c11 JWBS043-Rogers September 13, 2010 11:26 Printer Name: Yet to Come
LATTICE ENERGIES 177atom in CCl 4 , for example, but there is no clear way of finding where, along the C–Cl
bond axis, one radius leaves off and the other begins.
One approach to this difficulty is by finding the homonuclear bond distances in
molecules like ethane for which the C–C bond distance is 154 pm, and Cl–Cl for which
it is 200 pm. Under the assumption that homonuclear bond distances will be carried
over into the heteronuclear cases, one has (200/ 2 + 154 /2)= 100 + 77 =177 pm,
which successfully reproduces the experimental value forrC−Cl. Now, by studying
other compounds involving C and other compounds involving Cl, one can gradually
build up tables of covalent bond radii such as those found in elementary textbooks
(Ebbing and Gammon, 1999).
A number of points should be considered before using bond lengths or atomic
radii. For one thing, combination of X-ray data with neutron diffraction data is risky
because X-radiation is scattered by the electron cloud surrounding the nuclei in the
molecule and neutrons are scattered by the nuclei themselves. Clearly the first is
useful in studying bonds and the second is useful for structure. Also, there is no
reason to expect ionic radii and covalent radii to agree with one another because of
the different modes of chemical bonding involved. Tables of bond distances, ionic
radii, and covalent radii should be used with some degree of reserve because of
potential inconsistencies and approximations.11.6 COMPUTATIONAL GEOMETRIES
Most present-day molecular structure–energy computer programs contain a routine
thatoptimizesthe geometry of the molecule under study so that each of the constituent
atoms resides at the bottom of its unique potential energy well. Once knowing the
complete molecular geometry, the bond lengths and angles can be calculated with
great precision. The results, however, are not exactly comparable to experimental data
because the energy minimum found by computational optimization for atoms in the
force field of all other nuclei and electrons does not coincide with the average position
of the vibrating atom. Current estimates of atomic radii and bond lengths are in good
agreement overall but differ slightly according to the method used to determine them.
Using the Spartan©C package, the homonuclear distancerH−H= 73 .6 pm and the
heteronuclear distancerH−F= 90 .0 pm are found, as compared to the experimental
values of 74.2 and 91.7 pm.11.7 LATTICE ENERGIES
Along with their geometry, we would like to know how firmly ionic crystals are
held together. A quantitative measure of the energy or enthalpy holding the crystal
together is itslattice energy. The lattice energy is the energy necessary to draw ions
out of the crystal lattice and propel them into the gaseous state.NaI(crystal)→Na+(g)+I−(g)