11.6 Binding Interactions Between Atoms
527
Table 11.1 Radial behavior
of molecular interactions
Interaction
Radial (r) behavior
Coulomb
±1/r
Screened Coulomb
± exp (−ar)/r
Charge and dipole
±1/r 2
Charge and induced-dipole −1/r 4
Dipole and dipole
±1/r 6
Hydrogen bonding
−1/r 6
Direct London
−1/r 6
Spin-spin (magnetic)
±1/r 6
Retarded London
−1/r 7
‘Shadow’ effect
−1/r
Pauli exchange
+1/r 12 (approx)
11.6.1 Chemical Binding
Since the development of quantum electrodynamics (after 1948), electromagnetic
interactions and quantum theory have been sufficient to describe all the known
properties of chemical binding of atoms to form molecules, including those of life.
As atoms are brought together, the wave functions for outer atomic electrons
(‘valence electron’) are disturbed first. The valence electrons which are strongly
affected in light atoms are typically in combinations of l = 0 (s) and l = 1 (p)
orbitals. Above atomic number Z ≈ 18, the l = 2 (d) orbitals can also be strongly
affected. If the result of the interaction between the atoms is an attractive force,
the atoms can bind together. As the atoms are squeezed together even closer than
bond separations, electron Pauli repulsion opposes electric and quantum attraction.
Further compression and the Coulombic repulsion between nuclei becomes just as
important as the electron Pauli repulsion.
11.6.2 Molecular Orbitals
If a pair of electrons is shared between two atoms, the bonding is called ‘covalent’.
If the orbital for those electrons has a higher probability near one of the atoms, the
bond is called ‘polar covalent’. Multiple such bonds between pairs of atoms may
occur. For example, acetylene has a triple covalent bond between its two carbon
atoms (Figs. 11.2 and 11.3).
A ‘sigma bond’ is a covalent bond with axial symmetry about the line joining
the two atoms. A sigma bond allows one atom to rotate around the symmetry axis
relative to the second atom without any energy change. Sigma bonds can be formed
by pairs of atomic s-wave or axially aligned p-wave atomic orbitals which have the
two atomic waves in phase in the region between the atoms. ‘In phase’ waves have
the same sign in a given region at a given time. Having the atomic waves in phase
527
Table 11.1 Radial behavior
of molecular interactions
Interaction
Radial (r) behavior
Coulomb
±1/r
Screened Coulomb
± exp (−ar)/r
Charge and dipole
±1/r 2
Charge and induced-dipole −1/r 4
Dipole and dipole
±1/r 6
Hydrogen bonding
−1/r 6
Direct London
−1/r 6
Spin-spin (magnetic)
±1/r 6
Retarded London
−1/r 7
‘Shadow’ effect
−1/r
Pauli exchange
+1/r 12 (approx)
11.6.1 Chemical Binding
Since the development of quantum electrodynamics (after 1948), electromagnetic
interactions and quantum theory have been sufficient to describe all the known
properties of chemical binding of atoms to form molecules, including those of life.
As atoms are brought together, the wave functions for outer atomic electrons
(‘valence electron’) are disturbed first. The valence electrons which are strongly
affected in light atoms are typically in combinations of l = 0 (s) and l = 1 (p)
orbitals. Above atomic number Z ≈ 18, the l = 2 (d) orbitals can also be strongly
affected. If the result of the interaction between the atoms is an attractive force,
the atoms can bind together. As the atoms are squeezed together even closer than
bond separations, electron Pauli repulsion opposes electric and quantum attraction.
Further compression and the Coulombic repulsion between nuclei becomes just as
important as the electron Pauli repulsion.
11.6.2 Molecular Orbitals
If a pair of electrons is shared between two atoms, the bonding is called ‘covalent’.
If the orbital for those electrons has a higher probability near one of the atoms, the
bond is called ‘polar covalent’. Multiple such bonds between pairs of atoms may
occur. For example, acetylene has a triple covalent bond between its two carbon
atoms (Figs. 11.2 and 11.3).
A ‘sigma bond’ is a covalent bond with axial symmetry about the line joining
the two atoms. A sigma bond allows one atom to rotate around the symmetry axis
relative to the second atom without any energy change. Sigma bonds can be formed
by pairs of atomic s-wave or axially aligned p-wave atomic orbitals which have the
two atomic waves in phase in the region between the atoms. ‘In phase’ waves have
the same sign in a given region at a given time. Having the atomic waves in phase