Reprinted from THE JOURNALOF CHEMICALPHYSICS, Vol. 25, No.4,
779-780, October, 1956
Printed in U. S. A.
Electrostatic Interpretation of Directed Valence
B. F.
Department
GRAY
AND
H. O.
PRITCHARD
of Chemistry, Univel'sity of Manchester,
Manchester 13, England
(Received July 19, 1956)
SINCE
early 1930's,
it has been
common
to discuss
bond
angles the
in terms
of directional
properties
of atomic
orbitals.
It is clear, however, that there is no causal relationship between
the mathematical convenience of the orbital approximation and
the occurrence of directed valences. We will take the two molecules
BeH2 and H20 as typifying the problem of directed valence and
show that their difference in shape can be understood qualitatively
in terms of an electrostatic model.
First, consider the symmetrical approach of two protons P to a
hydrogen-like atom M: the energy of repulsion between the three
nuclei will be a minimum when they are in a straight line
P-k[ -P, but the energy of attraction between the electron and the
nuclei is a maximum when the two P nuclei are superimposed, i.e.,
[2PJ-M (compare the H3++ molecule-ion, where approximate
electronic attraction energies for 4ao separation are 1.2: 0= 180°,
E~-2.6IH;
0=60°, E~-3.3IH;
0=0, E~-4.5IH).
For any
given M - P distance, the expected bond angle will depend on the
absolute magnitudes of these two energy terms and the way in
which they vary with the P - M - P angle. The equilibrium molecular configuration arises from a compromise between these
considerations and the way in which the two energy terms vary
with internuclear separation.
The compounds MH n may be divided into two classes, (1) where
the nuclear repulsion term dominates and (2) where the net
electronic attraction term dominates. Consider the approach of
two protons to a Be-- ion to form BeH2; the nuclear repulsion
term is dominant and a linear molecule is formed (similarly BH3
will be trigonal and CH4 tetrahedral because these arrangements
minimize the nuclear repulsion energy for any given internuclear
separation). However, 0-- has ten electrons confined to a rather
smaller volume than the six electrons in Be-- (0 is smaller than Be
and we have assumed that this is also true for the corresponding
negative ions). Thus the two protons encounter a much greater
electron density in the region of the equilibrium internuclear
separation causing the net attraction term to dominate, thereby
reducing the H-O-H
angle from 180° to 104° where the attractive force tending to superimpose the two nuclei balances the
nuclear repulsion.
Thus for case (1) molecules (M belonging to the left-hand side of
the periodic table) we have a common explanation of the bond
angles which occur, but for case (2) molecules (i.e., M on the
right-hand side of the periodic table), we have to consider each one
separately. The reason for the phenomenon of directed valence is
conceptually much simpler than hitherto realized, but the hope of
being able to calculate explicitly any case (2) bond angles becomes
far more remote. One could formalize these arguments in terms of a
suitable charge density function situated on the M-- ion and is
functions on the protons by ignoring the electronic kinetic energy.
However, the kinetic energy does not remain constant during the
molecule-forming process envisaged and such formalization is not
therefore of much value. However, some generalizations, supported by experimental observation, about case (2) can be made:
the greater the electron density around the central atom, the
smaller will be the bond angle (compare the successive reduction in
bond angle along the series NH3, PH3, AsH" SbH3); also an atom
in a low valence state may be case (2), but in a higher valence
state may pass over into case (1) because of the increasing number
of nuclear repulsions (e.g., H2S is angular but in SF6 the fluorine
atoms take up a symmetrical arrangement of minimum nuclear
repulsion). Also, SeCI. is case (1) whereas lower down the table
TeCI. is a case (2) molecule in accordance with the previous
generalization (compare also the series SF6- UF6).
1 G. S. Gordadse, Z. Physik 99, 287 (1936).
2
D. R. Bates and T. R. Carson, Proc. Roy. Soc. (London) A234, 207
(1956).