Page 53 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

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CHAPTER 1
Chemical Bonding
and Molecular Structure
Hückel’s rule also pertains to charged cyclic conjugated systems. The cyclo-
propenyl (2 electrons), cyclopentadienyl anion (6 electrons), and cycloheptatrienyl
(tropylium) cation (6 electrons) are examples of stabilized systems. We say much
more about the relationship between MO configuration and aromaticity in Chapter 9.
+
–
+

1.2.2. Semiempirical MO Methods

Beginning in the 1960s, various more elaborate MO methods were developed
and applied to organic molecules. Among those that are historically significant are
extended Hückel theory (EHT), 46 complete neglect of differential overlap (CNDO), 47
and modified neglect of differential overlap (MNDO). 48 In contrast to HMO theory,
these methods include all the valence shell electrons in the calculation. Each of these
methods incorporates various approximations and parameters. The parameters are
assigned values based on maximizing the agreement for a set of small molecules. The
CNDO findings were calibrated with higher-level computational results, while MNDO
was calibrated to experimental stability data. These parameters are then employed for
computations on more complex molecules. The output provides molecular geometry,
atomic coefficients, and orbital energies. Each method had both strengths and limita-
tions with respect to the range of molecules and properties that could be adequately
described. At the present time, the leading semiempirical methods, called AM1 49 and
PM3, 50 are incorporated into various MO computational programs and are widely
employed in the interpretation of structure and reactivity. In Section 1.2.6, we illustrate
some of the problems that can be addressed using these methods.

1.2.3. Ab Initio Methods
Ab initio computations are based on iterative calculations of a self-consistent
electronic field (SCF), as is the case in the semiempirical methods just described, but do
not use experimental data to calibrate quantities that appear in the calculations. These
methods are much more computationally demanding than semiempirical methods, but
their reliability and range of applicability has improved greatly as more powerful
computers have permitted more sophisticated approaches and have enabled handling
of more complex molecules. The computations are carried out by successive series
of calculations minimizing the energy of the electron distribution and the molecular
geometry. The cycle of the calculations is repeated until there is no further improvement
(convergence).

46 R. Hoffmann, J. Chem. Phys., 39, 1397 (1963).
47
J. A. Pople and G. A. Segal, J. Chem. Phys., 44, 3289 (1966).
48 M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc., 99, 4907 (1977).
49 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. P. Stewart. J. Am. Chem. Soc., 109, 3902 (1985).
50
J. P. Stewart, J. Comput. Chem., 10, 209, 221 (1989).