Concise Physical Chemistry

c20 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

SPLIT VALENCE BASIS SETS 331

The energy, taken from a much more detailed output file, is

TOTAL ENERGY=-1.0934083240

The value calculated here used two Gaussian basis functions STO-2G and arrived

at an energy of−1.09340Ehwhich replicates the output from File 20.6. The bond

energy BE is the difference between the molecular energy and the level of the atoms,

which have an energy of 2(.5000):

BE=− 1. 0934 − 2 (− 0. 5000 )=− 0. 0934 Eh=−245 kJ mol−^1

This is about half of the experimental value of 435 kJ mol−^1 ,slightly better than

the one calculated using the estimated coefficients in File 20.5. Using six Gaussian

functions improves the result to 0.0991Eh=260 kJ mol−^1 , which is about 57% of

the experimental value:

TOTAL ENERGY=-1.0991105267

20.9 METHANE

The carbon atom can be combined with four hydrogen atoms to form input File 20.8

for methane. The geometry for methane is given in approximate coordinates, which

will be changed during the program run. Once carbon and hydrogen can be combined,

the whole vista of alkanes, alkenes, and alkynes (many thousands of molecules) is

open. Extension to heteroatomic molecules other than hydrocarbons follows by the

same method (Example 20.1).

An optimized geometry is part of the output file. Neither the basis set nor the

optimized coordinate set is unique. Many (strictly, infinitely many) sets are possible.

Center Atomic Atomic Coordinates (Angstroms)

Number Number Type X Y Z

--------------------------------------------------------------

1 6 0 0.000000 0.000000 0.000162

2 1 0 0.000000 0.000000 1.089051

3 1 0 0.000000 1.026565 -0.363340

4 1 0 -0.889032 -0.513283 -0.363340

5 1 0 0.889032 -0.513283 -0.363340

FILE 20.8 One of many possible STO-2G optimized coordinate sets for methane. The carbon

atom has been arbitrarily placed at the origin of a Cartesian coordinate system.

20.10 SPLIT VALENCE BASIS SETS

A hundred years of theory and experiment persuades us that the electrons in atoms

reside in one or more “shells” surrounding the nucleus, each at a more or less fixed