Page 195 - Academic Press Encyclopedia of Physical Science and Technology 3rd Organic Chemistry

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442 Organic Chemical Systems, Theory

not seen much use. An approach that is almost universally Atomic orbitals are characterized by a principal
adopted nowadays is the quantum mechanical molecular quantum number n (there are n − 1 radial nodes in an
orbital (MO) theory of electronic structure. This is compu- AO) and a letter indicating their shape as dictated by the
tationally manageable and is described in some detail later. angular nodes: An ns orbital has no angular nodes and
Even the mathematically simpler MO approach to elec- is of spherical symmetry; each of the three equienergetic
tronic structure requires the use of large computers for np orbitals has one angular mode (usually taken to be
any quantitative applications. Although large-scale com- a plane through the nucleus, with respect to which the
putations have been extremely valuable in enhancing the orbital is antisymmetric); each of the five nd orbitals has
understanding of organic molecules, they are in them- two angular nodes; and so on. Shorthand abbreviations
selves not appropriate for the day-to-day thinking of bench for orbital shapes are shown in Fig. 1A. These are meant
chemists. However, they have had a great influence on the to indicate the regions of space in which the numerical
much simpler qualitative models of electronic structure value of the AO is the largest, also known as the lobes of
adopted for daily use by organic chemists and even some an AO, as well as their signs.
effect on that ill-defined body of knowledge generally re- In the ground state of an atom, the AOs are assumed
ferred to as the organic chemist’s “intuition.” The current to be occupied by the available electrons in the order of
qualitative model of molecular electronic structure based increasing energy of the subshells: 1s, 2s, 2p, 3s .... The
on the qualitative notions of MO theory represents a sig- last at least partially occupied subshells and the more sta-
nificant advance over the structural theory outlined in the ble ones of the same principal quantum number represent
preceding sections, but is not easy to describe unequivo- the valence shell [in transition metals this contains the
cally, since its form varies among individuals. nd, (n + 1)s, and (n + 1)p subshells]. Only valence-shell
Current qualitative thinking about the electronic struc- AOs are normally considered important for bonding: the
ture of organic molecules is based on the independent- 1s orbital in hydrogen and the 2s in lithium and beryllium
particle model, in which it is assumed that the motion of (2p areverycloseinenergyandcouldbeincludedaswell),
each electron is dictated by the field of stationary nuclei 2s and 2p in boron through neon, 3s in sodium and mag-
and the time-averaged field of all the other electrons. In nesium (3p could be included), 3s and 3p in aluminum
this model, any correlation of the instantaneous positions through argon, and so on.
of the many electrons present is neglected. The qualitative theory of bonding also makes use of
Only in several well-recognized and more or less ex- combinations of valence AOs known as hybrid orbitals.
ceptional situations are correlation effects explicitly in- Combining an s with a p orbital produces two equivalent
troduced. This is particularly true in the treatment of bi- sp hybrids pointing in opposite directions. Combining an
2
radicals, which represent an important class of reaction s with two p orbitals produces three equivalent sp hy-
intermediatesbutwhicharenotdiscussedhere,inthetreat- brids pointing to the corners of an equilateral triangle.
ment of several other unusual bonding situations, and in And combining an s with three p orbitals produces four
3
the treatment of photochemical processes (e.g., in the con- equivalent sp hybrids pointing to the corners of a regular
sideration of differences in the reactivity of excited singlet
and triplet states).

A. Atomic Orbitals
The independent-particle model is well known from the
quantum mechanical description of atomic structure. Each
electron in an atom is assumed to reside in an atomic or-
bital (AO) with a maximum of two electrons (of opposite
spin) in any one orbital (Pauli principle). The AO is a
function of the coordinates of one electron. The square
of its magnitude at any point in space gives the proba-
bility density for finding the electron at that point. The
magnitude itself can be positive or negative, with zero
values at the boundaries of the positive and negative re-
gions. The boundaries are referred to as nodal surfaces
(planes, spheres, etc.). The energy of an electron residing
in an orbital increases with the increasing number of nodal
surfaces in the orbital. FIGURE 1 (A) Atomic orbitals. (B) Hybrid orbitals.