Concise Physical Chemistry

c04 JWBS043-Rogers September 13, 2010 11:24 Printer Name: Yet to Come

64 THERMOCHEMISTRY

4.7 
fH^298 (g)FROM CLASSICAL MECHANICS

One of the drawbacks of the hydrogen-atom counting method is that account is

not taken of classical mechanical properties of molecules such as mechanical strain

energy induced in distorted or crowded molecules. Other mechanical features not

accounted for are those due to the quantum mechanical influences on electron

probability densities which, in turn, influence both molecular energy and molecular

structure.

The influence of molecular strain can be seen in the discrepancy between the

hydrogen-atom counting estimate of
fH^298 (cyclopentane(g))=− 24 .9kJmol−^1

as contrasted to the experimental value of−16.3 kJ mol−^1. The experimental value

is higher (less negative) than the estimate. Evidently, crowding 10 hydrogen atoms

into the small space afforded by a 5-membered ring increases the interatomic in-

terference energy that contributes to
fH^298. N. L. Allinger at the University of

Georgia has developed a series of molecular mechanics programs called MM1 to

MM4 that incorporate energies due to bond bending, bond stretching, ring distortion,

and so on, into the calculation of molecular structure and
fH^298. The method as

implemented on a computer is extremely fast and is therefore well-suited to large

molecules.

4.8 THE SCHRODINGER EQUATION ̈

In 1926 Erwin Schrodinger published an equation that gives correct solutions for the ̈

energy levels of the hydrogen atom. Shortly afterward, Heitler and London showed

that the Schr ̈odinger equation, as it has come to be called, predicts the existence of a

chemical bond between H and H and that it gives an approximate strength of the H H

bond. A powerful refinement and extension of thismolecular orbitalcalculation called

GAMESS is available asa site license at no costfor your microcomputer (academic

or similar affiliation must be specified):

http://www.msg.ameslab.gov/GAMESS/GAMESS.html

We shall use the GAMESS program to determine the bond energies of a number of

molecules starting with the simplest case, that of the hydrogen molecule when it is

formed from two hydrogen atoms:

2H·→H H

The GAMESS output for calculation of the total energy of H·isE=−0.4998Eh,

whereEhis thehartree, a unit of energy. A GAMESS output for the molecule H His

E=− 1. 1630349978 Eh