Concise Physical Chemistry

c19 JWBS043-Rogers September 13, 2010 11:29 Printer Name: Yet to Come

PROBLEMS AND EXAMPLES 315

water 0 3 0 0 0 0 10.0

0 0 0.0000000 2 0 0 0 0 0 0 1 0

2123

-0.76769 0.52221 0.00000 H 21( 1)

0.00000 -0.06580 0.00000 O 6( 2)

0.76769 0.52221 0.00000 H 21( 3)

FILE 19.3 The MM4 geometry output TAPE9.MM4 for water.

catTAPE9.MM4 to display the optimized geometry of your input file. File 19.3

shows an MM4 output for water. The output File 19.3 has the same format as the

input File 19.2, but it contains some more information beyond column 65 which

we do not need at this point. These differences notwithstanding, the geometry is

clear. The simple angle>has been up-ended to a V and moved down 0.06580A ̊

during the optimization. By a Pythagorean calculation, we get an O H bond length of

0.967A. This length is confirmed by a calculation within the program. We find, along ̊

with much other information in TAPE4.MM4,

H( 1)- O( 2) 0.9670

O( 2)- H( 3) 0.9670

A search toward the end of the output file will reveal a computed dipole moment

(Section 18.7):

DIPOLE MOMENT= 2 .0188 D

The experimental value is 1.85 D.

Example 19.3 An MM4 Calculation of the Geometry and
fH^298 of Methane

Convert the H 2 O input file to a methane input file and run it in the MM4 protocol.

The atomic identifiers are 1 for ansp^3 carbon and 5 for an alkane hydrogen. A 1 in

column 65 of line 2 requests
fH^298.

Solution 19.3 Assuming considerable ignorance about the structure of methane,

let us place the carbon atom at the origin and suppose that the projection of each

atom upon the Cartesian coordinates centered on the carbon is 1.0A. For conve- ̊

nience, it is useful to orient the molecule with two C H bonds in thex, yplane.

Examination of the TAPE4.MM4 file circumvents awkward trigonometric hand cal-

culations within the tetrahedral output geometry and gives the C H bond length

asC(1)- H(2) 1.1070expressed in Angstroms. The experimental value is

109.3 pm=1.093A. The tetrahedral H ̊ C H bond angles areH(2)- C(1)-

H(3) 109.471expressed in degrees. The experimental value is 109.5◦.Avery

important line in TAPE4.MM4 is the
fH^298 “heat” (enthalpy) of formation that was

requested in entry 2, 65 of the input file:

HEAT OF FORMATION (HFN) AT 298.2 K= -17.89 KCAL/MOLE