9.1 Types of molecular bonds  (Page 4/14)

As we discuss later, the total wave function of two electrons must be antisymmetric on exchange. For example, two electrons bound to a hydrogen molecule can be in a space-symmetric state with antiparallel spins $\left(\uparrow \downarrow \right)$ or space-antisymmetric state with parallel spins $\left(\uparrow \uparrow \right)$ . The state with antiparallel spins is energetically favorable and therefore used in covalent bonding. If the protons are drawn too closely together, however, repulsion between the protons becomes important. (In other molecules, this effect is supplied by the exclusion principle.) As a result, ${\text{H}}_2$ reaches an equilibrium separation of about 0.074 nm with a binding energy is 4.52 eV.

Quantum mechanics excludes many types of molecules. For example, the molecule ${\text{H}}_3$ does not form, because if a third H atom approaches diatomic hydrogen, the wave function of the electron in this atom overlaps the electrons in the other two atoms. If all three electrons are in the ground states of their respective atoms, one pair of electrons shares all the same quantum numbers, which is forbidden by the exclusion principle. Instead, one of the electrons is forced into a higher energy state. No separation between three protons exists for which the total energy change of this process is negative—that is, where bonding occurs spontaneously. Similarly, ${\text{He}}_2$ is not covalently bonded under normal conditions, because these atoms have no valence electrons to share. As the atoms are brought together, the wave functions of the core electrons overlap, and due to the exclusion principle, the electrons are forced into a higher energy state. No separation exists for which such a molecule is energetically favorable.

Bonding in polyatomic molecules

A polyatomic molecule    is a molecule made of more than two atoms. Examples range from a simple water molecule to a complex protein molecule. The structures of these molecules can often be understood in terms of covalent bonding and hybridization    . Hybridization is a change in the energy structure of an atom in which mixed states (states that can be written as a linear superposition of others) participate in bonding.

To illustrate hybridization, consider the bonding in a simple water molecule, ${\text{H}}_2\text{O}\text{.}$ The electron configuration of oxygen is $1s^{2}2s^{2}2p^4.$ The 1 s and 2 s electrons are in “closed shells” and do not participate in bonding. The remaining four electrons are the valence electrons. These electrons can fill six possible states ( $l=1$ , $m=0$ , $\pm 1$ , plus spin up and down). The energies of these states are the same, so the oxygen atom can exploit any linear combination of these states in bonding with the hydrogen atoms. These linear combinations (which you learned about in the chapter on atomic structure) are called atomic orbitals, and they are denoted by $p_x,p_y,$ and $p_z.$ The electron charge distributions for these orbitals are given in [link] .

The transformation of the electron wave functions of oxygen to $p_x,p_y,$ and $p_z$ orbitals in the presence of the hydrogen atoms is an example of hybridization. Two electrons are found in the $p_z$ orbital with paired spins $(\uparrow \downarrow )$ . One electron is found in each of the $p_x$ and $p_y$ orbitals, with unpaired spins. The latter orbitals participate in bonding with the hydrogen atoms. Based on [link] , we expect the bonding angle for $\text{H—O—H}$ to be $90\text{°}$ . However, if we include the effects of repulsion between atoms, the bond angle is $104.5\text{°}$ . The same arguments can be used to understand the tetrahedral shape of methane $({\text{CH}}_4)$ and other molecules.

Summary

• Molecules form by two main types of bonds: the ionic bond and the covalent bond. An ionic bond transfers an electron from one atom to another, and a covalent bond shares the electrons.
• The energy change associated with ionic bonding depends on three main processes: the ionization of an electron from one atom, the acceptance of the electron by the second atom, and the Coulomb attraction of the resulting ions.
• Covalent bonds involve space-symmetric wave functions.
• Atoms use a linear combination of wave functions in bonding with other molecules (hybridization).

Conceptual questions

Problems