Page 47 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

26 Table 1.6. Van der Waals Radii in Å

CHAPTER 1 Bondi a Structural b
Chemical Bonding H 1 20 1 09
and Molecular Structure
C 1 70 1 75
N 1 55 1 61
O 1 52 1 56
F 1 47 1 44
S 1 80 1 79
Cl 1 75 1 74
Br 1 85 1 85
I 1 98 2 00

a. A. Bondi, J. Phys. Chem., 68, 441 (1964).
b. R. S. Rowland and R. Taylor, J. Phys. Chem., 100, 7384
(1996).

Van der Waals dimensions are especially significant in attempts to specify the
“size” of molecules, for example, in computational programs that attempt to “fit”
molecules into biological receptor sites. In the next chapter, we discuss the effects of
van der Waals interactions on molecular shape (conformation). These effects can be
quantified by various force fields that compute the repulsive energy that molecules
experience as nonbonded repulsion.

1.2. Molecular Orbital Theory and Methods

Molecular orbital (MO) theory is an alternative way of describing molecular
structure and electron density. The fundamental premise of MO theory is that the
orbitals used to describe the molecule are not necessarily associated with particular
bonds between the atoms but can encompass all the atoms of the molecule. The
properties of the molecule are described by the sum of the contributions of all orbitals
having electrons. There are also empty orbitals, which are usually at positive (i.e.,
antibonding) energies. The theoretical foundation of MO theory lies in quantum
mechanics and, in particular, the Schrödinger equation, which relates the total energy
of the molecule to a wave function describing the electronic configuration:

2
E = H d when d = 1 (1.11)
where H is a Hamiltonian operator.
The individual MOs are described as linear combinations of the atomic orbitals
(LCAO):
x
= c +c +c c n (1.12)

2
1
2
1
n
3
3
The atomic orbitals that are used constitute was is known as the basis set and a
minimum basis set for compounds of second-row elements is made up of the 2s,2p ,
x
2p , and 2p orbitals of each atom, along with the 1s orbitals of the hydrogen atoms.
y z
In MO calculations, an initial molecular structure and a set of approximate MOs are
chosen and the molecular energy is calculated. Iterative cycles of calculation of a self-
consistent electrical field (SCF) and geometry optimization are then repeated until a