Page 81 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

60 Qualitative VB theory uses resonance structures and bond polarity relationships
to arrive at an indication of relative charge distribution. For example, in propenal
CHAPTER 1 the combination of a preferred resonance structure and the higher electronegativity of
Chemical Bonding oxygen relative to carbon leads to the expectation that there will be a net negative
and Molecular Structure
charge on oxygen and compensating positive charges on C(1) and C(3) (see p. 21).
How much the hydrogen atoms might be affected is not clear. As a first approximation,
they are unaffected, since they lie in the nodal plane of the conjugated system, but
because the electronegativity of the individual carbons is affected, there are second-
order adjustments.
δ–
O
δ+ δ+

Numerical expression of atomic charge density in qualitative VB terminology
can be obtained by use of the electronegativity equalization schemes discussed in
Section 1.1.4. The results depend on assumptions made about relative electronegativity
of the atoms and groups. The results are normally in agreement with chemical intuition,
but not much use is made of such analyses at the present time. MO calculations
give the total electron density distribution as the sum of the electrons in all the filled
molecular orbitals. The charge distribution for individual atoms must be extracted
from the numerical data. Several approaches to the goal of numerical representation
of electron distribution have been developed. 79

1.4.1. Mulliken Population Analysis
In MO calculations, the total electron density is represented as the sum of all
populated MOs. The electron density at any atom can be obtained by summing the
electron density associated with the basis set orbitals for each atom. Electron density
shared by two or more atoms, as indicated by the overlap integral, is partitioned equally
among them. This is called a Mulliken population analysis. 80

N occ

P = 2 c c X X (1.21)
$
#$ #
#=1
$

P = c c X X for % on A (1.22)
A #$ # $ #
The Mulliken population analysis, and all other schemes, depend on the definition
used to assign charges to atoms. For example, the orbital in formaldehyde has two
electrons, and according to HF/3-21G calculations they are assigned as shown at the left
below. When all the basis set orbitals are considered, the charge distribution is as shown
81
ontheright. OutputfromtypicalMOcalculationscanprovidethiskindofatomiccharge
distribution. No great significance can be attached to the specific numbers, since they are
dependent on the particular basis set that is used. The qualitative trends in redistribution
79
S. M. Bachrach, Rev. Comput. Chem., 5, 171 (1994).
80 R. S. Mulliken, J. Chem. Phys., 36, 3428 (1962).
81
W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley-
Interscience, New York, 1986, pp. 118–121; A. Szabo and N. S. Ostlund, Modern Quantum Chemistry:
Introduction to Advanced Electronic Structure Theory, Macmillan, New York, 1982.