Page 205 - Academic Press Encyclopedia of Physical Science and Technology 3rd Organic Chemistry

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452 Organic Chemical Systems, Theory

potential contour maps can be constructed, indicating the puter time is needed for the semiempirical computations.
nature of the electric fields to be expected in the vicinity This great reduction in computational effort is to a large
of the molecule. degree due to the almost universal use of the so-called zero
differential overlap approximation, which greatly reduces
the number of electron repulsion integrals needed in the
3. Ab Initio and Semiempirical Methods
computations.
The approach described so far is of the so-called ab ini- Some of the best known examples of semiempirical
tio type, in which the whole computation is done from methods are those developed for the treatment of elec-
first principles, taking from experiment only the values tronic ground states by Dewar and collaborators (MNDO,
of fundamental constants such as electron charge. As al- AM1, and MINDO/3) and the methods developed by Jaff´e
ready indicated, accurate results cannot be obtained by (INDO/S), Zerner (INDO/S), and their respective collab-
these methods for most molecules of interest in organic orators for calculations involving electronically excited
chemistry, but the approximate solutions obtained at the states. A very simple procedure is the extended H¨uckel
SCF or improved SCF level provide much useful informa- method popularized by Hoffmann. Others are the older
tion. For certain properties, such as molecular geometries, methods developed for the treatment of π electrons only:
dipole moments, and the relative energies of conformers, the PPP method of Pariser, Parr, and Pople and the ex-
the agreement with experiment is excellent. tremely crude but also extremely simple HMO method of
An alternative approach to the problem of molecular H¨uckel.
electronic structure is provided by semiempirical mod- These semiempirical models should not be confused
els. In these no attempt is made to derive the properties with approximate models that are designed to mimic the
of atoms from first principles. Rather, they are taken as results of ab initio calculations in a simpler manner rather
described by a set of parameters obtained by fitting ex- than to mimic the results of experiments. The best known
perimental data, and an attempt is made to find a model approximate MO methods are the CNDO and INDO meth-
Hamiltonian that will provide a good description of inter- ods developed by Pople and collaborators.
atomic interactions. The form of the model Hamiltonian
is patterned after the ab initio analysis. In the most com-
C. Molecular Properties
mon semiempirical methods it is still a fairly complicated
many-electron Hamiltonian, so that its exact stationary Although we have indicated how the electronic wave func-
wave functions cannot be found for molecules of interest, tion of an electronic state and its energy are calculated, we
and only approximate solutions are obtained. One almost have said very little about the calculation of other mole-
invariably starts with a minimum basis set of AOs and pro- cular properties once the wave function is known.
ceeds to an SCF type of wave function, possibly followed The calculation of molecular equilibrium geometry in a
by a limited amount of improvement toward the FCI wave given electronic state, usually S 0 , is performed by varying
function. The parameters that enter the Hamiltonian are the assumed nuclear geometry and repeating the calcu-
optimized so as to bring about close agreement between lation of the energy by one of the methods referred to
the molecular properties computed from the approximate earlier until a minimum is found. This search is normally
wave function (usually SCF) and those observed experi- performed by computer routines that compute surface gra-
mentally. Most commonly, the properties fitted are heats dientsinordertospeedupconvergencetowardalocalmin-
of formation, molecular equilibrium geometries, or suit- imum in the (3N − 6)-dimensional nuclear configuration
able spectroscopic properties. In this way one attempts to space. From the computed curvatures of the surface at the
incorporate intraatomic correlation energies and a large minimum one obtains the force constants for molecular
part of interatomic electron correlation energies into the vibrations and the form of the normal modes of vibration.
model through parameter choice, although one works only For a true local minimum, all the force constants must be
at the SCF level or at least not much beyond it. positive. A similar type of procedure, minimization of the
The agreement of the calculated properties with exper- norm of the gradient, can be used for finding transition
iment is roughly comparable to the agreement obtained states. After a transition point is found, it is essential to
by extended basis set ab initio methods at the level of the convince oneself that a normal mode analysis produces
SCF approximation or slightly better, at least for those only one vibration with a negative force constant. This
classes of molecules for which the semiempirical pa- mode corresponds to the path from one catchment basin
rameters were originally optimized. However, even for to the other, and the corresponding vibration has an imag-
molecules quite different from those on which the original inary frequency (the restoring force is negative). Other
optimization was performed, the agreement is frequently modes of vibration are ordinary and permit the evaluation
striking considering that orders of magnitude less com- of the entropy of the transition state.