent bonds.

Primary valency refers to the charge over the metal ion e.g. Co(III) has +3 charge, which can be balanced by −3 charge-forming compounds like CoCl3. The primary valency is ionic and is satisfied in the second coordination sphere, as shown in Figure 3.

Figure 3. First and second coordination spheres in [Co(NH3)6]Cl3.

Secondary valency is the number of empty valence orbitals, as illustrated for [Co(NH3)6]Cl3 in the figure. The Co(III) ion has six empty valence orbitals. Hence its secondary valency is six. Secondary valency is a coordinate covalent valency, and it is satisfied in the first coordination sphere of the metal ion, as shown in Figure 4.

Figure 4. Secondary valency of Co(III) in [Co(NH3)6]Cl3.

Coordination number is a property of the metal ion representing the total number of donor atoms directly attached to the central atom. In the above case, the coordination number of Co(III) is six, as six nitrogen donor atoms are directly connected to the central metal ion (cobalt(III)).

Ligand is any atom, ion or neutral molecule capable of donating an electron pair and bonded to the central metal ion or atom through secondary valency.

Dentate character is a property of a ligand representing a number of coordinating atoms.

In the case of [Co(NH3)6]Cl3, ammonia, NH3 the ligand contains one donor atom (N). Hence its dentate character is one and is classified as a monodentate ligand. Similarly, chloro (Cl−) is an anionic, monoatomic and monodentate ligand, while hydroxo (OH−) is a diatomic, monodentate and anionic ligand. Aquo (OH2) represents a neutral triatomic monodentate ligand. A few popular ligands and their characteristics are shown in Figure 5.

Figure 5. Structures and characteristics of a few important ligands.

Due to a higher dentate character of ligands, a variety of complexes known as chelate is also formed sometimes. Chelate is a compound formed when a polydentate ligand uses more than one of its coordinating atoms to form a closed-ring structure, which includes the central metal ion. Five- and six-membered rings are known to provide extra stability to the chelates. The process of chelate formation is known as chelation. A polydentate ligand involved in chelate formation is also known as a chelating ligand. Chelates generally exhibit higher stability than analogous complexes.

A polydentate ligand may be attached to the central metal ion through more than one kind of functional group. The number and kind of linkages by which the metal ion is attached with the ligands can thus become a criterion for the classification of chelates. The covalent bonds are formed by the replacement of one or more H-atoms, while coordinate covalent bonds are formed by the donation of an electron pair from the ligands. Some of the chelates involving a variety of polydentate ligands and linkages are shown in Figure 6. The coordinate covalent linkages are shown by thin, thread-like bonds.

Figure 6. Structures and characteristics of a few chelates.

Polynuclear complex is a complex with more than one metal atom/ion. These metal ions are sometimes bridged through appropriate ligands, resulting into the formation of a bridged polynuclear complex.

1.3.3 Covalent binding

Covalent bonds are mostly formed between side-chain-exposed functional groups of proteins and suitably modified transducer surface, resulting in an irreversible binding and producing a high surface coverage [71,72]. One of the most commonly used methods for covalent immobilization is to couple the antibody randomly via their free amino groups to an activated sensor surface (Fig. 1.5). Chemical coupling agents, such as carbodiimides and succinimidyl esters, may be used to activate carboxylic acids on sensor surfaces. Amines or alcohols can be activated by isothiocyanates, epoxides, glutaraldehyde (GA), or other aldehydes. Oxidation of alcohols is achieved with periodate to yield aldehydes, which react readily with amines. In addition, conversion of alcohols to a highly reactive ester by cyanogen bromide allows for further reaction with amines of antibody. For example, the ultrasonication treatment of carbon nanotubes (CNTs) in concentrated acid condition can produce abundant carboxyl groups on their surface. When CNTs are modified on the electrode surface, the carbodiimide/N-hydroxysuccinmide system is commonly applied to link antibodies with the activated carboxyl groups [60].

Another approach is to use bifunctional cross-linking reagents [73]. The cross-linking reagents contain two different reactive groups, thereby providing a means of covalently linking two dissimilar target groups on the sensor surface and protein biomolecules. A wide variety of these linkers such as (3-aminopropyl)triethoxysilane (APTES) [74], (3-glycidoxypropyl)-trimethoxysilane (GPTMS) [75], 3-mercaptopropyltrimethoxysilane (MPTMS) [76], diazonium cation [77], and various thiol derivatives [78–80] are commercially available to cover a broad range of functional groups necessary. For example, the silanization reaction of APTES at the hydroxyl group-containing substrate (e.g., glass, electrode, and microwell plate) can provide amino groups at the surface. Then antibodies can be coupled to the substrate via the cross-linking of GA (Fig. 1.6).

3.2.4 Prediction of the activation volume

When covalent bonds break during non-ionic reactions, the contribution to ΔvR# of the elongation, Δl, of the bond whose initial length was l, can be roughly calculated. Hamann [3] has assumed that the stretching occurs along the axis of a cylinder of constant cross-section. For a diatomic molecule, the cross-section can be taken to be the mean of the van der Waals cross-sectional areas of the separating atoms. Using the van der Waals radii, rA and rB, it follows that

(3.2-44)ΔvR ,b#=π(rA2+rB2)2⋅Δl

The elongation, Δl, can be evaluated from quantum mechanical calculations. For a rough estimation, a value of

(3.2-45)Δl=(0.10to0.35)⋅l

can be assumed. From eqn. 3.2-44 it can be seen that the activation volume is positive when covalent bonds break.

Similarly, when covalent bonds are formed, ΔvR,f# can be estimated from the relationship:

(3.2-46)ΔvR,f#=π(rA2+rB2)2⋅[(l+Δl)−(rA+rB)]

The initial distance of the reactants is taken to be the sum of the van der Waals radii, rA and rB. The transition state distance is again (l + Δl) and can be roughly estimated from equation 3.2-45. A negative activation volume results when covalent bonds are formed, because (rA+rB)>(l + Δl). Comparison of equation 3.2-44 and 3.2-46 shows that the value of the activation volume, ΔvR, f#, for the formation of covalent bonds is invariably greater than ΔvR,b# for bond breaking. When bond-formation and the breaking of another bond occur simultaneously, ΔvR,f# predominates, and the net activation volume, ΔvR#, will be negative.

2.1.1. The covalent bond

The covalent bond may be described in terms of the more qualitative VB (valence bond) theory by overlapping atomic orbitals occupied by unpaired valence electrons (fig. 1). Its strength depends on the degree of overlapping and is given by the exchange integral. In terms of the more quantitative LCAO–MO (linear combination of atomic orbitals – molecular orbitals) theory, molecular orbitals are constructed by linear combination of atomic orbitals (fig. 2). The resulting bonding, non-bonding and anti-bonding molecular orbitals, filled up with valence electrons according to the Pauli exclusion principle, are localized between the bonding atoms with well defined geometry. Generally, covalent bonds can be characterized as strong, directional bonds. Increasing the number of atoms contributing to the bonds increases the number of molecular orbitals and their energy differences become smaller and smaller. Finally, the discrete energy levels of the molecular orbitals condense to quasicontinuous bands separated by energy gaps. Since in a covalent bond each atom reaches its particular stable noble gas configuration (filled shell) the energy bands are either completely filled or empty. Owing to the localization of the electrons, it needs much energy to lift them from the last filled valence band into the empty conduction band. The classic example of a crystal built from only covalently bonded atoms is diamond: all carbon atoms are bonded via tetrahedrally directed sp3 hybrid orbitals (fig. 3). Thus the crystal structure of diamond results as a framework of tetrahedrally coordinated carbon atoms (fig. 4).