Physical Chemistry Third Edition

21.10 More Advanced Treatments of Molecular Electronic Structure. Computational Chemistry 909

of Chapter 16.

exp(̂T) 1 +̂T+

1

2!

+̂T^2 +

1

3!

̂T^3 + ··· (21.10-5)

The operator̂Tis itself a sum of terms that corresponds to excitation of one electron to

a previously unoccupied orbital, excitation of two electrons to previously unoccupied

orbitals, and so on. We do not discuss the method, which is discussed in some graduate-

level quantum chemistry textbooks.^20

Molecular Mechanics

Molecular mechanics is a branch of calculational chemistry that has achieved

considerable success in predicting geometries of molecules and reactive intermediates

without any use of quantum mechanics. The potential energy of the molecule is

expressed as a sum of functions of the bond lengths and angles, using various

empirical formulas for different bonds. Different formulas have been developed by

Allinger and others, using trial and error and curve-fitting techniques. These sets of

formulas are known by different acronyms such as MM2, MM3, MMFF94, AMBER,

and so on.^21 The potential energy functions are built into a computer program,

which then carries out the process of finding the conformation of minimum potential

energy by varying bond distances and angles. For a molecule containing many atoms

the energy minimization can be a difficult problem, and various techniques exist

for its solution.^22

Since the energy change in a chemical reaction is a small fraction of the total energy

of the molecules, the total energies must be calculated to very high accuracy in order

to get a good approximation to the energy change of a chemical reaction. The energy

change in a reaction is typically near 500 kJ mol−^1 (about 5 eV per molecule) while

the total energies of the molecules might be several thousand eV per molecule (several

hundred thousand kJ mol−^1 ). Achieving an error of 10% in the energy change of reaction

requires an uncertainty of less than a tenth of a percent in the molecular energies. This

degree of accuracy is not yet routinely achievable.

There are some things that are inherently very difficult to observe experimentally,

and any quantum chemical calculation giving information about such a process can

be useful. For example, the elementary steps in a chemical reaction might take place

in 10−^13 second or less, making experimental study difficult. Quantum-chemical cal-

culations giving the energies and geometries (bond angles and lengths) of reactive

intermediates can be a source of such information, even if great accuracy is not

achieved.

Quantum Chemistry Software

With presently available programs, it is possible for any student of chemistry to carry

out a calculation in a few seconds that would have constituted a Ph.D. dissertation fifty

(^20) I. N. Levine,op. cit., p. 568ff (note 2).
(^21) N. L. Allinger and L. Yan,J. Am. Chem. Soc., 115 , 11918 (1993); T. A. Halgren,J. Comput. Chem., 20 ,
730 (1999).
(^22) U. Burkert and N. L. Allinger,Molecular Mechanics.ACS Monograph 177, American Chemical
Society, Washington, DC, 1982.