Page 56 - Advanced Organic Chemistry Part A - Structure and Mechanisms, 5th ed (2007) - Carey _ Sundberg

This may be accomplished by perturbation methods such as Moeller-Plesset (MP) 51 35
or by including excited state determinants in the wave equation as in configurational
52
interaction (CISD) calculations. The excited states have electrons in different orbitals SECTION 1.2
and reduced electron-electron repulsions. Molecular Orbital
Theory and Methods
The output of ab initio calculations is analogous to that from HMO and semiem-
pirical methods. The atomic coordinates at the minimum energy are computed. The
individual MOs are assigned energies and atomic orbital contributions. The total
molecular energy is calculated by summation over the occupied orbitals. Several
schemes for apportioning charge among atoms are also available in these programs.
These methods are discussed in Section 1.4. In Section 1.2.6, we illustrate some of
the applications of ab initio calculations. In the material in the remainder of the book,
we frequently include the results of computational studies, generally indicating the
type of calculation that is used. The convention is to list the treatment of correlation,
e.g., HF, MP2, CISDT, followed by the basis set used. Many studies do calculations
at several levels. For example, geometry can be minimized with one basis set and
then energy computed with a more demanding correlation calculation or basis set.
This is indicated by giving the basis set used for the energy calculation followed by
parallel lines (//) and the basis set used for the geometry calculation. In general, we
give the designation of the computation used for the energy calculation. The infor-
mation in Scheme 1.3 provides basic information about the nature of the calculation
and describes the characteristics of some of the most frequently used methods.

1.2.4. Pictorial Representation of MOs for Molecules

The VB description of molecules provides very useful generalizations about
molecular structure and properties. Approximate molecular geometry arises from
hybridization concepts, and qualitative information about electron distribution can be
deduced by applying the concepts of polarity and resonance. In this section we consider
how we can arrive at similar impressions about molecules by using the underlying
principles of MO theory in a qualitative way. To begin, it is important to remember
some fundamental relationships of quantum mechanics that are incorporated into MO
theory. The Aufbau principle and the Pauli exclusion principle, tell us that electrons
occupy the MOs of lowest energy and that any MO can have only two electrons, one
of each spin. The MOs must also conform to molecular symmetry. Any element of
symmetry that is present in a molecule must also be present in all the corresponding
MOs. Each MO must be either symmetric or antisymmetric with respect to each element
of molecular symmetry. To illustrate, the MOs of s-cis-1,3-butadiene in Figure 1.13
can be classified with respect to the plane of symmetry that dissects the molecule
between C(2) and C(3). The symmetric orbitals are identical (exact reflections) with
respect to this plane, whereas the antisymmetric orbitals are identical in shape but

51 W. J. Hehre, L. Radom, P. v. R. Schleyer, and J. A. Pople, Ab Initio Molecular Orbital Theory, Wiley-
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E. G. Zoebisch, E. F. Healy, and J. P. Stewart. J. Am. Chem. Soc., 109, 3902 (1985); J. P. Stewart, J.
Comput. Chem., 10, 209, 221 (1989); ; J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Phys.
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J. A. Pople, M. Head-Gordon, and K. Raghavachari, J. Phys. Chem., 87, 5968 (1987).