54 STRUCTURE AND BONDING
/O-H...O
H 3 C—C^NO ...H—O
Hydrogen bonding is not restricted, however, to bonding between
like molecules; it can exist between two different molecules (for
example water and ethanol) or between a molecule and an ion (for
example the species [H • • • • F • • • • H] ~ already mentioned). Hydrogen
bonding also plays a vital role by providing cross linkage in proteins.
It is, therefore, a very important bond; although it is usually weak,
having a strength of approximately 20 kJ compared with a normal
covalent bond strength of 200-400 kJ, certain hydrogen bonds can
have strengths up to 80 kJ (see p. 57)
THE MODERN THEORY OF THE COVALENT BOND
The idea that a shared electron pair constitutes a covalent bond
ignores any difficulty about the actual position and nature of the
electrons in the combining atoms or in the resulting molecule. The
idea that electrons are particles revolving in 'orbits' or situated in
'shells' is inadequate when we desire to picture electrons in covalent
bonds. It is, however, known that a beam of electrons can undergo
diffraction, and that they therefore possess a wave-like nature
like light waves. It has also been found that there is a simple rela-
tionship between the momentum of an electron (characteristic of
its particle-nature) and the wavelength (characteristic of its wave-
nature). But if we give a definite wavelength or amplitude to an
electron, then its position in space becomes uncertain, i.e. it cannot
be pin-pointed. Instead, the wave amplitude (strictly, the square of
the amplitude) can be used to represent the probability of finding
the electron at a given point in an atom or molecule. This amplitude
is usually given the symbol \l/ (psi) and is called a wave function.
For hydrogen (or helium), with one (or two) electron in the K
'shell', \// is found to depend only on the distance from the nucleus,
diminishing as this distance increases; hence our picture of the
hydrogen atom is that shown in Figure 2.7.
The intensity of shading at any point represents the magnitude of
^^2 , i.e. the probability of finding the electron at that point. This
may also be called a spherical "charge-cloud'. In helium, with two
electrons, the picture is the same, but the two electrons must have
opposite spins. These two electrons in helium are in a definite
energy level and occupy an orbital, in this case an atomic orbital.